®l|g ^. ^. Igm pkarg 511555 Wv5 -^ UNlVEBSnV LIBRARIES S00601843 M Date Due [ ,j< > ^ ' • xoiw^' jyc ,,;^jJ^J^.; JANl 1964 AprI4'3l Wb4 ^^tir29^^f wm MavU'3l febi8'32 Novir33 ^^^^^^^-;2i-- • ..•,.;. giJanid AP^ ^"9iqftn '■•S .iOreo'36 t;^^'} ■i ii 199^ 28~eb'36 t'-tr- ' - ^ ' ^^ ■•: 2.::r--' 34Feb'3e MMay'f^f ) \0 HANDBOOK OF FIELD AND OFFICE PROBLEMS IN FOREST MENSURATION BY HUGO WINKENWERDER Dean, College of Forestn/, University of Washington AND ELIAS T. CLARK Associate Professor of Forestry, University of Washington SECOND EDITION NEW YORK JOHN WILEY & SONS, Inc London: CHAPMAN & HALL, Limited 1922 Copyright, 1915, 1922, by Hugo Winkenwerder and Elias T. Clark PRESS OF BRAUNWORTH & CO. BOOK MANUFACTUREBO BROOKLYN. N, V. LIBRARY N, C. State Colleg e PREFACE The problems in this handbook were originally prepared as an aid to the laboratory instruction in forest mensuration at the University of Washington, and were first published by the authors in 1915. Numerous changes and addi- tions were made in this edition, particularly with reference to making them more generally useful to the practical field and office men and more generally applicable to all sections of the country. In the few instances where they are not applicable they can readily be made so by slight modifications at the instance of the instructor in charge. In each problem the forms for recording and for working up the data have been definitely indicated. It has been found that this will result in greater uniformity and better standards of comparison for the work of the individual students. Although different schools are using forms that differ in some of the details they can readily be made applicable by adopting form numbers to coincide with those adopted in this handbook. These forms are illustrated in the Appendix on pages 90 to 97. In the preparation of the handbook the object has not been to present a complete series of problems covering the entire field of forest mensuration, but rather a series of carefully selected type exercises which may be used as practical illustrations to supplement the recitation and text-book work. A number of the newer methods recently developed but not yet thoroughly established have been purposely omitted. References to various new methods will be found in the Appendix, in connection with the Bibliography. The authors have included only problems of standard character. It is hoped that the value of the handbook will be due as much to what is omitted as to what is actually included. Ex-perience has shown that a few funda- mental type exercises, carefully worked out in the field and laboratory, and their relation to associated problems then brought out in class-room discussions will give the student a more thorough grounding in the subject than a multitude of exercises hurriedly worked over but not assimilated. A second feature sought in these problems is the elimination of an undue amount of duplication in clerical work. The function of a university is to teach the how and the wherefore. Our time is too limited to use more than a reasonable amount of it for drill work, and it has been our experience that clerical drudgery often obscures the fundamental object of an exercise. Though a student works over only a limited number of data in the field or laboratory this is no excuse for iii 13236 iv PREFACE an instructor to allow the student to gain a false impression concerning the actual number of data required in an extensive investigation. A third object sought is a thorough correlation of the individual fundamental problems in forest mensuration and to show their relation to the larger problems which are usually dependent upon a combination of the fundamentals. It has been sought to accomplish this by keeping the fundamental problems wholly distinct from each other in the early exercises. This should serve to prevent obscuring their broad field of usefulness for other purposes. In the sudceeding exercises the fundamental problems have, however, been combined with the more extensive ones so as to coordinate them and to emphasize their special rela- tionships. The directions for the fundamental problems are also given in consid- erable detail; in the succeeding problems, however, wherein the former are used only as a step in the solution, the student is made to depend upon his knowledge of the methods outlined in preceding problems by having the directions in the latter made more general. Nearly all of these problems have been used in about their present form by the students at the University of Washington. Only such changes have been made as were necessary to bring the manuscript up to date and otherwise put it in proper form for publication. Although the majority of forest schools now have their work so arranged that in connection with the field work they can obtain data for the greater part of the office problems, every locality does not contain the conditions that would furnish the proper kind of data for all of them. For this reason data have been supplied for use in connection with all of the office problems presented. However, in order to keep the price of the book within reasonable limits it has been neces- sary to limit the quantity of these data included. Though they are therefore not adapted for extensive practice it is hoped they may be of considerable help for illustrative purposes. Wherever these data are supplied in any limited quantity, a special effort was made to select them with reference to average conditions but not so as to destroy their general illustrative value. That the data are only in a few cases presented on the complete field forms should not detract from their value, but should rather help the student to remember just what measurements are required for a certain problem. The authors wish to acknowledge their indebtedness to Mr. Bror L. Grondal, of the College of Forestry, University of Washington, and Mr. T. T. Munger and Mr. L. A. Nelson, both of District 6, United States Forest Service, Port- land, Oregon, and to the instructors in other Forest Schools who have used the "Exercises" for helpful suggestions. Hugo Winkenwerder. Eli AS T. Clark. University of Washington, January, 1922. TABLE OF CONTENTS PAGE Preface i" SECTION I. PRELIMINARY MEASUREMENTS PROBLEM 1. (Field) Pacing - . . 1 2. (Field) The Determination of the Diameters of Standing Trees 2 3. (Field) The Determination of the Heights of Standing Trees 4 4. (Office) The Construction of a Dendrometer 6 5. (Office) The Construction of a Hypsometer 6 6. (Field) The Collection of Data for Volume Studies 8 7. (Field) The Collection of Data for Growth Studies 12 SECTION II. USE OF GRAPHIC METHODS 8. (Office) The Fundamental Principles in the Use of Graphic Methods . . 15 SECTION III. LOG RULES 9. (Office) The Construction of a Scientific Log Rule 18 10. (Office) The Graphic Comparison of Log Rules 19 11. (Office) The Extension of Log Rules 19 SECTION IV. PRELIMINARY CALCULATIONS 12. (Office) The Determination of the Merchantable Contents in Board Feet of Felled Trees 22 13. (Office) The Determination of the Total Cubic Contents of Felled Trees 23 14. (Office) The Determination of the Merchantable Contents of Trees in Standards 2o 15. (Field) The Determination of the Contents of Standing Trees by Short Methods 25 y vi TABLE OF CONTENTS SECTION V. THE CONSTRUCTION OF VOLUME TABLES PROBLEM PAGE 16. (Office) The Construction of a Merchantable Volume Table in Board Feet Based on D.B.H. Only 29 17. (Office) The Construction of Full Stem Cubic Foot Volume Table Based on D.B.H. and Total Heights 31 18. (Office) The Construction of a Table of Stem Form Factors Based on D.B.H. Alone 34 19. (Office) The Construction of a Merchantable Volume Table in Board Feet Based on D.B.H. and Number of 16-Foot Logo by the Frustum Form Factor Method 35 20. (Office) The Construction of a Taper Table 37 SECTION VI. SCALING 21. (Field) Scahng Logs 38 SECTION VII. DETERMINATION OF THE CONTENTS OF STANDS 22. (Field) Obtaining the Contents of a Small Tract by Different Methods 45 23. (Field and Office) Cruising without the Aid of a Volume Table 47 24. (Field and Office) Cruising with the Aid of a Volume Table , 51 SECTION vilL GENERAL GROWTH STUDIES 25. (Field) The Determination of Total Ages of Trees 57 26. (Office) The Determination of Diameter Growth in Even-aged Stands 58 27. (Office) The Determination of Growth in Uneven-aged Stands 60 28. (Office) The Transposing of a Table of Diameter Growth at the Stump to Growth at D.B.H 61 29. (Office) The Determination of Height Growth 62 30. (Office) TheDeterminationof Volume Growth of an Individual Tree.. 63 31. (Office) The Determination of Volume Growth by Graves' Modifica- tion of Mlodjianski's Method 66 32. (Office) The Determination of Maximum Growth 68 SECTION IX. SAMPLE PLOT STUDIES 33. (Field) The Determination of Contents of Stands by Means of Felled Sample Trees 69 34. (Field) The Determination of the Rate of Growth in Even-aged Stands by the Analysis of Felled Sample Trees 72 35. (Field) The Determination of Growth in Even-aged Stands by the Measurement of Standing Trees 74 TABLE OF CONTENTS vu SECTION X. STUDIES IN GROWTH PER CENT PROBLEM P^«^ 36. (Field) The Determination of Future Volume by Growth Per Cent Calculated from Felled Sample Trees 76 37. (Field) The Determination of Future Volume in Immature Even- aged Stands by Gro^\i:h Per cent, Calculated from Standing Trees "^ 38. (Field) The Prediction of Future Volume in Mature Stands from Standing Trees 79 SECTION XL YIELD TABLE STUDIES 39. (Office) The Construction of Yield Tables for Even-aged Stands 80 40. (Field) Method of Using a Yield Table for Even-aged Stands Uneven-aged Stands ^^ APPENDIX PAGE Diagram-Correlation of Methods in Growth Studies 84 Explanation of Diagram-Growiih Studies 85 Bibhograph}' 85 Units of Measurement 89 Mensuration Forms 90 I. Cross Section Sheet 90 2A. Analysis Sheet, front 91 2B. Analysis Sheet, back 92 3A. D.B.K. Only, Cruising Sheet, front 93 3B. D.B.H. Only, Cruising Sheet, back 94 4A. D.B.H.— Height Cruising Sheet, front 95 4B. D.B.H.— Height Cruising Sheet, back 96 5. Scaling Sheet 97 Columbia River Grading Rules 98 Puget Sound Grading Rules 99 Tables 100 I. Schiffel Formula D.B.H. Basal Areas 100 II. Schiffel Formula Middle Diameter Basal Areas 102 III. Basal Area of Circles 103 IV. Volumes of Frustums of Cones 105 V. Douglas Fir Volume Table 106 VI. Western Red Cedar Volume Table 107 VII. Silver Fir Volume Table 108 VIII. Western Hemlock Volume Table 109 IX. Scribner Dec. C. Log Rule 110 X. Yield Table for Douglas Fir 112 Data Series 113 I. Douglas Fir Stem Measurements 113 II. Periodic Growth Western Yellow Pine 121 III. Stump Analysis, Second Growth Douglas Fir 122 IV. Height Growth Data, Second Growth Douglas Fir 124 V. Complete Stem Analysis, Western Yellow Pine 125 VI. Yield Table Data, Second-Growth Douglas Fir 131 ix FIELD AND OFFICE PROBLEMS IN FOREST MENSURATION SECTION I— PRELIMINARY MEASUREMENTS PROBLEM 1. (Field.) Pacing. Explanation. — A great deal of the work in forest mensuration requires accurate pacing. The student should therefore at the outset learn to establish a distance of a surveyor's chain or mile with a fair degree of accuracy. In learning to pace the student should use his ordinary walking step. A longer step may be used with accuracy for short distances but cannot be kept up in long distance pacing without fatigue. Directions. A. Parties. — Each man will do individual work in this problem. B. Equipment Required. 1 hand compass. 1 100-foot steel tape. 1 field note book supplied with Form 1. C. Method of Procedure. 1. With the aid of another member of the class carefully lay off a quarter mile course over fairly rough country with a steel tape and a hand compass. 2. Go over the course several times using your ordinary step in order to determine how many double paces you take to cover the course. Then adjust the number of paces you take to the quarter mile to a certain even number which can readily be broken up into chains and rods; i.e., 240, 250, 260, etc. After establishing a standard step, go over the course repeatedly until you can cover the distance with practically the exact number of your standard paces. You should not be satisfied until your limit of error is within 3 double paces. 2 PRELIMINARY MEASUREMENTS Note. — In practically all engineering and mensuration work the distance between two points is expressed in terms of horizontal distance. Therefore in pacing across broken country the horizontal distance must be secured. Where the topography is rolling this may be accomplished by slightly lengthening the step, but where the slopes are steep resort should be made to one of the following expedients: a. Take extra steps to secure the unit pace. b. With a Jacob staff or a stick lay off the pace horizontally on the ground. c. Estimate the distances in terms of some unit of distance, i.e., pace rod, or chain. . When you can pace the original course satisfactorily, lay olT a dis- tance of a quarter of a mile in some other direction by means of pacing and a hand compass. During the actual process of pacing make a rough plat to a suitable scale of the physical features such as woods, trails, creeks, fences, etc., of the country you cross and note on the plat the distance in feet of each from the starting point. Draw the plat on Form 1 of the Field Note Book. 4. Check the accuracy of your pacing. With the aid of another mem- ber of the class go over the course covered in 3 above with compass and steel tape and note on the plat the exact measured distances from the starting point to each of the physical features indicated. D. References. — Consult table of units of measure in Appendi.x. PROBLEM 2. (Field) The Determination of the Diameters of Standing Trees. Explanation. — The object of this exercise is to give practice in estimating the diameters of trees by eye, to show the use of different types of in- struments, and to compare the efficiency of the different methods in use Directions. A. Parties. — Parties will consist of two men each. The men should alter- nate in the use of the instruments and in tallying results. B. Equipynent Required per Party. 1 pair tree calipers. 1 Biltmore stick. 1 diameter tape. 1 dendrometer. 1 field note book supplied with Form 1. C. Method of Procedure. 1. Obtain the diameters at breast height (D.B.H., 4.5 feet above ground) in inches and tenths, of at least 20 trees with each of the above instruments after first estimating the diameter by eye. The average diameter should always be taken . This can best be obtained by taking two measurements at right angles to each other. In using the instruments note the following: DIAMETERS OF STANDING TREES 3 The Calipers. — See that the calipers are in adjustment. If •they are, the closed arms will just fit together nicely when the handles of the arms* are pressed together. It they are out of adjustment, adjust by means of the set screw on the movable arm. In using the calipers he sure that the movable arm is -pressed hack against the scale-beam, and that the scale-beam is placed against the tree. This will lessen inaccuracies due to the arm being out of adjustment. In calipering a large number of trees care is also necessary that the measurements be taken at a point 4.5 feet (D.B.H.) above ground. The Biltmore Stick is based upon similar triangles, and assumes that the trees are perfectly round in circumference. To measure a diameter with this instrument place the stick flat against the tree at the point where the diameter is to be measured, being careful tha^ it is held horizontal and perpendicular to the line of sight from the eye to the center of the tree. The eye should be arm's length, 25 inches, from the stick. Move the stick to right or left until the line of sight from the eye to the edge of the tree passes over the zero end of the stick. The diameter is then read where the line of sight to the opposite side of the tree strikes the stick. . In making the reading be careful that the head is not moved and that the stick is not placed on a ridge or in a depression of the bark. The Diameter Tape. — No especial directions concerning the use of the diameter tape should be necessary. If a diameter tape is not available use an ordinary tape graduated into feet and tenths and divide by tt. Reduce to inches by multiplying by 12. The Dendrometer .—Since the types of dendrometers available are so varied special directions for using will have to be given by the instructor. In this connection the author has devised and exten- sively used an instrument termed a "tree cross" which is based upon the principle of the Biltmore stick except that the scale is attached by means of a sliding and swiveling joint fifteen inches from the end of a staff which is sixty inches long. The measurement is taken by placing the end of the staff nearest the scale against the cheek, the other end against the tree pointing towards the center and reading the scale as is done with the Biltmore stick. Tally the measurements of each tree according to the following form of notes: Tree Ocular Diameter Biltmore Dendrom- Tree No. estimate tape stick eter calipers When all measurements have been taken on the 20 trees, add up the total inches in each column; find the difference between each one of these totals and the total value secured with the calipers. 4 PRELIMINARY MEASUREMENTS Using the calipers as a standard now fmd the ])er('entage of error by divifUng tlie (HtTerenee ()l)tained V)y the total number of eaUpered inches. Comment on the comparative efhciency of the various methods and instruments as to accuracy, portabihty, etc. 3. In order to develop proficiency in estimating diameters by eye now make an ocular estimate of a large number of trees, checking each estimate with the calipers. D. References. Numbers 1, 2, 3, 5, 6, and 10. Note. — All numbers to references in this and succeeding problems refer to Bibliography in the Appendix. PROBLEM 3. (Field.) The Determination of the Heights of Standing Trees. Explanation. — The object of this problem is to give practice in estimating the heights of standing trees by eye and other rough methods, and by means of hypsometers, and to compare the efficiency of the various methods. Directions. A. Parties. — Students will work in two-man parties, alternating in the use of instruments and in tallying results. B. Equipment Required. — All the different types of hypsometers available, a 100-foot tape, and notebook supplied with Form 1 . C. Method of Procedure. 1. Select a tree standing in the open and measure its height accurately by means of a transit or other accurate method designated by the instructor. In using the transit, set up at any convenient horizontal distance measured from the tree, and read the vertical angle to the top of the tree. With a table of natural tangents of a right angle triangle compute the height of the tree above the level of the center of instrument. In a similar manner obtain the height below this level and add the two for the total height of the tree. 2. Measure this tree by the following rough methods: {a) shadow, (6) two-pole, (c) prostrate, and {d) with single pole, and with as many of the following hypsometers as are available: (e) Klauss- ner, (/) Faustman, {(j) Weisc, (/?) Winkler, {i) Christen, (j) Brandis, (A:) Goulicr, (/) omnimeter, (w) Abney level, (n) Barbow compass, (o) Forest Service Standard, (p) Forest Service Compass. (See note for description of rough methods.) HEIGHTS 0F» STANDING TREES 5 Note. — The various rough methods are described below: Sfiadoiv Method (a) Stick a pole of any convenient length, upright in the ground and measure its heiglit above the ground. (6) Measure the shadow oi the pole and the shadow of the tree and by proportion compute the height of the tree. Two-Pole Method (o) Stick a pole about 4 feet long, upright in the ground at any convenient distance from the tree. (6) About 6 feet away from this pole and in line with the first pole and the tree place a second pole about 10 feet high. (c) Sight from top of the short pole and make marks on the long pole at the intersections of the lines of sight to the top and to the base of the tree. (d) Measure the length between these marks, the distance from the top of the short pole to the base of the tree and the distance from the top of the short pole to the lower mark on the long pole. (e) By proportion compute the height of the tree. Prostrate Method. This method is similar to the two-pole method, except that the short pole is dispensed with and the observer takes the sight by lying on his back on the ground with his foot against the long pole. Sinch-Poh Method (a) Hold a pole about 5 feet long at arm's length loosely between the fingers of one hand, so that it will swing into an upright position and so that the portion of the pole above the hand is equal in length to the distance of the hand from the eye. (6) Without changing the position of the hand with reference to the eye, step slowly forward or backward until the line of sight to the bas ,■ of the tree strikes across the hand, and the line of sight to the top of the tree just. includes the tip of the pole. (e) The height of the tree then equals the distance of the observer from the tree. 3. After using the rough methods, use the different hypsometers. 4. Tally all measurements, on Form 1, according to the following form of notes: Instrument Total Error from Remarks or m.ethod Height Standard Two pole 83 1 Faustman. . . 84 The third column will be used for entering the error of each instru- ment or method from the height as measured by the transit or other accurate method. The ''Remarks" column will be used for enter- ing the estimator's reasons for condemning or recommending the instrument or method. 6 PRELIMINARY MEASUREMENTS 5. In order to develop proficiency in securing heights by eye now estimate the heights of a large number of trees by eye. Check each estimate with the hypsometer found to be the best. D. References. — Numbers 4, 8, 10, 11 and 12. PROBLEM 4. (Office) The Construction of a Dendrometer. Explanation. — The object of this problem is to illustrate the principles under- lying the construction of dendrometers such as the Biltmore stick or other similar diameter measures, and to construct an instrument which can V)e used in later field problems. The formula for securing the length of graduatioo of the Biltmore stick is: 25D V252+25D where a: = the length of graduation; D = the diameter of the tree ; 25 = distance in inches from the eye of the observer to the circumference of the tree. Directions. A. Method of Procedure. 1. Draw a diagram illustrating the principle of the Biltmore stick de- scribed in Problem 2. 2. Work out the complete algebraic proof of the formula given above for securing the length of graduation of the stick in terms of the 25-inch distance and the diameter of the tree. 3. Compute the exact length of graduation for each two-inch diameter class for trees from ten to sixty inches. 4. Select a hardwood stick approximately | inch scjuare and of a suitable length, and bevel off one side. Upon this side mark the graduations just computed, B. References. — Numbers 1, 2 and 3. C. Discussion. 1. In what respects would the proof of the principle of the tree cross mentioned in Problem 2 be different from that for the Biltmore stick? 2. Give a list of the advantages and disadvantages of the tree cross as compared with the Biltmore stick. PROBLEM 5. (Office) The Construction of a Hypsometer. Explanation. — The object of this problem is to illustrate the principles underlying the construction of a hypsometer such as the Christen or the THE CONSTRUCTION OF A HYPSOMETER 7 Merritt (Biltmore Stick) and to construct an instrument which can be used in later field problems. Either of the illustrations may be used. Illustration 1. — Construction of the Christen Hypsometer. Explanation. — The Christen hypsometer consists of a flat piece of brass or wood with a notch near each end between which are placed graduations representing heights of trees. The lengths of these graduations are secured by the following formula : AXB x = C where .c = length of graduation, measured upward from the lower notch, inches; A = distance between notches, inches ; B = length of the pole, feet; C = height of the tree, feet. In using the instrument the observer holds the upper end of the instru- ment suspended between his fingers, in front of his eyes and at any convenient distance away. An assistant holds upright against the base of the tree a pole of the certain length upon which the graduations of the instrument are based. The observer obtains the height of the tree by moving towards or from the tree until it is just included between the notches and then reads as the height of the tree the graduation intersected by the line of sight to the top of the pole. Directions. A. Method of Procedure. 1 . Draw a diagram illustrating the principle upon which the instrument is based and write out the complete algebraic proof. 2. For finding the length of graduations of the instrument in terms of the distance between the notches of the instrument, the height of the tree, and the length of the pole used with the instrument, proceed as follows: (a) Using 10 feet as the length of the pole and 12 inches as the dis- tance between the notches of the instrument, work out the length of the graduation measured upw^ard from the bottom notch for each five feet of height for trees from 20 to 100 feet in height. (6) Shape a stick 13X1 X0.25 inches with notches 12 inches apart and to a thin beveled edge between the notches, and mark the com- puted lengths of graduations on the beveled edge of the stick. Illustration 2.* — Construction of the Merritt Hypsometer. Explanation. — Markings may be placed upon the reverse side of the Biltmore stick. It should be held upright in the hand 25 inches from the eye of an observer when stationed 1^ chains from the tree. ♦Note — A third type of hypsometer easily may be made by attaching near one corner of a board ix3^x8 inches, a piece of wire which may swing as a pendulum. Graduations for tree heights may then be computed and marked along the opposite long edge of the board. 8 PRELIMINARY MEASUREMENTS A. Method of Procedure. 1. In a manner similar to that explained above draw a diagram illustrat- ing the principle and work out the formula for deriving the length of graduations of the Biltmore stick when used for securing the 16.2-foot log lengths in standing trees. 2. Compute the length of graduation measured upward from the zero end of the Biltmore stick for each 16.2-foot log from one to eight. 3. Mark these graduations on the reverse side of the Biltmore stick con- structed in Problem 4. PROBLEM 6. (Field) The Collection of Data for Volume Studies. Explanation. — The object of this problem is to illustrate practically the methods of taking measurements necessary for volume studies of every character. The student should realize at the outset that certain special studies require only certain of the measurements here called for and that when such special studies are to be made the first step in the work should be to determine just what measurements are necessary, so that all unnecessary measurements may be eliminated. The organization of parties and the routine as here suggested have been found efficient in Pacific Coast timber, though it may not prove so for the timber of other regions without slight modifications. Likewise, when a smaller variety of measurements is required, some changes in this routme' may be necessary. The proper key to the situation has been found only when each member of the party is kept busy without any "waits," for if any man has to wait on any of the others, the party is not efficiently organized. The lengths in which the sections will be measured and the top diameter limit to which D.O.B. (diameter outside bark) will be taken will ordinarily depend upon the use which is to be made of the data. If they are to be used for the construction of a rough "Used Volume Table" showing the average contents of trees as utilized at a specific logging operation, measurements will be taken to the last saw cut, and the length of sections will correspond with the log lengths cut by the logger. If on the other hand the data are to be used in the construction of a general volume table, a practically uniform volume should be secured for all trees of the same size and shape. To do this the sections muEt be taken in regular lengths up to a certain fixed diameter in the top, independent of the variable lengths into which different trees are cut by the logger. In such cases a certain length, such as 10.2 feet, 16.2 feet, or other regular length with a slight overlength above the even foot to allow for trimming in the mill, is determined upon in advance of the work, and trees are all measured in this length of section up to a certain fixed limit in the top, as for example 6, 8 or 10 inches. The tree will then be divided into sections of this length up to the fixed top diameter limit, regardless of whether the bole is broken or defective or of how the tree has been cut into logs by the logger. In case the bole of the COLLECTION OF DATA FOR VOLUME STUDIES 9 tree from the stuinp-cut (or from a fixed height above the ground should the measurement of the log sections not be started from the stump) up to the top diameter limit does-not contain an even number of regular sections, the last section and the fractional section will be broken into two even-foot lengths of as nearly equal length as possible. Example: In measuring to an 8-inch top diameter limit with 16.2-foot sections, suppose there results a section at the top 10.2 feet long. Instead of taking the last two sections in these lengths, they should be broken into a 14.2-foot length and a 12.2-foot length with the short length at the top and the D.O.B. measurements taken at the top ends of these sections. Care must be used in selecting the trees for measurement in order that a range of sizes may be obtained and in order that only normal specimens are . included. Abnormal trees or trees with any kind of malformation should not be measured. However, trees which are broken or are defective, as long as the defect does not affect their shape, may be taken, but they should be measured as entirely sound with no attention given to the defect. Illustratiox. — To Collect Data for a General Full Stem Volume Study. Directions: A. Parties. — The following organization of the men into 3-men parties, with the duties of each as indicated, will be found efficient: 1. The Notekeeper, who is chief of party, is responsible for all work, and tallies all measurements called out to him. 2. The Caliperman measures the D.B.H. and all other diameters outside of bark with the calipers, and the average width of bark with the analysis rule. 3. The Poleman locates the D.B.H. and measures the length of all sections including the stump and tip, and the clear length. B. Equipment Required for Each Party. 1 pair tree calipers. 1 six-inch flat boxwood or metal rule graduated into inches and tenths. 1 8-foot pole, graduated into feet and tenths, and with the D.B.H. point (4.5 feet) plainly indicated. 1 piece carpenter's crayon. 1 belt axe. 1 field notebook supplied with Form 2A. C. Summary of Measurements Required. Measurements Unit Instrument 1. Stump height Foot to nearest 0.1 ft. 8-foot pole 2. Stump diam. outside bark (D.O.B.) Inch to nearest 0.1 in. Tree calipers 3. Width of bark on stump Inch to nearest 0.1 in. Boxwood rule 4. D.B.H. outside bark Inch to nearest 0.1 in. Calipers 5. Length each section and tip Foot to nearest 0.1 ft. 8-foot pole 6. D.O.B. end of each section Inch to nearest 0.1 in. Calipers 7. Width bark end each .section Inch to nearest 0.1 in. Boxwood rule 8. D.I.B. end of each section Inch to nearest 0.1 in. (Calculated by notekeeper) 9. D.O.B. at middle of total height Inch to nearest 0.1 in. Calipers 10 PRELIMIXARV MEASUREMENTS D. Method of Procedure. 1. The chief of party should systematize the work as soon as i)ossil)Ic, for not until each man knows exactly what to do, and follows the same routine for each tree, will the work progress rapidly and efficiently. 2. The following method of procedure has been found efficient in Pacific Coast timber: The Poleman. (a) The poleman first approaches the stump of a tree, marks it with the crayon to prevent repetition, and then, setting the 8-foot pole alongside it, obtains its height. Care must be used not to measure the longest nor the shortest height, but the average. The poleman then calls out the measurement to the notekeeper and before proceeding further waits for him to repeat the figure to avoid errors in tallying. (6) Keeping his thumb on the pole at the point which indicates the height of the stump, he lays the pole along the first log with his thumb against the saw cut. The breast high point on the pole now shows where the D.B.H. measurement should be taken. This point is kept until the caliperman takes the D.B.H. or it is indicated by an axe or crayon mark. (c) Starting from the saw-cut at the butt of the first log the poleman now proceeds along the bole (up the tree) measuring the lengths of all sections, including the tip, and the clear length, in feet and tenths. The length of the tip should be carefully measured to the terminal bud, and if broken, a little time and care should be used to find the missing pieces. If they cannot be found, however, the length actually found should be measured and recorded as "found top"; and the missing part should then be estimated, and recorded as "estimated top" on the tally sheet (analysis sheet.) The clear length, which is the length from the large end of the butt log to the first prominent green limb, should be measured as the poleman proceeds up the bole. The Caliperman. (a) The caliperman follows close behind the poleman, measures and calls out to the notekeeper the various diameters and thickness of bark measurements as they are obtained in order. First, he obtains the D.B.H. at the point indicated by the poleman. This, since it is the most important of all measurements, should be obtained with great care by taking the longest and shortest diameters, or, when this is obviously impractical, by two measurements at right angles. COLLECTION OF DATA FOR VOLUME STUDIES 11 (b) Next, he measures the D.O.B. at the stump, again taking an average of the longest and shortest diameters, and the average width of bark determined by t\^o or more measurements. Every time he calls out a measurement he should wait for the notekeeper to repeat it. (c) In a similar manner he proceeds along the bole and obtains the D.O.B. , and width of bark at the top end of each section. Should the sections not be measured in the same lengths as cut by the logger, the width of bark will have to be secured by chopping through it, taking care to have the cut surface perpendicular at the point where the D.O.B. is secured. Often when the saw cut is not over a few feet from the point where the measurement is to be taken, or in rough work, the width of the bark of the nearest saw cut may be entered as that of the section being measured. A few trials will readily show to what extent this is permissible. (d) The D.O.B. at the middle of the total height of the tree will be measured in order to compare the two methods of com- puting volumes of trees explained in Problem 13. It is not required in ordinary work. The Notekeeper. (a) The notekeeper should always repeat the values as they are called out to him as a check in tallying the measurements. (6) Before leaving a tree he should check over his tally sheets to ascertain whether any necessary measurements have been omitted. At odd moments he should also make the follow- ing calculations and record them in the proper spaces on the tally sheet. 1. Diameter inside bark at each section, obtained by doubling the width of bark and subtracting from the D.O.B. 2. The total height, obtained by adding together the length of all sections, including stump and tip. 3. The used length, which represents the sum of the log sections just as used by the logger, and hence does not include stump and tip. 4. The merchantable length. This may be the same as the used length though not necessarily.' It is usually not when it is determined between a fixed diameter limit in the top, irrespective of the sections as cut by the logger. E. Discussion. 1. Supposing that the field data were to be obtained for the construction of a volume table on the D.B.H. only, and intended to show the con- tents of trees as cut by the logger, how would the above method of 12 PRELIMINARY MEASUREMENTS procedure be varied as to the list of the measurements taken, the organization of the work, and the accuracy required? 2. How woukl you proceed if you were to collect data in a tie operation for the construction of a tie table? 3. Give the method of procedure, measurements necessary, etc., for col- lecting data for a cordwood table. 4. In the collection of volume table data, why are broken or defective sections of a tree scaled as if sound? 5. Why are the measurements for a general table usually taken in regular length sections {i.e. 16.2), rather than in the same lengths as cut by the logger? 6. Explain the difference between fixed, merchantable, and used limits for the top diameters of trees measured . 7. How would the organization of the work in a full stem volume study be changed if there were only two men in the party? 8. What is the object of taking the clear length, and when should it be omitted? PROBLEM 7. (Field) The Collection of Data for Growth Studies. Explanation. — The illustration given below aims to include all measurements required in any growth study concerning itself with the stem of the tree (hence it does not include branches), and unless a specific problem involves a full stem analysis all of the measurements enumerated below may not be required. As in Problem 6, the student should realize that the first important step in the collection of data for any specific problem will be to determine just what measurements are required. Illustration. — To make a Complete Stem Analysis, Directions. A. Parties. — The organization of men into parties will be the same as for Problem 6, except that the taking of the D.B.H. and the D.I.B. measurements of each section will be added to the duties of the pole- man; and the caliperman now becomes the ring counter. The duties of the latter will be to count the rings at each cut, to make the decade measurements, and to obtain the thickness of bark. B. Equipment Required for Each Parti/. — Same as for Problem 6, with the addition of a small hand magnifying glass to aid in counting the annual rings and an analysis or similar rule graduated into inches and twen- tieths. If the trees are more than 2 1 inch(>s in diameter inside the bark at the stump, the analysis rule should be 24 inches long. It will also be found a great aid to the work if this is sui)plied with a centering point attached at the zero mark . COLLECTION OF DATA FOR GROWTH STUDIES 13 C. Measurements Required .—The measurements will correspond to those outlined for Problem 6, except that the D.I.B. at the top end of each section will be taken instead of the D.O.B. The following additional measurements will also be necessary: Measurements Unit Instrument Total age Years To be determined by a sepa- rate special study on seed- lings; see Problem 25 Age at each cross-cut Years Hand lens Measurements taken on average radius in ten- Inches to Analysis rule year periods (decades) nearest 0.05 D. Method of Procedure. 1. The Poleman. The Poleman, with the added duties of caliperman, will follow the same routine as before (see Problem 6), except that both series of measurements will be made at the same time as he proceeds along the tree. 2. The Ring Counter. (a) (c) id) The Ring Counter first obtains the average width of the bark. Then with the D.I.B. as obtained by the poleman he computes the average radius, and with the centering pin at the pith of the tree he swings the analysis rule until the length of the average radius just cuts the outer edge of the last ring. A straight line is now drawn from the pith to the bark along this radius. The rings are then counted from the bark to the pith and the tenth ring of each decade marked with a soft pencil. Care should be used to place the mark within the tenth ring. The total age at the cut and the distances from the pith to each tenth ring are then read off to the note-keeper m inches to the nearest 0.05. In reading off the decade measurements care should be taken to read to the inner edge of the early wood of each of the marked rings. 3. The Tallyman. (a) The Tallyman records the measurements in the proper column on the Tree Analysis Blank (Form 2A and B.) In recording the first decade measurement it will be found that it usually does not represent a full period of ten years. The number of rings included in this measurement should therefore be indicated in the upper left-hand corner of the space allotted to this measure- ment on the back side of the sheet (Form 2B.), and divided off from this space by a diagonal line. (6) He should make the following checks on the analysis sheet. 14 PRELIMINARY MEASUREMENTS 1. The last decade measurement should equal one-half the D.I.B. as previously tallied. 2. The age at any cut should be equal to the total number of decades minus one, times 10, plus the number of rings recorded in the upper left-hand corner of the space allotted to the first decade measurement. 3. The consecutive cross-sections should show a decrease in age from stump to tip. 4. Before leaving the tree he should carefully check over the entire tally sheet to see that none of the necessary measurements have been omitted, (c) In making the necessary calculations he determbies the D.O.B. at each cut instead of the D.I.B. as was done in Problem 6. This is done by adding twice the thickness of the bark to the recorded D.I.B. E. References. — Numbers 7, 9 and 80. SECTION II— USE OF GRAPHIC METHODS PROBLEM 8. (Office.) The Fundamental Principles in the Use of Graphic Methods. Explanation. — In this problem one of the simplest problems involving the plotting of curves has been chosen and outlined primarily with reference to illustrating the fundamental principles of determining averages by means of plotted values, and to show something of the significance of bringing out a series of related results by graphic representation. Illustration. — To Make a Table of Average Heights on Diameters by Plot- ting the Values on Co-ordinate Paper. Directions : A. Data Required. — Measurements showing the total heights of trees of dif- ferent diameters at breast height. Use Data Series I in the Appendix. B. Method of Procedure. (a) Preparing the Co-ordinate Paper. 1. The problem used to illustrate this exercise aims to determine an average height for certain specified diameters, i.e., the diameters of the trees are independent variable quantities and the heights dependent variables. As it is customary to let abscissae on the cross-section paper represent the independent values and ordinates the dependent values, in this problem let the abscissa? represent diameters and the ordinates heights. It is a rule to let horizontal distances from the vertical axis represent abscissae, and vertical distances from the longitudinal axis ordinates. 2. Having determined which values shall be represented by abscissae and which by ordinates, the next step is to determine the limits of variation which the data will represent {i.e., in this problem, what are the smallest and the largest values for diameters and for heights that it will be necessary to plot?), so that the unit best adapted for each of the co-ordinate axes can be decided upon. In deciding this unit, remember that the larger the unit the more accurate will be the results (so that the entire sheet of paper should be utilized as far as practicable), and also that 15 16 USE OF GRAPHIC METHODS the general aim should he io choose such unils (hot (lie curve loill be neither very Jlat nor very sleep. This aim is (icconiplished if the largest ordinate is not more than one and one- half times the largest abscissa. Remember this in connection with all curves. 3. Having determined the units for ordinates and abscissae, starting from the lower left-hand corner of the page lay off and mark the respective values on each axis. Always label these carefully along the edge of the paper; i.e., "Diameters in Inches," "Heights in Feet," etc. 4. In plotting the values remember, as before stated, that the hori- zontal distances from the vertical axis represent the values of the abscisstr. (diameter values in this case), and that the ver- tical distances from the horizontal axis represent the ordinates (heights in this case.) The two variable quantities, the height for a specified diam- eter, can be expressed by a single point on the co-ordinate paper ; namely, that point at which the perpendicular lines extending from the respective abscissa and ordinate axes cross. After the location of the first point has been determined plot the values of all other trees in the data supplied. Where a second point occurs at the intersection of the same lines place a small figure "2" beside the point already plotted, for a third point of the same value a small figure "3," and so on. (6) Averaging the Values. 5. When plotting is completed, the next step is to average the values in accordance with the object sought. In this problem the average height will be determined for each 2-inch diameter class in even inches. Remember that in all of these problems two sets of averages must be obtained. In this problem we have (1) the average heights for the diameter classes and (2) the average diameter of each diameter class. Let each of the diameter classes begin with the fractional part of the preceding whole odd inch and end with the next succeeding whole odd inch, of the diameter class, i.e., 5.1 inches to 7.0 inches inclusive will comprise the 6-inch class. In 1-inch classes it should be from 5.6 inches to 6.5 inches inclusive. The average abscissa for each diameter class will be found by adding horizontally the values of all points plotted within each diameter class, and dividing by the total number of points. Similarly the average ordinate for each diameter class will be found by adding vertically the values of the same points, and dividing by the number of points. With these two average values at hand now plot the average point in its proper place as was done with the points for the individual trees. In order that this point may be distinguished from the others FUNDAMENTAL PRINCIPLES 17 enclose it within a small circle or square. Opposite the average point enter the number of trees that the point represents. Note. — The following short cut in averaging saves a great deal of time. Instead of adding the actual values represented by the plotted points, let the first heavy line below and a similar one to the left of the group of points to be averaged represent zero lines. Now find the value of each point in terms of the number of spaces it is located from the new zero. Average, and locate the new point accordingly. (c) Draicing the Curve. 6. Connect the average points by fine straight hncs. This will help to show the general direction of the curve. 7. Next locate the direction of the curve by eye. In doing this imagine the curve as a flexible steel band so placed that the aver- age points, which are considered as magnets of a strength dependent on the number of trees represented, are about equally located on either side of it. The band will then take a position nearest the points with the greatest attractive force. After locating the direction of the curve by the eye, sketch in it free- handed as smoothly and regularly as possible, and finally smooth off the irregularities by means of a spline or adjustable curve. 8. From this curve construct a table of heights for each diameter in whole inches by noting the points where the respective perpen- dicular lines from the co-ordinate axes meet the curve. C. Discussion. 1. Supposing that the method of first averaging and then plotting the averaged points were used instead of that described above, explain in detail how the method of proced\ire would be varied. 2. Why can not the data be averaged in the above problem just as well without plotting values and drawing a curve? SECTION III— LOG RULES PROBLEM 9. (Office.) The Construction of a Scientific Log Ruls. Explanation. — The object of this problem is to illustrate the fundamental principles underlying the determination of the contents of logs in board measure. A thorough preliminary study of a rule such as the International, which is constructed upon scientific principles, should give the student a thorough understanding of the determination of the contents of logs in board feet, and a scientific foundation upon which to base his general study of log rules. Illustration. — The International Log Rule. The formula for securing the volume of a log 4 feet in length by the International log rule is F = 0.22D2-0.71D, where V = the volume of the log in feet B.M . ; D = the diameter in inches at the top end of the log. This formula is based upon the assumption of a loss for each 1 inch board of i-inch in saw kerf, and ye inch for shrinkage and that the loss in slabbing, edging and surface waste is equivalent to a board 2.12 inches thick, of the same width as the diameter of the log and the same length as the length of the log. Directions: A. Methods of Procedure. 1. Work out the complete algebraic proof of the International rule for 4-foot lengths, noting the reason for each step. 2. Using the formula for 4-foot lengths, and allowing ^-inch taper for each 4 feet, compute the volumes of the logs of all diameters from 6 inches to 16 inches inclusive, and each length in even 4-foot lengths from 8 feet to 24 feet {i.e., 8-, 12-, 16-, 20- and 24-foot lengths) . Arrange the results in table form leaving blank spaces for the alternating even-foot lengths (i.e., 10-, 14-, IS-, and 22-foot lengths.) 3. Now determine the values for the missing alternating lengths by plot- ting a separate curve for each diainc^tor from 6 inches to 12 inches using abscissa) as lengths, and ordinates as volumes. IS THE GRAPHIC COMPARISON OF LOG RULES 19 4. From these curves read off the vohimes for the missing lengths, and enter in the table. 5. Take a smooth stick-0.5XlXl3 inches and enter on it the values in the table, in the same manner as they occur on the ordinary scale stick. B. References. Numbers 17, 18, 25, 26, and 27. C. Discussion. 1. Write brief directions for using the scale stick in scaling logs. 2. What is the object in drawing the curve in this problem? 3. What particular fundamental principles make the International Rule more accurate than other formula rules such as the Doyle. 4. What advantages has a formula rule over a diagram rule? PROBLEM 10. (Office.) The Graphic Comparison of Log Rules. Explanation. — To illustrate the extreme variations in values obtained by scaling with different log rules. Illustration. — The International, Scribner, and Doyle Rules. Directions : A. Method of Procedure. 1. On a sheet of co-ordinate paper lay off diameters in inches as abscissa on the long edge of the sheet, and volumes in board feet as ordinates. Be sure first to determine the number of spaces you will allow to each unit by an examination of the data to be plotted. 2. With values read from a scale stick, or from the respective tables in Graves' Mensuration or the Woodsman's Handbook, Bull. 36 U. S. Dept. of Agr., construct on the same sheet of cross-section paper curves representing the values of the 16-foot logs of all diameters given by the International, the Scribner, and the Doyle Rules. B. References. Numbers 16, 19, 20, 23 and 24. C. Discussion. 1. Comment on the relationships as illustrated by the curves. 2. Could a combination table for the " Doyle-Scribner " Rule be con- structed so as to yield low values? PROBLEM 11. (Office.) The Extension of Log Rules. Explanation. — The object of this problem is to show how log rules with values reading only to a certain point may be extended so that the rule may be applied to logs of other dimensions. The method of procedure here outlined for log rules may also be used in the extension of volume, growth, or any other 20 LOG RULES tables in which the values vary more or less regularly according to some definite law. Illustration 1. — Extension by prolonging a curve. Explanation. — The Drew Rule has been chosen for this illustration because it gives values only for logs above 20 feet in length. The object will be to extend the values for 16-inch logs so that they may be scaled down to 10-foot lengths. Directions : A. Method of Procedure. 1. With lengths in feet as abscissae and volumes in board feet as ordinates, plot the following values for 16-inch logs by the Drew Rule. Length, Volume, Length, Volume, Feet B.M. Feet B.M. 20 194 32 311 22 214 34 330 24 233 36 350 26 252 38 369 28 272 40 388 30 291 2. Extend the curve backward to 10 feet. Be careful that the extended portion of the curve follows the spme general trend as the original curve. 3. Read values from the curve for lengths from 20 feet down to 10 feet in 2-foot classes and tabulate. 4. The values for other inch classes may be extended backward in a sim- ilar manner, and the values thus secured tabulated. Illustration 2. — Extension by interpolation. Explanation. — The Vermont Rule gives the following board foot contents for 16-foot logs. Diameter, Volume, Diameter, Volume, Inches B.M. Inches B.M. G 24 16 170 8 43 18 217 10 66 20 267 12 96 22 320 14 130 24 384 The object will be to extend this rule so that volumes for logs "d to 36 inches in diameter can be obtained. THE EXTENSION OF LOG RULES 21 Directions : A. Method of Procedure. 1. Find the difference in volume between the diameters of 14 and 16 inches, 16 and 18 inches, 18 and 20 inches, 20 and 22 inches, 22 and 24 inches. 2. Find the average of these differences. 3. Find the average increase of these differences. 4. To the vahie of a 24-ifich log as given in the table add the average difference found in 2, plus the average increase found in 3 and the volume of a 26-inch log will be obtained. 5. Secure the volume of a 28-inch log similarly by adding to the value of a 26-inch log the average difference plus twice the average increase. 6. Continue this operation for all even diameters up to 36 inches and tabulate. 7. The values for other log lengths may be extended in a similar manner and the values thus secured tabulated. B. References. Number 21. C. Discussion. 1 From this problem and the preceding one would you say that there is ever any justification for extending a log rule by tacking one rule onto another? 2. What are the different uses of plotted curves as illustrated in Prob- lems 8, 9, 10 and 11. SECTION IV— PRELIMINARY CALCULATIONS Explanation. — The object of this section is to give the student sufficient practice in making calculations by means of the various units used in forest mensuration, so that such calculations may be largely dispensed with in suc- ceeding problems wherein they become merely clerical work. PROBLEM 12. (Office.) The Determination op the Merchantable Con- tents IN Board Feet of Felled Trees. Directions : A. Data Required. — Use the tree measurement data collected in Problem 6. B. Method of Procedure. 1, With the aid of a Scribner decimal C log table or scale stick determine the volume in board feet of each log section measured except stump and tip, as shown by the length of the section (log) and the diameter inside of bark at the small end of the section. Round off all diam- eters to the nearest whole inch above or below the actual diameter. In rounding off diameters classify logs with diam- eters exactly half-way between inches (0.5 inch) in the next lower inch. Place all lengths in the even 2-foot length next below the actual size, unless "penalty scaling" is practised in which case place logs which exceed a certain amount allowed for trimming in the sawmill, in the next higher even-foot length. Enter the volumes in the proper columns on the analysis blank. (Form 2A.) Since in the construction of the Scribner decimal C rule the end figure is dropped, add a cipher to the volume of each section as read from the table to secure the full scale of the log to the nearest 10 feet. Note. — Where the Scribner decimal C. rule is used for scaling Pacific Coast timber, the maximum scaling length of any section should not exceed 32 feet; i.e., logs up to and including 82 feet in length should be scaled as one log, and logs longer than this as two logs of as nearly equal even-foot lengths as possible, the shorter length to be taken nearer the smaller diameter. In this case the diameter at the end of the larger log will be determined in Pacific Coast species by allowing one inch increase for every 10 feet of length for taper; i.e., for lengths from 5 to 15 feet allow 1 inch, for lengths from 16 to 25 feet 2 inches. To illustrate further, a 36-foot log should be broken into two 18-foot sections, and the diameter at the end of the butt section as 2 inches larger than the top diameter at the small end of the whole (36-foot) log. Similarly, a 38-foot log would be broken into a 20-foot section and an 18-foot section, the longer section at the butt end with a diameter 2 inches larger than the top section. 22 . TOTAL CUBIC CONTENTS OF FELLED TREES 23 2. Add the volumes of all sections to determine the total merchantable volume of the entire tree, and record in proper space. C. References. Number 45. PROBLEM 13. (Office.) The Determination of the Total Cubic Contents OF Felled Trees. Explanation. — The object of this problem is to show the comparative value of the different methods and to develop proficiency in making the various fundamental calculations required in the determination of the cubic contents of trees. Illustration I. — To compute the cubic contents of felled trees by cubing the tree in sections. Explanation. — In this method each section in the tree is compared to a geometric figure and for that reason logs, stumps, tips and branches each require the use of a distinct formula . The various formulae follow : A. The Cubic Contents of Logs. 1 . Let B = basal area in square feet of large end of log ; 6 = basal area in square feet of small end of log; L = length of log. Then the cubic contents may be expressed by Smalian's formula as follows : 2. Determine basal areas in square feet by, — 4 ^144' Where d = the diameter of the area in inches and — is used to 144 reduce to square feet. B. The Cubic Contents of Stumps. A stump is treated as a cylinder whose diameter is equal to the top diameter of the stump. The formula for the cylinder is BXL. C. The Cubic Contents of Tips. A tip is treated as a cone whose basal area is equal to the basal area of the tip, and whose altitude is equal to the length of the tip. The formula is, \BXL. M f State College 24 «'• *" PRELIMINARY CALCULATIONS D. The Cubic Contents of Branches. A branch is treated as a cylinder whose diameter is equal to the diam- eter of the middle of the branch. Letting Bi equal the middle diameter and L the length, the formula becomes, BiXL. Directions. A. Data Required. — Use the data collected in Problem 6. B. Method of Procedure. 1. Compute the contents of one tree according to the formula) given in the Explanation. 2. In the remaining data use, in place of the formula for basal areas, the table of basal areas given in the Appendix (Table IIL). 3. Tally all volumes in the proper column on the analysis blank and total. Illustration 2. — To Compute the Cubic Contents of Felled Trees by Cubing the Tree as a Whole (Schiffel Method). Explanation. — The following formula for securing the full stem volumes of trees, devised by Professor Schiffel of the Austrian Experiment Station, has recently been introduced in this country. Cubic contents of a tree = (0.16 B-\-O.QQb)H, where J5=area in square feet at the D.B.H. point; h = basal area in square feet at the middle of the total height ; H = total height in feet. This formula is explained in the ''Centralblatt fiir das gesamte Forst- wesen" for December, 1906. It has not yet gained general use in the United States as its accuracy has not been completely established. This illustra- tion serves to compare its accuracy with the SmaUan method of cubing trees. Directions. A. Data Required. — Use the same data as in Illustration 1. B. Method of Procedure. 1. Compute the cubic volume of one tree using the Schiffel formula. 2. In the remaining data use tables Number I and II in the Appendix for finding value of 0.16 B and 0.66 b. C. References. — Numbers 28, 29 and 31. D. Discussion. 1. Comment on the relative accuracy of this method as compared with that of cubing each section separately outlined in Illustration I. CONTENTS OF TREES IN STANDARDS 25 2. In what way will tlii's method decroase the necessary field work involved in securing the tree measurements? PROBLEM 14. (Office.) The Detek.mi.xatiun of the Merchantable Contents OF Trees in Standards. Explanation. — A Standard is a log of specified dimensions used as a unit of volume. It is based on the principle that the contents of logs vary directly as their lengths and the squares of their respective diameters. The volume of any log in terms of a specified standard may be obtained as follows : ''Square the diameter at the small end, and divide by the square of the diameter of the standard log; then divide by the length of the standard log and multiply by the length of the log measured." Illustration. — To compute the Merchantable Contents of Trees in the " 19- inch Standard." Explanation. — The "19-inch Standard" is a log 13 feet long and 19 inches in diameter at the small end. The formula for determining the contents of a given log by this rule is, D2 L where V = volume in standards ; Z) = diameter inside of bark in inches at the small end of the log to be measured ; L = length in feet of the log to be measured. Directions. A. Data Required. — Use the data collected in Problem 6. B. Method of Procedure. 1. Compute the volumes of all vSections except stump and tip in 19-inch standards. 2. Enter the values in a blank column on the analysis sheet, label properly and total. PROBLEM 15. (Field.) The Determination of the Contents of Standing Trees by Short Methods. Explanation. — It is often necessary to determine the contents of standing trees by some short rule of thumb when no volume table or other better means is available. The student will find it very convenient to have one or more of these short rules at his constant command. Each of these methods should be tried out on 12 trees, except method II of Illustration 1, which will be used in connection with Problem 23. Illustration 1.— To Compute Contents in Board Feet of Standing Trees by the Spaulding Rule. 26 PRELIMINARY CALCULATIONS Explanation. — The Spaulding Rule is well adapted for Pacific Coast timber. The original Spaulding Rule was based u[)on diagrams but the following rule of thumb gives approximately the same result. Vol = (/^-— 3D)— plus 3 per cent to G per cent of the value obtained by this formula. D R H -I--D R H where D = — '—^ — — - — '- '- — and in which the D.B.H. is the diameter breast high inside the bark, in inches. L = length from top of stump to point at which diameter inside bark is equal to one-half the D.B.H. inside bark. In practice it makes little difference whether this length be estimated with the \ D.B.H. point taken as one-half the D.B.H. outside the bark or one half the D.B.H. inside the bark as long as both measurements are taken either inside or outside the bark. The first part of the fo nula, namely that without the addition of the 3 to 6 per cent will give thv. volume of the tree up to the \ D.B.H. point. The additional 3 to 6 per cent will give the value of the merchantable portion of the tree above the \ D.B.H. point. In the case of trees with very tapering tips above the \ D.B.H. point, the lower percentage, namely 3 per cent, should be used, while for trees without excessive taper above the \ D.B.H. point a higher percentage, up to 6 per cent should be used. To compute the volume by this formula two measurements of the tree are necessary, the D.B.H. and the length from stump to \ D.B.H., which will be obtained as outlined in the method of procedure. Directions. A. Parties. — Men will be organized in two-man parties, each man alternating as cruiser and tallyman. B. Equipment Required per Party. 1 pair tree calipers. 1 hypsometer. 1 dendrometer (if available). 1 field note book supplied with Form 3 A, C. Method of Procedure. Method 1. — By tallying D.B.H. and merchantable length for each tree. 1. Caliper D.B.H. outside bark of the trees whose volumes are to be computed. 2. By estimate determine width of bark at breast height, and check thickness of bark occasionally by chipping through it. CONTENTS OF STANDING TREES BY SHORT METHODS 27 3. Estimate, checking the estimate occasionally with hypsometer, the height from stump up to 5 D.B.H. outside bark. 4. Tally these three measurements on Form 3 A, using one vertical column for each species. On the left-hand side of the column, opposite the proper D.B.H. class, enter the width of bark and on the right-hand side the height up to | D.B.H. for each tree cal- ipered. 5. From these field measurements compute the volume inside bark of each tree from the formula . Method H. — By tallying the D.B.H. of each tree and securing heights from a height curve. 1. Caliper D.B.H. outside bark of the trees whose volumes are to be computed. Note. — When the D.B.H. of a tree falls at a point where the bole is swell- butted the measurement should be reduced so as to give the tree the average amount of taper which in the judgment of the cruiser the conditions will warrant, for otherwise the formula will give results too high. 2. Take measurements of D.B.H., width of bark, and merchantable length to ^ D.B.H. on at least 30 fallen trees of various sizes. 3. From these measurements construct a height curve showing mer- chantable heights for different diameters breast high outside bark. 4. Using an average width of bark for each D.B.H. and with heights obtained from the height curves, compute volumes inside bark with the Spaulding Log Rule, for trees 20, 30, 40, 50, 60, 70 inches D.B.H. outside bark. 5. Plot the volumes of the sizes thus computed, connect with a curve, and read off the volumes of the intermediate diameters breast high outside bark. 6. Tally the volumes thus obtained in tabular form, and use this table for computing the volumes of trees calipered. Illustration 2. — To Compute the Contents of Standing Trees in Board Feet by the Doyle Rule. Explanation. — The Doyle Rule is simpler than the one described above but is not accurate for Pacific Coast timber, since it will give high results, as is the case when this rule is used with large-sized logs in any region. The rule follows : Volume of tree = ( — — - ) XL. m D = middle diameter inside bark obtained by averaging the diameters at the top and base of the merchantable length of the tree; L = merchantable length. Directions. To apply the Doyle Rule follow Illustration I, Method I, described above, except that the middle diameter should be tallied instead of D.B.H. 28 PRELIMINARY CALCULATIONS Illustration 3. — To Compute Contents of Standing Trees in Cubic Feet or Cords. Explanation. — The object of this illustration is to demonstrate a method of determining the volume of standing trees in cubic feet or in cords. The Schiffel formula (see Problem 13, Illustration 2) may be used for computing the volumes in cubic feet and the contents in cords may be determined by dividing the total cubic volume by 90. This converting factor of 90> is based upon the supposition that a cord of wood contains 70 per cent solid wood. This of course will vary with the method of piling, and the size and form of the pieces. Should the trees be crooked or knotty, and the wood be split in small pieces, or should wood be wasted in the stump or top a converting factor between 80 and 90 should be used; on the other hand, should the timber be very smooth, straight and be cut in very large pieces a factor between 90 and 100 should be used. Directions. A. Parties. — Use the same party organization as for Illustration 1. B. Equipment Required Per Party. — Use the same equipment as for Illus- tration 1, except that Form 1 should be substituted for Form 3 A. C. Method of Procedure. 1. Prepare Form 1 with the following column headings on a separate sheet for each species : 0. D.B.H. Total Height D.M.H. Vol. Cu. Ft. Vol. Cords The D.M.H. column will be used for tallying the diameter at the mid- dle of the total height. The D.M.H. and total height of each tree should be tallied opposite its D.B.H. Caliper the D.B.H. outside the bark of each tree. Estimate, checking occasionally with a hypsometer, the total height of each tree. Estimate, checking with a dendrometer if available, the D.M.H. out- side the bark of each tree. With the Schiffel formula work up the cubic volume including the bark of all trees and total. Divide the total volume of each species in cubic feet by 90 to redu(;e to cords. D. RrftTcnccs. — Numbers 51, G4, and tif). SECTION V— THE CONSTRUCTION OF VOLUME TABLES Explanation. — The problems in this section have been chosen with reference to illustrating a number of fundamental problems which may serve as a basis for all volume table studies. Each problem illustrates some one or more specific features. These are emphasized in each instance in the ital- icized portions of the titles. The relation of the specific features to related problems are brought out by special questions. Caution. — In the problems of this section the student should use special care to label all work completely. The co-ordinate axes should be labeled with the unit being used, as ''Volume in cubic feet"; and each completed curve and table should contain all the information necessary to give it scientific accuracy. Substantial reductions in grade will be made for any work turned in that is not properly and completely labeled. The following points should be considered in the title of a completed volume table, though not all need be included, because some one condition may be wholly obvious from some others already stated : 1. Kind of table. 2. Species. 3. Forest type. 4. Locality. 5. Number of trees upon which table is based. 6. Top diameter-limit used. 7. Date. PROBLEM 16. (Office.) The Construction of a Merchantable Volume Table in Board Feet Based on D.B.H. Only. Directions. A. Method. — Averaging the values first and then plotting the averaged points. B. Data Required. — The student should determine first just what field measurements are necessary for the construction of a volume table of this kind. (See Problem G.) Before beginning the work he should ask the instructor whether his conclusions on the j^oint arc right. Use Data Series I or the data collected in Problem 6. In case the latter are used the field work of the entire class should be used by each student. 29 30 THE CONSTRUCTION OF VOLUME TABLES C. Method of Procedure. A. Tabulation 1 . Divide a piece of blank note paper into tabular form with the following headings. One Inch Tallied Values Averaged Values D.B.H. Classes Tallied D.B.H. Volumes B.M. No. of Trees Average D.B.H. Average Volumes 11" Class 10.6 to 11.5" 12" Class 11.6" to 12.5" The horizontal lines should be spaced far enough apart to allow the data for all trees included in any 1-inch diameter class to be listed between them in a vertical column . Label the spaces successively with the diameter classes they are to represent. 2. Tally in a vertical column in the space allotted to the D.B.H. measure- ments the actual breast high diameters to the nearest 0.1 of an inch, placing each in the space allotted to its class, as determined by the rule that each class shall contain all trees whose diameters ' range from .6 of the one inch to .5 of the next inch higher, inclusive. 3. In the second column enter opposite each D.B.H. tallied the calculated volume of the tree in board feet. 4. In the third column enter the number of trees in each diameter class. 5. When all the trees have been tallied, add the actual D.B.H. measure- ments in each class, as recorded in the first column, and divide by the total number of trees in the class as recorded in the third column to obtain the average D.B.H., and record it in the fourth column oppo- site its diameter class. 6. In a similar way add the separate volumes in each class as recorded in the second column, and divide by the number of trees in the class to obtain the average volume, and record in the fifth column . B. Plotting. 7. On a sheet of cross-section paper lay off diameters (D.B.H.) and vol- umes as co-ordinates. Determine first which will be abscissa; and which ordinates and be careful to select values for each commensurate with the limits of variation in the data and the size of the cross- section paper. 8. Plot the average values as determined and recorded in the tables, and enter beside each plotted point the number of trees it represents. FULL 8TEM CUBIC FOOT VOLUME TABLE 31 9. Connect the consecutive average points by fine straight hnes. 10. Draw a free-hand curve, giving weight to the various points according to the number of trees represented, and smooth off the curve with a si)hne or other curve rule. 11. Read off from this curve the volumes for whole inches as indicated, and tabulate in one corner of the sheet of cross-section paper. 12. Label the exercise and indicate the species, forest type, locality, total number of trees used, and date. D. References.— lumbers 31, 32 and 36. PROBLEM 17. (Office.) The Construction of a Full Stem Cubic Foot Volume Table Based on D.B.H. and Total Heights. Method. — Averaging the values first and then plotting the averaged values. For this problem diameters will be taken in 2-inch classes, and heights in 20-foot classes. (Ordinarily heights are taken in 10- or 16-foot classes.) Directions. A. Data Required. — Determine first just what field measurements are neces- sary for this problem. They differ slightly from those of Problem 16. Ask the instructor if you are right before proceeding. B. Use Data Series I, or the data collected in the field in Problem 6. C. Method of Procedure. I. Tabulation. 1 . Prepare a blank form for tabulation like the following : 20-FooT Height Classes Two-inch D.B.H. Classes 80 100 120 140 Etc. 1 D.B.H. Vol- ume D.B.H. Vol- ume 1 D.B.H. ""'- ume D.B.H. ^'>'- ume D.B.H. Vol- ume 12" Class 11.1" to 13.0" 14" Class 13.1" to 15.0" Each diameter class will be imderstood to include all trees from .1 over the whole inch of one diameter to the whole inch of the second higher diameter inclusive; i.e., the 12-inch class includes all trees 32 THE CONSTRITCTION OF VOLUME TABLES from 111 inclics to !;>.() iiiclics iiu'liisivc; and all lici^htclasses from 9 feet below to the even 10 feet above the value iiulicating the class; i.e., the 80-foot height class includes all trees from 71 feet to 90 feet inclusive. 2. Record the D.B.H. and computed volume of each tree in the space allotted to it according to its D.B.H. and total height. Tally D.B.H. in inches and tenths, and full stem volume in cubic feet and tenths. 3. When all the trees are tallied, determine the total diameter and total volume for each diameter-height class by adding the recorded values and divide each by the total number of trees added to obtain the average diameter and average volume of that class. n. Plotting A new feature in plotting the values for this exercise arises which has not been explained heretofore. (See Problem 8.) Instead of having one dependent and one independent variable we now have two independent variables namely, diameters and heights; and the volumes as the one dependent variable. Hence three distinct values must be considered. Since a single plotted point on a piece of cross-section paper cannot express more than two values it now becomes necessary to draw a series of harmonized curves b}^ means of which it is possible to express the three values. This is done by first plotting separate "volume-on- diameter" curves for each height class. From the resulting series of curves we obtain the volumes according to -the different diameters irrespective of average heights. With the average volumes read from this series of curves we now con- struct a series of " volume-on-height " curves for the different diameter classes, and from them obtain the final values as follows: a. Averaging the Diameters. 1. On a piece of cross-section paper lay off diameters as abscissae and volumes as ordinates. Since several curves must be drawn on a single sheet of cross-section paper it will be well, in order to avoid confusion, to use a scale such that 1 inch on the paper will repre- sent at least 2| inches in D.B.H. values. It will also aid if the different points of each height class are connected with lines in different colored inks or crayons. 2. Plot a curve for the first height class using each of the average values and average heights under that class; i.e., plot a curve for the 80-foot height class using the D.B.H. and volumes on the tabulation sheet in a vertical column under this class. Besides each plotted point place the number of trees represented. Join the points by fine lines and draw a smooth curve. Label this curve with the height class it represents. 3. In a similar manner, with the same values for abscissae and ordi- nates, and on the same sheet of cross-section paper, plot the FULL STEM. CUBIC FOOT VOLUME TABLE 33 values and draw smooth curves for each one of the remaining height classes. Label each. If any of these height classes con- tain but few or chiefly abnormal trees, the curve for this class must be interpolated between the next higher and lower classes. 4, From each height curve now read the average volume for the respective average diameters in 2-inch classes by taking the reading at every even inch. . Averaging the Heights. — Up to this point we have evened off the volumes according to the average diameters, irrespective of heights. Hence it will now be necessary to determine what the average volumes will be according to the average heights. 1. On a piece of cross-section paper lay off heights as abscissa; and volumes as ordinates. ~ 2. Now construct a set of curves similar to those constructed under ''rt," except that a separate curve is constructed for each diameter class, using the new volumes read from the first set of curves on the average heights. Use for the heights in this plotting the value indicating the cla'^s. 3. Read off the values for every even 20 feet and tabulate in the final form as follows: D.H.B. Height Classes Classes 80 100 120 140 Etc. 12 14 16 Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Volume Label every curve of this exercise completely, and put a legend on the final table showing the type of volume table constructed, the species, the number of trees upon which the table is based, the unit of measure, and the diameter limit used in computing the volumes of the trees. D. /^e/cre^e.s.— Numbers 39, 41, 42, 43, 44 and 62. E. Discussion. 1. Of what use is a volume table? Can it be applied accurately for securing the value of a single tree? Why, or why not? 2. In what respect would the method of procedure, outlined above, be varied if the table should be constructed in board feet instead of cubic feet? 34 THE CONSTRUCTION OF VOLUME TABLES 3. What is the difference in the data required for the construction of a table based on D.B.H. only and one based on D.B.H. and total heights? 4. Which of the two tables would be the more accurate and why? Which would be easier to use? 5. How many trees would ordinarily be considered the minimum for a good D.B.H. only volume table? For a D.B.H. and total height table? 6. Outline stej) by step and in detail the nu^thod of procedure in a manner similar to that used in Problem 17 for making a table based on D.B.H. and number of 16-foot logs. 7. What are the chief details in which the construction of a table based on D.B.H. and merchantable lengths differ from the method of procedure outlined in Question 6? 8. Describe briefly how a cordwood table based on D.B.H. would be constructed. 9. Describe briefly how a tie table based on D.B.H. would be constructed. PROBLEM 18. (Office.) The Construction of a Table of Stem Form Factors Based on D.B.H . Only. Explanation: The object of this problem is to illustrate the method of constructing a table of form factors and to show the difference between such a table and a volume table. Directions: A. Data Required. Use the data collected in Problem 6. B. Method of Procedure. 1. First compute the full stem volumes of the trees in cubic feet as explained in Problem 13, Illustration I. 2. Divide the computed volume of each tree by the cubic contents of a cylinder whose diameter is the same as the D.B.H. of the tree, and whose height is equal to the total height of the tree. Call the results the "form factor fractions." For determining the contents of the respective cylinders use the tables of Basal Areas in the Appendix and multiply by the heights. 3. From this point on, the method of constructing the tajjie will be the same, step by step, as outlined for Problem 16, except that the expression "form factor fraction" is used in place of "volume in board feet" throughout the exercise. Note. — For rough work the Schiffel formula may be used for securing the form factor directly without the necessity of first finding the cubic volume and then dividing this volume by the volume of a cylinder. By the Schiffel formula the form factor of a tree is equal to 0.16 + 0.GGXQ2 where Q is the form quotient, which is the D.M.H. divided by the D.B.H., where the D.M.H. equals the diam- eter at the middle height of the tree. VOLUME TABLE IN BOARD FEET BASED ON D.B.H. 35 C. Discussion. 1. What is the difference between a table of form factors and a volume table? 2. What is the difference in their uses? 3. Which is the more practical for ordinary timber estimating? PROBLEM 19. (Field.) The Construction of a Merchantable Volume Table in Board Feet Based on D.B.H. and Number of IQ-Foot Logs by THE Frustum Form Factor Method. Explanation. — A method of constructing volume tables based on D.B.H. and log lengths which much lessens the office work involved and which will give a better table with a lesser number of trees has been devised by Mr. Donald Bruce and is described by him in the Forestry Quarterly, Volume X, Number 2 and in the Proceedings of the Society of American Foresters, Volume VIII, Number 3. This method has not gained universal use and its accuracy compared with the usual method of constructing volume tables has not been entirely established. Several tests have, however, shown that excellent results can be obtained with the method. The following problem will demonstrate this method of constructing a volume table. Directions: A. Data Required. — About 25 trees will be required for Method I and 100 or more for Method II. Use data collected in Problem 6, or trees of different sizes w^hich show the volumes of boles in board feet measured in 16-foot lengths to an 8-inch diameter in the tops selected at random from Data Series I. B. Method of Procedure. Method I. To construct a volume table with a small number of trees. 1. Tabulate the sizes of the trees to be used in this problem according to the following form : D.B.H. Inches No. 16-ft. Volume Logs B.M. to 8" Top j to 8" Top Diameter ' Diameter Frustum Form Factor Compute the frustum form factor for each tree by dividing the volume of the tree by the volume of the corresponding frustum of a cone as secured from the table of frustums of cones in the Appendi.x (Table IV). Interpolate in this table the volumes for diameters breast high to 0.1 inch and lengths to the nearest ^ of a 16-foot log. 36 THE CONSTRUCTION OF VOLUME TABLES 3. Find the averago frustum form factor by obtaining the sum of the individual form factors of all trees and dividing by the number of trees. 4. Obtain the volume taV)le by multiplying each volume in the frustum table in the Appendix by the average frustum form factor. Method IL To construct a volume table with a considerable number of trees. 1. Compute the frustum form factor as in Method L 2. Devise a convenient form of tabulation and group the trees into 5-inch diameter classes. Secure for each class the average frustum form factor. 3. Round off the values of these average frustum form factors by means of a curve. 4. Obtain the final volume table by multiplying each value in the frustum table in the Appendix by the average frustum form factor for the diameter class in which the value is included. Note. — Should the table in the Appendix giving the volumes of frustums of cones not contain a sufficient range of values it may be extended by the method illustrated in the following two examples: Example 1. To find the volume of the frustum of a cone with 8-inch top, 10 inches D.B.H. and H logs in length. Tree: 10 inches D.B.H. with 8-inch top and 1 log in length yields 1 8-inch log containing 32 feet B.M. Tree: 10 inches D.B.H. with 8-inch top and 2 logs in length yields 1 8-inch log containing 32 feet B.M. 1 9-inch log containing 42 feet B.M. Total volume. . . .■ 74 feet B.M. By Interpolation Tree: 10 inches D.B.H. 8-inch top 1| logs in length yields 32 + K74-32) = 43 feet B.M. Example 2. To find the volume of the frustum of a cone with 8-inch top, 16 inches D.B.H. and 4 logs in length. Total taper = 8 inches. Taper per log = 2 inches. Tree yields 1 8-inch log containing 32 feet B.M. 1 10-inch log containing 54 feet B.M. 1 12-inch log containing 79 feet B.M. 1 14-inch log containing 114 feet B.M. Total volume 279 feet B.M. THE CONSTRUCTION OF A TAPER TABLE 37 C. References. — Numbers 33, 34 and 40. D. Discussion. 1. What is gained over Method I by using IVIethod II? 2. Compare the frustum form factor method and the regular method of constructing volume tables as to time required and as to accuracy. 3. How might the table bo constructed by averaging according to the number of 16-foot logs as well as according to D.B.H. as explained in Method H? PROBLEM 20. (Office.) The Construction of a Taper Table. Expl.\nation: Taper Tables show for each D.B.H. the top diameter inside the bark of the respective 16-foot logs (the usual length employed). Such tables can be used in place of volume tables in cruising where the trees are tallied according to the D.B.H. and number of 16-foot logs. This method has an advantage over volume tables in that an estimate can be worked up according to any log rule or any one of the units of log measure. It presents the disadvantage of requiring more subsequent calculations for securing the volume of an estimate than does the use of volume tables. Directions: A. Data Required. — Use data collected in Problem 6. B. Method of Procedure. (Prerequisite study — Reference Number 38.) 1. On a separate sheet of cross-section paper for each 20-foot total height class, lay off heights above the ground as abscissae and diameters inside of bark as ordinates. 2. Plot all trees in 2-inch D.B.H. classes. 3. For each D.B.H. class plot points representing the D.I.B. at the top end of each 16-foot log section. If possible, plot all curves on one sheet using a different symbol (., x, o, O,) for each diameter class in order to keep the various classes separate. 4. Average points for each 16-foot section of each D.B.H. class, and construct regular curves for each D.B.H. class. 5. Assume an arbitrary stump height (e.g., 3 feet), and read off the D.I.B. values for each 16-foot section. 6. For the same 20-foot total height classes and u^ith the same ordi- nates but using D.B.H. for abscissae, replot and average the data in separate 16-foot classes above the stump. 7. From the averaged data found in 6, for each 2-inch D.B.H. class plot a series of 16-foot curves above the stump, using the same ordi- nates and the total heights of trees as abscissae. 8. With the averaged data from 7 now plot a fourth set of curves exactly as was done in 1 and then, with the data thus obtained, plot a fifth set of curves as was done in 6. Retain the data thus obtained in graphic form or read off a set of tables. SECTION VI— SCALING PROBLEM 21. (Field.) Scaling Logs. Explanation: The method of scahng sound logs free from any defect or malformation is very simple. All it requires is that the diameter inside the bark at the small end of the log and the length of the log be measured and with these two measurements the corresponding volume in board feet may be found on a scale stick or in a table giving contents of logs according to the log rule used. Should the lengths of logs to be scaled be limited to a certain maximum length, logs longer than this length should be scaled in two sections of as nearly equal even-foot lengths as possible, the shorter length to be taken at the small end of the log. The diameter of the section nearest the large end of the log should be increased over the diameter at the small end by an amount corresponding to the taper, estimated for each log. The sum of the volumes of the two sections will give the volume of the log. However, no method of scaling is accurate unless the sound volume is discounted to allow for defects which may occur in the log. The following formulae and tables together with an explanation of the method of their use will demonstrate typical methods of allowing for defect in scaling. FormuloB for Scaling Defect Pitch Seams OC^C^^i^E^ T = DDXL V 12 7 5 15 W= width of seam across end of log, inches; A = waste thickness, inches; 12 = dividing factor, to reduce to B.M. DD = defect deduction per lineal foot in feet B.M, L = length of defect, feet; 1^ = reducing factor, to allow 20 per cent for sawkerf; T = total number feet B.M. defect caused by seam. SCALING LOGS 39 Pitch Rings DD=(''-^Y = 0.2iDXA) T = DDXL. \ 12 / 5 D = diameter of ring, inches; 7r = 3.14. Remaining factors same as for pitch seams. Rot 4 W^ DD= { — ]- = —, T = DDXL. \12/- TT^=side of a square which can be circumscribed around the defect, inches; Shingle Bolts 144 ^ = area of end of bolt, square inches; L = length of bolt, inches ; 144 = dividing factor to reduce to B.M.; .70 = per cent of utilization; y = total number feet B.M. in bolt. Explanation of Scaling Formulae There are various systems of m.aking allowance for the defects which occur in logs but the simplest and most logical is to consider the amount of the defect as equivalent to the piece of lumber which would be lost in sawing it out in the saw mill. As tl^ Scribner rule makes an allowance for sawkerf of J inch for each 1-inch board or a deduction of 20 per cent of the volume of the log this deduction should also be taken into account in making the defect allowance. In the formulae the defect deduction is first found per lineal foot and then multiplied by the length of the defect as this is the easiest procedure for the scaler to follow in practice as will be e.xplained below for each type of defect. Pitch Seam. — To determine the amount of defect in a log with a pitch seam or seams the scaler should determine if they show on both ends of the log and whether they are straight or twisted, for the greater the twist the 40 SCALING LOGS greater will be the amount of waste. Sometimes a seam at one end of the log will be at right angles to its position on the opposite end. If the seam shows on one end only, the scaler should estimate the length it extends into the log .and take as the width of the seam its width as it shows. If the seam shows at both ends of the log the width of the seam should be taken at Avhich- ever end it is the greatest. Measure the width of the seam across the end of the log and the inches of waste that will result from sawing out the seam. Multiply the width of the seam by the thickness of the waste, divide by 12, and multiply the result by ^, which will give the number of feet B.M. defect per lineal foot. Multiply this by the length of the defect and the result will be the total number of feet B.M. defect caused by the seam.* Pitch Ring. — To determine the amount of defect in a log with a full pitch ring the scaler should first determine if the ring shows on both ends of the log. If it does not show on both ends he should estimate the number of feet it extends in the log, and then measure the diameter of the ring. If it shows on both ends he should average the diameters of the rings on both ends. Care should be used in getting this average diameter in swell butted logs so as to get a fair average, for the ring generally tapers with the swell and if the swell is very great the measured diameter will be too large. Multiply the diameter of the ring thus obtained by 3.14 to obtain the circumference and then measure or estimate the number of inches of waste necessary to saw out the ring — the inches of waste depending upon the irregu- larity of the ring. When two rings occur close together a large factor of waste must be taken as no lumber can be cut between the rings. Multiply the circumference by the thickness of waste, divide by 12 and multiply the result by ^. This will give the number of feet B.M. defect per lineal foot. Multiply this result by the length of defect and the result will be the total number of feet B.M. defect caused by the pitch ring. Rot. — To determine the amount of defect in a log with center or stump rot, the scaler should first determine if it shows on both ends of the log. If it does not show on both ends he should estimate the number of feet it extends into the log and then measure its diameter. If it shows on both ends he should average the diameters if the rot is uniform throughout the length of the log. Care must be taken with swell butted logg to get an average diameter as the rot usually tapers very rapidly in such logs. When such logs have rot of large diameter at one end and rot of small diameter at the other end it is well to divide the length of the rot into sections and give each section a diameter estimated according to the taper of the rot. Each section would then be treated as a unit by itself and the total of the defect for each would * Since in scaling with most log rules all material outside the cylinder represented by the top end diameter is considered as lost in slabbing, a defect which shows at the butt end of a log should never be taken as larger than the top diameter of the log unless the log is scaled in two sections, as explained in Problem 12. In this case the defect at the butt of the log should not be taken as larger than the top diameter of the butt section. SCALING 41 give the total defect for the lojj;. It will be noted that the ro(. formula is similar to the pitch seam formula except that the width of the defect is taken as equal to the diameter of the rot. Slab. — Western red cedar logs in the course of handling very often si)lit up into slabs which can not be acciu*ately scaled as logs. The method used on the Pacific Coast in this case is to estimate the volume of the slab in shingle bolts and reduce this volume to feet B.M. by the formula given above. A ''shingle bolt " in the formula is a piece 52 inches in length with roughly, equilateral triangular ends, the sides of this triangle being 12, 14, 16, or 18 inches in length. To determine the number of feet B.M. in a shingle bolt, first measure the end and compute the area of it in square inches, then multiply by the inches m length and divide by 144. Multiply this result by .70 and the result will be the number of feet B.M. in the bolt. Example: How many feet B.M. in a bolt 52 inches in length which has a triangular cross section 18 inches on a side? Area of triangle (18 by 18 by 18) X 52 ^ ^ , , X./0 = 35 feet B.M. 144 Miscellaneous Defects. — The formula? just given for seams, rings, and rot can be applied to nearly all other interior defects. There are, however, several other types of defects to which they do not exactly apply, such as crook, cat face, sap rot, worms, broken ends, etc. Allowance for crook can be made by a lump percentage of the total contents of the log or by deducting the equivalent of the piece of lumber which it is visualized would be lost. No allowance is made for cat face or similar side defects unless they extend inside the cylinder represented by the top diameter of the log, in which case the equivalent of the piece of lumber lost should be computed and deducted. Allowance for sap rot will be made by scaling the log with a diameter inside the exterior decay. Worms and broken ends can be allowed for by reducing the length of the log sufficiently to eliminate the defect. Method of Using Scaling Tables In order to simplify the application of the method to actual scaling, by means of the scaling formulae, the tables on page 42 have been computed to show the defect per lineal foot for the most common sizes encountered in scaling. A copy of these tables should be carried by the scaler for reference at all times. Included with the scaling tables is a legend for use in indicating on the scaling sheet (Form 5) the kind of defect found in each log. This legend may be used as follows: If a log has a pitch ring, use the letters P. R. as show^n in legend instead of writing the words in full. If a log has a pitch seam and ground rot, use the letters P. S. and G. R. If a cedar slab is scaled, place the letters SI in the defect column. 42 SCALING TABLES FOR SCALING DEFECT Legend for Defect P.R. PS. S. SI. Sp. Sh. c. Cr. Ch. Ck. R. G.R. W. B. O. L. Pk. Y. Pitch ring Pitch seam Shake Slab Split Shatter Conk Crook Check Chunk Rot in cedar Ground or stump rot Worms Broken end Overlength Punk or sap rot Crotch Shingle Bolts No. of Bolts Size 18X18 16X16 14X14 12X12 Bolts per Cord 20 25 33 44 Board Feet 35 70 105 140 175 i 210 i 245 280 315 350 28 56 84 112 140 168 196 224 252 280 21 42 63 84 105 126 147 168 189 210 16 32 48 64 80 96 112 128 144 160 Length 4' 4' 13' 17' 21' 26' 30' i 34' I 39' I 43' Pitch Rings Pitch Seam Rot Diameter or Width 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ,35 36 Waste, Thickness Inches 4 5 2 3 4 Defect per Lineal Foot 4 5 6 1 2 4 6 7 1 2 5 6 8 2 2 5 7 9 2 2 6 8 10 2 3 7 9 11 1 2 3 7 10 12 2 2 3 8 10 13 2 3 3 8 11 14 2 3 4 9 12 15 2 3 4 10 13 16 2 3 4 10 14 17 2 3 5 11 14 18 2 4 5 11 15 19 2 4 5 12 16 20 3 4 5 13 17 21 3 4 6 13, 18 22 3 4 6 14 18 23 3 5 6 14 19 24 3 5 6 15 20 25 3 5 7 16 21 26 3 5 7 16 22 27 4 5 7 17 22 28 4 6 8 17 23 29 4 6 8 18 24 30 4 6 8 19 25 31 4 6 8 1« 26 32 4 6 9 20 26 33 4 7 9 20 27 34 4 7 9 21 28 35 5 7 9 22 29 36 5 7 10 SCALING LOGS 43 / Pif.ch Ring, Pitch Seam and Rot Tables. — These tables have been com- puted by use of the defect formulae explained in the first part of this problem. In the pitch ring table the first column gives the diameter of the ring, the figures below "Waste Thickness" give the inches waste necessary to saw out the ring and the figures under columns 3, 4, 5 show the number of feet B.M. of defect per lineal foot. The pitch seam table similarly shows the defect for different waste thicknesses and widths. The rot table shows the defect for different average diameters. In each case the defect per lineal foot should be multiphed by the total length of the defect and the result subtracted from the full scale. Example: If a log has a pitch ring 20 inches in diameter and a waste thickness of 4 inches, the defect in board feet per lineal foot wiU be found in the column headed "4" under "Pitch Rings" opposite 20 in the "Diam." column, which in this case is 16 board feet. Multiply this defect per lineal foot by the distance the pitch ring extends into log and the result will be the total number of feet B.M. defect caused by the ring. Example: If a log has a pitch seam 16 inches in width across the end of the log and a waste thickness of 2 inches the defect in board feet per lineal foot will be indicated in the column headed "2" under "Pitch Seam" oppo- site 16 in the "Diam." column, which in this case is 2 board feet. Multiply this defect per lineal foot by the distance the seam extends into the log, and the result will be the total number of feet B.M. defect caused by the seam. Example: If a log has a uniform rot 16 inches in diameter, the defect in board feet per lineal foot will be indicated in the column headed "Rot" opposite 16 in the "Diam." column, which in this case is 17 board feet. Multiply this defect per lineal foot by the distance the rot extends into the log and the result will be the total number of feet B.M. defect caused by the rot. Shingle Bolt Table. — By means of the formula for securing the contents of shingle bolts the table above has been computed to show the contents in board feet of bolts 52 inches long with triangular ends 18X18X18, 16X16X16, 14X14X14, and 12X12X12 inches. Under each column heading giving the size of the bolt is showm a figure representing the number of bolts of that size contained in a cord and in the table below is shown the board foot contents of any number of bolts from one to ten inclusive. In the last column under "length" is shown the length in feet corresponding to the number of bolts indicated in the first column. In using this table for scaling slabs the scaler should first ascertain what size bolts the cross section of the piece is equivalent to and then estimate the number of that size bolts contained in the piece. The number of board feet in the piece may then be secured by referring to the shingle bolt table. Should the cross section of the slab be larger than an 18X18X18 bolt it may be divided into bolts of two sizes {i.e., 18X18X18 and 12X12X12, etc.), and the number of such bolts and their equivalent board-foot contents secured. 44 SCALING Example: A slab triangular on the ends measuring 18 inches on the side and 40 feet in length contains nine bolts. The scaler looks in column "No. of Bolts" and finds 9; then, in column "18X18" opposite "9," in the first column, he finds that the slab contains 315 board feet. If the piece con- tained 9 bolts 14X14 and 9 bolts 16X16, the table indicates that 9 bolts 14X14 contain 189 board feet, and 9 bolts 16X16 contain 252 board feet, and the sum of these two gives the total number of 441 board feet in the slab. Directions: A. Parlies. — Each man will work by himself in this problem. B. Equipment Required. 1 scale stick; 1 blue lumber crayon; 1 field note book supplied with Form 5; 1 copy of table for scaling defect. C. Method of Procedure. 1 . In an area in which logs are available select a specified number of logs for scaling. 2. Number the top end of each log consecutively and place this number in the proper column in the form in order that the instructor may check the scaled contents. 3. Scale the sound contents of each log in accordance with directions given in Problem 12. Estimate or actually measure the taper of a log when it is divided into two or more sections in applying the maximum scaling length. 4. Inspect the log carefully to ascertain whether it has any defects and if it has make the deductions by means of the scaling table in accord- ance with the principles outlined above. 5. Tally the net scale in the proper column. In the "Defect Column" show the defect by symbol and amount. If the scaling is done by the Scribner Dec. C. Rule, both the defect and the net scale should be tallied to the nearest ten feet B.M. and the zero to show the full scale added only to the total net scale at the bottom of the page. D. i^e/erences.— Numbers 45, 46, 47, 48, 53 and 54. SECTION VII— DETERxMINATION OF THE CONTENTS OF STANDS Explanation: This section has been outhned especially with reference to Pacific Coast timber. Very shght modifications to suit the needs of the different sections of the country will, however, make it available for use anywhere. The blank pages at the end of the problems may be used for noting such modifications. The work has been arranged to illustrate several methods of cruising, so as to allow the student to compare them, and to give him practice in estimating the total volumes of trees and stands by ocular estimate. PROBLEM 22. (Field.) Obtaining the Contents of a Small Tract of Timber by Different Methods. Directions: A. Parties. — Men will be organized in two-man crews, each man alternating as tallyman and as cruiser. B. Instruments. 1 pair tree cahpers. 1 compass. 1 hypsometer. 1 field notebook, supplied with Forms 1, 3 A, B and 4 A, B. C. Method of Procedure. 1. Select a representative area in the stand, and with the aid of the compass and paced distances run out a square acre (208.7 feet on a side) . 2. Secure the volume of the acre tract by the following five methods: (a) Ocular estimate. ih) Commercial cruising method. {c) D.B.H. volume table method. {(I) Diameter-height volume tabic method. {c) Spaulding rule method. These methods should be carried out in the following way: Each of these methods, except (c) and {d) which may be combined in the field, should be worked out separately in the order given, and the volume computed on the ground before proceeding with the next 45 46 DETERMINATION OF THE CONTENTS OF STANDS method, in order best to compare them. Make no deduction for defect or breakage and include all standing live or dead trees above 12 inches D.B.H. since the object of the exercise is to compare total volumes. (a) Ocular estimate. Before measuring or counting any of the trees make an estimate of the total volume of the tract. The succeeding methods will show the accuracy of your estimate. Use Form 1. (6) Commercial cruising method. Count all the trees on the tract, and estimate the volume of the average tree. Multiply this volume by the number of trees to secure the total volume of the stand. Check the method by actual measurement of what is judged to be an average tree, calipering its D.B.H., measuring the height with the hypsometer, and computing the volume by the Spaulding Rule of Thumb (See Problem 15, Illustration 1, Method I). Use Form 1 for recording the measurements and estimate. (c) D.B.H. volume table method. Caliper the diameter breast height outside the bark of all trees on the tract. Compute the volume of the tract by use of the volume table constructed in Problem 16, or any other volume table based on diameters breast high only, which would be applicable to the conditions. Use Form 3 A for recording the measurements and estimate. (d) Diameter-height volume table. Cahper the diameters breast high outside the bark, and estimate the total heights of all trees on the tract. As a check measure with a hypsometer the heights of the first trees taken. Compute the volume of the tract by use of the volumes given in Tables V-VIII in the Appendix, or any other tables based on D.B.H. and total heights that would be applicable to the conditions. Use Form 4 for recording the measurements. (e) Spaulding rule method. Tally the D.B.H. inside the bark and the length of all trees on the tract from the breast height point to a point on the bole where the D.B.H. is equal to h D.B.H. (outside bark). Measure this length by means of a hypsometer. Compute the volume of the tract by the Spaulding rule of thumb explained in Problem 15, Illustration 1, Method I. Use Form 3 A. CRUISING WITHOUT THE AID OF A VOLUME TABLE 47 D. References. — Numbers 14, 56, 58 and 60. E. Discussion. 1. Which method is most accurate? 2. Which method is the most rapid? 3. Which method would you choose to cruise a given tract? Why? 4. Can the first two methods be safely used by inexperienced men? PROBLEM 23. (Field and Office.) Cruising Without the Aid of a Volume Table. Explanation: The object of this problem is to illustrate a method of cruising a large tract of timber when there are no volume tables available. Directions : A. Equipment Required. 1 Forest Service staff compass, or hand compass when the former is not available. 1 pair of tree caHpers. 1 field notebook with Forms 3 A and B. B. Parties and Organization. Men will be organized in two-man parties, one man acting as compass- and tallyman and the other as caliperman. Each crew will cruise a quarter section tract. One man will act as cruiser and the other as compassman on the first eighty acres covered, and the second man as cruiser for the second eighty. In this way each man will cruise one-half of the tract. The men should assist each other in working up the data, but each will hand in only the data for the area he has cruised. C. Method of Procedure. The estimate will be obtained by running two strips, four rods wide, through each ''forty"; on each strip diameters breast high of trees 10 inches and over will be tallied; the heights will be obtained from a height curve constructed from data collected in the field as suggested under Section II; the volumes will be computed by means of the Spaulding Rule of Thumb. Part I. Running the Strips The compassman will pace, run the compass line, and tally the sizes called off by the cruiser who will take the D.B.H. to the nearest even inch of all trees 10 inches and over on the four- rod strip. The cruiser should be careful to look out for defects in the trees calipered. As he approaches a tree when at a distance from it where he can see the whole stem, he should look up the hole for conk, fungus or other defects. The volumes 48 DETERMINATION OF THE CONTENTS OF STANDS of trees showing eonk should bo discounted by reducing the sound volume 50, 75 or 100 per cent, according to the cruiser's judgment as, to the extent of the fungus attack. Trees with other defects such as fire-scars, hollow butts, broken tops or any other visible defects should be reduced in volume by the proper percentage estimated in the field for each tree tallied. All snags which have not been dead over four years and are apparently sound should be tallied. All windfalls which originally stood upon the strip and which are sound enough to produce lumber should be tallied. In this respect it should be remembered that cedar remains sound for a great many years and that cedar windfalls can hence be taken much more closely than any other species. The taper of swell -butted cedars must be taken into account by reducing the D.B.H. several inches so as to give the cedar no more swollen butts than normal fir trees, as otherwise the Spaulding rule will give too high volumes. Defects such as pitch, spike tops, butt rot, shake, and all other hidden defects and breakage will be discounted by deducting a lump per- centage from the total volume at the end of work. This percentage should be estimated by the cruiser in the field. Instructions for making discounts for defects must be given by the instructor on the ground. Special directions cannot be given here. For tallying, the cruising sheet (Form 3 A) will be used which has the page divided into columns for different species. One column will be used for tallying each species by means of the regular dot system as follows : The trees are tallied by dots and lines, in blocks of ten, as indicated in the following table, which shows the marks corresponding to different numbers, 3.3456 -7 89 10 '**::: r. n n n K Dead trees or snags which have merchantable contents should be tallied in the same column with the living trees with an "x" instead of a dot to distinguish them. Defective living trees should be tallied in the same columns with the sound, but should be kept separate by tallying them with the following symbols: For 10 per cent deducted from the sound volume: Q For 25 per cent deducted from the sound volume: r\ For 50 per cent deducted from the sound volume: J) For/75 per. cent deducted from the sound volume: ^^ For a tree tallied by mistake: Dead defective trees should be tallied in a similar way, except that an "x" will be used in place of the dot. The number of snags over 12 inches in diameter without merchantable contents may be tallied in the column provided on the right hand side of the sheet should the purpose of the cruise require these data. The percentage of estimated hidden defect for each species and the breakage for the whole "forty " should be tallied in the proper spaces at the bottom of the sheet. CRUISING WITHOUT THE AID OF A VOLUME TABLE 49 Each forty cruised will be taUied on a separate sheet, and the tallyman should hence change sheets when a forty has been completed, taking care that the forty number, section number, and direction of course at the top and in the lower right- hand corner of the tally sheet are completely filled out so that the forty can always be located. The different species will be tallied in separate columns. Part II. Securing the Height Data Since heights will not be tallied in the field it will be necessary to construct a height curve from data collected for each species. For this purpose sufficient time should be taken during the cruising to obtain the necessary measurements. These measurements are made on down trees and as many should be taken as possible. For each down tree measure the D.B.H. outside of bark, width of bark at D.B.H. or as near this point as possible, and the merchantable length from stump to ^ D.B.H. outside bark. Part III. The Forest Description While running the strips, or at any other convenient time, the cruiser should take notes to be used as a basis in writing a detailed forest description of the tract. Use Form 3 B. All information called for on the form should be obtained. Part IV. Office Computations The estimate will be worked up and totaled by 40-acre tracts. The volume of all trees above 22 inches D.B.H. except hemlock will be computed in feet B.M. by the method explained in Problem 15, Illustration 1, Method II. Hemlock 16 inches D.B.H. and over will be computed in feet B.M. All fir from 16 inches to 22 inches D.B.H. inclusive wih be computed as pihng, and all cedar from 10 inches to 22 inches as poles, by cimply noting the number of pieces. All fir and hemlock from 10 inches to 14 inches D.B.H. inclusive will be computed in ties. This will necessitate an estimate of how many No. 1 ties (6"X8"X8') or No. 2 ties (6"X6"X8') an average 10-, 12- or 14-inch tree will contain. The following data should be handed in by each party: (1) A height curve and a volume curve both on D.B.H. for each species, together with the accompanying tables read from them. (2) All tally sheets. (3) Summary sheet, showing the cruise by species for each forty and totals for the tract. (4) A forest description of each eighty. Arrange all in neat, logical order. D. Reference. — Number 56. 50 DETERMINATION OF THE CONTENTS OF STANDS Note. — This page should be used for noting special instructions, relating to the pre- ceding exercise, in order to meet the conditions of a particular tract or region. CRUISING WITH THE AID OF A VOLUME TABLE 51 PROBLEM 24. (Field and Office.) Cruising with the Aid of a Volume Table.* ExPLAN.\TiON : The object of this problem is to illustrate a method of cruising a tract of considerable size with volume tables showing values for trees of differ- ent diameters and total heights. DiRECTIOX.S: A. Equipment Required. 1 hand compass or Forest Service Compass and Staff. 1 pair of tree caUpers. 1 hypsometer. 1 field notebook with cruising Forms 4 A and B. B. Parlies and Organization. The same organization as outlined for Problem 23 will be followed in this exercise. C. Method of Procedure. The estimate will be obtained by running four strips four rods wide through each forty. On each strip the diameters breast high and the total heights of all trees 10 inches and over in diameter will be tallied. The volumes will be obtained by means of the volume tables given in the Appendix or any other tables based on diameters breast high and total heights, applicable to the conditions. Part I. Running Strips The compassman will pace, run the compass line and at the end of each acre. (4 rods wide by 40 rods long) cruised will see that the cruiser changes the tally sheets. If the object of the work requires a topographic map the compassman will make such a map while the cruiser tallies the trees. If no topographic map is required he need only run the compass line and pace the distances unless the area of the stand be irregular in which case he should plat a diagram to scale on Form I of the field notebook showing the shape of the tract, boundaries of the timber, limits of forest types, location of burns or other features affecting the forest cover. The cruiser will tally the diameters breast high and total heights of all trees 10 inches and over in diameter. At the end of each acre he will carefully fill out on the reverse side of the tally sheet the acre number, direction of course, section number, etc., which will locate the acre, and he will then change tally sheets. Tallying will be done on Form 4 A, using the thirty-foot height classification given on these sheets, i.e., up to 75 feet, 75 to 105, 106 to 135, 136 to 165, 166 to 195, 196 to 225, 226 to 255, and from 256 feet up. In case the volume table used * As in Problem 23, this exercise will need to be modified if used anywhere except in the Pacific Coast region. The modifications may be noted on the blank page following the problem. 52 DETERMINATION OF THE CONTENTS OF STANDS is constructed with a diffcront classification of heights than that given hero, the same height classes used in the table should be usetl in cruising. The dot system of tallying described in the previous exercise should be used. Each of the species will be talhed separately in one of the three sets of columns provided on the tally sheets. Should more than three species be found on the area to be cruised the three species found in greatest number should be tallied in the columns provided and other species tallied at the bottom of the sheet by name and size, i.e., a white pine 35 inches D.B.H. 125 feet high would be tallied W. P. -35 -125, or if it had 10 per cent defect, W. P. -35 -125 -10 per cent. Deductions for all defects which would affect the amount of lumber which can be cut from the tree, will be made exactly as outhned in Problem 23, except that the diameters of swollen-butted cedars need not be reduced unless thesweUing is excessive. Part II. Office Computations After completing the field work the next step is to compute the contents in board feet of each species on each tally sheet. If a considerable amount of this kind of work has to be done a multiplication volume table should be made. This is made by expanding the volume table so that it will show for each different D.B.H. and height class the volumes of trees from one to ten in number. For example, Volume Table Number V in the Appendix if converted into a multipli- cation volume table would have the following form : D.B.H. 10 12 Etc. to 75 76-105 1 2 Etc., to 1 2 3 Etc., to tree trees 10 trees tree trees trees 10 trees 80 160 100 200 300 100 200 140 280 420 Etc. With such a table the volume of any number of trees up to ten may be read off at a glance or the volume of any other number of trees secured by a short computation and the work will be much hastened; i.e., the volume of 13 trees would be the sum of the volume of 10 trees and 3 trees. Using the multij^lication volume table one man should call off the number of trees in each D.B.H. -height class of a certain species to the other man of his party who will immediately give him their volume as read from the table. The first man will enter this volume on the tally sheet and total for each species, or better still will enter the volumes, as called out, in an adding machine and secure the total with the machine. The totals for each species should be entered at the foot of the proper column and sliould be kept separate for the sound live trees, the defective live trees, and the sound and defective dead trees. In the case of the defective trees the totals should have defect properly discoimted. CRUISING WITH THE AID OF A VOLUME TABLE 53 Each distinct total for oach species should then be multiplied bj' 5, since the strips tallied covered 20 per cent of the total area. These totals should then be reduced by the percentage estimated in the field for hidden defect and breakage. The total of each species and the grand total of all species for each forty should then be computed by adding together the totals on each tally sheet included in the forty. Should any acre tallied be of full size but the tract it represents of irregular size, the area of the fractional tract should be obtained before the estimate is calculated. This can be done with a planimeter by measuring the plat made in the field, or by estimating the number of squares on the plat included in the irregular tract and calculating their equivalent area. The volume of this tract is then secured by multiplying the volume of the acre tallied by the number of acres in the irregular tract. For example, in a 20 per cent cruise each acre talhed represents 5 acres and the total cruise were the area perfectlj^ regular, would be secured by multiplying the volume of the acre tallied by 5. Suppose, however, that one cornev of the tract is logged ofT and from the plat it is found that 2 acres contain no timber. The volume of the acre sheet would then be multiplied by 3 instead of 5. If neither the acre tallied nor the tract it represents were complete the volume of the equivalent full acre should be found by dividing the volume of the fractional acre by its area expressed in tenths of an acre. The volume of the fractional tract would then be found as explained above. For example, the last tally sheet coveis but 0.8 of an acre and it represents but 3 acres instead of 5 as normally. The volume of the fractional acre would then be divided by 0.8 to reduce the fractional acre to terms of a whole acre. This volume would then be multii^lied by 3 to find the volume of the tract. The same method might also be applied to the forty as a unit instead of the acre. Each party, upon the completion of the work, should hand in all tally sheets and a summary sheet showing the total stand by species for each forty and the grand total for the whole area. D. References.— lumbers 37, 55, 57, 59, 61 and 63. E. Discussion. 1. How would the method of procedure outlined above be modified if the volume tables to be used were based upon merchantable lengths instead of total heights? 2. How would the method of procedure be modified if the heights of the individual trees were not tallied but the trees on each forty were given one of three height classifications and the volume tables used were constructed with similar height classifications. 3. Discuss the respective merits of deducting for defect by a percentage for each individual tree or by a lump percentage to cover all defects for each acre cruised. 4. What is the advantage in changing tally sheets at the end of each acre rather than at the end of each forty? 54 DETERMINATION OF THE CONTENTS OF STANDS 5. Discuss llio advanlagos aiul disadvantasos of using a correction factor to adapt the cruise to stands outside of the strip cruised whi(;h have a greater or a lesser vohmie per acre than the stand on the strip. 6. What criticisms of the method of procedure given above for carrying on the office work might be made and why? CRUISING WITH THE AID OF A VOLUME TABLE 55 Note. — This page should be used for noting special instructions to be given by the instructor in order to meet the conditions of a particular tract or region. SECTION VIII— GENERAL GROWTH STUDIES Explanation. — Studies in the growth of trees are made chiefly for the pur- pose of determining the number of years required for trees to become mer- chantable in size, for the prediction of future yield in volume, as a basis for silvicultural practice and as steps in organizing forests for continuous timber production. Studies are made on growth in diameter, height, basal area, and volume. These may be made for individual trees or as an average for small groups or even for extensive areas. As a basis for predicting the vol- ume growth of stands studies are usually made in terms per acre and are then known as yield studies. Growth in diameter and height form the direct basis for the volume and yield studies. In many studies it is necessary to distinguish growth with reference to time. Thus we have (C. A. G.) Current Annual Growth, that for any one specific year; (M. A. G.) Mean Annual Growth, the average annual rate of growth during the life of the tree; the (P. G.) Periodic Growth, the rate for any specific period of years. In some problems, particularly the prediction of growth in the future, we have growth per cent, which is determined by means of a simple interest formula that shows the per cent of increase in relation to the present size of the tree or stand. Prerequisite Study. — Before taking up the exercises included in this section the student should review the general method of collecting data for growth studies, Problem 7. Caution. — In all growth studies it should be remembered that the number of measurements required both as to kind and quantity will vary with the specific problem to be solved. Since separate studies must be made for trees growing under different conditions, a completed curve or table will have no value unless it is labeled with all the conditions of growth. This is even more important in growth studies than in volume studies. All of the points enumerated in the outline below should be considered in the title or label for each distinct growth study, though not all need be included because some conditions may be wholly obvious from some others already stated. For example, if a study had been made of the growth of Virgin Yellow Pine in Eastern Oregon, it would be practically obvious that it represents the growth in an uneven-aged stand. Points to he Considered in Connection with Title.* 1. The general problem. 2. Species. * Those italicized should appear in the title of each problem. 56 DETERMINATION OF THE TOTAL AGES OF TREES 57 3. Even- or uneven-aged stand. 4. Pure or mixed stand. 5. Forest type. 6. Soil or site quality. 7. Density. 8. Number of trees upon which the study is based. 9. Locality. 10. Virgin or second growth. 11. Date. 12. Be sure to indicate units of measurement (feet, inches, B.M., etc.) and kind of growth (Dia., Vol., P. A. G., C. A. G., etc.) on all curves and tables, PROBLEM 25. (Field.) The Determination of the Total Ages of Trees. Explanation. — In this problem it is assumed that we have determined the ages at the stump of a large number of trees. In order to determine the total ages of these trees it would be necessary to cut the trees near the sur- face of the ground because that is the only portion where a growth ring has been added each year from the time the tree was a one year old seedling, several inches high, to the time of cutting. To cut large trees near the sur- face of the ground would, of course, be impracticable. Hence the ages at the stumps must be corrected by a separate study of height growth on seedlings whose total heights vary about as the stump heights. Illustration. — To determine the total ages of the trees analyzed in Prob- lem 7. Directions: A. Parties. — Each student can work to advantage by himself. B. Equipment. 1 sharp pocket knife. 1 rule or tape graduated to inches. 1 hand lens. Pencil and field notebook with Form 1. C. Method of Procedure. 1. Select trees of the same species and of about the heights of the stumps and under the same conditions of growth as those whose total ages it is desired to find. 2. With the pocket knife cut from 10 to 15 seedlings at about one inch from the surface of the ground. The heights should vary about as the heights of the stumps of the trees whose ages are to be corrected. 3. Determine the age and height of each. In conifers this may be done by countmg the whorls of branches and checking by ring counts: 58 GENERAL GROWTH OF STUDIES in hardwoods usually ring counts alono can be used, though often these may be checked by the annual nodes, or terminal bud scars. Record the measurements in a table of two columns with ages opposite heights. Note. — When the annual nodes are conspicuous it is often possible to obtain a number of height measurements from each individual seedling as follows: 1. After the total age and the total height of a seedling are determined, subtract one from the total age and measure the height to the first annual node below the tip. 2. In a similar manner determine the values with reference to each of the remaining annual nodes. (The same may be done by cutting the seedlings into 6-inch lengths and constructing a height growth table. See Problem 29.) 4. On a sheet of cross-section paper (Form 1 of Field Notebook) lay otT heights as abscissae, and ages as ordinates. Plot the values, in half-foot height classes, draw a smooth curve and read off a table showing the average ages of the heights for each 0.5 of a foot, and label. 5. Apply this table directly to the stump ages as follows, and record in the proper spaces in the data blanks, (a) Look up the stump height of each tree on the front of the Analysis Blank (Form 2 A). (6) Determine in the table just constructed the number of years it took the tree to grow to stump height. (c) Add this number of years to the age at the stump and record as ''Total Age." PROBLEM 26. (Office.) The Determination of Diameter Growth in Fjver)- aged Stands. Explanation. — The object of this exercise is to ilhistrate the fundamental principles involved in all diameter growth studies in even-aged stands. In all cases tables are to be prepared that will show the average diameter a tree may be expected to attain at some one or more points (certain prescribed distances above the ground) along the bole of the tree. The growth at each of these points is determined by a separate study. The method of procedure . will be practically the same for all problems involving diameter growth in even-aged stands, as that outlined in the illustration given below. It is cus- tomary to make these studies in ten-year age-periods. Illustration. — To Construct a Table of Average Diameter Growth at the Stump for Even-aged Stands, not Thinned. A. Data Required. — Stump analysis and total ages. Use Data Series III. B. Method. — Plotting the values before averaging. Note. — When this problem is completed do not erase any of the plotted points. They will be of use in succeeding problems. When these data are not to be used DIAMETER GROWTH IN EVEN-AGED STANDS 59 for other purposes it may be more convenient to average before plotting, especially when a large number of trees are used. In this case rule a large sheet of paper so that there will be one vertical column for each age from one year to the age of the oldest tree. Record the radius measurements in their proper age columns, average and finally even off by means of a curve. Method of Procedure.— (Using method of plotting before averaging.) 1. Ages in this case are the independent variables, diameters the depend- ent variables; hence, lay off the cross-section paper with ages ui ten-year periods on the abscissa axis, and diameters in inches on the ordinate axis. Label. 2. Before plotting the values from any analysis sheet it should be checked according to the instructions for the tallyman, Problem 7. If it does not check do not use it. All data in this book supplied for use with this problem have been checked. 3. Determine the respective values of the points to be plotted as follows, and plot them accordingly : (a) The successive diameter values by multiplying the radius measure- ments, as recorded, by 2. (6) The age corresponding to the first radius measurement is taken as recorded in the upper left-hand corner of the space allotted to the first decade. The succeeding ages are determined by adding 10 years to the age of the first decade for the age of the second decade, and 10 years more for each successive decade; or the age at any decade is equal to: [(No. of the decade minus 1) times 10] plus number of years in the first decade. This, however, gives the age at the stump and not the total age of the tree; hence, in order that our study may be based on the total age, it will be necessary to add also the number of years it took the tree to grow to stump height. The formula then becomes: The total age for any decade measurement equals [(No. of the decade minus 1) times 10] phis the number of years in first decade plus the number of years required to grow to stump height. During the actual process of plotting it is neces- sary to determine this value only for the first point to be plotted. The values (ages) of the succeeding abscissae can be determined very rapidly by simply adding ten years to each preceding value. 4. When all the values are plotted average for each ten-year period as follows : (a) The average ages: By averaging separatelj', in a horizontal direction, all plotted points in each ten-year period, letting to 10 inclusive represent the first period, 10.1 to 20 inclusive the second, and so on. (h) The average diameter: By averaging separately, in a vertical direction, all points in each age period as in (a). 60 GENERAL GROWTH OF STUDIES 5. Draw a smooth curve and read off a table showing the average diameters at the end of each ten-year period. 6. Label. PROBLEM 27. (Office.) The Determination of Growth in Uneven-aged Stands. Explanation. — Growth in uneven- or many-aged stands differs from growth in even-aged stands in that the individual trees grow more nearly like the trees of a certain diameter than they do like trees of a certain age. Hence, except when it is desired to determine the mean annual growth of trees, growth studies in uneven aged stands are usually based on diameters (D.B.H.) instead of ages. This holds true and, as described below, is applicable to all kinds of growth in uneven-aged stands. The object, then, is to determine how fast a tree of a certain diameter is growing, either in diameter, height, volume, or other dimensions. This immediately makes it evident that when a tree of one diameter class has grown to the next higher diameter class it has a different rate of growth. Our problem then becomes one of determining first of all the periodic annual growth for each diameter class and from this the number of years required to grow one unit; i.e., in diam- eter, one inch. The independent variables, then, will be diameters breast high, and the dependent variables, periodic growth as determined in 5- or 10-year periods. Unless there is some special reason for determining the mean annual growth use periodic growth on D.B.H. for all problems in mamj- (or uneven-) aged stands. Illustration. — To Construct a Table of Diameter Growth at the Stump for Uneven-aged Stands, Based on D.B.H. Directions: A. Data Required. — The D.B.H. and measurements of the last 10 rings at the stump, or at D.B.H. Note. — The data for this problem can be obtained at D.B.H. from standing trees with the increment borer, but usually more satisfactory work can be done on felled trees in con- nection with a logging operation. The data supplied for this exercise were obtained in the latter manner. Use Scries II. The data in this series are somewhat limited for the purpose but show admirably what a small variation enters into the final results even with limited data. Compare the results obtained under " D " of this problem as worked out by different members of the class. The problem also illustrates the need for a large number of data for absolute accuracy in all problems dealing with averages. B. Method. — Averaging before plotting. C. Method of Procedure. 1. Group all trees into 1-inch D.B.H. classes {e.g. 8-inch class 7.6-8.5, inclusive) , DIAMETER GROWTH AT THE STUMP 61 2. Average the periodic growth and the diameter class of all trees of each class separately. (See Problem 16 for method.) 3. Even off by a curve. 4. Construct a table showing for each D.B.H. inch class: (a) The periodic growth as read from the table. (b) The periodic annual growth. (c) The number of years required to grow 1 inch. D. Discussion. 1. Solve the following problem from the above table: If you are cutting to a 14-inch diameter limit, in how many years will the 8-inch trees be ready to cut? Show how you derived the result. PROBLEM 28. (Office.) The Transposing of a Table of Diameter Growth at the Stump to Growth at D.B.H. Explanation. — Since for practical purposes all measurements of trees are based on the D.B.H., outside of bark, the most valuable diameter growth tables are those which show the growth at that point. For obvious reasons it is in most cases impracticable to analyze trees at the D.B.H. The object of this exercise is to construct a table showing the rate of growth at D.B.H, outside of bark from analyses made at the stump (D.I.B.) Directions: A. Data Required. — D.B.H., complete stump analyses, and total ages. Use the same data (Series III) used in Problem 26. The curve for average D.I.B. growth at the stump constructed in that exercise will be taken as a basis for the work. B. Method of Procedure. 1. Lay off a sheet of cross-section paper as in Problem 26, and transfer the average curve from that sheet to the new sheet by plotting the values from the table made in Problem 26. Do not prick the points through the paper as this often results in inaccuracies. Label this, "Curve I, (D.I.B. Stump)." 2. On this same sheet now draw Curve II to show the ratio between D.I.B. (stump) and D.B.H. (outside of bark) as follows: (a) Let ordinates represent D.I.B. values as for Curve I. Now lay off D.B.H. values as abscissa), the abscissa) to have the same value (in number of spaces on the paper alotted to each unit) already established for the ordinates; i.e., if one large space represents 2 inches on the ordinate axis, it shall also represent 2 inches on the abscissa axis. These values may be placed directly below the age figures. Be sure to label each set of figures. Confusion 62 GENERAL GROWTH OF STUDIES may often be avoided by using a distinct color for all points, curves, figures, and labels belonging together. (6) Plot values of D.I.B. (ordinates) on D.B.H. (abscissa) for each tree as recorded on the Tree Measurement Blank. Select the trees, so that they will be well distributed over the various diameters. D.I.B. values can be obtained from Data Series III by doubling the last radius measurement. (c) Average; draw a curve. Label this "Curve II (Ratio Curve)." It may cross Curve I. 3. These two curves now show the relationship between growth at D.I.B. • (stump) and D.B.H. on age. The D.B.H. for any age may be determined as follows: (a) Beginning on the abscissa axis at the desired age, trace the per- pendicular at that point to the point where it crosses the D.I.B. curve (Curve I). (6) From this point trace the horizontal line straight across to the Ratio Curve (Curve II). The line dropped from this point perpendicular to the abscissa axis will indicate the D.B.H. for the age started with. Show by dotted line and arrrows on the cross-section sheet how this reading is obtained. 4. It is customary to draw a third curve representing growth at D.B.H. as follows : (a) On the same sheet of cross-section paper let ordinates as there laid ofT for Curves I and II now represent D.B.H., and ages as established for Curve I abscissa;. (b) From Curves I and II read off the values of D.B.H. on age in 10-year periods, as explained in 3, (a) and (h), and plot them according to 4 (a) . (c) Even off by a curve. Call this Curve III. 5. Read off two tables. 1. Showing the diameters (D.B.H.) at different ages in 10-year periods. 2. Showing ages for the different diameters (D.B.H.) in even inches. PROBLEM 29. (Office.) The Determination of Height Growth. Explanation. — The determination of height growth depends upon the prin- ciple that the number of annual rings at any point along the bole of the tree represents the number of years it took the tree to grow from that point to the tip. Thus the total age represents the number of years it took the whole tree to grow from the ground to the tip, and the number of rings at any cross-cut the number of years to grow from that point to the tip. In order to find how many years it took the tree to grow from the surface of the ground to any point intermediate between it and the tip subtract the number of annual rings that occur at the desired point from the total age. Illustration 1 —To construct ;i T;i))lo of Ileighl Growth for Eirn-df/cd Stands. VOLUME GROWTH IN AN INDIVIDUAL TREE 63 Directions: A. Data Required. — Total ages and ring counts (decade measurements not needed) at various intervals along the boles of the trees, recorded with the heights above the surface of the ground at which the counts are made. Whenever height growth studies are made in connection with some study, not involving complete stem analysis, such for example, as diameter growth at the stump, it is necessary to make ring counts at various intervals along the bole for the height determinations. Usually a good height growth table can be made from a much smaller number of trees than required for diameter growth. Use data Series IV. B. Method of Procedure. 1. Determine which is the independent and which the dependent variable. Ask the instructor if you are right, then lay off the cross-section paper accordingly. 2. Determine the number of years required to grow to the height of the cross-cut in question by subtracting the number of rings at the various cross-cuts from the total age. 3. Plot the values, average, and read off the proper kind of table. Note in this problem the value of plotted points for interpolating values. Illustration II. — To Construct a Table of Height Growth for Uneven, or Many-aged Stands, Based on D.B.H. Explanation. — This exercise aims to throw the student upon his own responsi- bility and should be written out instead of being worked out. Directions. A. Data. — Determine first what data (enumerating all measurements) are required. B. Method of Procedure. 1. Outline the method step by step. Suggestion. — Take into consideration the fundamental differences in the construction of growth tables in even- and in uneven-aged stands as illustrated in Problems 26 and 27, and apply to Height Growth. Determine first which is dependent and which independent variable, and whether you would use M. A. G. or Per. G. according to the pro- cedure in many-aged stands. If you have any difficulties read again the Explanation to Problem 27. PROBLEM 30. (Office.) The Determination of Volume Growth in an Individual Tree. Explanation. — Volume growth may be based on stem analysis data or on measurements taken on a large number of standing trees of different ages. In the first case the trees are analyzed in the field as in Problem 7 and the volumes of the trees at different ages are reconstructed from the analysis. In the second case average trees in even-aged stands of different ages are meas- 64 GENERAL GROWTH OF STUDIES ured and the volumes calculated and plotted. The object of this problem is to illustrate the fundamental principles involved in all volume growth determinations based on analyses. In the different problems involved slight modifications are of course necessary in the method of collecting data and in the method of working them up into the final table. These will be empha- sized in the succeeding problems. The underlying principle in the study is to reconstruct each tree analyzed on the basis of its dimensions 10, 20, etc., years ago. Illustration. — To Determine the Volume Growth of an Individual Tree in Cubic Feet and in Board Feet, Based on Age. A. Data Required. — Complete stem analysis. Use tree number 116 in Data Series V. B. Method of Procedure. 1. Calculate the volume in cubic feet without bark of the whole stem for each 10-year period in the life of the tree, using Smalian's formula for contents of logs, the cylinder formula for stumps, and the cone formula for tips above the last log, as follows: (Calculations for 5 to 7 ten-year periods will illustrate the problem.) (a) On a sheet of note paper arrange a blank form like the following. Preserve all calculations on this form. Cross Cut Diameter Inside Bark, Inches Area, Square Feet Section Length of Section Volume, Cubic Feet Volume, B.M. 1 2 3 4 Etc. Stump 1st Log 2d Log Etc. Present Time (Give Age) Total 1 Stump 2 1st Log 3 2d Log 4 Etc. Etc. Tree 10 Years Ago (Give Age) Total Volume. VOLUiME GROWTH IN AN INDIVIDUAL TREE 65 (b) Calculate the volume of the tree according to its present dimen- sions by calculating the volume of each section separately, and add all of them for total volume. The dimensions of the diam- eters may be determined from the last set of figures recorded on the analysis sheet, for each section analyzed. As they are radius measurements they should be doubled. (c) In a similar manner calculate the volume of the tree by recon- structing from the analysis its dimensions at 10, 20, 30, 40 years ago and so on down to within the first 10-year period in the life of the tree. (Make only 5 to 7 calculations.) The diameters of the successive 10-year periods are again determined from the radius measurements recorded on the analysis sheet. For ten years ago, for example, the radius at each cross-section will be represented by the next to the last series of radius measure- ments; for twenty years ago by the third from the last, and so on. The lengths of the logs or sections are recorded on the front of the analysis sheet, including the height of the stump and the length of the tip of the present tree. The lengths of the tips of the reconstructed trees, however, must be determined by special calculations, because the tips usually end somewhere between the last cross-cut and the original tip, or between two successive cross-cuts. Determine the lengths of the individual tips by proportion as follows : (1) Determine the periodic annual height growth of the section above the last log in the reduced tree under consideration by dividing the length of the section by the number of years it took the tree to gi-ow that length. (2) Multiply the periodic annual height growth by the number of rings at the base of the tip whose height you wish to find. If the tip of the reduced tree happens to be in the tip of the present tree, the length of the present tip divided by the number of rings at its base will equal the periodic annual height growth. If the tip of the reconstructed tree falls within any of the sections below the present tip, the total number of rings at the top of the section sub- tracted from the total number of rings at the bottom of the section will equal the number of years it took the tree to grow the length of the section. Then divide the length of the section by this number of years, as just determined, to obtain the periodic annual growth (P. A. G.) in height. Multiply this by the number of rings at the base oj the tip U'hose height it is desired to find. (d) Determine volume of tip as usual B.A.X^H. (e) Enter the volumes of the separate sections of each reconstructed 6G GENERAL CiKOWTH OF STUDIES tree in the proper place on the blank form and add for total volume. 2. Now determine the rate of volume growth in board feel in a similar manner to that just described, except as follows: (a) Use only the merchantable portion of the stem, assuming -every- thing merchantable above the stump down to 6 inches D.I.B. at the top of the log. Tii)s and stumps, of course, must be omitted, also logs whose top diameters are less than 6 inches. (6) Use the International Log Rule as worked out in Problem 9 or any other rule giving values down to 6 inch top diameters, for determining the board foot values. (c) Record the values in their proper places in the blank forms, and total. (d) Make a final table showing only the volume in cubic feet and in board feet in 10-year age periods. C. Discussion. 1. What would be some of the practical applications of such a table. PROBLEM 3L (Office.) The Determination of Volume Growth by Graves' Modification of Mlodjianski's Method. Explanation. — A table showing growth based on age might be constructed from analysis data by first calculating the volume growth of each individual tree as was done in Problem 30, and averaging the results to determine the average rate of growth. The student will realize fully from the foregoing exercise without further emphasis the tremendous amount of work necessary if a number of trees sufficient to give good average results are used. The object of the method described in this problem is to reduce the number of cal- culations to a minimum. Mlodjianski's principle is first to determine by means of separate curves the average dimensions of the trees at different ages, and from them to calculate the volume growth rather than to calculate the volumes first and then determine the averages. Graves' modification con- sists in arranging the averaged curves in graphic form on one sheet of cross- section paper in such a manner that the dimensions of a tree of any age may be determined at a glance. The principle underlying the method as proposed by Graves is to have the curves for the diameter growth at each cross-cut placed on the co-ordinate paper with reference to the total age of the tree instead of the number of rings at the cross-cut in question. Remember, that the age at the stump does not represent the total age of the tree, because no rings are represented in the cut surface of the stump for those years during which the tree grew to stump height. The problem, then, is to show in the diameter growth curve for the stump how many years in the whole life of the tree it took to produce a stump of a certain diameter and not how many years after the tree had grown to stumj) height. In this problem the curve for each cross-cut GRAVES' MODIFICATION OF MLODJIANSKI'S METHOD 67 will then begin to the right of the original zero, at th(> intersection of the co-ordinate axes, as many units (years) as it took the tree to grow from the ground to the respective cross-cuts. Directions: A. Data Required. — Complete stem analysis of trees cut into logs of equal length where possible. Unless other data are available the three selected trees of Data Series V. will suffice for purposes of illustration. B. Method. — Plotting the values before averaging. C. Method of Procedure. 1. Construct a height growth table showing the average time required for the trees to grow from the ground to the various cross-cuts. 2. Determine the average stump heights. 3. Draw a diameter growth curve for the stump just as was done in Problem 26. Label it Stump Curve and indicate the average stump height on it. 4. In a similar manner, and with the same values for abscissae and ordi- nates, draw a separate diameter growth curve for each of the suc- ceeding cross-cuts, i.e., if the average stump height is 2 feet and the logs are cut in 16-foot lengths, the second curve will represent the growth at a point 18 feet above the ground, the third at a point 34 feet above the ground and so on. Label each with its average distance above ground 5. Now transfer all the curves to one sheet in such a manner that the growth at the respective cross-cuts will be shown on the basis of total age, i.e., let each curve begin as many years to the right of the intersection of the two axes as it took the tree to grow to the height of the cross-cut in question. Determine this point in each case from the height growth table. Do not transfer the curves by means of pin pricks, but plot the average values. 6. Determine the average height of the oldest trees from the height growth curve. Indicate this average by drawing a short perpen- dicular through the age axis at the proper point, and label it "Aver- age Total Age," below the axis. Just above the axis at this point write in the average total height and label. 7. These curves represent the diameter growth at their respective dis- tances above ground, on the basis of total age (the age at the ground) and not on the basis of the age at the respective cross-cuts. The points on the age axis together with the average total age, the average total height and the points where the curves at different heights cross the axis represent height growth. Hence this series of curves will give for any age the dimensions of the trees, D.I.B. at various points along the bole, and the total heights. For points at distances above the ground that are intermediate between the 68 GENERAL GROWTH OF STUDIES curves constructed interpolate. A D.B.H. growth curve mav also be added l)y the method of Problem 28. 8. Determine the dimensions of the trees — D.I.B. at the stump, and at the end of each section (log) and the total height — for even 10-year periods beginning with 10 years, and proceeding through to the time the trees were cut. Arrange in table form. 9. From the preceding table construct a Volume Growth Table showing (a) the growth of the entire stem in cubic feet, and (6) the growth in board feet of the merchantable stem, for each 10-year period. Consider 6 inches D.I.B. for the merchantable top diameter limit. Use the International Log Rule, or any other with values down to 6 inches top diameter for determination of board foot contents. PROBLEM 32. (Office.) The Determination of Maximum Growth Explanation. — The object of determining maximum growth is chiefly for the purpose of finding out how fast all the trees in an unthinned stand would grow assuming that each could be made to grow as fast as the most rapidly growing trees, providing they were given the proper treatment. Thie method of procedure as given in the accompanying illustration would be applicable to any of the various kinds of growth studied and may be applied to any of the succeeding growth exercises. The data for this exercise may be obtained either by analysis of a large number of trees of different sizes, or by selecting only the maximum trees for analysis. In the latter case the maximum growth would be determined directly from these analyses by the same method of procedure as described in Problem 26, if collected by first method referred to, as described in the illustration below. Illustration. — To Determine the Maximum Diameter Growth at the Stump in Even-aged Stands by Constructing a Maximum Diameter Growth Curve. Directions: A. Data Required. — Stump analyses and total ages of selected trees of differ- ent sizes. As the values are plotted exactly as in Problem 26, the same sheet of cross-section paper with its plotted points may be used. B. Method of Procednre. 1. Using the same sheet of cross-section paper with its plotted points that was used in Problem 26, draw a smooth curve as an upper boundary to the main body of the plotted points, being careful to exclude all points that indicate abnormally high values. 2. Read off a table showing the diameters of the maximum trees for each even 10 years. SECTION IX. SAMPLE PLOT STUDIES Explanation. — Sample plot studies are useful for the determination of the contents of stands, for solving certain problems in growth, and as a prelimi- nary step in the construction of yield tables. In order that all of these different problems may be worked out as laboratory exercises from the same felled sample trees, and that unnecessary duplication of work may be avoided, this section is placed immediately following the section on Growth Studies. The underlying principle in all sample plot studies is to obtain the desired information by the measurement of a few carefully selected average trees in sample plots representing average conditions, and then to apply the com- bined average results as obtained from the sample plots to an entire tract. It should not be necessary to emphasize here that the greater the number of plots used the greater will be the accuracy of the results. For a rough check in practical work, or where sample trees ^an not be felled a standard volume table may be used to determine the volumes of the sample trees. Do not do this where great accuracy is required. PROBLEM 33. (Field.) The Determination of the Contents of a Stant) BY Means of Felled Sample Trees. ExPLitN ATiON . — The accompanying illustrations include three distinct methods. With them as a foundation the student should have no difficulty in understanding the underlying principles of any method. It is suggested that this e.xercise be carried out in young, nearly even-aged stands. They will serve the purpose of illustration fully as well as older stands, and, further, will result in a considerable saving of time and unnecessary manual labor. Each student should have a complete set of all the data and calculations obtained by the other members of his party. These should be collected from the other members immediately after each problem has been completed. In each of the accompanying illustrations arrange the data and the results in logical order so that each step will be indicated in the proper place. Illustration I. — The Mean Sample Tree Method. Principle. — The principle of this method is to base the contents of the sample plot on the contents of one or more trees, each of which represents the average of all the trees within the sample area. 69 '0 SAMPLE PLOT STUDIES DlKLX'TlONS: • A. Parties. — A men. 'I'lic organization of (he work for each man is loft to the "Chief of I^irty " designated by the instructor. lie will be marked on the efficiency with which his party carries out the work. Remember that every man should be kept busy. B. Equipment Required. 1 100-foot steel tape. 1 surveyor's compass, or 1 angle mirror. 2 pairs of tree calipers. 1 cross-cut saw. 1 hand axe. 2 bark scratchers (white carpenter's chalk often answers the purpose even better) . 3 field notebooks (one per man), with blank Forms 1, 2 A, and 3 A, and cross-section paper. C. Method of Procedure. 1. Determine the area of the tract. In order to save time assume an arbitrary area of 40 acres. 2. Make a careful examination of the entire tract for the purpose of selecting a plot that will represent average conditions. 3. Carefully lay off a sample plot (i to r& acre will do to illustrate the problem). Mark the bovmdaries carefully. 4. Cafiper all the trees in the sample area at D.B.H. to the nearest inch, down to a minimum diameter of 2 inches. Mark each tree calipered, to avoid repetition. For convenience in recording the measurements use a form similar to that used when cruising on the basis of diameters only. (Form 3 A.) 5. Arrange all data, including the calculated values, in a convenient tabular form. 6. Determine the diameter of the average tree by the formula: 6ini+52n2+63^i3 4-etc. '' = - N • in which 6 = the average basal area of all trees on the plot; 6i, hi, etc. = basal areas of the ditTerent diameters; Ml, n-,, etc. = number of trees of each diameter; A^ = total number of trees on the plot. Use table of basal areas for getting the diameter values of h. 7. Cut three trees whose diameters fall within 0.5 of an inch of the diam- eter of the average tree. Be careful to select trees of average height and crown development. Number the stump of each tree to corre- spond ivith the number of the record sheet so that both may be used for future problems. Record measurements on Form 2 A. STAND BY MEANS OF FELLED TREES 71 8. Determine the volume of each in cubic feet bj^ Smahan's method, using 10-foot sections. 9. In order to correct any error resulting from a difference in the diameters of the sample trees and that of the average tree as calculated deter- mine the contents of the average plot by the formula : vXB ^ ~ b ' in which l' = the volume of the average acre; /' = average volume of test trees; /?= total basal area of the plot; 6 = average basal area of the test trees. Reduce to acre terms. 10. Determine the contents of the entire stand. (40 acres assumed.) Illustration II. — The Arbitrary Group Method. Principle. — The principle of the method is to group all the trees measured on the plot into arbitrary D.B.H. classes. Each group is then treated in exactly the same manner as were all the trees in the Mean Sample Tree Method. The chief difference between this and all other methods in which the trees are grouped is in the manner of grouping and the number of test trees to be cut. Directions: A. Parties ami Equipment a.s in Illustration I. B. Method of Procedure. 1. Use the same area for the tract, the same plot and the same diameter measurements of the standing trees as in Illustration I. Note. — The same plot is here suggested for each illustration given in order to give the student a thorough basis for comparing the different methods. Sometimes the plots can be located in timber which will be cut before the completion of the course in mensuration. In that case all the trees can be carefully measured, and the contents can be computed accu- rately from the felled trees and then compared with the results obtained by the different sample plot methods. 2. Group the diameter measurements into three or four groups, so that each group or diameter class does not, so far as possible, vary by more than 4 inches. 3. Proceed with each group (diameter class) just exactly as was done for all the trees in Illustration I. Record sample tree measurements on Form 2 A. 4. Arrange all data in tabular form similar to that used in Illustration I. 5. From these measurements now determine the cubic foot contents of the 40-acre tract. 72 SAMPLE PLOT STUDIES Illustration III. — The Volume Curve Method. Principle. — This method differs from all others in that no determination of average trees is necessary. The underlying principle depends upon the construction of a volume curve based on D.B.H. made from a few trees selected so that the small, the medium and the large sized trees are repre- sented. Directions: A. Parlies and Equipment as in Illustrations I and II . B. Method of Procedure. 1. Use the same area and the same sample plot with its tree measurements as in Illustrations I and II. 2. Select 6 sample trees without reference to any particular diameter but apportioning them so that the large and the small trees will be represented, and so that in a measure the diameters for which the largest number of trees have been recorded will be given the largest number of sample trees. 3. Fell the sample trees, and determine their total cubic foot contents, without bark, by means of ten-foot sections. 4. On a sheet of cross-section paper now plot the volumes of the sample trees on their diameters (D.B.H.) . Draw a smooth curve, and read off a table of volumes for diameters in whole inches. 5. Apply the volume table to the measurements of the trees on the plot to determine the contents of the whole plot and from the latter the contents of the tract. C. Discussion. 1. Comment on the three methods giving your views on the advantages and disadvantages of each with reasons. 2. Outline methods of procedure for the Urich and for the Draudt methods. 3. What per cent of a tract should be measured to insure a good estimate? PROBLEM 34. (Field.) The Determination of the Rale of Growth in Even-aged Stands by the Analysis of Felled Sample Trees. Explanation. — This exercise endeavors to illustrate in a practical manner the chief problems in growth in even-aged stands that may be solved by means of felled sample trees. As the details of the method of procedure have been illustrated in connection with previous problems the student should be able to carry out the work of the accompanying illustration from very general directions, and the directions in the Method of Procedure have been so made. The scheme will serve, in addition to illustrating the problems RATE OF GROWTH IX EVEN-AGED 8TAXDS 73 involved, as a thorough review of the prorediire in growth stucUes. Refer- ences are made to previous problems, but the student will gain the greatest benefit from this exercise if he does not make use of them until he has found by actual Irial that he cannot work out the problems without using the references, Directions: A. Parties. — 3 mer. B. Equipment. — After reading over the exercise the student should deter- mine what equipment is required. (See Problems 6 and 7.) Ask the instructor if yo\i are right before starting for the field. The chief of party will be held responsible. C. Method of Procedure. 1. Use the original data and the felled sample trees obtained in the Mean Sample Tree method of Problem 33. 2. Make a complete stem analysis of the felled sample trees. (Use regular analysis sheet for recording measurements. Forms 2, A and B.) 3. Work out the following problems. Arrange all work in logical order: (a) Construct a table of diameter growth at the stump. (See Problem 26.) (6) Construct a height growth table on total age. (See Problem 29.) (c) Construct a cubic foot volume growth table in 10-year periods. Use Graves' Modification of Mlodjianski's Method. (See Problem 31.) {d) From (r) determine the volume growth per acre in cubic feet. D. Discussion. 1. Under what conditions would the method of this problem give satis- factory results concerning growth? When applied to mature stands, of which trees onhj does it show the growth throughout the entire life of the stand? 2. Which of the following methods would give the most satisfactory results for a growth study: Mean Sample Tree, Arbitrary Group, Draudt, or Urich? Why? 3. How many plots would be considered sufficient for a reliable study in any one type? How large would you say, judging from your studies involving the use of plots, should plots ordinarily be to insure getting average conditions? 4. How would you modify the method of procedure if this problem were to be carried out in a mixed stand? 74 SAMPLE PLOl^ STUDIES PROBLEM 35. (Field and OHicc.) Tmo J^ETioiiiMiNyVTioN of (Iuowth in Even-aged Stands by the Measurement ok Standing 'J' ires. Explanation. — In the method of the last problem (No. 33) it will be remem- bered that good results can be obtained only when worked up in mature stands, and that the results will then show the rate of growth of only those trees which reach maturity. The method of this exercise will show the average rate of growth of all trees throughout the life of the stand. As it is only a comparatively small step from this exercise to the fundamental prob- lems involved in the construction of yield tables showing the average total stand per acre at any period in the life of the stand, the exercise is here out- lined so as to cover the necessary work for these, namely to select the plots located in different site qualities and to calculate values in terms per acre. This problem requires second growth even-aged stands of diiferent ages. In order that a sufficient number of plots may ])e measured to insure CTiough to illustrate the exercise the instructor should at the outset arrange the work of each party in such manner that as large a range of ages will be olitained as the conditions of the locality and the sis^e of the class will warrant. The students should now be able to carry out this work without much super- vision by the instructor, and the different parties can be scattered over a wide territory. Directions: Part I.— l^ield Work A. Parties. — 3 men in each. B. Equipment. — Determine what instruments and other equipment are necessary for each party, and have the instructor check your list before starting for the field. The chief of party will be held responsible. C. Method of Procedure. 1. Carefully lay off sample plots of re"? a-cre in stands of different ages. If good average conditions cannot be found in ^-acre plots, larger plots should be used. In order that these same data may be used in connection with the work in yield tables, some effort should be made to secure them from different site qualities. 2. Measure all trees at D.B.H. and record as in cruising. 3. Number and describe the locality of each plot on the tally sheet. Use U. S. land subdivisions where possible. 4. Determine the following information in the field with reference to each plot, using the Mean Sample Tree Method for determining any points requiring felled sample trees, (a) The number of trees per acre. {h) The diameter of the average tree, (c) The volume of the average tree. {d) The average height. (Measure 6 to 10 representative trees of the average diameter with the hypsometer and average.) ie) The average age. GROWTH IN EVEN-AGED STANDS 75 Part II.— Office Work Note.— In order that enough data for the construction of a table may be at hand the field work of the entire class should be collected for the use of each student. (For schools 8o situated that it is impracticable to collect appropriate data, Data Series VI has been included in the Appendix.) A. Construct a table giving the following information in 10-year periods: (a) The average number of trees per acre; ib) The dianieter of the average tree; (c) The average diameter; (d) The average total basal area in acre terms; (e) The average height; (/) The average volume in cubic feet in acre terms. Note. — All average values should be evened off by curves. B. Arrange all data, curves and other work in logical order. C. Discussion. 1. Outline the measurements and office work required as if the object were to show only the growth at D.B.H. in 10-year periods. 2. Compare this method with that of Problem 33 with reference to the conditions under which each would be applicable. 3. Could this method be modified for the determination of growth in uneven-aged stands? If so, show how you would modify it. If not, why not? Consider in your reply the difference in the character of the stands, and in the silvicultural conditions of growth, and the method of studying growth in uneven-aged stands. (See Problem 27.) 4. Would the method be applicable to mixed stands? Show how, or, if not applicable, wh}^ not? 5. Which would you consider the more accurate for the determination of the average age, the average age of the sample trees or the aver- age age of the dominant trees? Why? SECTION X— STUDIES IN GROWTH PER CENT Explanation. — Growth per cent is chiefly' useful in the prediction of volume growth for short periods, and is a method used in connection with the prepa- ration of working plans for even-aged stands, and in the determination of the final volume to be cut. Equipment required for field work is not listed with the exercises of this section. The chief of party will in each case be held responsible for checking out the necessary equipment. PROBLEM 36. (Field.) The Determination of Futuhe Volume by Means of Growth Per Cent Calculated Frotn Felled Sample Trees. Explanation. — This exercise aims to illustrate three of the fundamental methods. For purposes of comparison it is suggested that all of them be carried out on the same sample plot. IL1.USTRATION. — To Determine What the Volume in Cubic Feet of a 40-acre Tract (area assumed) Will Be 10 Years Hence. Method 1. — By comparing the Average Volume Growth for the past ten years as interest to the Volume 10 years ago as Principle. Directions: A. Formula. V-v :v = p:100, n V-v p = xioo vn where p = growth per cent; V = present volume ; «; = volume 10 years ago; n = 10 years. B. Parties. — 3 men in each. C. Method of Procedure. 1. Select and carefully lay out an average plot of j acre. 2. Proceeding as in the Mean Sample Tree Method, determine the volume of the plot and the average tree. 3. Select and fell three average trees for measurement. 76 FUTURE VOLUME BY MEANS OF GROWTH 77 4. Determine the present full-stem volume (inside bark) and the volume 10 years ago, of each bj^ means of 10-foot sections, and average. 5. Determine the growth per cent by substituting in the formula th.e values obtained in 4. 6. Calculate from the growth per cent what the volume of the tract (assume 40 acres) will be 10 years hence. Method 2. — By Comparing the Average Volume Growth for the past 10 years as interest to the Average of the Present Volume and the Volume 10 years ago as Principle. DiRECTION.S: A. Formula. V-v V+v n 2 V-v 200 V-\-v n The symbols are the same as in Method 1. This is considered the most satisfactory formula for all general purposes. B. Method of Procedure. 1. Proceed as in Method 1 using the same felled sample trees. Method 3. — By Comparing the Average Volume Growth for the past 10 3^ears as interest to the Volume one year ago as principle. Directions: A. Formula. n \ n I V-v V = X 100. ^ F(n-1)+^' B. Method of Procedure. — Proceed as in 1 and 2, using the same felled sample trees. C. Di'iC'i'ifiion. 1. Present the mathematical derivation of each of the formula) used. 2. Arrange the results of the three methods in a comparative series. Give your opinion of their relative values. 3. Which of the above methods are applicable to mature, and which to young stands? 4. Outline a method of ])r()cedur(' for use in mixed stands. 5. Are any of the above methods applicable to uneven-aged stands? If not, why not? 100, 78 STUDIES IN GROWTH PER CENT PROBLEM 37. (Field.) The Determination of Future Volume in Immature Even-aged Stands by Means of Growth Per Cent Calcu- lated FROM Standing Trees. Illustration. — To determine what the volume of a stand will be ten years hence by means of Pressler's formula for immature trees. Explanation. — In this formula Presslcr starts with the factors of volume, ■kD'^HF V = as a basis and eliminates F, the form factor, by assuming that trees will not materially change in form in ten years, and by further assuming that the change in height is proportional to the change in diameter he elimi- nates the height factor, H, by finding its value in terms of the diameter thus evolving the formula as given below for immature trees. For mature trees he evolves the formula, D2-d2 200 assuming that there is practically no change in either height or form factor. Directions: A. Formula. D^-d^ 200 D^+d^ n where p = growth per cent; D = D.B.H. of present tree; d = D.B.H. of tree 10 years ago; n = 10 years. B. Method of Procedure. 1. Use the same plot used in the preceding problem. 2. Find 3 standing trees of the requisite diameter, either on this plot or adjacent to it. 3. With calipers find the average present diameter of each tree by means of two measurements at right angles to each other. 4. With the increment borer, by means of two borings at right angles to each other on each tree, find the average diameter ten years ago. 5. Substitute the averaged values for D and d of the three trees in the formula for growth per cent. 6. Calculate what the volume of the tract (assume 40 acres) will be 10 years hence. C References. — Numbers 06 and S2. D. Discussion. 1. Show by means of the mathematical derivation of Pressler's formula how he justifies the uso of this formula for immature stands. FIXTURE VOLUME IX MATURE STANDS 79 2. Compare the results of this exercise with tliose derived by the three different methods of the previous exercise, and conmient on the efficiency of Pressler's formula. 3. What is Pressler's formula for mature or nearly mature stands? PROBLEM 38. (Field.) The Prediction of Future Volume in Mature Stands BY Means of Growth Per Cent. Explanation. — Schneider's formula is applicable only to mature trees. It has been found to be one of the most reliable and easily used formulae. Illustration. — To determine what the volume of a stand will be 10 years hence by means of Schneider's formula. Explanation. — Schneider's formula uses the periodic annual growth as determined by the last inch radius as interest and the average of the volume one year ago and one year hence as principle. He assumes there will be no change in height or form factor. DiRECTION.s: A. Formula. 400 nD where j) = growth per cent ; D = present D.B.H. (outside bark) ; n = number of rings in the last inch radius. B. Method of Procedure. 1. Lay off a sample area of ^ acre in an old stand of timber. (If the trees are very large or scattered use 1 acre.) 2. Determine the average tree by means of the Mean Sample Tree Method. 3. Make the necessary measurements on three trees. Average and apply in the formula for growi:h per cent. 4. By means of the growth per cent calculate the volume of the tract (40 acres) 10 years hence. C. Discussion. 1. Show step by step how your results were derived. 2. Show by means of the mathematical derivation of Schneider's formula why it is not applicable to immature trees. SECTION XL— YIELD TABLE STUDIES Explanation. — Yield tables are tabular statements which show the average stand of timber per acre. As in volume and growth studies separate tables are made for stands growing under different conditions or having distinct characters. »They are made both for even-aged stands and for uneven- aged stands. Two forms are recognized for the even-aged stands : 1. The Normal Yield Table, showing the stand per acre of normal or fully stocked stands, and 2. The Empirical Yield Table, showing the average stand in any locality irrespective of stocking. By a fully stocked stand is meant one with the average maximum yield obtainable under the existing conditions. The construction of yield tables for even-aged stands does not present any great difficulties. Yield tables for many-aged stands, however, offer a number of serious difficulties. Up to the present time there has been no general method devised for constructing these that is wholly satisfactory. For this reason problems for many-aged stands have been omitted, but a list of references to the various methods is included at the end of this section. In dealing with yield tables the student should remember that he is dealing with values per acre. PROBLEM 39. (Office.) The Construction of Yield Tables for Even- aged Stands. Explanation. — In the foregoing problems the student has had practice in nearly all the steps necessary for the construction of the different kinds of yield tables for even-aged stands. The Method of Procedure in Problem 35 covers practically all of the points necessary for the collection of field data. In fact in that exercise the student has virtually constructed an Emjyirical Yield Table. All that is now necessary to further illustrate the work is to take up the special problems that arise in connection with the construction of Normal Yield Tables. Illustration. — To Construct a Normal Yield Table for IJuthinned Pure Stands. Directions: A. Data Required. — The measurement of permanent sample plots would of course give the best results. However, when time is an important consideration these are out of the question, since it would take years to collect the necessary data by this means. To overcome the difficulty 80 YIELD TABLES FOR EVEN-AGED STANDS 81 of the time element we measure a large number of sample plots in even-aged stands from youth to maturity, in different site qualities, and as fully stocked as possible. Use data collected (or used) in Problem 35. B. Method of Procedure. 1. Group the plots into 3 site qualities. Method I.— Bauer's Method of Bands. (a) Plot the volumes (cubic feet) in acre terms on age. In each case be sure to place the number of the plot with the plotted points. (The data of Series IV are arranged according to site quahties.) (6) Enclose the plotted points between 2 regular curved lines. Divide the space between them into 3 equal bands by first indicating the proportional distances on the vertical lines from the abscissa axis at each 10- or 20-year point and then join the indicating marks by regular curves. (c) Include all plots in the highest band in Site Quality I, those in the middle in Site Quality II, and those in the lowest in Site Quality III. Method II.— The Site Factor Method. (a) Determine the site factor for each plot by means of the following formula : a in which F = the site factor; /i = the height of the average tree, which is to be determined from a height-diameter curve. The height of the average tree is to be taken as the height shown for the tree of average diameter; B = basal area in square feet per acre; a=the average age of the stand. (6) Divide all the site factors into 3 groups of equal numerical range in volume. All plots whose site factor falls within the range of the highest group ^nW belong to Site Quality I, those of the middle group into Quality II, and those of the lowest into Quality III. (c) Determine the basal areas and plot. id) Arrange the results obtained by the two methods in a compara- tive table. 2. Determine the normality of stocking by Bauer's Method as follows: (a) Draw an average curve and exclude from the investigation all I)lots whose volumes vary by more than 7.5 per cent from the average. These are either abnormally stocked or understocked. 82 YIELD TABLE STUDIES (b) Normality ran also l)o determined, and that often more rapidly by comparing the basal areas of all plots of the same age and site cjuality without curves as follows: 1. Determine the average total basal areas of plots of same average age. 2. Plots whose areas do not fall within 7.5 per cent of this average are discarded. 3. Average the plotted points of each site quality separately, even off with a regular curve, read ofT the average volume per acre in 10-year periods, and arrange in table form. 4. In addition to the yield the Normal Yield Table should also include the following information for each 10-year age period : (a) The average height; (6) The average diameter (D.B.H.); (c) The number of trees per acre; (d) The total basal area in acre terms; (e) Sometimes also the form factor and the growth per cent. All of the above are determined just as they were in Prob- lem 34, except that stands not normally stocked are not in- cluded and all calculations are made separately for each site quality. C. References. — Numbers 71, 74 and 86. D. Discussion. 1. Name in the order of procedure all the important steps necessary in the collection of data for the construction of a Normal Yield table. 2. What other factors beside volume may be used to determine normality of stocking? Under what circumstance would it be more advan- tageous to use a different factor? 3. What factor beside volume may be used to determine site quality by Bauer's Method of Bands? 4. What would be the chief difference in the collection of data for Normal and Empirical Yield Tables? 5. Outline briefly the main steps in the method of procedure for collect- ing data for a yield table thinned for the first time in late life. 6. Outline briefly a method of procedure for a yield table for mixed stands, assuming that we have an even-aged stand of Douglas Fir with an under-story of hemlock. PROBLEM 40. (Field.) Method of Using Yield Tables in the Field. Explanation. — Yield tables are used to show the future returns from planta- tions and immature stands, for estimating, for the determination of site quality, and, with reference to working i)lans, the growing stock, the normal yield and the rotation. That the students may work this exercise out prac- METHOD OF USING YIELD TABLES IN THE FIELD 83 tically, it will be necessary to i)lace in their hands a yield table applicable to the section of the country in which they are working. A yield table for Second Growth Douglas Fir will be found in the Appendix. Others can sometimes be obtained in Forest Service publications dealing with the particular region in question, or they may in some cases be obtainable from the Forester at Washington, D. C. The illustrations given below are out- lined with reference to Normal Yield Tables. If these are not available Empirical Tables will do, but in that case provision should be made in the directions for the discrepancy that will arise in connection with the question of normality of stocking. Choose for the purpose of illustrating this exercise young, even-aged stands, preferably under 50 years old, and as fully stocked as possible. Illustration I. — To Estimate the Contents of a Stand. A. Parties. — 3 men in each. B. Equipment. — To be determined by chief of party. C. Method of Procedure. — Lay out a representative plot of ^ acre in the tract to which the table is to be applied and by means of the Mean Sample Tree IMethod determine the following: 1. The average age of the stand as the age index. When the age is not an even multiple of 10, all calculations will need to be reduced by proportion to the nearest 10-year period in the table. 2. The average height * of the stand as an index to the site quality. 3. The total basal area (in acre terms) as in index to the normality of stocking. This should be stated in terms of the per cent of the total basal area indicated in the table. 4. The ijield. Reduce the yield indicated in the table by the per cent of stocking. Illustration II. — To determine what the Volume of the Stand will be when it is 100 years old. A. Method of Procedure. — With the information obtained in Illustration I it is now only necessary to refer to the table to obtain the future yield. The yield indicated for the 100-year-old stand should be reduced by the per cent of stocking. B. References. — Number 68. C. Discussion. — In the two illustrations given above no use was made of: (a) The number of trees i)er acre; (b) The average diameter at the different ages; (c) The form factor. What is the object of including these in a yield table? Uneven-aged Stands The following references may be helpful in understanding the question of yield tables for uneven-aged stands: Numbers 69, 70, 75, 77, 78 and 79. * If the site factor has been established for the region it may be used. APPENDIX A DIAGRAM FOR THE CORRELATION OF METHODS IN FOREST MENSURATION (Explanation) The accompanying diagram will show with reference to the character of the stand (forest description) the data required and the method of computation for practically all problems in growth studies. It also serves to correlate and illus- trate the relationship between the various different individual problems. To use the diagram begin at the center and follow an imaginary radius line straight from the center through the sections that will indicate the character and previous treatment of the stand (forest descrii)tion) to Data Required; read the data indicated opposite diameter, height, volume or yield as required; continue the same radius into the circle marked Computations and read as indicated for the type of study. E.xample* Desired a volume growth tal)lc for Even-aged, Pure Stands, Regularly Thinned: Begin at center — Follow a radius that cuts the even-aged sector, the pure- stand sector, and the regularly-thinned sector to "data required." In this circle we have indicated opposite "Vol." the data required for this study. Continue this same radius to the circle marked "Computations," the methods of working up the data, as indicated opposite "Vol." BIBLIOGRAPHY The Following lu /."rencefi arc Confined Entirely to American Works and Periodicals PRELIMINARY MEASUREMENTS 1. Biltmore Pachymeter. Ralph G. Burton, Forestry Quarterly, Vol. IV, No. 1, p. 9. 2. Biltmore Stick. A. G. Jackson, Forestry Quarterly, Vol. IX, No. 3, p. 406. 3. Notes on the Biltmore Stick. Donald Bruce, Proceedings of the Society of American Fcfresters, Vol. IX, No. 1, p. 46. 4. A New Ilypsometer. H. D. Tieman, Forestry Quarterly, Vol. II, No. 3, p. 145. 5. Relative Accuracy of Calipers and Diameter Tape. N. VV. Scherer, Proceedings of«the Society of American Foresters, Vol. IX, No. 1, p. 102. o. A New Measuring Instrument (For Heights and Diameters). H. W. Siggins, Forestry Quarterly, Vol. XII, No. 2, p. 141. 84 DIAGRAAI— CORRELATION OF METHODS IN GROWTH STUDIES A Diagram for the Correlation of Methods in Growth Studies 85 86 APPENDIX 7. Difficviltics ami Errors in Stem Analysis. A. S. Williaiiis. Forestry Quarterly, Vol. I, No. 1, p. 12. 8. New Aspects Regarding Use of the Forest Service Standard Ilypsonieter. Herman Krauck, Journal of Forestry, Vol. XVI, No. 7, p. 772. 9. Method of Taking Impressions of Year Rings in Conifers. L. S. Higgs, Forestry Quarterly, Vol. X, No. 1, p. 1. 10. A New Timber Scale. Judson F. Clark, Forestry Quarterly, Vol. XI, No. 4, p. 467. 11. Comparative Test of the Klaussner and Forest Service Standard Hypsometers. D. K. Noyes, Proceedings of the Society of American Foresters, Vol. XI, No. 4, p. 417. 12. A Practical Xylometer. J. S. lUick, Journal of Forestry, Vol. XV, No. 7, p. 859. 13. Mensuration in France. Donald Bruce, Journal of Forestry, Vol. XVII, No. G, p. G86. 14. Determination of the Middle Diameter of a Standing Tree. P. d'Aboville, Journal of Forestry, Vol. XVII, No. 7, p. 802. 15. English Units for Measuring Lumber. Trotman, West Coast Lumberman, February 1, 1915, p. 21. LOG RULES 16. Comparison of the Maine and Blodgett Rules. Irving G. Stetson, Forestry Quarterly, Vol. VIII, No. 4, p. 427. 17. The Measurement of Saw Logs. A. L. Daniels, Forestry Quarterly, Vol. Ill, No. 4, p. 339. 18. The Measurement of Saw Logs. Judson F. Clark, Forestry Quarterly, Vol. IV, No. 2, p. 79. 19. Woodman's Handbook, Bulletin 36, U. S. Forest Service, Washington, D. C. 20. Mill Scale Studies. Louis Margolin, Forestry Quarterly, Vol. IV, No. 1, p. 5. 21. Extending a Log Rule. Edward A. BranitT, Forestry Quarterly, Vol. VI, No. 1, p. 47. 22. Recent Log Rules. H. S. Graves, Forestry Quarterly, Vol. VII, No. 2, p. 144. 23. Comparison of the Doyle and Scribner Rules with Actual Mill Cut for Second Growth White Pine in Pennsylvania. N. R. McNaughton, Forestry Quarterly, Vol. XII, No. 1, p. 27. 24. Comparative Study of Scribner and Universal Rules. J. Bentley, Forestry Quarterly, Vol. XII, No. 3, p. 390. 25. Log Scale in Theory and Practice. H. D. Tieman, Proceedings of the Society of American Foresters, Vol. V, No. 1, p. 18. 26. Standardization of Log Measures. E. A. Ziegler, Proceedings of the Society of American Foresters, Vol. IV, No. 2, p. 172. 27. Log Rules, their Limitations and Suggestions for Correction. H. E, McKenzie, Bulletin 5, California State Board of Forestry. PRELIMINARY CALCULATIONS 28. New Method of Measuring Volume of Conifers (Schiffel Method). B. E. Fernow, Forestry Quarterly, Vol. V, No. 1, p. 29. 29. Form of Bole of the Balsam Fir. Judson F. Clark, Forestry Quarterly, Vol. I, No. 2, p. 56. 30. Alinement Charts in Forest Mensuration. Donald Bruce, Journal of Forestry, Vol. XVII, No. 7, p. 773. THE CONSTRUCTION OF VOLUME TABLES 31. Volume Tables and the Bases upon Which They May Be Built. Judson F. Clark, Forestry Quarterly, Vol. I, No. 1, p. 6. 32. Canadian Volume Tables. Ellwood Wilson, Forestry Quarterly, Vol. IX, No. 4, p. 588. BIBLIOGRAPHY 87 33. A New Method of Constructing Volume Tables (By Frustum Form Factors). Donald Bruce, Forestry Quarterly, Vol. X, No. 2, p. 215. 34. Use of Frustum Form Factors for Constructing Volume Tables. Donald Bruce, Proceed- ings of the Society of American Foresters, Vol. VIII, No. 3, p. 27S. 35. Taper Curves in Relation to Linear Products. F. S. Baker, Proceedings of the Society of American Foresters, Vol. IX, No. 3, p. 380. 36. Graded Volume Tables for Vermont Hardwoods. I. W. Bailey and P. C. Heath, Forestry Quarterly, Vol. XII, No. 1, p. 5. 37. Multiple Volume Table. Lincoln Crowell, Forestry Quarterly, Vol. IX, No. 2, p. 261. 38. Construction of a Set of Taper Cvirves. W. B. Barrows, Proceedings of the Society of American Foresters, Vol. X, No. 1, p. 32. 39. Reading and Replotting Curves. W. B. Barrows, Proceedings of the Society of American Foresters, Vol. X, No. 1, p. 65. 40. Top Diameters as Affecting the Frustum Form Factor for Longleaf Pine. H. H. Chapman, Proceedings of the Society of American Foresters, Vol. XI, No. 2, p. 185. 41. Logarithmic Cross-section Paper in Forest Mensuration. Donald Bruce, Journal of Forestry, Vol. XV, No. 3, p. 335. 42. The Problem of Making Volume Tables for Use on the National Forests. T. T. Munger, Journal of Forestry, Vol. XV, No. 5, p. 574. 43. A Volume Table for Hewed Railroad Ties. J. W. Girard and U. S. Swartz. Journal of Forestry, Vol. XVII, No. 7, p. 839. 44. The Height and Diameter Basis for Volume Tables. Donald Bruce, Journal of Forestry, Vol. XVIII, No. 5, p. 549. SCALING 45. Scaling Regulations. The National Forest Manual, Forest Service, U. S. Department of Agriculture, Washington, D. C. 46. History and Evolution of Scaling. American Lumberman, December 24, 1910, p. 29. 47. Scaling Government Timber. T. S. Woolsey, Forestry Quarterly, Vol. V, No. 2, p. 166. 48. Method Making Discounts for Defects. H. D. Tieman, Forestry Quarterly, Vol. Ill, No. 4, p. 354. 49. General Regulations Concerning Scaling in British Columbia. Andrew Haslam, Proceed- ings of the Second Pacific Logging Congress, p. 23. 50. Red and White Fir Xylometer Cordwood Test. Taylor, Forestry Quarterly, Vol. XII, No. 1, p. 24. 51. Factors Influencing the Volume of Wood in a Cord. Raphael Zon, Forestry Quarterly, Vol. I, No. 4, p. 126. 52. British Columbia Log Grades. West Coast Lumberman, March 15, 1914, p. 32. 53. Early History of Log Scaling Practice. C. E. Knouf, West Coast Lumberman, July 15, 1920, p. 41 and August 1. 1920, p. 40. 54. Log Scaling in Douglas Fir Region. E. I. Karr, The Timberman, April, 1920, p. 32o. DETERMINATION OF THE CONTENTS OF STANDS 55. A Manual for Northern Woodsmen. Cary, Published by Harvard University, Cambridge, Mass., 1901. 56. Average Log Cruise (Spaulding Rule Method). W. J. Ward, Forestry Quarterly, Vol. V, No. 3, p. 268. 57. Errors in Estimating Timber. Louis Margolin, Forestry Quarterly, Vol. XII, No. 2, p. 167. 88 APPENDIX 58. A Method of Estimating. Clyde Leavitt, Forestry Quarterly, Vol. II, No. 3, p. 161. 59. Forest Service Method of Check Cruising. Editorial, The Timberman, November, 1913, p. 25. 60. A Short Cut Method of Cruising. C. S. Judd, Forestry Quarterly, Vol. XI, No. 3, p. 380. 61. Timber Estimating. H. H. Chapman, Proceedings of the Society of American Foresters, Vol. IV. No. 1, p. 114. 62. The Factor of Top Diameter in Construction and Application of Volume Tables Based on Log Lengths. H. II. Chapman, Proceedings of the Society of American Foresters, Vol. XI, No. 2, p. 221. 63. Timber Estimating in the South Appalachians. R. C. Hall, Journal of Forestry, Vol. XV, No.. 3s p. 310. 64. A Formula Method for Estimating Timber. E. I. Terry, Journal of Forestry, Vol. XVII, No. 4, p. 413. 65. Comment on "A Formula Method of Estimating Timber." Donald Bruce, Journal of Forestry, Vol. XVII, No. 5, p. 691. GROWTH AND YIELD STUDIES 66. Suggestions on Predicting Growth for Short Periods. J. C. Stetson, Forestry Quarterly, Vol. VIII, No. 3, p. 326. 67. Growth of Red Pine in Ontario. A. H. D. Ross, Forestry Quarterly, Vol. XI, No. 2, p. 160. 68. Use of Yield Tables in Predicting Growth. E. E. Carter, Proceedings of the Society of American Foresters, Vol. IX, No. 2, p. 177. 69. Measurement of Increment in All-aged Stands. H. H. Chapman, Proceedings of the Society of American Foresters, Vol. IX, No. 2, p. 189. 70. Determination of Stocking in Uneven-aged Stands. W. W. Ashe, Proceedings of the Society of American Foresters, Vol. IX, No. 2, p. 204. 71. Determination of Site Qualities for Even-aged Stands by Site Factors. E. J. Hanzlick, Proceedings of the Society of American Foresters, Vol. IX, No. 2, p. 229. 72. Permanent Sample Plots. T. S. Woolsey, Forestry Quarterly, Vol. X, No. 1, p. 38. 73. Method of Calculating Yield in India. A. D. Blaschock, Forestry Quarterly, Vol. VIII, No. 3, p. 330. 74. Determination of Quality of Locality by Fibre Length of Wood. C. D. Mell, Forestry Quarterly, Vol. VIII, No. 4, p. 419. 75. Yield in Uneven-aged Stands. Barrington Moore, Proceedings of the Society of American Foresters, Vol. IX, No. 2, p. 216. 76. Relation of Crown Space to Volume of Present and Future Yellow Pine Stands. Kerr, Forestry Quarterly, Vol. XII, No. 3, p. 330. 77. Method for Regulating the Yield in Selection Forests. Walter J. Morrill, Forestry Quarterly, Vol. XI, No. 1, p. 21. 78. Methods of Investigating Yields in Many-aged Stands. H. H. Chapman, Forestry Quarterly, Vol. X, No. 3, p. 458. 79. Coordination of Growth Studies, Reconnaissance and Regulation of Yield on National Forests. H. H. Chapman, Proceedings of the Society of American Foresters, Vol. VIII, No. 3, p. 317. 80. Stem Analysis. John Bentley, Jr., Forestry Quarterly, Vol. XII, No. 2, p. 158. SI. Increment Measurements. Brief, Forestry Quarterly, Vol. XIII, No. 4, p. 550. 82. Notes on a Method of Studying Growth Per cent. B. A. Chandler, Forestry Quarterly, Vol. XIV, No. 3, p. 453. UNITS OF MEASUREMENT 89 S3. Plan for Permanent Sample Plots in the Adirondacks. Journal of Forestry, Vol. XVI, No. 8, p. 922. S. N. Spring, et al. 84. A Simplified Method of Stem Analysis. T. W. Dwight, Journal of Forestry, Vol. XV, No. 7, November, 1917, p. 8G4. 8.5. Mechanical Aids in Stem Analysis. Ernest C. Pegg, Journal of Forestry, Vol. XVII, No. 6, October, 1919, p. 682. 86. Classifying Forest Sites by Height Growth. E. H. Frothingham, Journal of Forestry, Vol. XIX, No. 4, April, 1921, p. 374. UNITS OF MEASUREMENT Used in Land Surveying and Forest Mensuration 1 Mile 5280 feet 80 chains (66 feet each) 320 rods (16^ feet each) 16 tallies (5 chains each) 1000 standard double paces (5. 28 feet) 2000 standard single paces (2 . 64 feet) 1 Acre 43,560 square feet 10 square chains 160 square rods 2 chain strip, 1 tally in length -1 Section 640 acres 16 "forties" (square forty acre tracts) 1 mile square DIMENSIONS OF FRACTIONAL ACRE TRACT Size of Fractional Tract (Acres) Area of Fractional Length of Side Tract if Square (Square Feet) (Feet) 43,560 208.7 21,780 147.6 10,890 104.4 5,445 73.1 2,722.5 52.2 Length of Radius if Circular (Feet) 117.8 83.3 58.9 41.6 29.4 90 APPENDIX MENSURATION FORMS Form 1 i i I I MENSURATION FORMS Form 2A 91 Series Species . . Locality S . M Regular Volume Measurements As Used by Logger < it \'olume t-3 p > 1 St 2 3 4 5 6 7 8 9 10 11 1? 13 14 15 16 17 18 19 26 Tree No . SUMMARY Plot No . 3 « Volume, B.M. s§ Name Date 92 APPENDIX 2 T t^ 3 O 3 O o a 3 rjj 1 CO T (M 5 O - 2 2 O a o Li 3 'i 05 oo - CD o o 3 lO -3 5 -f fO (N - c =1 ""a c^ cc t IT t^ X c- c - ^ 't 15 u s MENSURATION FORMS 93 P'ORM 3A UNITED STATES DEPARTMENT OF AGRICULTURE FOREST SERVICE D-6 DOUGLAS FIR REGION TIMBER SURVEY TALLY SHEET N Form 494— D 6b (Revised, 1917) 4 3 2 1 5 '^ s^ 8 12 11 s r^io 9 13 14 15 16 Ht. Class Site . R W Compassman . Estimator. . . Sec Date 40 No f Est. \ Sheet [ Tot.. 19. Applies to { Acres Tot. D.B.H. D.F. 1 ' ' ^ D.B.H. D.F. 10-14 1 1 i 54 16 1 1 56 18 58 20 60 22 62 24 64 26 66 28 68 30 70 32 72 34 74 36 76 38 78 40 80 42 Sound, D.F. 44 Def.. D.F. 46 Total 48 Snags over 30 ft. tall 50 i D.B.H. 52 20-36 Gross vol. on strip 37-48 Cull % B D 49 up Vol. strip Net No. per A. Vol. on 40 Net Avei stand T age 3er A. 94 APPENDIX Form 3B Forest Types: Age Classes: Condition of Timber: Thrifty Mature Decadent Fire killed %. ■ %. % ; damaged . Insect killed % ; damaged . Other killed % ; damaged . Name of disease Species affected 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.] Logging factors: Undergrowth — Light, medium, dense. Wind fall — Light, medium, dense. Boulders and broken rock — Numerous, occasional, absent. Other factors Reproduction: Speciea. No reproduction Ground J stocked Ground § stocked Ground fully stocked Additional Notes: Per cent. MENSURATION FORMS 95 Form 1A Douglas Fir Western Red Cedar D.B. H. to 75 76 to 105 106 to 135 136 to 165 166 to 195, etc. to 75 76 to 105 106 to 135 136 to 165 166 to 195, etc. to 75 76 to 105 106 to 135 136 to 165 166 to 195, etc. 14 • 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 ! 96 APPENDIX Form 4J} Acre No Sec T Course Offset Ch's from Compassman Date Cruiser Per rent of eruise Width of strip . . . Type Slope Asoect FOREST DESCRIPTION Rock Soil Humus Ground Cover Undergrowth Reoroduction Density Quality of Locality Condition of Stand Age of Stand Remarks MENSURATION FORIMS 97 Form 5 Locality Brand . Where Scaled Date . Log 1 5 a Contents by Species Defects, Kind, No. Doug. Fir Hem- lock Cedar Amount Deducted, Overlengths 1 i 1 1 i 1 1 1 1 1 II 1 3 >> c a u 1 Totals for Page 1 i APPENDIX COLUMBIA RIVER L(3G SCALING AND GRADING BUREAU LOG GRADING RULES FOR DOUGLAS FIR 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. 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 6 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 pro- ducing 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 permitted 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 not be 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 33^ per cent of sound lumber. PUGET SOUND GRADING RULES 99 PUGET SOUND LOGGERS ASSOCL\TION LOG SCALING AND GRADING RULES FOR DOUGLAS FIR A^o. 1 Logs. No. 1 logs shall be logs in the lengths of 16 to 32 feet and 30 inches in diameter inside the bark at the small end and logs 34 to 40 feet, 28 inches in diameter inside the bark at the small end, and shall be logs which in the judg- ment of the scaler shall contain at least 50 per cent of the scaled contents, in lumber in the grades of No. 2 clear and better. No. 2 Logs. No. 2 logs shall be not less than 16 feet long and having defects which prevent its grading No. 1, but which in the judgment of the scaler will be suitable for the manufacture of lumber principally in the grades of merchant- able and better. No. 3 Logs. No. 3 logs shall be not less than 16 feet long and having defects which pre- vent its cutting into higher grades and in the judgment of the scaler will be suitable for the manufacture of common lumber. Cull Logs. Cull logs shall be any logs which in the judgment of the scaler will not cut 33^ per cent of sound lumber. 100 AI'PENDIX 1ABLES TABLE I ScHiFFEL Formula D.B.H. Basal Areas, 0.16 of the Area of a Circle at Breast Height Diam- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 eter, Square Square S(iuare S(iuare Square Square Square Square Square Sciuare Inches Feet Feet Feet Feet Feet Fee:: Feet Feet Feet . Feet 1 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.003 0.003 0.003 2 0.003 0.004 0.004 0.005 0.005 0.005 0.006 0.006 0.007 0.007 3 0.008 0.008 0.009 0.010 0.010 0.011 0.011 0.012 0.013 0.013 4 0.014 0.015 0.016 0.017 0.018 0.018 0.018 0.019 0.020 0.021 5 0.022 0.083 0.024 0.025 . 025 0.026 0.027 0.02S 0.029 . 030 6 0.031 0.032 0.034 0.035 0.036 0.037 0.038 0.039 0.040 0.042 7 0.043 0.044 0.045 0.047 0.048 0.049 0.050 0.052 0.053 0.054 8 0.056 0.057 0.059 0.060 . 062 0.063 . 065 0.066 0.068 0.069 9 0.071 0.072 0.074 0.075 0.077 0.079 0.080 0.082 0.084 0.086 10 0.087 0.089 0.091 0.093 0.094 0.096 0.098 0.100 0.102 0.104 11 0.106 0.108 0.109 0.111 0.113 0.115 0.117 0.119 0.122 0.124 12 0.126 0.128 0.130 0.132 0.134 0.136 0.139 0.141 0.143 0.145 13 0.147 0.150 0.152 0.154 0.157 0.159 0.161 0.164 0.166 0.169 14 0.171 0.173 0.176 0.178 0.181 0.183 0.186 0.189 0.191 0.194 15 0.196 0.199 0.202 0.204 0.207 0.210 0.212 0.215 0.218 0.221 If) . 223 0.226 0.229 0.232 0.235 0.238 0.240 0.243 0.246 0.249 17 0.252 . 255 0.258 0.261 0.264 0.267 0.270 0.273 0.276 0.280 18 0.283 0.286 0.289 0.292 0.295 0.299 . 302 0.305 0.308 0.312 19 0.315 0.318 0.322 0.325 0.328 0.332 0.335 0.339 0.342 0.346 20 0.349 0.353 0.356 0.360 0.363 0.367 0.370 0.374 0.378 0.381 21 0.385 0.389 0.392 0.396 0.400 0.403 0.407 0.411 0.415 0.419 22 0.422 0.426 0.430 0.434 0.438 0.442 0.446 0.450 0.454 0.458 23 0.462 0.466 0.470 0.474 0.478 0.482 0.486 0.490 . 494 0.498 24 0.503 0.507 0.511 0.515 0.520 0.524 0.528 0.532 0.537 0.541 25 0.545 0.550 0.554 0.559 0.563 0.567 0.572 0.576 0.581 0.585 2G 0.590 0,594 0.599 . 604 0.608 0.613 0.617 0.622 0.627 0.631 27 0.636 0.641 0.646 . 650 . 655 0.()60 . 665 0.670 0.674 . 679 28 . 684 0.689 0.694 0.699 0.704 0.709 0.714 0.719 0.724 0.729 29 0.734 0.739 0.744 0.749 0.754 0.759 0.765 0.770 0.775 0.780 30 0.785 0.791 0.796 0.801 0.806 0.812 0.817 0.822 0.828 0.833 31 0.839 0.844 0.849 0.855 0.860 0.868 0.871 0.877 0.882 0.888 32 0.894 0.899 0.905 0.910 0.916 0.922 0.927 0.933 0.939 0.945 33 0.950 0.956 0.962 0.968 0.974 0.979 0.985 0.991 0.997 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 1.125 36 1.131 1 . 137 1.144 1 . 150 1 . 156 1 . 163 1.169 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 1.362 1.368 1.375 1.382 1.389 40 1 . 396 1 . 403 1.410 1.417 1.424 1.431 1 1.438 1.446 1.453 1.460 TABLES 101 TABLE I— Continued Diam- 0.0 o;i 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 eter, Square Square Square Square Square Square Square Square Square Square Inches Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet 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 1.659 1.667 1.674 1.682 44 1.689 1.697 1.705 1.713 1.720 1.728 1.736 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 1.863 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 2.061 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 2.369 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 2.516 2.526 2.535 54 2.545 2.554 2.564 2.573 2.583 2.592 2.602 2.611 2.621 2.630 55 2.640 2.649 2.659 2.669 2.678 2.688 2.698 2.707 2.717 2.727 56 2.737 2.746 2.756 2.766 2.776 2.786 2.796 2.806 2.815 2.825 57 2.835 2.845 2.855 2.865 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 3.058 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 3.365 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 3.563 64 3.574 3.586 3.597 3.608 3.619 3.630 3.642 3.653 3.664 3.676 65 3.687 3.698 3.710 3.721 3 . 733 3./'44 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 3.964 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 4.167 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 4.486 4.499 4.511 72 4.524 4.536 4.549 4.562 4.574 4.587 4.600 4.612 4.625 4.638 73 4 . 650 4.663 4.676 4.689 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 4.961 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 5.269 5.282 5.296 78 5 . 309 5.323 5.337 5.350 5.364 5.378 5.391 5.405 5.419 5.433 79 5.446 5.460 5.474 5.488 5.502 5.515 5.529 5.543 5.557 5.571 80 5.585 5 . 599 5.613 5.627 5.641 5.655 5.669 5.683 5.697 5.711 102 APPENDIX TABLE II ScHiFFEL Formula Middle Diametek Basal Areas, 0.G6 of tue Area of a Circle at THE Middle Height of the Tree Diam- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 eter, Square Square Square Square Square Square Square Square Square Square Inches Feet Feet Feet Feet Feet Feet Feet Feet Feet, I'eet 1 0.004 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.012 0.013 2 0.014 U.016 0.017 0.019 0.021 0.023 0.024 . 026 0.028 . 030 3 0.032 0.035 0.037 0.039 0.042 0.044 0.047 . 049 0.052 . 055 4 0.058 0.061 0.064 0.067 0.070 0.073 0.076 0.080 0.083 0.086 5 0.090 . 094 0.097 0.101 0.105 0.109 0.113 0.117 0.121 0.125 6 0.130 0.134 0.138 0.143 0.147 0.152 0.157 0.162 0.166 0.171 7 0.176 0.182 0.187 0.192 0.197 0.202 0.208 0.213 0.219 0.225 8 0.230 0.236 0.242 0.248 0.254 0.260 0.266 0.273 0.279 0.285 9 0.292 0.29S 0.305 0.311 0.318 0.325 0.332 0.339 0.346 0.353 10 0.360 0.367 0.375 0.382 0.389 0.397 0.405 0.412 0.420 0.428 11 0.436 0.444 0.452 0.460 0.468 0.476 0.484 0.493 0.501 0.510 12 0.518 0.527 0.536 0.545 0.554 0.563 0.572 0.581 0.590 . 599 13 0.608 0.618 0.627 0.637 0.646 0.656 0.666 0.676 0.686 0.696 14 0.706 0.716 0.726 0.736 0.746 0.757 0.767 0.778 0.788 0.799 15 0.810 0.821 0.832 0.843 0.854 0.865 0.876 0.887 0.899 0.910 16 0.922 0.933 0.945 0.956 0.968 0.980 0.992 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 1.411 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 1.603 1.618 1 . 633 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 2.196 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 2.663 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 3.756 3.779 3 . 802 3.826 3.849 3.873 3.896 33 3.920 3.944 3.968 3.992 4.016 4.040 4.064 4.088 4.112 4.137 34 4.161 4.186 4.210 4.235 4.260 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 5.253 5 . 280 5.308 5.336 5.363 5.391 5.419 5.447 39 5.475 5.503 5.532 5 . 560 5.588 5.616 5.645 5.673 5 . 702 5.731 40 5.760 5.788 5.817 5.846 5.875 5.904 5.934 5.963 5.992 6.022 41 6.051 6.081 6.110 6.140 6.170 6.200 6.230 6.260 6.290 6 320 42 6.350 6.380 6.411 6.441 6.471 6.502 6.533 6.563 6.594 6.625 43 6.656 6 . 687 6.718 6.749 6.780 6.812 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 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 9.108 9.144 9.180 9.217 9.253 9.290 9.326 TABLES 103 TABLE III Areas of Circles for Diameters of 1 Inch to 60 Inches Diam- Area, Diam- Area, Diam- Area, Diam- Area, Diam- Area, Diam- Area, eter, Square eter, Square eter, Square eter, Square eter, Square eter, Square Inches Feet Inches Feet Inches Feet Inches Feet Inches Feet Inches Feet 1.0 0.006 5.0 0.136 9.0 0.442 13.0 0.922 17.0 1.576 21.0 2.405 1.1 0.007 5.1 0.142 9.1 0.452 13.1 0.936 17.1 1.595 21.1 2.428 1.2 0.008 5.2 0.147 9.2 0.462 13.2 0.950 17.2 1.614 21.2 2.451 1,3 0.009 5.3 0.153 9.3 0.472 13.3 0.965 17.3 1.632 21.3 2.475 1.4 0.011 5.4 0.159 9.4 0.482 13.4 0.979 17.4 1.651 21.4 2.498 1.5 0.012 5.5 0.165 9.5 0.492 13.5 0.994 17.5 1.670 21.5 2.521 1.6 0.014 5.6 0.171 9.6 0.503 13.6 1.009 17.6 1.689 21.6 2.545 1.7 0.016 5.7 0.177 9.7 0.513 13.7 1.024 17.7 1.709 21.7 2.568 1.8 0.018 5.8 0.184 9.8 0.524 13.8 1.039 17.8 1.728 21.8 2.592 1.9 0.020 5.9 0.190 9.9 0.535 13.9 1.054 17.9 1.748 21.9 2.616 2.0 0.022 6.0 0.196 10.0 0.545 14.0 1.069 18.0 1.767 22.0 2.640 2.1 0.024 6.1 0.203 10.1 0.556 14.1 1.084 18.1 1.787 22.1 2.664 2.2 0.026 6.2 0.210 10.2 0.568 14.2 1.100 18.2 1.807 22.2 2.688 2.3 0.029 6.3 0.216 10.3 0.579 14.3 1.115 18.3 1.827 22.3 2.712 2.4 0.031 6.4 0.223 10.4 0.590 14.4 1.131 18.4 1.847 22.4 2.737 2.5 0.034 6.5 0.230 10.5 0.601 14.5 1.147 18.5 1.867 22.5 2.761 2.6 0.037 6.6 0.238 10.6 0.613 14.6 1.163 18.6 1.887 22.6 2.786 2.7 0.040 6.7 0.245 10.7 0.625 14.7 1.179 18.7 1.907 22.7 2.810 2.8 0.043 6.8 0.252 10.8 0.636 14.8 1.195 18.8 1.928 22.8 2.835 2.9 0.046 6.9 0.260 10.9 0.648 14.9 1.211 18.9 1.948 22.9 2.860 3.0 0.049 7.0 0.267 11.0 0.660 15.0 1.227 19.0 1.969 23.0 2.885 3.1 0.052 7.1 0.275 11.1 0.672 15.1 1.244 19.1 1.990 23.1 2.910 3.2 0.056 7.2 0.283 11.2 0.684 1 15.2 1.260 19.2 2.011 23.2 2.936 3.3 0.059 7.3 0.291 11.3 0.697 15.3 1.277 19.3 2.032 23.3 2.961 3.4 0.063 7.4 0.299 11.4 0.709 15.4 1.294 19.4 2.053 23.4 . 2.986 3.5 0.067 7.5 0.307 11.5 0.721 15.5 1.310 19.5 2.074 23.5 3.012 3.6 0.071 7.6 0.315 11.6 0.734 15.6 1.327 19.6 2.095 23.6 3.038 3.7 0.075 7.7 0.323 11.7 0.747 15.7 1.344 19.7 2.117 23.7 3.064 3.8 0.079 7.8 0.332 11.8 0.760 15.8 1.362 19.8 2.138 23.8 3.089 3.9 0.083 7.9 0.340 11.9 0.772 15.9 1.379 19.9 2.160 23.9 3.115 4.0 0.087 8.0 0.349 12.0 0.785 16.0 1.396 20.0 2.182 24.0 3.142 4.1 0.092 8.1 0.358 12.1 0.799 16.1 1.414 20.1 2.204 24.1 3.168 4.2 0.096 8.2 0.367 12.2 0.812 16.2 1.431 20.2 2.226 24.2 3.194 4.3 0.101 8.3 0.376 12.3 0.825 16.3 1.449 20.3 2.248 ' 24.3 3.221 4.4 0.106 8.4 0.385 12.4 0.839 16.4 1.467 20.4 2.270 24.4 3.247 4.5 0.111 8.5 0.394 12.5 0.852 16.5 1.485 20.5 2.292 24.5 3.275 4.6 0.115 8.6 0.403 12.6 0.866 16.6 1.503 20.6 2.315 24.6 3.301 4.7 0.121 8.7 0.413 12.7 0.880 16.7 1.521 20.7 2.337 24.7 3.328 4.8 0.126 8.8 0.422 12.8 0.894 16.8 1.539 20.8 2.360 24.8 3.335 4.9 0.131 8.9 0.432 12.9 0.908 16.9 1.558 20.9 1 2.383 24.9 1 3.382 104 APPENDIX TABLE III— Continued Diam- eter, Inches Area, Square Feet 25.0 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25 . 8 25.9 26.0 26.1 26.2 26.3 3.409 3.436 3.464 3.491 3.519 3.547 3.574 3.602 3.631 3.659 3.687 3.715 3.744 3.773 Diam- Area, eter, Square Inches Feet 26.4 3.801 26.5 3.830 26.6 3.860 26.7 3.888 26.8 3.917 1 26. 9 3.947 27.0 3.976 27.1 4.006 27.2 4.035 27.3 4.065 27.4 4.095 27.5 4.125 27.6 4.155 27.7 1 4^ IS.. Diam- eter, Inches 27.8 27.9 28.0 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29.0 Area, Square Feet I 4.215 4.246 4.276 4 . 307 4.337 4.368 4.399 4.430 4.461 4.493 4.524 4.555 4.587 Diam- Area, eter, Square Inches Feet 29.1 4.619 29.2 4.650 29.3 4 . 682 29.4 4.714 29.5 4 . 746 29.6 4.779 29.7 4.811 29.8 4.844 29.9 4.876 30.0 4.909 31.0 5.241 32.0 5.585 33.0 5.940 34.0 i 6 . 305 Diam- eter, Inches Area, Square Feet 35 . 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 6.681 7.069 7.467 7.876 8 . 296 8.727 9.168 9.621 10.085 10.559 11.045 11.541 12.048 Diam- Area, eter, Square Inches Feet 48.0 12.566 49.0 13.095 50.0 13.635 51.0 14.186 52.0 14.748 53.0 15.321 54.0 15.904 55.0 16.499 56.0 17.104 57.0 17.721 58.0 18.348 59.0 18.986 TABLES 105 TABLE IV Volumes of Frustums of Coxes. Scaled with Scribxer Rule in 16-foot Logs Down TO 8-INCH Tops Height in Number of Logs D.B.H.j U 2 3 4 5 6 7 8 9 10 10 43 74 115 159 11 44 80 128 175 12 46 86 137 192 13 47 91 150 212 271 14 48 96 165 232 300 15 50 103 179 257 331 405 16 52 111 195 279 366 449 528 17 54 120 210 311 406 496 598 684 18 56 129 231 338 438 548 650 756 855 968 19 137 253 363 485 591 707 822 938 1065 20 146 270 395 530 651 780 908 1030 1165 21 160 291 435 572 710 828 982 1126 1278 22 174 317 472 618 775 931 1095 1227 1391 23 182 342 510 675 843 998 1155 1329 1507 24 191 364 550 720 895 1097 1265 1439 1725 25 204 391 584 772 972 1182 1346 1532 1760 26 217 426 624 836 1052 1250 1458 1669 1886 27 231 449 666 901 1105 1337 1566 1804 2038 28 245 476 719 954 1194 1441 1699 1916 2199 29 259 508 755 1026 1285 1552 1848 2062 2337 30 272 539 809 1092 1363 1639 1908 2208 2482 31 292 569 868 1160 1446 1732 2019 2324 2626 32 312 595 926 1233 1536 1837 2161 2451 2802 33 324 636 982 1299 1608 1930 2274 2582 2965 34 336 682 1029 1355 1704 2059 2410 2772 3103 35 351 717 1072 1424 1808 2128 2527 2897 3262 36 366 754 1117 1509 1896 2272 2654 3041 3433 37 388 792 1180 1587 1987 2374 2773 3171 3591 38 409 827 1243 1662 2085 2473 2920 3340 3773 39 422 851 1296 1745 2127 2613 3063 3493 3954 40 436 887 1331 1805 2236 2743 3195 3683 4164 41 464 929 1401 1878 2366 2874 3375 3864 4395 42 1 ... 491 973 1455 1940 2501 3037 3515 4030 4545 43 1 ... 511 1018 1506 2040 2637 3153 3647 4214 4739 44 532 1048 1593 2174 2730 3243 3846 4399 5000 45 1 '• 1084 1 1658 2269 2838 3384 4011 4629 5202 106 APPENDIX TABLE V ' VOLUMK Tahle— Douglas Fi„, ,n Fekt, B.M., Based on D.B.H. and 30-foot Height Classes D.B.H. to 75 76 to 105 106 to 135 136 to 165 166 to 195 196 to 225 220 to 255 256 Up 10 80 100 130 160 12 100 140 190 240 310 14 140 200 250 330 430 540 IG 190 220 320 440 540 690 18 240 320 410 550 680 840 980 20 290 380 480 680 850 1,010 1,170 22 350 460 580 810 980 1,190 1,360 24 430 550 700 910 1,150 1,390 1,580 26 510 640 810 1000 1,340 1,600 1,820 28 590 750 930 1250 1,550 1,820 2,080 30 680 860 1080 1440 1,770 2,080 2,310 32 780 980 1230 1620 2,020 2,300 2,610 34 890 1100 1400 1830 2,280 2,590 2,930 36 1000 1240 1570 2040 2,550 2,700 3,270 3,630 38 1400 1760 2260 2,850 3,230 3,030 4,020 40 1560 1980 2510 3,170 3,600 4,030 4,410 42 1740 2190 2720 3,510 3,970 4,040 4,870 44 1910 2420 2950 3,810 4,300 4,870 5,390 46 2660 3360 4,180 4,770 5,200 5,870 48 2920 3690 4,570 5,200 5,730 6,330 50 3190 4030 4,950 5,650 6,200 6,860 52 3480 4400 5,400 6,090 6,680 7,470 54 4800 5,900 6,140 7,210 8,070 56 .... 5200 6,350 7,070 7,760 8,660 58 5620 6,800 7,000 8,320 9,330 60 6150 7,260 8,150 8,910 10,010 62 6420 7,710 8,650 9,570 10,740 64 6790 8,280 9,220 10,200 11,590 66 7150 8,730 9,870 10,900 12,470 68 7470 9,240 10,510 11,770 13,330 70 7790 9,870 11,200 12,540 14,250 72 10,260 11,880 13,320 15,240 74 10,670 12,600 14,190 16,160 76 11,050 13,440 15,050 17,190 78 11,410 14,140 15,840 17,850 80 11,760 14,850 16,080 18,540 82 15,480 17,400 19,230 84 16,030 18,010 19,980 86 16,510 18,550 20,640 88 10,930 19,040 21,240 90 17,370 19,500 21,810 92 19,920 22,340 94 20,300 22,810 96 20,080 23,210 98 :::: j 21,020 23,610 100 .... 21,360 23,970 Note.— Tables V, VI, VII, VIII are based upon data collected in the lower slope, Douglas fir-cedar type of King and Snohomish Counties in Western Washington. The trees were scaled by the Scribner Decimal C Rule to a point 8 inches in diameter at the tops inside the bark. The Douglas fir table is based upon the measurement of about 600 trees and the other tables each are based upon the measurement of about 300 trees. TABLES 107 TABLE VI Volume Table — Westekn Red Cedar — in Feet B.M. Based on D.B.H. and 30-foot Height Classes D.B.H. to 75 re to 105 L06tol35 136 to 165 166 to 195 1 1 196 to 225 226 to 255 256 Up 12 90 102 14 120 192 210 16 158 209 265 18 196 256 322 20 235 302 386 510 570 22 275 352 456 590 710 24 406 528 700 875 26 460 598 818 1.045 28 557 670 910 1,200 30 629 749 1016 1,360 32 836 1145 1,560 34 940 1303 1,780 36 1122 1498 1,990 38 1272 1718 2,200 40 1700 1945 2,425 2,650 2,875 42 1855 2178 2,670 2,875 3,080 44 .... 2015 2412 2,915 3,165 3,415 46 2180 2768 3,175 3,475 3,775 48 2340 2940 3,435 3,800 4,165 50 2500 3480 3,690 4,090 4,490 52 2670 3500 3,9.50 4,425 4,900 54 .... 2840 3740 4,225 4,750 5,275 56 3010 3815 4,500 5,100 5,700 58 3190 4160 4,800 5,470 6,140 60 3375 4390 5,105 5,825 6,545 62 3555 4615 5,410 6,200 6,990 64 3750 4850 5,725 6,560 7,395 66 .... 3925 5075 6,030 6,920 7,810 68 .... 4100 5300 6,340 7,280 8,220 70 4280 5520 6,640 7,600 8,560 72 4470 5750 6,935 7,950 8,965 74 .... .... 4650 5970 7,220 8,275 9,330 76 4825 6190 7,505 8,600 9,695 78 5010 6425 7,795 8,925 10,055 80 5200 6670 8,080 9,2.50 10,420 82 .... i '.'.'.'. .... 6925 8,400 9,.575 10,750 84 .... 7200 8,700 9,975 11,250 86 7475 9,000 10,350 11,700 88 7750 9,300 : 10,750 12,200 90 .... 8000 9,600 11,200 12,800 92 8265 9,940 11,575 13,210 94 8550 10,265 11,980 13,695 96 88.50 10,600 12,350 14,100 98 9125 1 10,900 12,675 14,450 100 j .... 9400 ; 11,200 13,000 i 14,800 108 APPENDIX Volume Table — Silver Fir- TABLE VII -IN Feet, B.M., Based on D.B.H. and 30-foot Height Classes D.B.H. To 75 76 to 105 100 to 135 136 to 165 166 to 195 196 Up 10 60 65 75 12 95 110 135 ' 14 140 160 250 16 190 240 360 500 18 240 315 470 610 20 310 405 580 770 1,190 22 380 510 700 920 1,360 24 480 620 840 1,110 1,540 26 590 740 950 1,290 1,730 28 700 870 1100 1,470 1,920 30 820 1020 1270 1,660 2,140 2,660 32 930 1170 1450 1,870 2,370 2,900 34 1090 1380 1650 2,100 2,620 3,170 36 1240 1530 1860 2,360 2,900 3,450 38 1390 1720 2090 2,650 3,190 3,760 40 1560 1930 2330 2,880 3,490 4,080 42 1730 2160 2590 3,200 3,840 4,440 44 1900 2400 2880 3,500 4,180 4,750 46 2080 2640 3170 3,790 4,.520 5,090 48 2260 2890 3480 4,110 4,860 5,440 50 2450 3150 3790 4,410 5,200 5,780 52 2630 3420 4100 4,730 5,.540 6,140 54 3670 4430 5,080 5,580 6,500 56 3950 4750 5,460 6,240 6,850 58 4220 5090 5,820 6,570 7,230 60 4500 5450 ■ 6,200 6,940 7,620 62 4770 5800 6,570 7,290 8,020 64 6150 6,960 7,670 8,440 66 6510 7,340 8,000 8,970 68 6880 7,710 8,460 9,310 70 .... 7250 8,110 8,850 9,750 72 .... 7610 8,.500 9,260 10,200 74 8,870 9,650 10,630 76 9,230 10,030 11,030 78 9,570 10,380 11,380 80 9,900 10,700 11,750 82 10,200 11,010 12,080 84 10,470 11,320 12,380 86 11,600 12,600 88 .... 11,860 12,920 90 12,100 13,150 92 12,330 13,380 94 13,000 96 13,820 98 100 14,020 14,220 TABLES 109 TABLE VIII Volume Table — Western Hemlock — in Feet, B.M., Height Classes Based ox D.B.H. and 30-fc)ot To 75 50 80 130 200 260 350 430 510 590 76 to 105 106 to 135 60 100 150 220 280 370 460 550 650 760 900 1050 1200 1390 80 140 220 300 390 490 580 700 830 980 1140 1300 1500 1710 1940 2190 2480 2800 3150 3550 3950 4430 4860 5260 136 to 165 480 590 710 850 1000 1170 1360 1560 1780 2040 2300 2650 2850 3200 3600 4080 4580 5070 5480 5840 6170 6460 6750 7020 7260 7460 7640 7820 166 to 195 1200 1380 1600 1840 2100 2350 2750 3150 3560 3980 4410 4850 5300 5700 6120 6450 6750 7030 7270 7500 7710 7920 8110 8290 8450 8610 8770 8920 9060 9180 9290 9400 9500 9580 9670 196 Up 2,710 3,050 3,460 3,910 4,420 4,920 5,400 5,840 6,220 6,570 6,890 7,180 7,260 7,640 7,860 8,060 8,270 8,440 8,620 8,790 8,950 9,100 9,230 9,360 9,480 9,570 9,660 9,740 9,820 9,900 9.970 10,030 10.100 10,160 10,210 10.270 110 APPENDIX TABLE IX ScRiBNER Decimal "C" Log Rule for Logs 6 to 32 Feet in Length Length- -Feet 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Contents, Board Feet m Tens 0.5 0.5 1 1 1 2 2 2 3 3 3 4 4 5 0.5 1 1 2 2 3 3 3 4 4 4 5 5 6 1 1 2 2 2 3 3 3 4 4 5 6 6 7 1 2 3 3 3 4 4 4 5 6 6 7 8 9 2 3 3 3 4 6 6 7 8 9 9 10 11 12 2 3 4 4 5 7 8 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 5 6 7 8 10 11 12 13 15 16 17 18 19 4 6 7 9 10 11 13 14 16 17 19 20 21 23 5 7 9 11 12 14 16 18 20 21 23 25 27 28 6 8 10 12 14 16 18 20 22 24 26 28 30 32 7 9 12 14 16 18 21 23 25 28 30 32 35 37 8 11 13 16 19 21 24 27 29 32 35 37 40 43 9 12 15 18 21 24 27 30 33 36 39 42 45 48 11 14 17 21 24 28 31 35 38 42 45 49 52 56 12 15 19 23 27 30 34 38 42 46 49 53 57 61 13 17 21 25 29 33 38 42 46 50 54 58 63 67 14 19 23 28 33 38 42 47 52 57 61 66 71 75 15 21 25 30 35 40 45 50 55 61 66 71 76 81 17 23 29 34 40 46 52 57 63 69 75 80 86 92 19 25 31 37 44 50 56 62 69 75 82 88 94 100 21 27 34 41 48 55 62 68 75 82 89 96 103 110 22 29 36 44 51 58 65 73 80 87 95 102 109 116 23 31 38 46 53 61 68 76 84 91 99 107 114 122 25 33 41 49 57 66 74 82 90 99 107 115 123 131 27 36 44 53 62 71 80 89 98 106 115 124 133 142 28 37 46 55 64 74 83 92 101 110 120 129 138 147 29 39 49 59 69 78 88 98 108 118 127 137 147 157 30 40 50 60 70 80 90 100 110 120 130 140 150 160 33 44 55 66 77 88 98 109 120 131 142 153 164 175 35 46 58 69 81 92 104 115 127 138 150 161 173 185 39 51 64 77 90 103 116 129 142 154 167 180 193 206 40 54 67 80 93 107 120 133 147 160 174 187 200 214 42 56 70 84 98 112 126 140 154 168 182 196 210 224 45 60 75 90 105 120 135 150 166 181 196 211 226 241 48 64 79 95 111 127 143 159 175 191 207 223 238 254 50 67 84 101 117 134 151 168 185 201 218 235 252 269 52 70 87 105 122 140 157 174 192 209 227 244 2^9 279 56 74 93 111 129 148 166 185 204 222 241 259 278 296 57 76 95 114 133 152 171 190 209 228 247 266 286 304 59 79 99 119 139 159 178 198 218 238 258 278 297 317 62 83 104 124 145 160 186 207 228 248 269 290 310 331 65 86 108 130 151 173 194 216 238 260 2S1 302 324 346 67 90 112 135 157 180 202 225 247 270 292 314 337 359 70 94 117 140 164 187 211 234 257 281 304 328 351 374 73 97 122 146 170 195 219 243 268 292 315 341 365 389 76 101 127 152 177 202 228 253 278 304 329 354 380 405 79 105 132 158 184 210 237 263 289 316 341 368 395 421 82 109 137 164 191 218 246 273 300 328 355 382 410 437 85 113 142 170 198 227 255 283 312 340 368 397 425 453 88 118 147 176 206 235 264 294 323 353 382 411 441 470 91 122 152 183 213 244 274 304 335 365 396 426 457 487 95 126 158 189 221 252 284 315 347 379 410 442 473 505 98 131 163 196 229 261 294 327 359 392 425 457 490 523 101 135 109 203 237 270 304 338 372 400 439 473 507 541 TABLES 111 TABLE lX~Continued Length —Feet Diam- eter, Inches 6 8 10 12 14 16 18 20 22 24 26 2S 30 32 Contents Board Feet in Tens 61 105 140 175 210 245 280 315 350 385 420 455 490 525 560 62 108 145 181 217 253 289 325 362 398 434 470 506 542 679 63 112 149 187 224 261 299 336 373 411 448 485 523 560 597 64 116 154 193 232 270 309 348 387 425 464 503 541 580 619 65 119 159 199 239 279 319 358 398 438 478 518 558 597 637 66 123 164 206 247 288 329 370 412 453 494 535 576 617 659 67 127 170 212 254 297 339 381 423 466 508 550 593 635 677 68 131 175 219 262 306 350 393 437 480 524 568 611 655 699 69 135 180 226 271 316 361 406 452 497 542 587 632 677 723 70 139 186 232 279 325 372 419 465 512 558 605 651 698 744 71 144 192 240 287 335 383 430 478 526 574 622 670 717 765 72 148 197 247 296 345 395 444 493 543 592 641 691 740 789 73 152 203 254 305 356 406 457 508 559 610 661 712 762 813 74 157 209 261 314 366 418 471 523 576 628 680 733 785 837 75 161 215 269 323 377 430 484 538 592 646 700 754 807 861 76 166 221 277 332 387 443 498 553 609 664 719 775 830 885 77 171 228 285 341 398 455 511 568 625 682 739 796 852 909 78 176 234 293 351 410 468 527 585 644 702 761 819 878 936 79 180 240 301 361 421 481 541 602 662 722 782 842 902 963 80 185 247 309 371 432 494 550 618 680 742 804 866 927 989 81 190 254 317 381 444 508 572 635 699 762 826 889 953 1016 82 196 261 326 391 456 521 586 652 717 782 847 912 977 1043 83 201 268 335 401 468 535 601 668 735 802 869 936 1002 1069 84 206 275 343 412 481 549 618 687 755 824 893 961 1030 1099 85 210 281 351 421 491 561 631 702 772 842 912 982 1052 1123 86 215 287 359 431 503 575 646 718 790 862 934 1006 1077 1149 87 221 295 368 442 516 589 663 737 810 884 958 1031 1105 1179 88 226 301 377 452 527 603 678 753 829 904 979 1055 1130 1205 89 231 308 385 462 539 616 693 770 847 924 1001 1078 1155 1232 90 236 315 393 472 551 629 708 787 865 944 1023 1101 1180 1259 91 241 322 402 483 563 644 725 805 886 966 1047 1127 1208 1288 92 246 329 411 493 575 657 739 822 904 986 1068 1150 1232 1315 93 251 335 419 503 587 671 754 838 922 1006 1090 1174 1257 1341 94 257 343 428 514 600 685 771 857 942 1028 1114 1199 1285 1371 95 262 350 437 525 612 700 788 875 963 1050 1138 1225 1313 1400 96 268 357 446 536 625 715 804 893 983 1072 1161 1251 1340 1429 97 273 364 455 546 637 728 819 910 1001 1092 1183 1274 1365 1456 98 278 371 464 557 650 743 835 928 1021 1114 1207 1300 1392 1485 99 284 379 473 568 663 757 852 947 1041 1136 1231 1325 1420 1515 100 289 386 482 579 675 772 869 965 1062 1158 1255 1351 1448 1544 101 295 393 492 590 688 787 885 983 1082 1180 1278 1377 1475 1573 102 301 401 502 602 702 803 903 1003 1104 1204 1304 1405 1505 1605 103 307 409 512 614 716 819 921 1023 1126 1228 1330 1433 1535 1637 104 313 417 522 626 730 835 939 1043 1148 1252 1356 1461 1565 1669 105 319 425 532 638 744 851 957 1063 1170 1276 1382 1489 1595 1701 106 325 433 542 650 758 867 975 1083 1192 1300 1408 1517 1625 1733 107 331 442 553 663 773 884 995 1105 1216 1326 1437 1547 16.58 1768 lOS 337 450 563 675 788 900 1013 1125 1238 1350 1463 1575 1688 1800 109 344 459 573 688 803 917 1032 1147 1261 1376 1491 1605 1720 1835 110 350 467 583 700 817 933 1050 1167 1283 1400 1517 1633 1750 1867 111 356 475 594 713 832 951 1069 1188 1307 U26 1545 1664 1782 1901 112 362 483 604 725 846 967 1087 1208 1329 1450 1571 1692 1812 1933 113 369 492 615 738 861 984 1107 1230 1353 1476 1599 1722 1845 1968 114 375 501 626 751 876 1001 1126 1252 1377 1502 1627 1752 1877 2003 115 382 509 637 764 891 1019 1146 1273 1401 1528 1655 1783 1910 2037 116 389 519 648 778 908 1037 1167 1297 1426 1556 1686 1815 1945 2075 117 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 118 403 537 672 806 940 1075 1209 1343 1478 1612 1746 1881 2015 2149 119 410 547 683 820 957 1093 1230 1367 1503 1640 1777 1913 2050 2187 120 417 556 695 834 973 1112 1251 1390 1529 1668 1807 1946 2085 2224 112 APPENDIX TABLE X* [ELD FOR Even-aged Stands of Douglas Fir on Quality 1 Soils, Based on Two-site Qualities for the Type, Namely, Western Foothills of the Cascade Mountains IN Washington and Oregon. (Read from Curves.) Average Average No. of Total Diameter of Height of Yield Annual Growth Yield Annual Growth Age Trees per Acre Basal Area Average Tree Average Tree per Acre per Acre in Each Decade per Acre per Acre in Each Decade Years Sq. Ft. Inches Feet Cu. Ft. Cu. Ft. Ft. B.M. Ft. B.M. 10 1,000 20 990 116 4.6 32.0 2,150 115 30 580 149 6.9 46.0 3,550 140 40 410 177 8.9 59 . 5,400 185 12,400 50 340 199 10.4 69.5 7,550 215 28,000 1560 60 265 218 12.3 82.0 9,650 210 41,000 1300 70 208 234 14.4 95.0 11,500 185 51,700 1070 80 107 247 16.5 107 . 5 13,100 160 61,100 940 90 137 261 18.7 120 . 5 14,400 130 70,300 920 100 115 275 20.9 134.5 15,000 120 79,800 950 110 100 288 23.0 147.0 16,750 115 90,300 1050 120 92 301 24.5 156.5 17,800 105 101,500 1120 130 90 312 25.2 161 . 18,850 105 113,000 1150 140 88 323 25.9 166.0 19,900 105 122,000 960 Based on 252^ acres (361 sample plots). Note. — Including only Douglas fir, western hemlock, grand fir, and Sitka s^iruce; over 95 per cent of the trees are Douglas fir. The yield in cubic feet includes the contents of the whole stem of all the trees; that iu board feet includes only the merchantable contents of trees 12 inches and more in dianictor at breast height, taken to a top diameter of 8 inches inside the bark. *From Cir. No. 175, Forest Service, U. S. Dept. Agr., Growth and Managoinent of Douglas Fir in the Pacific Northwest, by T. T. Munger. DATA SERIES 113 DATA SERIES DATA SERIES I DouGL.\s Fir Stem Measurements Collected in the West Coast Lower Slope Type of Washington and Oregon D.B.H. Total Height Mer. Length to 8 inches No. of 16.2-foot Sections to 8 Inches Volume, B.M., 16.2-foot Sections to S Inches Volume, Cubic Feet (stem) Used Length Volume, B.M. (as cut into logs by logger) 31.1 180.6 140.0 81 1401 255.5 120.3 27.1 25.0 141.2 129.2 116.6 97.6 7i 6 1046 710 185.3 130.0 67.0 71.9 24.5 119.8 92.1 ol 730 144.3 70.6 22.2 24.2 27.0 159.1 148.7 130.2 117.5 114.1 115.6 7k 7z 7i 590 890 1000 120.2 172.1 174.4 97.6 96.2 105.5 31.0 24.2 179.7 150.3 151.1 96.1 9§ 6 1550 540 253.1 120.4 79.5 78.6 13.8 139 . 8 86.0 5^ 204 53.2 80.0 31.2 27.0 17.0 23.5 26.0 27.0 32.5 178.1 158.1 115.6 161.4 153.7 158.1 184.2 85.6 139 . 8 121.1 126.3 5i SI 7h 8 1290 1140 314.2 255.5 72.5 206.2 202 . 3 255.5 271.8 123.2 80.6 65.0 127.4 99.0 83.6 126.3 1550 1256 336 980 1510 12.5 17.0 113.2 124.8 69.6 68.2 4i 4i 160 . 240 40.3 76.9 408.8 37.1 140 160 35.0 183.0 157.4 91 3620 394.9 112.2 2590 19.8 16.7 123.9 127.3 85.8 o\ 690 101.4 78.1 81.0 64.6 440 440 26.1 174.7 135.3 H 1162 193.7 101.9 1000 32.7 175.0 149.4 9i 1720 285.9 131.2 1660 17.1 152.1 103.0 6^ 360 86.3 70.3 340 26.3 149.3 198.7 105.0 1040 29.0 39 5 156.7 222.4 231.1 321.5 85.9 135.9 • 1180 2650 12 1 115.2 36.6 80 17.8 101.8 64.8 4 260 61.0 49.4 190 12.1 97.0 43.2 21 80 23.7 24.7 60 11.2 96.3 41.4 2h 70 24.5 36.1 50 18.7 110.0 73.5 61.0 330 27.1 160.7 136 . 1 8i 182.7 103.2 870 29.0 173.2 134.6 8^ 201.6 87.6 1860 32.0 166.8 146.8 91 260.8 103.9 1430 30.9 199.4 162.0 10 1920 305.4 139.4 1990 38.5 225.4 162.0 10 2780 406.8 162.0 2710 35.0 254.3 194.4 12 4030 515.2 162.0 3840 33.5 226.3 178.2 11 2610 426.1 116.2 2180 29.3 197.7 162.0 10 1820 225.0 114.1 1560 114 APPENDIX DATA SERIES I— Continued No. of 16.2-foot Sections to 8 Inches Volume, Volume, D.B.H. Total Height Mer. Length to 8 Inches B.M., 16.2-foot Sections to 8 Inches Volume, Cubic Feet (stem) Used Length B.M. (as cut into logs by logger) 44.0 216.6 178.2 11 4210 625.3 133.2 3130 23.3 182.5 145.8 9 910 182.6 98.9 890 31.0 200.5 162.0 10 2110 383.9 105.7 1660 37.5 214.8 162.0 10 2750 422.5 131.1 2460 45.5 215.0 194.4 12 5190 721.2 135.1 4870 24.0 168.0 145.8 9 1330 203.2 104.6 1100 44.4 266.8 178.2 11 4210 614.5 131.4 3560 39.4 196.8 194.4 12 4590 655.2 157.8 4380 23.5 201.5 145.8 9 1480 238.2 102.3 1080 19.1 190.2 129.6 8 520 122.3 97.2 510 32.7 208.3 178.2 11 2390 375.1 102.1 1860 19.2 179.5 113.4 7 680 134.2 65.3 470 36.2 199.2 178.2 11 3280 469.5 118.2 2650 26.0 184.7 145 . 8 9 1260 207.6 106.3 1080 25.0 198.3 162.0 10 1610 252.9 145.1 1570 33.0 191.0 162.0 10 2310 344.1 130.4 1980 21.2 165.5 113.4 7 680 110.6 97.5 500 31.6 222.0 162.0 10 2320 326.9 148.0 2290 26.3 146.1 129.6 8 1000 189.6 97.5 820 22.9 144.0 129.6 8 780 124.2 72.5 620 13.5 147.0 81.0 5 220 49.6 64.9 160 24.4 181.0 129.6 8 910 149.2 129.9 820 24.4 180.1 145.8 9 990 178.3 130.0 880 25.0 189.1 145.8 9 1310 188.4 129.6 1150 30.5 191.5 178.2 11 2420 381.2 162.0 2191 17 . 5 135.7 113.4 7 560 103.1 97.7 430 26.5 183.6 129.6 8 1040 188.4 129 . 6 860 27.5 181.0 129.6 8 1340 219.5 98.0 1240 21.1 134.7 113.4 7 770 140.3 80.0 710 23.8 160.0 145.8 1120 191.2 102.0 1100 21.7 147.0 113.4 7 1040 110.5 104.0 1010 32.5 197.3 162.0 10 2640 394.0 149.5 2390 22.5 143.3 113.4 7 500 104.4 89.1 370 17.9 114.5 81.0 5 350 91.2 74.0 300 32.0 183.3 162.0 10 1890 314.8 140.0 1740 27.8 204.2 162.0 10 1630 215.0 125.5 1420 28.0 195.0 162.0 10 1910 253.3 119.3 1530 21.0 163.0 129.6 8 900 158.1 146.0 780 26.5 181.4 162.0 10 1710 275.6 145.2 1670 30.6 194.0 162.0 10 1970 314.4 106.5 1916 28.5 191.8 162.0 10 2110 319.4 143.1 1660 24.5 176.5 145.8 9 1260 215.7 145 . 3 1100 .24.5 192.8 162.0 10 1570 252.1 135.8 1210 24.5 195 . 3 162.0 10 1650 257.7 81.3 1130 37.5 208.6 178.2 11 3330 609.3 104.6 2390 DATA SERIES DATA SERIES I— Continued 115 No. of 16.2-foot Sections to 8 Inches Volume, Volume, D.B.H. Total Height Mer. Length to 8 Inches B.M.. 16.2-foot Sections to 8 Inches Volume, Cubic Feet (stem) Used Length B.M. (a» cut into logs by logger) 25.5 188.6 145.8 9 1440 242.7 70.1 960 23.5 174.0 145.8 9 1190 197.2 100.0 890 38.0 215.4 194.4 12 3670 464.2 162 . 3240 32.0 183.9 162.0 10 1820 277.2 109.0 1280 26.0 147.1 129.6 8 1070 148.9 94.2 890 32.4 208.4 178.2 11 2500 378.8 137.0 2200 29.0 198.1 162.0 10 1780 298.6 101.6 1540 34.5 205.7 178.2 11 2800 424.2 133.7 2330 34.6 206.4 178.2 11 2930 369.8 155.1 2830 29.0 182.3 129.6 8 1730 246.9 113.5 1640 27.5 195.4 162.0 10 1470 210.9 100.4 1220 17.2 180.1 113.4 7 570 131.6 72.9 500 41.3 196.3 178.2 11 3940 542.8 153.1 3600 29.2 204.7 158.0 9f 1680 270.0 147.5 1550 23.2 187.9 156.0 9i 1130 189.6 145.5 950 31.0 204.5 178.2 11 1950 346.4 148.3 1850 26.0 186.9 145.8 9 910 170.9 145.3 880 24.2 151.6 113.4 7 900 132.2 99.4 810 15.0 125.0 81.0 5 270 47.4 67.9 230 15.6 137.8 81.0 5 340 73.3 60.0 230 41.2 241.0 194.4 12 4610 688.9 186.6 4360 18.0 157.7 97.2 6 420 87.5 89.2 340 36.5 210.6 162.0 10 3940 446.3 117.6 2510 31.0 194.3 162.0 10 1660 292.3 142.1 1490 33.0 199.3 178.2 11 2040 320.7 98.6 1500 37.3 226.5 178.2 11 3180 466.2 151.3 2820 32.3 190.9 162.0 10 2110 269.6 123.4 1760 47.2 229.8 210.6 13 5810 699.2 167.8 5110 31.9 225.2 178.2 11 1910 299.5 162.3 1830 24.8 184.9 145.8 9 1340 167.5 103.0 1080 25.0 193.2 162.0 10 1360 187.0 97.4 860 34.0 222.9 194.4 12 3700 428.8 131.9 2710 31.0 203.6 162.0 10 1990 294.2 66.0 1000 37.8 211.0 194.4 12 4250 589.6 154.9 4000 35.2 195.0 178.2 11 3240 464.6 131.0 3120 38.5 209.2 162.0 10 2920 331.4 133.3 2720 34.0 205.0 178.2 11 2590 413.5 120.1 2140 32.0 205.0 178.2 11 2890 360.0 135.6 2050 17.0 130.5 97.2 6 490 88.5 96.0 360 40.0 189.8 45.8 9 2930 455.4 67.8 2060 31.5 195.0 162.0 10 1980 332.6 65.0 1210 29.5 166.4 129.6 8 1310 224.9 60.8 890 36.1 193.2 162.0 10 2830 422.4 114.8 2240 19.8 150.1 113.4 7 660 116.3 101.9 590 40.0 195.0 178.2 11 2900 569.0 66.5 2470 116 APPENDIX DATA SERIES I— Continued No. of l().2-foot Sections to 8 Inches Volume, Volume, D.B.H. Total Height iMor. Length to 8 inches H.M., 16.2-foot Sections to 8 Inches V'olunie, Cubic Feet (stem) Used Length B.AL (as cut into . logs by logger) 50.0 233 . 5 210.2 13 7310 703.9 130.0 5900 26.0 176.4 145 . 8 9 1310 238.6 112.0 1140 32.0 196.5 162.0 10 2540 376.1 136.0 2340 25.0 151.3 145.8 9 1190 158.4 108.2 790 39.5 224.9 176.2 11 3970 623.4 129.9 3010 29.7 194.0 162.0 10 2170 340.2 103.0 1720 39.0 206 . 5 176.2 11 3980 577.4 110.0 3590 20.9 190.0 145.8 9 850 150.8 129.6 790 18.9 118.4 81.0 5 450 85.6 64.8 360 14.8 107.0 56.8 3^ 200 53.3 15.4 102.0 64.8 4 270 57.5 14.8 95.5 60.8 3f 210 46.5 14.7 104.0 62.8 4 230 50.3 13.0 91.0 48.6 3 160 36.1 14.5 90.0 46.6 3^ 150 36.3 13.2 103.0 52.8 3i 140 38.1 11.6 95.0 40.6 2h 80 28.1 15.7 99.5 60.8 3| 220 51.1 16.0 104.0 64.8 4 270 59.3 13.6 102.0 50.8 3i 110 40.3 13.6 99.0 52.8 3i 140 39.3 14.0 90.0 46.6 3 150 35.4 11.6 92.0 38.6 2^ 70 28.2 13.8 87.0 46.4 3 150 35.8 13.5 92.0 48.6 3 130 34.8 11.5 94.0 42.6 2f 80 28.3 11.6 86.0 40.6 2h 80 26.4 16.2 117.0 64.8 4 310 71.7 14.0 94.0 54.8 4 180 44.7, 13.6 95.0 54 . 6 4 150 41.1 11.2 69.0 16.2 1 40 17.9 13.6 108.0 58.8 3i 180 44.8 13.5 85.5 42.6 3! 130 32 . 5 12.0 93.0 48.6 3 150 33.4 11.2 90.0 40.6 2h 90 28.9 12.4 95.0 48.6 3 160 38.1 11.7 83.0 42.6 2f 110 26.4 12.1 106.6 28.6 n 160 38.4 13.0 80.0 48.6 3 150 28.4 15.8 102.0 69.8 3f 210 51.6 15.8 97.0 71.0 4^ 230 68.1 16.6 104.0 64.8 4 270 58.2 14.3 114.0 56.8 31 200 49.9 15.2 96.0 54.8 3| 170 44.1 14.3 122.0 56.8 31 200 47.2 DATA SERIES 117 DATA SERIES I — Continued Volume, Volume, Mer. No. of B.M., i Volume, B.M. (as D.B.H. Total Height Length to 8 Inches i 1 16.2-foot Sections to S Inches 16.2-foot Sections to 8 Inches Cubic Feet (stem) 1 Used Length cut into logs by logger) 16.0 135 . 3 91.2 i 5! 410 77.8 15.2 147.9 93.2 51 400 82.9 10 G 85.0 38.6 2^ 1 80 24.9 1 11. G 94.0 42.6 21 110 29.7 1 . 13.8 136 . 5 81.0 5 320 66.4 1 14.5 1 84.0 42.6 21 110 34.0 12.0 73.5 32.4 2 90 24.0 15.8 102.0 60.8 31 210 51.6 14.9 i 117.0 64.8 4 270 57.6 11.0 ! 90.0 40.6 2h 90 27.2 11.6 94.0 42.6 21 110 29.7 11.1 83.0 38.6 2i 70 23.0 11.6 87.0 46.6 ; 3 120 28.7 17.0 145.0 ' 97.2 6 410 82.3 16.0 136.0 91.2 51 360 73.0 18.0 133.0 97.2 6 450 89.3 17.8 132.0 97.2 6 460 86.1 16.5 142.0 95.2 6 370 79.2 21.4 162.0 127.6 8 860 145 . 8 23.5 167.0 121.6 7^ 1030 186.8 21.0 152 . 107.4 61 680 126.4 20.0 152.0 113.4 7 630 120 . 1 21.0 159.0 107.4 6i 650 129.8 17 . 5 157 . 97.2 6 450 94.5 23.5 170.0 129.6 8 1230 207 . 5 22.2 130.0 109.4 61 670 132.5 19.0 140.0 97.2 6 530 1 116.9 19.8 152.0 107.4 6| 680 123.6 18.6 137.0 113.4 7 1 580 96.9 19.2 152.0 1 107.4 6f , 490 1 99.8 20.0 ' 159.0 113.4 7 760 1 140.0 17.5 1 122.0 81.0 5 400 76.5 17.7 138.0 97.2 ' 6 570 99.3 17.1 147.0 91.2 H 440 i 86.2 19.0 148.0 111.2 7 660 115.9 18.8 i 144 . 97.2 6 490 99.6 31.7 174.0 145.8 9 1940 301.1 26.0 182.0 141.8 SI 1300 212.4 26.2 161.0 135.8 81 1300 195.2 22.6 162 . 129 . 6 8 890 144.9 25.0 171.0 129.6 8 1600 255.3 27.0 156.0 111.4 7 690 153.1 33.4 207.0 176.2 11 3300 477 . 3 33 . 5 210.0 176.2 11 3490 487.6 ' 21.7 183.7 1 145.8 9 950 167.8 1 118 APPENDIX DATA SERIES I— Continued No of Volume, Volume, D.B.H. Total Height Mer. Length to 8 Inches 16.2-foot ,f;,," c ,. , 16.2-foot Sections to „ . 8 Inches ««^tions to Volume, Cubic Feel (stem) Used Length B.M. (as cut into logs by 8 Inches logger) 19.2 138.2 113.4 7 690 102.5 22.8 178.6 129.6 8 910 164.6 21.6 176.6 139.8 8^ 1040 169.1 31.5 199.5 162.0 10 1980 311.8 24.5 190.8 143.8 9 1260 219.2 24.3 210.2 160.2 10 1620 263.0 24.4 183.0 145.8 9 1230 208.2 36.1 197.6 160.2 10 2670 426.9 36.0 204.2 174.2 10^ 2810 430.4 32.5 206.8 174.2 m 2580 401.3 33.9 207.0 162.0 10 2720 443.1 24.7 192.0 143.8 9 1400 233.4 34.2 200.6 162.0 10 2620 395.9 27.5 202.2 143.8 9 1530 265.0 17.8 165.0 97.9 6 420 86.8 27.5 202.2 143.8 9 1530 264.9 11.7 83.0 42.6 2i 110 26.4 13.5 85.5 43.6 21 130 35.8 16.5 117.0 72.8 4^ 340 70.6 15.5 112.0 64.8 4 280 59.4 19.5 135.0 97.2 6 1610 110.6 20.0 149.1 97.2 6 660 126.2 27.0 161.2 123.6 7i 1410 224.8 16.0 136.7 91.2 5- 360 74.2 16.3 126.2 81.0 5 460 89.4 15.6 136.3 93.2 H 360 75.7 16.0 136.8 81.0 5 340 75.0 15.6 136.9 97.2 6 440 83.9 13.9 116.8 60.8 3f 190 47.5 12.9 127.4 56.8 3^ 150 39.7 14.1 130.2 75.0 4f 270 59.8 14.5 137.2 91.2 5f 360 71.9 27.0 184.6 162.0 10 1780 288.6 31.5 206.2 176.2 11 2730 404.1 27.6 207.8 129.6 8 1460 305.2 20.3 188.8 143.8 9 1020 177.3 21.2 158.0 113.4 7 620 118.9 30.2 180.0 111.4 7 1310 244.6 21.4 160,0 125.6 7-J- 800 144.9 • 38.2 209 . 9 174.2 10 J 3870 559 . 2 25.0 191.3 160.0 10 1 3S() 240.6 25.0 176.0 145. S 9 1590 236.2 25.9 ISO. 6 145.8 9 1540 218.3 41.6 200.0 129.6 8 3330 528.3 30.0 201.5 162.0 10 1730 286.9 DAI. A SERIES 119 DATA SERIES I — Continued No. of 16.2-foot Sections to 8 Inches Volume, Volume, D.B.H. Total Height Mer. Length to 8 Inches B.M., 16.2-foot Sections to 8 Inches Volume, Cubic Feet (stem) Used Length B.M. (as cut into logs by logger) 18.9 162.0 113.4 7 600 116.0 17.8 151.3 107.4 6| 470 93.8 19.7 162.0 117.6 7i 770 132 . 1 17.8 165.0 97.2 6 420 86.8 ;12.5 185 . 8 162.0 10 2510 360.9 38.5 211.5 162.0 10 3180 471.4 34.4 217.0 162.0 10 3010 480.7 26.8 160.0 111.4 7 930 176.6 26.5 200.6 162.0 10 1840 299.2 28.1 196.0 162.0 10 1960 323.7 22.2 157.5 129.6 8 1010 161.0 41.0 204.0 139.8 81 3150 488.9 27.7 160.2 106.9 960 27.8 171.1 123.1 1250 30.5 149.2 101.0 1120 33.9 171.7 114.3 1120 34.0 168.8 129.8 1560 35.0 182.0 99.0 1830 37.0 167.0 114.0 1940 37.2 176.9 133.4 2360 38.1 178.0 • 111.0 2700 16.3 118.2 70.4 260 16.5 109.3 66.8 260 18.2 138.4 70.4 300 22.0 135.3 64.5 460 22.4 169.8 101.8 560 58.0 226.6 158.8 6280 53.5 219.7 153.5 7660 18.3 126.5 65.3 290 22.5 132.5 72.7 600 49.0 258.6 154.2 4890 57.1 255 . 2 1 164.4 4820 60.0 213.5 . 161.5 8170 57.0 205.5 128.0 6440 20.0 121.5 58.2 270 18.0 129.5 108.0 320 47.1 179.3 167.6 5070 30.5 182.0 1 149.2 1670 47.0 210.6 148.0 4580 39.0 189.3 114.5 2490 36.0 193.2 117.0 2510 52.2 202.4 111.7 4490 30.1 200.0 139.0 1570 43.5 230.0 1 121.7 3440 41.8 184.8 1 i 131.6 2510 120 APPENDIX DATA SERIES 1— Continued No. of Volume, Volume, Mer. B.M., Volume, B.M. (as D.B.H. Total Height Length to 8 inches 16.2-foot Sections to 8 Inches 16.2-foot Sections to 8 Inches Cubic Feet (stem) Used Length cut into logs by logger) 22.0 175.1 102.6 750 42.2 199.5 122.1 3310 47.0 202.3 134.5 6240 44.6 237.9 134.3 3080 42.4 214.6 135.1 3130 48.5 244.0 145.1 4030 45.5 221.2 122.6 3760 41.0 194.2 135.1 3290 42.2 182.5 101.8 2820 52.3 229.8 125.3 3980 48.4 212.9 130.9 3180 45.4 208.2 127.0 3350 42.5 216.3 156.6 4280 30.5 189.6 124.0 1510 35.7 187.2 127.8 2290 54.0 239.8 179.2 6770 59.7 175.6 6140 40.0 148.9 3870 52.2 186.7 8490 60.5 141.8 8150 45.5 179.6 4451 47.0 138.4 6050 54.0 136.4 5490 52.0 112.6 5500 53.0 151.6 6890 49.5 151.6 5690 48.0 192.6 4270 48.0 130.8 3510 49.0 147.3 5090 54.0 195.2 7130 49.0 142.5 5850 52.0 153.8 7140 48.0 154.9 3820 46.0 112.1 3640 38.0 155.8 2410 44.0 144.4 4310 44.0 154.2 4640 41.0 124.3 3610 52.0 176.8 8930 46.0 172.1 6130 46.0 156.3 4760 60.0 155.6 8580 DATA SERIES 121 DATA SERIES II Measurements of Periodic Growth at the Stump Collected in Pure Western Yellow Pine Stands at Manitou Park, Colo. Periodic Periodic Periodic Tree D.B.H., Growth, Tree D.B.H., Growth, Tree D.B.H., Growth, No. Inches Inches * (Radius) No. j Inches Inches * (Radius) No. Inches Inches * (Radius) 1 U.O 0.20 ! IS 11.0 0.40 37 11.0 0.60 2 9.5 0.30 19 9.0 0.55 38 13.0 . 50 3 6.0 0.55 1 21 13.0 0.20 39 9.0 0.60 4 13.5 0.30 , ' 22 11.5 0.40 40 10.0 0.50 5 17.0 0.20 24 5.2 0.55 42 7.0 0.55 6 10.6 0.25 ! 25 8.0 0.50 44 6.5 0.50 8 10.0 0.45 26 9.0 0.40 1 45 6.5 0.60 9 11.0 0.40 1 27 18.0 0.25 46 9.1 0.50 10 18.0 0.30 29 11.0 0.40 47 7.5 0.60 11 16.0 0.30 < 30 10.2 0.45 48 9.1 0.30 12 18.0 0.30 31 12.5 0.40 49 10.0 0.35 15 12.0 0.30 33 16.0 0.30 50 11.5 0.40 16 7.0 0.50 34 10.5 0.85 51 18.0 0.20 17 12.5 0.35 36 11.2 0.50 52 5.9 0.60 Measurements represent outermost ten rings on average radius. 122 APPENDIX CO % o Q t c I a 1 CO 3 03 Pi 1 <; c o c s ■* ^ 00 OOSrHOOCCiO iOT»i (n'm'th' CO OOCOCCt^t^i#iM0500^»oSt-(MQ005iMCCi2 O -*^^XC0005^CO'O>0C^G0(Nf0'*'-lO-*'-HiOt^00O00 - >0 lO >0 lO iC (N(Mt^>OCCi-<.O0OC^— iMt^-rHOiCC CCOiMt^QOOQOO^^COi-icOiM^'M'M'-i^O^O o CDt^rHCOiM(N-^OOOi-it^CO01'*<050a>COO'H^C^,-((M,.HrH,-i^O'-'O'-iOCSCO-*,-iOiOOt>. -HOr-it^OOOOOOlOOrHO-H^O^OOr^OOOO 00 ict-c«ioo500 o ■^CCXlMOO^-^t^OfOINOO^O^C^CD^rHMt- OOt-00?D1^000t^t^OOOOOOOOOCT>0500t^05t>-OOl> •o t^Tt<00cD-O0O0iC0l:^iM05O(N t^COt^'OOt^iOOt^t^t^t^t^OiaON.l^OOO'-Dt^I^ •* 05CCI>OOiM'-i05'-Hl:^(NCCiNOOOCDr(HiCeCCOOOOOOO-«*< 0»OCO»OCOCOiCiOOO«0?OCDOOt^incO»Ot^CO;DO'^iOCO M 00i-ll~-O-*(NCCi0>'-i0;00(N'--»-<(Ni-H-*(N-*00t^t>-'-Hi-t »0'*iO-':t<»0'OTf.0»«»OT}<«OiOiO»CCO-^iM IN eOQOO-^j^ost^^co^cci^ocoooi^TiHiNosOosoooiocnoo -*(MTj<(NCCCOCCCOCCTj*(N-Ct^.-i.-iOO'-iOC»«0 DATA SERIES 123 (M t^ t- •^ O >-0 05 GO (N O O CC lO 05 t» ^ IM ■>* iC CO Tj< (N CO - lO 'O '^ r^iOOCOt^05l^>*'-'!co-*»0'*co-*iocooo TjJcDoioJxt^ojcot^cdcdt^r^r^OQOio-^oi eCO>»COOOCDCDOCO'-H<-H>OCOCOCOOCOOOGO(N(>lO'*(NOOr>-COCD^0505"^0 CO t-' N^ t^; CO i-O CO lO r*; CO tT 'I'' O t-^ CO ^' ci t-^ t- OC CO 00 iC CO CD d CO CD CO lO I> ■*■ T}< 00 coOQOMCi^t--Hcot-^t-ooo»ocoocco-H-;co>ococoi>.'OcoMO>oco0 Tji C^" Tt-' Tf' Tt; CO CO ^' U'^ CS ^" b-' CO CO ^^ ^ CO TjJ Tli Tt* Tl< O »0 Tl< Tt< CO ^ Tt< CO Tji-*St-COCD^OiOCDC^t-T«OQOU:OOC50>"5Mt-.eO^COC^CDQ005t-.»COOO eO CO CO CO CO (N ^ C^' CO d M N CO Tfi -h' CO CD lO CO Tf' d ^' C^' ^1 CO C^ CO CO c^ OlQO(N'-^Tj 239 166 151 2.0 16.0 16.0 26.0 16.8 15.6 12.8 0.8 0.5 18.4 16.6 1 St. 2 3 Top i 4 5 6 7 8 9 10 ...... 11 12 13 14 15 1 1 16 1 17 18 ' 19 1 1 1 1 rree No. 67 SUMMARY Plot No 1* No. of Logs Volume, Cubic; Feet Volume, B.M. si is > 245 60 1 18 18. U \ ' Name, F. H. Rice. Date, 7, 17, '09. 126 APPENDIX DATA SERIES DATA SERIES Y—Continued 12' Regular Volume Measurements As Used by Logger c .2 1 i 15.0 13.8 10.0 6.6 ■5^ CD Q Volume g^ > 1 204 192 163 94 2.7 16.0 16.0 16.0 12.4 0.60 0.35 0.25 0.20 16.2 14.5 10.5 7.0 St. 2 S 4 f> Top 6 7 8 q 10 n 1"? 13 14 15 16 17 18 IQ ?0 Tree No. IK SUMMARY Plot No. _ 01 "5 > Volume, B.M. is > 16 212 63.1 22 7 Name, F. P. McKown. Date, 7, 17. "09. 128 APPENDIX 00 o o »o tN. § § lO iO o o s lO "O lO s g .0 ■^ •rf' § § -* ■<*< •«}< ^: g ^ ■* -* c^i CO CO CO M CO (N IM 0000 CO 00 o o ci (N C^ (N O ^ .-H j. CO - CO CO CO CO CO CO ^ ^ 00 'X) •0 ^ CO C4 (N g t^ g 1 ^ 5 DATA SERIES 129 DATA SERIES V— Continued Regular Volume Measurements As Used by Logger • c .2 1 < £^ 1.6 16.0 16.0 4.0 is Volume ¥ > 1 104 67 25 9.4 6.8 2.0 0.6 0.3 0.1 10.2 7.4 2.2 St. 2 3 4 Top 5 ... 6 7 8 9 10 11 1? 13 14 15 16 17 18 19 ?.o Tree No. IS SUMMARY Plot No. ^ JZ ^ H -5 si a -og III Volume, B.M. •Ul 3 73 (U H 6^ > 10 109 37.6 > Name, O. .1. Staunchfieid. Date, 7, 19, '09. 130 APPENDIX —I « c^ odd CO CO >o o CO 05 C^ IN QCO t>. 00 O O DATA 8EKIES 131 DATA SERIES VI Statistics of Sample Acre Plots in Pure Even-aged Stands of Douglas Fir Data collected by the U. S. Forest Service, 1909 and 1911, in Western Washington and Oregon. SITE QUALITY I Location and Plot Number Saddle Mt., Siuslaw, N.F. 96 95 97 89; 94 88 91 Cougar Cr., Ore. 44 49 48 58 55 62 Bacon Creek, Washington, N. F. 167 160 163 149 161 165 Parmelia Trail, Santiam, N. F. 125 129 139 138 137 136 Lucia, Wash. 7 1 5 504 510 502 No. of Trees Stand. Years Volume Basal Area, Square Feet Cubic Feet Feet, B.M. 208 38 4,704 15,604 131 347 38 6,327 19,920 179 231 38 5,285 17,878 148 263 38 6,813 23,847 190 386 38 7,288 20,514 195 186 38 6,306 25,263 172 252 38 7,022 24,397 194 367 51 7,266 17,481 179 262 51 9,888 35,766 227 286 51 9,668 30,036 206 547 51 9,818 14,389 254 347 51 9,192 28,305 218 373 51 9,253 22,675 211 265 62 8,119 28,779 185 233 62 11,725 49,757 261 302 62 12,073 45,097 271 241 62 11,469 48,012 255 186 62 10,740 47,816 238 182 62 10.139 43,030 217 260 107 18,324 103,134 368 228 107 20,500 120,096 394 177 107 19,168 111,741 366 219 107 18,709 102,64 363 216 107 19.421 113,284 370 176 107 22,589 140.570 432 84 121 19,021 108,860 342 70 121 14,429 79,250 263 95 121 25,560 154,517 458 93 121 24,047 141,234 431 72 121 16,476 95,458 296 67 121 18,841 112,992 337 1 D.B.H. of Average Tree, Inches 10.7 9.8 10.8 11.5 11.2 10.5 11.9 9.5 12.6 11.5 9.2 10.7 10.2 11.3 14.3 13.8 13.9 15.3 14.8 16.1 17.8 19.5 17.4 17.7 21.2 27.3 26.2 29.7 29.1 27.4 30.3 Height of Average Tree, Feet 88 85 88 91 89 87 92 95 110 105 93 101 98 108 117 115 116 120 118 135 141 148 140 141 155 173 169 178 177 173 180 * This table includes all species on the acre plot except cedar. The latter is considered an understory. Douglas fir is the predominating soecies, with scattering hemlock, firs, spruce, pines and hardwoods. All trees to 2 inches D.B.H. are tallied by inch classes. Board measure based on trees 12 inches and over in diameter. 132 APPENDIX DATA SERIES \I~iContinued) Statistics of Sample Acre Plots in Pure Even-aged Stands of Douglas Fir Data collected by the U. S. Forest Service, 1909 and 1911, in Western Washington and Oregon.* SITE QUALITY II No. of Trees Stand, Years Volume Basal Area, Square Feet D.B.H. of Average Tree, Inches Height Average Tree, Feet Location and Plot Number Cubic Feet Feet, B.M. Marmot, Ore. 308 208 257 236 235 252 184 215 254 264 222 448 400 582 412 305 212 277 295 261 228 183 250 190 269 278 50 50 50 57 57 57 57 98 98 98 98 98 98 98 119 119 119 119 6,101.5 5,750.0 4,979.0 6,376.0 6,373.0 6,484 . 6,433.0 6,334.2 7,108.8 7,728.8 6,747.8 8,909 . 8 8,674.8 8,650.4 10,380.0 13,108.0 12,970.0 13,351.0 12,327.0 14,842.0 12,482.0 15,433.4 14,879.5 15,355.1 14,764.6 15,429 15,476 11,812 19,485 18,360 21,953 21,233 19,442 21,331 29,277 12,742 27,894 17,218 25,750 44,055 64,428 62,240 61,142 .'^7,640 75,103 65,699 64,230 68,608 65,206 64,302 169.1 159.0 138.0 172.0 173.0 170.0 171.0 156.06 181.73 195.43 207.04 255.15 272.00 249.08 242.0 292.0 295.0 304.0 280.0 333.0 294.0 319.54 302.33 330.45 325.54 12.2 10.7 10.3 11.6 11.2 13.0 12.0 10.6 11.3 12.7 9.2 10.8 9.3 10.6 12.0 15.9 14.0 13.8 14.0 16.3 17.1 15.3 17.1 15.0 14.6 93 307 89 306 86 305 91 304 90 303 96 302 92 Morton, Wash. 262 93 261 97 260 103 Huckleberry Mt., Oregon N. F. 293 78 292 85 291 78 290 84 Santiam N. F., Minto Trail 123 102 112 119 lis 111 117 110 116 111 114 120 122 123 Columbia N. F. Racetrack Trail 21 127 22 132 23 126 24 125 * This table includes all species on the acre plot except cedar. The latter is considered an understory. Douglas fir is the predominating soecies, with scattering hemlock, firs, spruce, pines and hardwoods. All trees to 2 inches D.B.H. are tallied by inch classes. Board measure based on trees 12 inches and over in diameter. DATA SERIES 133 DATA SERIES VI— (Con(mued) Statistics of Sample Acre Plots in Pure Even-aged Stands of Douglas Fir Data collected by the U. S. Forest Service, 1909 and 1911, in Western Washington and Oregon.* SITE QUALITY III Location and Plot Number \f Volume Basal Area, D.B.H. of No. of Trees Stand, Years Cubic Feet Feet, B.M. Square Feet Tree, Inches 306 57 6,845.3 20,383 209.56 11.2 292 57 7,635.3 25,630 229.80 11.9 385 57 7,173.4 15,017 203.41 9.9 520 57 5,946.4 8,065 198.62 8.3 481 57 6,128.0 9,005 203.79 8.8 524 57 5,596.5 7,502 190.52 8.1 537 57 6,379.3 7,268 214.57 8.6 587 57 5,887.1 4,719 202.77 8.9 635 57 5,260.9 3,169 190.49 7.4 505 57 5,862.8 8,452 186.28 8.2 741 57 5,029.2 3,311 158.47 6.2 574 58 6,131.0 11,346 176.38 7.5 431 58 8,272.2 22,558 218.97 9.7 814 58 6,092.0 8,984 184.54 6.2 138 70 5,282.0 21,201 130.00 13.1 201 70 7.488.0 30,127 184.00 13.0 ' 196 70 9,790.0 42,071 240.00 14.3 133 97 9,046.0 37,032 205.00 16.8 146 97 10,435.0 42,160 234.00 17.7 130 97 7,743.0 34,137 182.00 16.0 143 97 11,326.0 45,555 247.00 17.8 134 97 10,074.0 41,064 222 . 00 17.4 179 97 8,740.0 29,935 191.00 14.0 179 97 11,775.0 47,922 261.00 13.1 145 97 10,480.0 42,210 230.00 17.0 164 97 10,358.0 41,108 235.00 16.2 158 120 9,127.0 44,507 191.00 14.9 133 120 12,327.0 64,703 243 . 00 18.3 149 120 7,649.0 31,596 155.00 13.8 105 120 6,742.0 35,762 145.00 15.9 176 120 8,825.0 45,524 176.00 13.6 137 120 10,987.0 53,522 215.00 16.9 Humphrey, Wash. 235 236 237 238 239 240 241 242 243 244 246 Morton, Wash., Handle Road 253 254 255 Columbia N. F., Racetrack Trail 2 3 6 Columbia N. F., Huckleberry Mt 30 29 31 32 33 38 39 40 41 Frank Brice Cr., Ore. 145 144 135 138 137 139 * This table includes all species on the acre plot except cedar. The latter is considered an understory. Douglas fir is the predominating species, with scattering hemlock, firs, spruce, pines and hardwoods. All trees to 2 inches D.B.H. are tallied by inch classes. Board measure based on trees 12 imihes and over in diameter. FMPEH.