3 1822 01088 2777 
 
 371 
 , C3 
 
 presented to the 
 
 UNIVERSITY LIBRARY 
 
 UNIVERSITY OF CALIFORNIA 
 
 SAN DIEGO 
 
 by 
 
 Mr. George Marshall
 
 A MANUAL 
 FOR NORTHERN WOODSMEN
 
 A MANUAL 
 
 FOR 
 
 NORTHERN WOODSMEN 
 
 AUSTIN CARY 
 
 Recently Assistant Professor of Forestry 
 in Harvard University 
 
 REVISED EDITION 
 
 CAMBRIDGE 
 
 HARVARD UNIVERSITY PRESS 
 1919
 
 FIRST EDITION 
 
 COPYRIGHT, 1909 
 
 BY AUSTIN GARY 
 
 One thousand copies issued in January, 1909 
 One thousand copies issued in January, 1910 
 One thousand copies issued in July, 1911 
 Five hundred copies issued in August, 1915 
 
 REVISED EDITION 
 
 COPYRIGHT, 1918 
 BY AUSTIN CARY 
 
 One thousand copies issued in January, 1918 
 One thousand copies issued in March, 1919 
 
 PRINTED AT 
 
 THE HARVARD UNIVERSITY PR! 
 CAMBRIDGE, MASS., D. 8. A.
 
 PREFACE 
 
 THE reception accorded this book since it was first 
 issued in 1909, particularly the appreciation expressed 
 by numerous woodsmen, has been gratifying. Letters 
 of commendation have been received from users in 
 all parts of the country. It is significant that the 
 first typographical error discovered (a wrong figure 
 in a logarithmic table) was pointed out by a ranger 
 on the largest tract of unsurveyed timber land in the 
 United States, in Idaho. The second correction was 
 sent in by a Canadian cruiser. 
 
 The incidents just mentioned illustrate the wide 
 distribution of the volume and explain the present 
 extension of it. As originally written, the book did 
 not aim at circulation west of the Lake states; but 
 from the first a large part of the demand for it came 
 from Westerners, chiefly those employed in the 
 United States Forest Service. Revisions have been 
 guided largely by this fact, and that is true especially 
 of the present and first considerable revision, for 
 aside from bringing the work up to date as concerns 
 appliances and methods which have come into use 
 since the first edition was written, the new matter 
 and tables which have been introduced are mainly 
 intended for the benefit of western woodsmen. As a 
 result, material additions have been made under the 
 heads Topographic Maps and Timber Estimating.
 
 VI PREFACE 
 
 The book, however, is not materially increased in 
 bulk, nor has there been any change in its chief pur- 
 pose, which is to serve the men who are carrying the 
 load of actual timber work in this country. To these 
 men, in whatever section they are, and whatever may 
 have been their training, the author extends greeting.
 
 CONTENTS 
 
 PART I. LAND SURVEYING 
 
 PAGE 
 
 SECTION I. THE SURVEYOR'S COMPASS 
 
 1. The Instrument 1 
 
 2. Adjustments of the Compass 4 
 
 3. Keeping the Compass in Order 6 
 
 SECTION II. THE MAGNETIC NEEDLE 7 
 
 SECTION III. MEASUREMENT OF DISTANCE 9 
 
 1. The Surveyor's Chain 9 
 
 2. The Tape 10 
 
 3. Marking Pins 11 
 
 4. Chaining Practice 11 
 
 5. Measuring Inaccessible Lines 15 
 
 6. Stadia Measurement ^17 
 
 7. Units of Distance and Area 19 
 
 SECTION IV. SURVEYING PRACTICE 19 
 
 1. Running a Compass Line (Backsight, Picketing, 
 
 Needle) 20 
 
 2. Try-Lines 22 
 
 3. Marking Lines and Corners 23 
 
 4. Original Surveys and Resurveys 26 
 
 5. Age of Spots or Blazes 26 
 
 6. Notes 28 
 
 7. Party and Cost 28 
 
 SECTION V. COMPUTATION AND OFFICE WORK .... 31 
 
 1. Traverse 31 
 
 2. Area 37 
 
 3. Plotting 40 
 
 SECTION VI. ON THE BEARING OF LINES 43 
 
 SECTION VII. ON OBTAINING THE MERIDIAN .... 51 
 SECTION VIII. THE UNITED STATES PUBLIC LAND 
 
 SURVEYS . 60
 
 Vlll CONTENTS 
 
 PART II. FOREST MAPS 
 
 PAGE 
 
 SECTION I. THE TRANSIT 73 
 
 1. Adjustments . '. 73 
 
 2. Care of the Transit 77 
 
 3. Stadia Measurement 77 
 
 4. Uses of the Transit 80 
 
 5. Summary 87 
 
 SECTION II. THE LEVEL 87 
 
 1. Adjustments 88 
 
 2. Uses of the Level 90 
 
 SECTION III. THE HAND LEVEL AND CLINOMETER . . 93 
 
 SECTION IV. COMPASS AND PACING 94 
 
 SECTION V. THE TRAVERSE BOARD 98 
 
 SECTION VI. THE ANEROID BAROMETER 103 
 
 SECTION VII. METHODS OF MAP MAKING 113 
 
 1. Introductory . . . 113 
 
 2. Small Tracts 117 
 
 3. Large Tracts 121 
 
 A. With Land already subdivided 121 
 
 B. Based on Survey of Roads or Streams . . . 121 
 
 C. Subdivision and Survey combined 123 
 
 D. Western Topography. Use of Clinometer . 129 
 SECTION VIII. ADVANTAGES OF A MAP SYSTEM . . . 133 
 
 ^PART III. LOG AND WOOD MEASUREMENT 
 
 SECTION I. CUBIC CONTENTS 137 
 
 SECTION II. CORD WOOD RULE 138 
 
 SECTION III. NEW HAMPSHIRE RULE 138 
 
 SECTION IV. BOARD MEASURE 139 
 
 1. General 139 
 
 2. Scribner and Decimal Rules .......... 141 
 
 3. Spaulding or Columbia River Rule 141 
 
 4. Doyle Rule . 141 
 
 5. Maine Rule 142 
 
 6. New Brunswick Rule 144 
 
 7. Quebec Rule 145 
 
 8. Theory of Scale Rules and Clark's International 
 
 Log Rule . . . 145 
 
 SECTION V. NEW YORK STANDARD RULE ..... 147 
 
 SECTION VI. SCALING PRACTICE 148 
 
 SECTION VII. MILL TALLIES . . 151 
 
 SECTION VIII. CORD MEASURE . 157
 
 CONTENTS IX 
 PART IV. TIMBER ESTIMATING 
 
 PAGE 
 
 SECTION I. INTRODUCTION 161 
 
 SECTION II. INSTRUMENTAL HELPS 162 
 
 SECTION III. HEIGHT MEASUREMENT 165 
 
 SECTION IV. VOLUME TABLES AND TREE FORM ... 167 
 
 SECTION V. PRACTICE OF TIMBER ESTIMATING . . . 173 
 
 A. Small and Valuable Tracts 174 
 
 B. Larger and Less Valuable Tracts 186 
 
 1. Type and Plot System 187 
 
 2. The Strip System 188 
 
 3. Line and Plot System 192 
 
 C. Summary 195 
 
 D. Pacific Coast Methods 196 
 
 PART V. TABLES 
 
 SECTION I. Tables relating to Parts I and II 
 
 1. STADIA REDUCTIONS 211 
 
 2. SOLUTION OF TRIANGLES 212 
 
 3. TRAVERSE TABLES 214 
 
 4. LOGARITHMS OF NUMBERS 220 
 
 5. LOGARITHMIC SINES, COSINES, TANGENTS, AND CO- 
 
 TANGENTS 222 
 
 6. SUPPLEMENTARY TABLES OF SMALL ANGLES .... 228 
 
 7. NATURAL SINES AND COSINES 230 
 
 8. NATURAL TANGENTS AND COTANGENTS 232 
 
 9. SPECIMEN LETTERING : . . . 234 
 
 SECTION II. Tables relating to Parts III and IV 
 
 VOLUMES OF CYLINDERS (Locs) IN CUBIC FEET . . 236 
 
 AREAS OF CIRCLES OR BASAL AREAS 238 
 
 CORD WOOD RULE 239 
 
 NEW HAMPSHIRE RULE 240 
 
 NEW YORK STANDARD RULE 242 
 
 SCRIBNER LOG RULE, LEGAL IN MINNESOTA . . . 243 
 
 DECIMAL RULE OF THE U. S. FOREST SERVICE . . . 244 
 
 DOYLE RULE 246 
 
 MAINE LOG RULE 248 
 
 QUEBEC RULE 250 
 
 NEW BRUNSWICK RULE . . 253
 
 X CONTENTS 
 
 PAGE 
 
 12. CLARK'S INTERNATIONAL RULE 254 
 
 13. SPATJLDING RULE OF COLUMBIA RIVER 255 
 
 14. BRITISH COLUMBIA RULE 258 
 
 15. VOLUME TABLES 
 
 A. Eastern 
 
 1. White Pine by the Scribner Rule 261 
 
 2, 3. Red (Norway) Pine by the Scribner Rule . . 262 
 
 4. White Pine as sawed in Massachusetts . . . 263 
 
 5. White Pine in Cords 264 
 
 6. Spruce in Cubic Feet 264 
 
 7. Spruce in Feet, Board Measure 265 
 
 8. Spruce in Cords 266 
 
 9. Hemlock by the Scribner Rule 267 
 
 10. Hemlock as sawed in New Hampshire . . . 268 
 
 11. White (paper) Birch in Cords 268 
 
 12. Red Oak as sawed in New Hampshire .... 269 
 
 13. Peeled Poplar in Cords 270 
 
 14. Second Growth Hard Woods in Cords .... 270 
 
 15. Form Height Factors for Southern Hard Woods 271 
 16, 17. Northern Hard Woods in Board Measure . 272, 273 
 
 18. Longleaf Pine in Board Measure 274 
 
 19. Loblolly Pine by the Scribner Rule .... 275 
 
 B. Western; Notes on Western Volume Tables .... 276 
 
 20. Western White Pine in Board Feet 281 
 
 21. Western Yellow Pine in Board Feet 282 
 
 22. Western Yellow Pine (16-foot log lengths) . . 283 
 
 23. Lodgepole Pine in Feet, Board Measure, and 
 
 in Railroad Ties 284 
 
 24. Western Larch in Board Measure 285 
 
 25. Engelmann Spruce in Board Measure .... 286 
 
 26. Douglas Fir of the Coast 287 
 
 27. Douglas Fir of the Interior 288 
 
 28. Washington Hemlock in Board Measure ... 289 
 
 29. Washington Red Cedar in Board Measure . . 290 
 
 30. California Sugar Pine in Board Measure ... 292 
 
 SECTION III. Miscellaneous Tables and Information 
 
 1. RULES FOR AREA AND VOLUME OF DIFFERENT 
 
 FIGURES . 294 
 
 2. WEIGHT OF MATERIALS 296 
 
 3. HANDY EQUIVALENTS . 297
 
 CONTENTS XI 
 
 PAGE 
 
 4. NUMBER OF PLANTS PER ACRE WITH DIFFERENT 
 
 SPACING 297 
 
 5. COMPOUND INTEREST TABLE 298 
 
 6. TIME IN WHICH A SUM WILL DOUBLE 298 
 
 7. TABLE OF WAGES AT GIVEN RATES PER MONTH . . 299 
 
 8. THE BILTMORE STICK . . 301
 
 PART I 
 LAND SURVEYING
 
 PART I. LAND SURVEYING 
 
 SECTION I. THE SURVEYOR'S COMPASS 
 
 1. The Instrument li 
 
 2. Adjustments of the Compass 4 
 
 3. Keeping the Compass in Order 6* 
 
 SECTION II. THE MAGNETIC NEEDLE 1 
 
 SECTION III. MEASUREMENT OF DISTANCE 
 
 1. The Surveyor's Chain 
 
 2. The Tape 10 
 
 3. Marking Pins 11 
 
 4. Chaining Practice 11 
 
 5. Measuring Inaccessible Lines 15 
 
 6. Stadia Measurement 17 
 
 7. Units of Distance and Area 19 
 
 SECTION IV. SURVEYING PRACTICE 19 
 
 1. Running a Compass Line (Backsight, Picketing, 
 
 Needle) 20 
 
 2. Try-Lines 
 
 3. Marking Lines and Corners 
 
 4. Original Surveys and Resurveys 
 
 5. Age of Spots or Blazes 
 
 6. Notes 28 
 
 7. Party and Cost 28 
 
 SECTION V. COMPUTATION AND OFFICE WORK .... 31 
 
 1. Traverse 31 
 
 2. Area 37 
 
 3. Plotting 40< 
 
 SECTION VI. ON THE BEARING OF LINES 43 
 
 SECTION VII. ON OBTAINING THE MERIDIAN .... 51 
 SECTION VIII. THE UNITED STATES PUBLIC LAND 
 
 SURVEYS .
 
 A MANUAL 
 
 FOR NORTHERN WOODSMEN 
 PART I. LAND SURVEYING 
 
 SURVEYING in forest land as compared with work done in 
 towns and on farms is carried out under unfavorable cir- 
 cumstances. In the first place, timber and brush growth 
 offer an obstruction to sighting; second, the work is often 
 done far from a well supplied base; third, the limits of 
 cost allowed are often the lowest practicable. These con- 
 ditions have a strong effect upon the methods employed, 
 and they also affect the choice of outfit. Equipment for 
 such work should not usually be expensive, it should be 
 as compact and portable as possible, and it should not 
 be so delicate or so complicated as to be likely to get 
 seriously out of order and so hold up a job. 
 
 SECTION I 
 THE SURVEYOR'S COMPASS 
 
 Compass and Chain are the instruments that at present 
 are most largely employed in forest land surveying, and 
 there is little doubt that they will continue to be so em- 
 ployed. The compass is one of the mainstays of the 
 practical woodsman. He should thoroughly understand 
 its capacities and limitations, and should have perfect 
 command of all parts of his own particular instrument. 
 
 1. THE INSTRUMENT 
 
 The essential parts of the surveyor's compass are a 
 magnetic needle for finding a meridian line, a horizontal 
 graduated circle for laying off angles from this meridian, 
 and sights attached for use in prolonging lines on the 
 ground.
 
 2 A MANUAL FOR NORTHERN WOODSMEN 
 
 The needle in compasses used for surveying purposes is 
 commonly between four and six inches in length. It rests 
 by a jeweled bearing at its center upon a steel pivot screwed 
 into the compass plate, and, turning freely in the horizon- 
 tal plane, its ends traverse the graduated circle. The plane 
 of the sights passes through the center of the circle, and 
 cuts its circumference at two points marked N and S, 
 known as the north and south points of the instrument. 
 From these points the graduation of the circle runs 90 in 
 each direction to the points marked E and W. These 
 
 PLAIN SURVEYOR'S COMPASS 
 
 points on the face of the surveyor's compass are reversed 
 from their natural position for convenience in reading 
 bearings. 
 
 In using the compass, point the north end of the 
 circle forward along the line and read from the north 
 end of the needle. 
 
 A compass bearing is the direction from the observer at
 
 THE SURVEYOR S COMPASS 3 
 
 the compass to any given object referred to the meridian. 
 It is read as so many degrees from the N or S direction, 
 up to 90; as, N 10 W, S 88 15' E. The graduations on 
 a surveyor's compass are commonly in half degrees, but it 
 is usual, if necessary, to set by estimation quarter degree, 
 or 15', courses. A bearing can be set, however, with a 
 surveyor's compass in first-class order, to about 5'. 
 
 A compass needle that is in good working order 
 takes some little time to settle, and its condition may be 
 told by the freedom and activity with which it moves. 
 Time can be saved in setting it by checking its motion 
 with the lifting screw. In its final settlement, however, 
 it must be left free. For important bearings, it is well to 
 let it settle two or more times independently. 
 
 A glass plate covers the compass box and two small 
 levels placed at right angles to each other are used to set 
 the instrument in the horizontal plane. It is very de- 
 sirable that the box of a compass employed for woods 
 work should be as nearly watertight as possible. In 
 general make-up, the instrument is subject to considerable 
 variation. 
 
 The plate of the Plain Surveyor's Compass is prolonged 
 in the north and south direction into arms on which the 
 sights are supported at a distance of twelve to sixteen 
 inches apart. The actual sighting is done through fine 
 vertical slits, and round apertures placed at intervals along 
 these are convenient for finding objects and for getting the 
 instrument approximately in line. 
 
 The Vernier Compass has the circle and the sights 
 upon separate plates which may be turned on one another 
 for 20 or more. Its advantage consists in the fact that 
 declination, or a change in declination, may be set off, 
 and the courses of an old survey set directly, or lines re- 
 ferred to the true rather than the magnetic meridian. 
 
 The Folding-Sight Compass possesses the advan- 
 tages of light weight and the utmost compactness, and is 
 therefore popular among woodsmen. The sights are set 
 upon the edge of the compass box, and fold down across 
 its face when not in use, the whole instrument with its 
 ' mountings slipping into a leather case which may readily
 
 4 A MANUAL FOR NORTHERN WOODSMEN 
 
 be carried in the pack or slung from the shoulder. A 
 folding-sight compass with too small a box and needle of 
 less than full length should not be employed on work of 
 importance, as it is impossible with such an instrument to 
 read bearings and set marks with accuracy. 
 
 Compasses are either mounted on a tripod or fitted for 
 attachment to a single staff called a Jacob-staff, which 
 the surveyor may make for himself, when needed, from a 
 straight sapling. The former is the firmer mounting and 
 better adapted to accurate work, but the latter is much 
 more portable, except on bare rocks is more quickly set up, 
 and is generally employed for the ordinary work of the 
 forest surveyor. 
 
 2. ADJUSTMENTS OF THE COMPASS 
 A compass in first-class order will meet the following 
 
 tests : 
 
 a. The plate must be perpendicular to the axis of the 
 
 socket. 
 
 6. The plane of the level bubbles must be perpendicular 
 
 to the same axis. 
 
 c. The point of the pivot must be in the center of the 
 graduated circle. 
 
 d. The needle must be straight. 
 
 e. The sights must be perpendicular to the plane of the 
 bubbles. 
 
 In these tests it is presupposed that the circle is accurately 
 graduated and that the plane of the sights passes through 
 the zero marks. These are matters that belong to the 
 maker of instruments, and in all modern compasses accu- 
 rate adjustment of them may be assumed. 
 
 The general principle of almost all instrumental adjust- 
 ments is the Principle of Reversion, whereby the error 
 is doubled and at the same time made more apparent. 
 Thorough mastery of this principle will generally enable 
 one to think out the proper method of adjusting all parts 
 of any surveying instrument. In the case of the compass 
 the above-named tests may be applied and the instrument 
 adjusted as follows. The order of the adjustments is 
 essential.
 
 THE SURVEYOR S COMPASS 5 
 
 a. The plate is exactly vertical to the spindle in a new 
 compass, but the soft metal of most instruments is liable 
 in use to become bent. If that occurs to any considerable 
 degree, it will be shown by the needle and the bubbles. 
 The instrument should then be sent to the maker for repairs. 
 
 b. To make the plane of the level bubbles perpendicular 
 to the axis of the socket, level the instrument, turn it 180, 
 and, if the bubbles are out, correct one half the movement 
 of each by means of the adjusting-screw at the end of the 
 bubble-case. Now level up again and revolve 180, when 
 the bubbles should remain in the center. If they do not, 
 adjust for half the movement again and so continue until 
 the bubbles remain in the center of their tubes for all posi- 
 tions of the plate. 
 
 c. d. When the pivot is in the center of the circle and 
 the needle is straight, the two ends of the needle will cut 
 the circle exactly 180 apart in whatever position the in- 
 strument may be set. If the needle does not so cut, one 
 or both of these conditions is not fulfilled. If the differ- 
 ence between the two end readings is constant for all posi- 
 tions of the needle, then the pivot is in the center of the 
 circle but the needle is bent. If the difference in readings 
 is variable for different parts of the circle, then the pivot is 
 off center and the needle may or may not be straight. 
 
 To adjust the pivot, first find the position of the needle 
 which gives the maximum difference of end readings; 
 then, using the small brass wrench commonly supplied 
 with the compass, bend the pivot a little below the point at 
 right angles to the direction of the needle until one half 
 the difference in end readings is corrected. Repeat the 
 test and adjust again if necessary. When the needle cuts 
 opposite degrees, or when it fails to do that by a constant 
 quantity in all parts of the circle, the pivot point is in the 
 correct position. 
 
 With the above adjustment attended to, straighten the 
 needle. To do this, set the north end of the needle on some 
 graduation mark and bend the needle until the south end 
 cuts the circle exactly 180 from it. 
 
 e. To make the sights perpendicular to the plane of the 
 bubbles, level the instrument carefully, hang a plumb
 
 6 A MANUAL FOR NORTHERN WOODSMEN 
 
 line some feet away, and then look through the sights upon 
 it. If the plumb line appears to traverse the forward slit 
 exactly, that sight is in adjustment. If not, file off the base 
 of the sight until the adjustment does come. Then revolve 
 the compass 180 and test the other sight in the same 
 manner. 
 
 3. KEEPING THE COMPASS IN ORDER 
 
 Sharpening Pivot. The pivot or center pin of a compass 
 much in use is liable to become dulled so that the needle 
 does not swing freely. To obviate this the needle should 
 always be raised off the pivot when the compass is being 
 carried. A much blunted pivot should be handed over to a 
 jeweller to be turned down in a lathe, but ordinary sharp- 
 ening can readily be accomplished by the surveyor him- 
 self with the aid of a fine whetstone and the small wrench 
 usually supplied with a compass, or a pair of pliers. The 
 pivot should be removed from the compass box and fixed 
 in the end of a small, split stick; the point may then be 
 sharpened by twirling it gently on the stone at an angle of 
 about 30 with its surface. When the point is made so 
 fine and sharp as to be invisible to the eye, it should be 
 smoothed by rubbing it on the surface of a soft, clean 
 piece of leather. 
 
 Remagnetizing Needle. Dulness of the needle may 
 be due to the fact that it has lost its magnetism and needs 
 to be recharged. For this purpose a permanent magnet is 
 required. The north end of the needle should be passed 
 several times along that pole of the magnet which attracts 
 it, and the south end passed similarly over the opposite 
 pole. The passes should be made from center to end of 
 the needle, and a circle described in bringing the two ends 
 successively into contact. In order to prevent the loss of 
 magnetism, the needle of a compass not in use for a con- 
 siderable time should lie in the north and south direction. 
 
 Balancing Needle. The needle is commonly balanced 
 on the pivot by a fine brass wire wound around the south 
 end. If change of latitude is made, the balance will be 
 destroyed, and the wire may be shifted to make adjustment. 
 
 Replacing Glass. In case of emergency, a piece of win-
 
 THE MAGNETIC NEEDLE 7 
 
 dow glass may be cut down with a diamond and ground 
 on a grindstone to fit its setting. It may then be set in 
 place, with putty if possible, and the binding ring sprung 
 into place over it. 
 
 SECTION II 
 THE MAGNETIC NEEDLE 
 
 All compass surveying is based on the tendency of the 
 magnetic needle to point north and south. The direction 
 of the needle, however, is very far from being constant. 
 
 Secular Change. There is a belt of country crossing 
 the United States in a general north and south direction 
 through the states of Michigan, Ohio, and South Carolina 
 along which the needle at the present time points due north 
 toward the earth's pole. This belt is called the agonic 
 line, or line of no variation. East of this line the needle 
 points westward of true north; west of this line it points 
 to the eastward of it. The direction from any place toward 
 the pole of the earth's revolution is for that place the true 
 meridian. The direction taken by the needle is the mag- 
 netic meridian. The angle between the two is called the 
 declination of the needle, west if the needle points west of 
 true north, east if the needle points east of it. The declina- 
 tion is greater the farther the agonic line is departed from, 
 amounting to more than 20 in the maritime provinces and 
 the Puget Sound country. The agonic line is not sta- 
 tionary but is moving slowly westward, as it seems to have 
 done constantly since the beginning of the last century. 
 The declination of the needle, therefore, is changing from 
 year to year and at a different rate in different parts of the 
 country. 
 
 These facts affect the work of the land surveyor impor- 
 tantly, and sections on the bearing of lines and on ascer- 
 taining the true meridian are given later on in this 
 volume. 
 
 Daily Change. The needle when free and undisturbed 
 swings back and forth each day through an arc amounting 
 commonly in the United States to about 10'. Early in the 
 morning, from four to six o'clock according to the season,
 
 8 A MANUAL FOR NORTHERN WOODSMEN 
 
 the north end of the needle begins to swing to the east, 
 reaching its maximum position between eight and ten 
 o'clock in the forenoon. It then swings west to a maximum 
 westerly position reached from one to two o'clock p. M. 
 Then it swings slowly east again to a mean position reached 
 between six and eight p. M., at which point it remains 
 practically steady during the night. 
 
 The effect of this variation is such that if a surveyor 
 starts a line in the morning and runs one course all day, he 
 runs, not a straight line, but a long curve. This variation, 
 however, like the slight variation thut occurs during the 
 course of the year, is in woods work commonly disregarded. 
 
 Irregular Changes. The needle is subject occasionally 
 to sudden and irregular changes in direction. They some- 
 times occur during thunder storms, and at other times are 
 attributed to so-called magnetic storms, related perhaps 
 to the aurora borealis. Trouble from this source is not 
 often experienced by the surveyor, but it is a matter which 
 needs to be understood and watched for. 
 
 Local Attractions. All users of the compass are on 
 guard against the disturbance caused by iron in its vicinity, 
 in the form, for instance, of chains, axes, and steel rails. 
 In addition, there are in most countries regions of greater 
 or less extent where the needle is subject to irregularities. 
 These are due to iron ore or other magnetic material located 
 in the vicinity, or to unknown causes. 
 
 A local disturbance is indicated when the compass does 
 not read the same on the two ends of a line, and in compass 
 running error from this source is guarded against by keep- 
 ing careful watch of the backsight. Local disturbances 
 vary much in intensity. When very strong, they are readily 
 detected, and if confined in area present little difficulty to 
 the surveyor, who will clear out his line across them with 
 especial care, and either picket ! through or set the compass 
 by backsight. Slight disturbances are harder to detect. 
 If the area of disturbance is large, particularly if the ground 
 is broken, the compass cannot be depended on to carry a 
 line through with accuracy, and a transit or solar instru- 
 ment must be used. 
 
 1 See page 21.
 
 MEASUREMENT OF DISTANCE 9 
 
 Electricity. A little caution is necessary in handling 
 the compass in order that the glass cover shall not be elec- 
 trified by the friction of cloth or the hand, so as to attract 
 the needle to its under surface. If, however, the glass does 
 become electric, the trouble may be removed by breathing 
 upon it, or by touching different parts of its surface with 
 the moistened finger. 
 
 Difference in Instruments. It is a well-known fact that 
 different instruments do not always give the same bearing 
 when read on the same marks at the same time. A differ- 
 ence of 15' is not uncommon. 
 
 Summary. The magnetic needle is thus seen to be sub- 
 ject to numerous variations and irregularities, and on that 
 account work with the needle compass cannot be expected 
 to give the most accurate results. The instrument has 
 great advantages, however, and a very large field of legiti- 
 mate use. It gives an approximately true direction from a 
 detached point. Except on open ground, it furnishes the 
 quickest and cheapest means of turning an angle or pro- 
 longing a line. Most authoritative land surveys have 
 been made with the needle compass and their renewal is 
 best accomplished by use of the same instrument. The 
 special advantages of the compass in forest conditions and 
 its most effective use therein are discussed under the head 
 of SURVEYING PRACTICE. 
 
 SECTION III 
 
 MEASUREMENT OF DISTANCE 
 1. THE SURVEYOR'S CHAIN 
 
 The word "chain" in connection with land surveying is 
 used to represent two things: a distance of 4 rods or 66 
 feet, and an instrument for measuring distance. The 
 chain in use for general land surveying is 66 feet long and 
 divided into 100 links, but woodsmen working in rough 
 ground find the 33 foot or half chain with 50 links much 
 more convenient. 
 
 A chain for surveying purposes should be made of steel 
 wire, and its links should be brazed to prevent stretching
 
 10 A MANUAL FOR NORTHERN WOODSMEN 
 
 by opening of the joints. Chains have every tenth link 
 marked by a brass tag, and these tags have one, two, three, 
 etc., teeth, so that the number of links may be readily and 
 accurately counted. 
 
 Chains change in length by use. The links may be bent 
 and the chain thus shortened, a matter which can readily 
 be adjusted by hammering; but more commonly a chain 
 increases in length from flattening of the links and wear 
 in the numerous joints. This may be corrected to a limited 
 extent by turning up the nuts which hold the handles. 
 Further effect may be had by taking out one or^more of the 
 rings which connect the links, or better still, by hammering 
 each link while it is held in a vise, and so distributing the 
 correction. 
 
 The chain is so liable to change in length that provision, 
 should be made for testing it frequently. An unused tape, 
 known to be of true length, kept at home or only taken 
 off on long jobs, is the best and most convenient safe- 
 guard. 
 
 2. THE TAPE 
 
 Steel tapes are in wide use for general surveying, but 
 not usually among woodsmen because of their liability to 
 breakage. They have, however, distinct advantages. 
 They are light, so as to be leveled readily when measure- 
 ment is being made on a slope. They do not stretch. 
 There are no links to get kinked and so cause a false 
 measure. A tape for field use should be made of steel 
 ribbon from i to J inch wide and No. 30 to 32 thick. 
 Wider and thinner tapes are a nuisance in woods 
 conditions. 
 
 Tapes are made of any length and graduated to suit the 
 work for which they are designed. One 66 or 33 feet long, 
 graduated to links, will best suit the needs of the timber 
 land surveyor. 
 
 Some precaution must be taken with steel tapes. When 
 in use, they should be kept out at full length and never be 
 doubled on themselves, for, if doubled, they are easily 
 kinked and broken. When done up, they should be wiped 
 clean and dry, and so cared for as to prevent rusting. A
 
 MEASUREMENT OF DISTANCE 11 
 
 broken tape can generally be repaired on the ground if there 
 are at hand a punch, a piece of another tape, and some pins 
 to serve as rivets. 
 
 3. ]\IARKING PINS 
 
 Woodsmen frequently manufacture their own marking 
 pins of wood or wire. Those bought from dealers are 
 made of heavy iron wire, are some fifteen inches in length, 
 with one end sharpened and a ring turned in the other for 
 convenience in handling. Strips of cloth are tied in the 
 rings, so that they can be readily seen. It is most con- 
 venient to use eleven pins in chaining. One of them is 
 stuck at the starting point, the leading man takes ten, 
 and thus there is always one in the ground to start from 
 when the tallies are finished. 
 
 4. CHAINING PRACTICE 
 
 Chains are standardized in length at about ten pounds 
 pull with their full length supported. In woods work it is 
 generally necessary that the chain should be suspended 
 above the ground and not lie upon its surface. Care must 
 be taken, therefore, in accurate measurement, to give it 
 proper tension. What tension is proper for a suspended 
 chain, in other words, what sag should be allowed to 
 compensate for the stretch of the chain under the greater 
 tension may be determined on perfectly smooth and level 
 ground, and this is a valuable exercise for inexperienced 
 chainmen. 
 
 In order to get true chainage between points, the chain 
 should be kept straight and free from kinks. It must also 
 be kept in approximately true alignment, though a con- 
 stant error of 1 in that matter, equivalent to seven inches 
 error in setting pins each two rods of distance, shortens 
 the line by only nine and a half inches in the mile. Simi- 
 larly, the chain must be levelled so as to give distance in 
 a horizontal line, not following the contour of the ground. 
 In this last connection, that is, in getting distance correctly 
 on slopes and over rough ground, are met the greatest 
 difficulties in practical chaining. What is necessary is 
 first, to determine when the chain is level, and second, to
 
 12 A MANUAL FOR NORTHERN WOODSMEN 
 
 carry the point occupied by the suspended end of the chain 
 vertically down to or up from the mark on the ground. 
 
 The use of plumb lines and plumbing rods for this pur- 
 pose is well known from standard works on surveying. It 
 is common woods practice to drop a pin from the head end 
 of the chain, and that practice, when a pin loaded near the 
 lower end is used, has been approved for United States 
 land surveys. Only one such pin is required in a set, as 
 after it is stuck in the ground another may be substituted 
 for it. Similarly, for the rear end of the chain, when it has 
 to be held above the ground, an ax held suspended beneath 
 the handle, with the bit turned across the line, enables one 
 to do quick and fairly accurate plumbing. For determin- 
 ing when the chain is level, a hand level or Abney clinom- 
 eter, such as is shown on page 93, may well be put in 
 the hands of the men. There is a strong tendency on the 
 part of unpracticed chainmen to hold the down-hill end of 
 the chain too low. 
 
 It is to be observed that all the above-mentioned sources 
 of error work in one direction, namely, to give too large a 
 valuation to the distance between two points. The young, 
 school-trained man particularly, with his aspiration after 
 exactness, is apt to undervalue these sources of error, and, 
 in consequence, not give land enough. 
 
 In view of all the facts and conditions, particularly be- 
 cause of the pressure for cheapness in this class of work, 
 many practical woods surveyors have concluded that it is 
 best and safest not to strive after too great mechanical 
 exactness, but to make a small constant allowance at the 
 rear end of the chain. On the other hand, the loose practices 
 of some old woodsmen, such as letting the chain run out 
 the length of a man's arm beyond the mark, have nothing 
 to be said in their defense. 
 
 The general method of procedure in chaining, to be 
 modified as circumstances may require, is as follows. 
 The two chainmen will be spoken of as head and rear 
 man. Commonly, the rear man is the better and more 
 experienced of the two, and is in general charge. 
 
 With one pin set at the starting point, the head man 
 takes his end of the chain or tape and ten pins and steps
 
 MEASUREMENT OF DISTANCE 
 
 13 
 
 off in the direction of the line to be measured. Just before 
 the chain is all drawn out the rear man calls out " chain" 
 or " halt," and prepares to hold his end of the chain on 
 the mark. The rear man lines in the other, by the com- 
 pass ahead, by stakes left, or by the marks and bushing 
 
 TABLE SHOWING ERROR CAUSED BY CHAINING ALONG 
 GROUND OF DIFFERENT DEGREES OF SLOPE 
 
 Slope. Error. 
 
 Infect 
 per 100. 
 
 In degrees. 
 
 In feet 
 per mile. 
 
 In links 
 per chain. 
 
 2 
 
 U 
 
 1.0 
 
 .02 
 
 4 
 
 2J 
 
 4.3 
 
 .1 
 
 6 
 
 31 
 
 9.5 
 
 .2 
 
 8 
 
 i 
 
 16.7 
 
 .3 
 
 9 
 
 fi 
 
 21.2 
 
 .4 
 
 10 
 
 51 
 
 26.1 
 
 .5 
 
 along the line. Kinks are shaken out, the chain is levelled, 
 and proper tension is applied. When all is ready and the 
 rear man has his handle firmly held on the mark, he calls 
 out " stick" to the leader who sets his pin at once and 
 calls " stuck." When the rear man hears this signal, and 
 not before, he pulls his pin and both men move quickly 
 forward, repeating the operation till the head man has 
 stuck his last pin or has reached the end of the line. 
 When the head man has stuck his last pin he calls 
 " tally." The rear man then drops his end of the chain, 
 counts the pins to make sure that none has been lost, and, 
 going forward, gives them to the head man who counts 
 them again. The tally is marked down and a stake left at 
 the point for reference in case of a lost pin or other cause 
 of debate in the next tally. Pins should be set plumb, and, 
 in general surveying practice, the point held to is the point 
 at which they enter the ground. In the brush and "down 
 stuff" of some woods lines, however, it is sometimes neces-
 
 14 A MANUAL FOR NORTHERN WOODSMEN 
 
 sary to chain by the top, not the bottom, of the pins. No 
 jerking of the chain should be allowed. The rear man 
 should not stop the head man with a jerk. The head man 
 must pull steadily on the chain when measuring. 
 
 When chaining on slopes which are so steep that the 
 full length of the chain cannot be levelled at once, the 
 head man first draws the chain forward the whole length 
 and in line. He then drops the chain and his marking 
 pins and returns to a point where he can level a part of the 
 chain. This distance is measured and one of the rear man's 
 pins stuck at the point. The rear man then comes forward 
 and, taking the chain at the same point, holds it to the 
 mark while a second section is measured, and so on till the 
 end of the chain is reached, when the head man sticks one 
 of his own pins. It is not usually necessary to note the 
 lengths of the parts of the chain measured. Take care 
 only to measure to and from the same points in the chain 
 and not to lose the count by getting the marking-pins of 
 the two men mixed together. 
 
 Accuracy. The requirements of woods chainage vary 
 so widely, its difficulties are sometimes so great, and the 
 expense permissible for the work is often so restricted that 
 only guarded statements can be made as to obtainable 
 accuracy. When chainmen, measuring the same line 
 twice, agree almost exactly, it does not prove that they 
 have given correct chainage, for two other men on the 
 same line may get a result considerably variant. Really 
 correct chainage is to be obtained only by strict attention 
 to the sources of error mentioned above, their amount and 
 nature. In general, it may be said that on smooth and 
 level ground, free from obstructions, chaining may be 
 done with error of a very few feet in the mile. On land as 
 it runs, however, chainage accurate to within a rod in a 
 mile is generally called entirely satisfactory. 
 
 Summary. Good chaining consists in keeping the chain 
 of right length, in true alignment, vertical and horizontal, 
 and in proper stretching, marking, and scoring. It is a 
 very important part of all surveying which employs that 
 method of measuring distance, and has been badly neg- 
 lected in much woods work of the past. It needs and de-
 
 MEASUREMENT OF DISTANCE 
 
 15 
 
 serves good men to carry it on, men who will get down to 
 the ground and take all needed pains in marking, level- 
 ing, and alignment. They should be brisk men, moving 
 quickly and doing their work in a prompt and business- 
 like manner. Much, too, depends on system, on tally- 
 ing, passing pins, etc., from habit and in regular order. 
 Some men never will make good chainmen because they 
 will not take sufficient pains about details. A few in their 
 strict attention to these are liable to make gross blunders. 
 The man in general charge of surveying work must give 
 careful attention to this part of the business. Chainmen 
 must be trained in good methods and watched till they 
 are perfectly trustworthy, while careful consideration must 
 be given to sources of error and to possible improvements 
 in method. 
 
 5. MEASURING INACCESSIBLE LINES 
 
 Ponds, bogs, and bluffs, over which it is impossible to 
 chain, are met in the practice of nearly every surveyor, and 
 quick and accurate measurement across them constitutes 
 one of the problems which he has frequently to solve. Each 
 problem of that kind has to be solved in the field according 
 to the ground and circumstances. The methods commonly 
 employed in such cases are as follows: 
 
 1. Offset. Frequently a short offset squarely to left or 
 right will clear the obstacle. 
 
 FIG. A 
 
 2. Method by 45 Angle. (A) With the compass at a, 
 set a stake in the line at b across the obstruction, and, 
 turning off an angle of 45, set another stake on that range
 
 16 A MANUAL FOR NORTHERN WOODSMEN 
 
 as x. Set up at b and, turning off a right angle, set a 
 
 stake c in the range a x. Then a b = b c. 
 
 3. Method by 26 34' Angle. (B) Proceed as before, 
 
 making the angle b a c = 26 34' ; then a b = 2 b c, as 
 
 may be found in the table of tangents. 
 
 4. Method by 30 Angle. (C) 
 With compass at a set a stake 
 in line at b, and, turning off an 
 angle of 60, set another stake 
 on that range, as x. Set up 
 at b and turn off a b c = 30, 
 setting a stake c in the range 
 a x. Then a b = 2 a c. 
 6. Method by Tangents. (D) With the compass at a 
 
 set a stake at 6, also run out a perpendicular line and set 
 
 a stake at c visible from b at any convenient distance. 
 
 Measure a c. With the compass at b, take the bearing of 
 
 c b and thus get the angle a b c. In the table of tangents 
 
 look up the tangent of this angle. Then a b = . 
 
 FIG. D 
 
 6. Method by Oblique Triangle. (E) The stake c may 
 be set at any convenient point visible from both a and b 
 and the angles at a and b measured. Measure also the side 
 a c or b c, whichever is easier. Then a 6 may be computed 
 as the side of an oblique triangle. For formulas neces- 
 sary, see pages 212-213. 
 
 7. Method by Traverse. (F) In the case of a large lake 
 or stream, several courses may be run along its banks, and 
 when the range of the line is again struck, as at e, the dis-
 
 MEASUREMENT OF DISTANCE 
 
 17 
 
 tance a e may be computed by traverse. If a e runs N and 
 S, the distance a e will be the latitude of the traverse, or, 
 stated in other words, it will be the sum of 
 the products of the cosines of the several 
 courses into their respective distances. The 
 departure of such a traverse should be zero. 
 Thus, if e is not visible from a, or if it is not 
 convenient to take the range a e, e may be 
 set when the sum of the departures figures 
 up 0. This process of surveying a lake or 
 river shore is called " meandering." It is the 
 method pursued in the United States land 
 surveys on considerable bodies of water. The 
 same method may also be employed to get 
 round a precipitous hill or some other inac- 
 cessible object. 
 
 An example of the computation necessary 
 for solving a problem of this kind is given on 
 page 33. 
 
 8. Method by 60 Angles. (G) A precipitous bluff or 
 impassable swamp may occasionally be passed most read- 
 ily in the following manner. With 
 the compass at a, lay off a 60 
 angle and run out a c, carefully 
 chaining. Next, making an angle 
 of 60 at c, run out c b to an equal 
 distance. Then, if the work has 
 been done accurately, b is in the 
 line and ab = a c = be. 
 
 In working by any of these 
 methods it is better, if possible, 
 to set b in range by the compass 
 from a rather than to rely for the range on any process of 
 figuring or angulation. 
 
 FIG. F 
 
 6. STADIA MEASUREMENT 
 
 A substitute for chaining, which has to some extent 
 been employed in forest land surveying and which deserves
 
 18 A MANUAL FOR NORTHERN WOODSMEN 
 
 wider use, is stadia measurement, or the measurement of 
 distance by wires placed in the focus of a telescope and 
 the space which they cut off on a graduated rod. The 
 principles of this method are stated on page 77. 
 
 For this purpose a light telescope may be fitted to 
 the rear sight of the compass, as shown in the illustra- 
 tion, a level and vertical 
 circle being added if the 
 instrument is to be used 
 on rough ground. The 
 cost of such an instrument 
 complete is about the same 
 as that of a compass. Its 
 adjustments will readily 
 be understood from its 
 construction and from 
 consideration of the ad- 
 justments required for the 
 transit. 
 
 The advantages of this 
 instrument in land sur- 
 veying are as follows : 
 1. Sights may be taken 
 on steeper ground, either 
 up or down hill, than can 
 be covered through com- 
 
 2. Distances over very 
 steep ground can be 
 measured more accurately 
 and quickly than by use 
 
 A TELESCOPIC SIGHT of the chain. 
 
 3. Distance across 
 
 gorges, swamps, and bodies of water can be obtained 
 directly and with ease. 
 
 4. It enables the surveyor himself to perform all the 
 particular work on a survey, and this on short jobs, or 
 wherever reliable chainmen cannot be had, may be a very 
 great advantage. 
 
 Stadia wires in an instrument used for land surveying
 
 SURVEYING PRACTICE 19 
 
 should be so spaced that one foot on the rod will be cut off 
 when it is held at a distance of 66 feet, or, if the wires are 
 fixed, the rod may be graduated to correspond. For occa- 
 sional use in land surveying, the rod may best be made 
 of painted canvas, which, in case of need, may be tacked 
 on any pole that comes to hand. 
 
 The Stadia Hand Level is a simpler form of the instru- 
 ment, adapted to the measurement of the width of gorges 
 or ponds. It is readily carried in the pack, and, when in 
 use, may be held in the hand or mounted on a staff. The 
 ready range of this instrument is 200-300 feet. 
 
 7. UNITS OF DISTANCE AND AREA 
 
 7.92 inches = 1 link. 
 
 25 links = 1 rod. 
 
 100 links = 66 feet = 1 chain. 
 
 320 rods = 80 chains = 1 mile. 
 
 160 square rods = 10 square chains = 1 acre. 
 
 640 acres = 1 square mile or section. 
 
 The vara, a measure of Spanish origin, prevails in Cali- 
 fornia and in Texas. The California vara is 33 inches. 
 The Texas vara is 33J inches, and 5645.376 square varas 
 make one acre. 
 
 In Louisiana and the Province of Quebec, the arpent, 
 an old French unit, is the measure of areas. This is .8449 
 acre. 
 
 The hectare = 10,000 square meters (meter = 39.37 
 inches) or 2.47 acres. This is also a French measure. 
 
 SECTION IV 
 SURVEYING PRACTICE 
 
 The starting point of a survey is generally settled for a 
 surveyor by outside controlling circumstances. When this 
 is recognized, the next thing to do may be to find out what 
 course to run by an observation for the true meridian, or 
 by finding the bearing of an old line. With the starting 
 point and course determined, the method of procedure is 
 about as follows.
 
 20 A MANUAL FOR NORTHERN WOODSMEN 
 
 1. RUNNING A COMPASS LINE 
 
 Set up the compass at the point from which the line is to 
 start; level the plate; free the needle, and when it has 
 settled, set the course to be run. It is desirable on starting 
 a line to let the needle settle two or more times independ- 
 ently. 
 
 An assistant, called the rodman or flagman, then goes 
 ahead with a pointed rod or flag, and, following him, go 
 the axemen, clearing out the bushes and other obstruc- 
 tions in such a manner as to secure both a clear line of 
 sight and a path for the chain. The rodman may use an 
 axe. He guides himself at first by the compass sights, later 
 by signals from the compassman or by the range of the line. 
 The axemen guide their work by him. 
 
 When the rodman has gone ahead a convenient distance, 
 at signal from the compassman or acting on his own judg- 
 ment, he selects a spot for a second setting of the compass, 
 attention being paid both to firm setting and clear ground 
 for the instrument, and to facility in getting sight ahead. 
 On uneven ground summits commonly meet best this last 
 requirement. 
 
 When setting the rod, the rodman should face the com- 
 pass, holding the rod plumb and directly in front of him. He 
 sticks it as directed by the compassman, who assures him- 
 self at the time that everything about the instrument is 
 right. Before taking up the compass, the man in charge 
 of it sets a stake near by and in line to be used in backsight. 
 The needle is then lifted, and the compass taken up and 
 carried forward to be set up at the point marked by the 
 rodman. If a Jacob-staff is used instead of a tripod, the 
 compass should be set up ahead of the rod with its cen- 
 ter in line, the exact position of the foot of the staff being 
 of no consequence. 
 
 The compass is then levelled again with its N mark 
 ahead as before and the sights turned on the object left 
 at the starting point. The needle is then freed, and if, 
 when it settles, the bearing reads the same as before, the 
 surveyor is assured that there is no local disturbance, and 
 may proceed confidently. The rod and axemen soon learn
 
 SURVEYING PRACTICE 21 
 
 to range for themselves, and lose no time waiting for the 
 set-up of the instrument. The chainmen keep behind the 
 instrument where they are out of the way. Each man 
 learns his exact duties, and all hands, particularly the corn- 
 passman and rodman, learn to work together. 
 
 Running by Backsight. The details of compass survey- 
 ing vary considerably in accordance with the accuracy re- 
 quired, cost allowed, and the make-up of the party doing 
 the work. If local attraction is suspected or, on short 
 lines, if great accuracy is required, obstructions are cleared 
 completely out of the line, and w r hen an assumed or trial 
 course has been started, it is prolonged by backsight en- 
 tirely, reference to the needle not necessarily being made. 
 In order to do this, either a rear rodman is employed or a 
 stake is set in line at each station occupied by the compass. 
 
 Picketing. The compass after the start, indeed, may not 
 be used at all, but straight stakes, preferably four to five 
 feet high and sharpened at both ends, may be ranged in 
 one after another along the line. This method of running 
 a line is frequently resorted to, and is called picketing. 
 
 To clear out in most woods a line open enough for con- 
 tinuous backsighting or picketing is an expensive process, 
 and, further, this method for long distances and uneven 
 ground is not to be relied on. If, in those circumstances, 
 close accuracy of alignment must still be had, resort must 
 be made to another class of instrument, a transit or solar, 
 which may carry the work out of the hands of the woods 
 surveyor. 
 
 Running by the Needle. Usually the compass will do 
 the work reasonably well and satisfactorily to all interested 
 parties, in which case the needle will be used at nearly 
 every setting. In all compass running it is well to carry a 
 light rod ahead, though that is sometimes dispensed with, 
 the compassman going up to a stake or even an axe set up 
 by the head axeman in line. When trees of some size are 
 run into, they are not commonly cut down, but the com- 
 passman notes, or has marked, the spot at which his line 
 of sight hits them, and, going forward, sets up beyond 
 them in the same range as nearly as he can. For back- 
 sighting it is not a great trouble to set stakes, but, in a
 
 22 A MANUAL FOR NORTHERN WOODSMEN 
 
 country where local attraction is infrequent it is sufficient 
 precaution to watch the blazes and bushing back along the 
 line. In any case, time is saved by setting up the com- 
 pass approximately by the backsight before letting the 
 needle go free. 
 
 2. TRY-LINES 
 
 When two unconnected points are to be joined, it is usual 
 first to run a line without spotting, a try-line so called, and 
 if the desired point is not hit, to measure at right angles the 
 distance between the line run and the point aimed at, fig- 
 ure the angle of error, and rerun the line. The angle re- 
 quired is obtained from a table of tangents. 
 
 Thus suppose a try-line to have been run N 4 E 120 
 rods or 30 chains and to have hit 32 links east of the mark 
 aimed at. Dividing 32 by 3000 (the distance run in links) 
 gives .0107, and the angle of which this is tangent is 
 found in the table of natural tangents to be 37'. The com- 
 pass may therefore be set N 3 23' E, and the line rerun. 
 
 Results near enough for most purposes may be had by 
 remembering that the tangent of 1 is .0175 (i. e., if feet in 
 100, or if links per chain) and that the tangents of small 
 angles are in proportion to the size of the angles. Thus 
 with the case above, the tangent of 1 being .0175 and 
 that of the angle required .0107, .0107 divided by .0175 
 equals .61 of 1, or 37'. 
 
 a c i . ; L__i___|Trial Line 
 
 Sch. 10 ch. 15 ch. 20 ch. 25 ch. 30 ch. 
 
 DIAGRAM SHOWING THE METHOD BY OFFSET 
 
 Or instead of using the compass to rerun the line, its 
 position may be fixed by offset, that is, by measuring at 
 right angles to the try-line, at different points along it, the 
 distance required to place points in the desired range. For 
 this purpose stakes should be left in the try-line at equal 
 distances apart, say every 5 chains, and the length of each 
 offset may be figured by tangents or as a simple problem 
 in proportion.
 
 SURVEYING PRACTICE 3 
 
 Thus with the case in hand. The tangent of the 
 angle between the try-line and the true line has been fig- 
 ured as .0107. This decimal multiplied by five chains 
 or 500 links gives 5| links, the offset from the 5-chain 
 point. Similarly 10 chains multiplied by .0107 gives 10.7 
 links, and so on until all the offsets have been computed. 
 
 By proportion the problem is even simpler. In the case 
 in hand the offset at the 15-chain mark should evidently be 
 half that at the finish, or 16 links. At the 5-chain mark it 
 is of it, or 5j links as found before. In the same way 
 offsets for any length of line and any error in closing may 
 be figured. When the points have been put in, the line 
 may be blazed through by eye, or with the aid of the 
 compass. 
 
 3. MARKING LINES AND CORNERS 
 
 Corners. Permanent corner marks are especially val- 
 uable in maintaining bounds and protecting property 
 rights; and the desirability of stone monuments, or, fail- 
 ing these, of earth mounds, iron rods, or charcoal, is not 
 to be disputed. Forest land is occasionally subject to 
 great mischances, as from clean cutting, wind, and fire, and 
 marks which can survive these have distinct and peculiar 
 value. 
 
 On the other hand, posts of durable wood, and trees that 
 are likely to remain in place a long time are generally 
 handiest, are easy to mark on, and frequently meet, better 
 than more elaborate and expensive marks, the ideas of 
 owners and the customs of the country. Supplemented 
 by blazed and marked witness trees, such markings for 
 corners are now in wide use on forest property and there 
 can be little doubt that their use will continue. Marks on 
 living trees should be placed in most cases on a peeled or 
 blazed surface of the wood, though bark marks, much dis- 
 torted it is true, have been known to remain legible for a 
 very long time. 
 
 Corners in every case should be plainly inscribed so that 
 any interested person may readily identify them. It is 
 usual in woods practice for the surveyor who establishes a
 
 24 A MANUAL FOB NORTHERN WOODSMEN 
 
 corner to leave there his initials, or some mark peculiar to 
 him which will identify it as his work, together with the 
 year in which the survey was made. The same thing may 
 be done by a succeeding surveyor. 
 
 Practice in all these matters, however, varies a good deal 
 in different parts of the country. The methods presciibed 
 for use in the United States land surveys will be found on 
 later pages of this volume. 
 
 Lines. A property line in the forests of Germany is kept 
 cleared out several yards wide and blocks of cut stone are 
 deeply set along it near enough together so that one may be 
 seen from another. In addition, the range of a transit line 
 is inscribed upon them. This renders the property limit 
 prominent and durable, and, further, defines it to within a 
 quarter of an inch. 
 
 Such ideal marking is seldom to be looked for in this 
 country, but the ends to be aimed at, which in the fore- 
 going case were attained, should be in the mind of every 
 man who has to do with forest boundaries. A property 
 owner's interests are first, to have his bounds prominent so 
 that he and other parties may know where they are and so 
 that there will be no excuse for trespass ; second, to have 
 them durably marked for obvious reasons ; and third, to 
 have them so closely defined that all possible causes of 
 dispute may be avoided. 
 
 Stone walls, ditches, and fences are the common bounds 
 of property in settled and half-settled countries, and each 
 of these methods of delimitation has its grade of efficiency, 
 considered from the above points of view. In large forest 
 areas blazed trees are the means almost universally em- 
 ployed for the purpose. That system has been reasonably 
 satisfactory in the past. It would have been more so had 
 care and system always been employed in the marking and 
 more attention paid to renewal. 
 
 The directions for marking lines in timbered lands, as 
 contained in the " Manual of Instructions for the Survey 
 of the Public Lands of the United States," are as follows : 
 
 All lines on which are to be established the legal corner boun- 
 daries will be marked after this method, viz. : Those trees which 
 may be intersected by the line will have two chops or notches cut
 
 SURVEYING PRACTICE 25 
 
 on the sides facing the line, without any other marks whatever. 
 These are called sight trees or line trees. A sufficient number of 
 other trees standing within 50 links of the line, on either side of 
 it, will be blazed on two sides diagonally or quartering toward the 
 line, in order to render -the line conspicuous, and readily to be 
 traced in either direction, the blazes to be opposite each other, 
 coinciding in direction with the line, where the trees stand very 
 near it, and to approach nearer each other toward the line, the 
 farther the line passes from the blazed trees. 
 
 Due care will ever be taken to have the lines so well marked 
 as to be readily followed, and to cut the blazes deep enough to 
 leave recognizable scars as long as the trees stand. This can be 
 attained only by blazing through the bark to the wood. Trees 
 marked less thoroughly will not be considered sufficiently blazed. 
 Where trees two inches or more in diameter occur along a line, 
 the required blazes will not be omitted. 
 
 Lines are also to be marked by cutting away enough of the 
 undergrowth of bushes or other vegetation to facilitate correct 
 sighting of instruments. 
 
 These directions are ample, have been tested by use, and 
 are practically the same as those issued for land survey 
 work in the Dominion of Canada. Plainly, however, they 
 are adapted to sparsely wooded land, for, in real timber 
 growth, blazed trees two rods away from the line would be 
 a source of confusion. In fact, the narrower a line is blazed, 
 so long as it is clear and durable, the better. A good 
 general rule to be applied in timber is to blaze those trees, 
 and only those, which a man can reach with his axe when 
 standing directly in the line. 
 
 A line in ordinary woods well blazed according to this 
 method is prominent, and reasonably durable, while the 
 quartering of the spots and special marking of the " line " 
 trees render it reasonably well defined. If decent care is 
 used in maintenance, and if when it has become dim or 
 doubtful it is thoroughly and carefully renewed, there need 
 be no great trouble or expense involved in that process, 
 and no trespass or dispute meanwhile. Certain identifica- 
 tion of the " line" trees of a previous authoritative survey 
 is a great help in renewal. In the United States system that, 
 is secured by notching those trees ; in the province of New 
 Brunswick they are blazed and the blazes hacked three 
 times upward. The same thing might be secured, and in 
 addition the work of the individual surveyor identified,
 
 26 A MANUAL FOR NORTHERN WOODSMEN 
 
 by a personal mark, such as a stamp cut on the poll of the 
 blazing axe. 
 
 4. ORIGINAL SURVEYS AND RESURVEYS 
 
 The woods surveyor has two broad classes of work to do, 
 the running of new lines, outlining property for sale or 
 administration, and the work of relocation. The first 
 class of work constitutes an original survey, which the sur- 
 veyor must carry out with due regard, on the one hand to 
 accuracy, on the other to cost. His ordinary duty here 
 consists of three parts: first, to duly outline and measure 
 the tract in question; secondly, to mark the bounds of it 
 in satisfactory fashion; third, to take notes of what he 
 does for record and the benefit of those who come after. 
 
 Resurveys. When a boundary has once been surveyed, 
 marked on the ground, and accepted, it becomes authorita- 
 tive, and the usual duty of the man who comes after is 
 simply to locate the work of the original surveyor. He 
 uses the compass commonly as the best means of finding 
 the old lines and corners. Hd may use the chain for the 
 same purpose, or to satisfy himself about area. But his 
 business, so far as the boundary itself is concerned, is to 
 find and remark the old one, not set up a new one ac- 
 cording to his notions of propriety. In relocating that 
 boundary the marks of the earlier surveyor are a more re- 
 liable guide than his notes : they must, however, be clearly 
 identified and not confused with those of irresponsible 
 parties. On the other hand, where monuments cannot be 
 found, reliable verbal testimony is admitted, while it has 
 further to be recognized that property boundaries may be- 
 come sanctioned by use or agreement, even though they 
 are crooked and astray from their original location. 1 
 
 5. AGE OF SPOTS OR BLAZES 
 
 A subject of special interest to the forest surveyor is 
 the determination of the age of spots on trees. This means 
 
 1 For both legal and practical guidance in resurvey work, see 
 "Restoration of Lost or Obliterated Corners," by the Land 
 Office, and Hodgman's "Land Surveying."
 
 SURVEYING PRACTICE 
 
 20 25 17 30 32 35 40 43 
 
 . BLAZE FIVE YEARS AFTER CUT WAS MADE : A, FRONT VIEW 
 SHOWING RIM OP CALLUS ; B, CROSS SECTION 
 
 C. BLAZE TWENTY-THREE YEARS AFTER CUT WAS MADE
 
 28 A MANUAL FOR NORTHERN WOODSMEN 
 
 of identifying a surveyor's work is recognized by all the 
 courts. The handling of the problem in the field may be 
 made clearer by the accompanying figures, reproduced 
 from Circular No. 16, Division of Forestry, United States 
 Department of Agriculture. 
 
 6. NOTES 
 
 Notes should be full and exact so as to furnish for the 
 benefit of later comers a complete record of the work done. 
 In the case of resurveys they should be particularly clear 
 as to the old marks found, so that the evidence which gov- 
 erned in the resurvey may be a matter of record. This 
 rule holds especially in regard to starting points and 
 corners. 
 
 The date of a survey is an important thing to record 
 clearly, along with the meridian which was used, whether 
 magnetic, true, or one assumed for the occasion. 
 
 Notes should be so plainly and clearly written that any 
 fairly intelligent man can understand them. They should 
 be honest as well, not concealing actual errors. When the 
 lines of a survey do not close in exactly, it may not be worth 
 while to rerun them, but there ought at least to be no dodg- 
 ing of the facts. It is only an incompetent surveyor who 
 will not acknowledge his errors. Errors are normal and 
 to be expected. They grow out of imperfections in 
 method that are imposed on the surveyor by limitations 
 in the matter of expense. Errors are not to be confused with 
 mistakes or blunders. 
 
 The notes of a timber land survey should also be full as 
 regards topography. Such notes often give great assist- 
 ance in the relocation of lines and corners. They are also 
 of value to the owner and operator of such property. 
 
 7. PARTY AND COST 
 
 The great advantages of compass and chain surveying 
 for woods work are that it is sufficiently accurate for most 
 purposes, and that the cost involved is very moderate. Six
 
 SURVEYING PRACTICE 29 
 
 /" Renew/ of souf/i tine of Tn/>., J/?.4, Oxford Co., Ma/ne Sept tt, /90s. 
 Line orig//?a//yrt//?fy.Ba//art/ntf94, fas beer? 0/azedo/er some s/nce.iut 
 
 never 
 
 resurveyed. .3. Dearborn, rear cAoin. 
 
 
 Hare traced dorm o/ra 'p/Tyrect 'tfte east ///re offtre tt>wns/rje> to a ///re 
 
 Ofspo 
 
 <y runnirig west supposed tobe/'ts souft ///K. Search afona tft/s -stows 
 
 nitfr/n 
 
 2orvds a spruce and ab/rth W//A rery o/d 6/azes nrfi/cb />rove as 
 
 near c 
 
 s rfrerifys can be counted fr> be ///years o/d. Ab/aze of /Me 
 
 age is 
 
 also fvi/ffd 3 rods /o the eastward. M> 5/ff/? -seen offfie ory/rxr/ 
 
 Corne. 
 
 ~ noted as 6e//ro /# a &//T;/?. 
 
 
 f/7 rawe of-ffie spots east- and nesf a/Kt/ntte //fre com//705ovft 
 
 Sfa 
 
 cedar post- andstv/?&s. 7/r/s /j in f/af s/>re/ce /and and S rvds 
 
 from 
 
 Cs/ar7d Fond to the easfwa/tf. Afar/tea 'tfre/xaf o/rMW. 7~S/?.4; 
 
 Of? ME. 
 
 T4. /J4.j or? 5. T-5 ft.3 , a/so 'L/.J.B.&OS.'' The M/TrcsslrveSfa/so mortal 
 
 J.J.B. 
 
 19OS, am a cedar sts/Td/n^r tf/O /O 6>rAs from tfie /oast, affotfrer 
 
 S.J0 
 
 /s//nto, a spruce s.3omo///?*s a. a fr'n* tf.45n /s///rte. 
 
 
 From ffieposff&natr/a/ '/// /V83W at ry/rt a/y/es to fire x*'* ^ brrc 
 
 After 
 
 esrods fotmd anot/rer ory/'/xr/ '6/aze 20 J/'/rAs to rte /efr. ffefur/redto 
 
 post a 
 
 vdnsr? tf.833O'rX 
 
 Rods 
 
 
 80 
 
 MarAed a b/rc/r rig ft f- of tine (*#+* 
 
 KO 
 
 Rising ontv the freight- ofar/dae w/?/c/7 fa//s o/f />nx/p/foe/s/y 
 
 
 2. rods to the 3ot/fft. Or/g//7a/ t/'mter 6/0 nr/? down a/rd roffex fans 
 
 
 and some rods afiead. f~0v/7rf3ofSa//a/Ttfs spots c/ase toSfi&SHOffy. 
 
 
 i^y afidjo/??e spots t>y /i/mber/Tres? of/e/7 w/'a<s of tt?e ///re. 
 
 
 B/azed tfiroty/r srmyfit: 
 
 160 
 
 Afarted a spruce rio/rf-of //tie. %M>* S/ope 3.IY 
 
 210 
 
 Don/i a sfrvnas/ope -5. W O/d^pots /rare eee/7 Aav/ty to t/rf right 
 
 
 and flow o/re on a o/rch with ///r//ys over /f is jo /wAs ry/rt: 
 
 
 Off-set to if, ft'// in the /ine t>ac/c over the o/ds/>ots, and contr'ne/e 
 
 
 on same oear/n.<7- 
 
 840 
 
 Set a cedar 5tafi e mar/ted %M++ 
 
 Z56 
 
 Watsr crosses tt> Soutfitvest- 
 
 17S 
 
 Lasf 40 rods tftroug/r swamp with main/yjot/nf ffrotvttr and no 
 
 
 SDO fs to oe see/7. 
 
 
 Old b/aze probao/y Sa//ards found now on a dead and down cedar. 
 
 Z95 
 
 Cross Canada /fay road. 
 
 320 
 
 A spof of Ba//ards age on a s/yrt/cejust oacA 2 rods 3oi/tfr ans 
 
 
 Spots of mucn /ess eye wh/ch come Sn/o rtrera/rtfe a feur svds 
 
 
 further 0/7. 0/azedthe tine ffrrvvaA s/m/pnf ^Sefa/nsffor 
 
 
 the corner Of -Secf/ons 3S & 36 mar/ted on /V.W "S.M93S. 
 
 
 on //.. "S.N 36." > onS. "T.S ft.3" MarAed /f and the witness 
 
 
 frees ^.B. &OS? 
 
 \^ , 

 
 30 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 /^ WoodsfocA, Mass., tfayft, M07 Survey made for C/arA Lumber Co of 
 ftreir farter Lot- SO Ca/fed Dec/, ofneed/e as near as Anontr //.' 'Jm/towS'ctoin 
 
 Begin at 
 
 Souffn 
 
 vest- corner cf /of- at 'June fro/7 ofsfoae wa//s marA/'/y 
 
 recoqn/z 
 
 ^/ bo 
 
 f/idar/es of f/re '/ofc Thence 
 
 Bearing 
 
 0/sf. 
 
 
 NJOE 
 
 847' 
 
 Along wa//to /f-s e#c/ 
 
 
 19/7' 
 
 ffirot/qh p'fte fy'm^er 6otf?s/tf&s nrM /ro s/'f/r ofproper/y 
 
 
 (iota/) 
 
 //ne, to a roffs/r f&rce runnim? easfer/y. T/re deeds ca///m? 
 
 
 
 for a /we ru/rn/'/y "Srr a norftter/y tf'necrwr" /Aibzec/ 
 
 
 
 the. ///7<e ffrrvvgSr orrtfre. ram?e of f-fre na// anrfxf a/XKt 
 
 
 
 and s fanes af/ts /ror/A emJ. 
 
 
 
 This is on /edgy ground IV/ff! a drop off /O feef- wes/: 
 
 S733S'. 
 
 IOS4- 
 
 Along Me o/c/ farce //ne Sma// brooA runs Maf68off: 
 
 
 
 fo 5 E corner of ffie /of- /y/ng north, as /nd/eafec/ ty 
 
 
 
 range of o/d far/n wa// rvn //? from f/re nortfr fo fhis possii: 
 
 
 
 Set a stone 6/ocfi on end and surrounded /f nM sfones 
 
 
 
 Setse/era/ heaps ofsfones a/any fhe //ne. 
 
 A//0 
 
 3SO' 
 
 Onrange of -farm yfaf/ffrenfib/Tecfandrouyn/ya/om? fne 
 
 
 
 bound of the cuff i/y, tnswam/y /and offer 2oo'. 
 
 
 
 Sef stakes a/ong fne //ne each 2OO 'andaffne e/rd a 
 
 
 
 post" w iff? heap of s/v/res. 
 
 S80 
 
 SO' 
 
 Alright ang/es fo ffre range //ne ft> Conasse ArooSc. 
 
 
 
 77r/s c/isfance /s ffre one (3 rods) Catted for /n f/ie cfeed 
 
 
 
 and is f he on/y means of f/jf/ng f/re /as f named corner 
 
 
 
 Off the norfh and soufn //ne . 
 
 SJSf 
 
 I7f\ 
 
 
 SSJ> 
 
 3/9\ 
 
 Along Cohasse brooA as /?es~ ca// of deed. 
 
 580E 
 
 33S 
 
 Jcross 6rooA, ffren 0/r south border of f/e/d //? passes 
 
 
 
 siorr of owners norfh, to ivesf s/de of/r/jhway. 
 
 
 
 7/r/s/x>/nf/s 7/6 ff sotrffrerfy from ffre forks of fhe h/g/r#qy. 
 
 
 
 the deedca//>nff for "about 40 rods" Set- /xzsf- andsfones. 
 
 S&Tr 
 
 /68' 
 
 Down h/ohway to br/dge orer Cofasse broofi as ca//ed 
 
 S^O3O' 
 
 2SO 
 
 for /n deed 
 
 S4030' 
 
 /SS- 
 
 
 S6W 
 
 7/2' 
 
 L//? the swamp c/ase fo foot of fne r/ctge 
 
 5 /aw 
 
 ^ss' 
 
 Offset freauenf/y to get exacf area of the "hare/ tend 
 
 53a'w 
 
 720' 
 
 Hhtch was con i/eyed /n ffre deed To stone tva//,rt?e 
 
 szz'w 
 
 S62'- 
 
 recogn/zed South bound of the /of 
 
 /V84W 
 
 296' 
 
 Along wa//, up a /yrec//)'fvi/s sfope 
 
 M73JO'lV 
 
 1086 
 
 Along the rva// fo p/ac e of oeynnrna 
 
 This surrey 
 
 M/ows 
 
 ff/e terms oftfie deeds as near as ffre/ can be //rfer/refet? 
 
 jUtoArmsfi 
 
 ity,ar 
 
 Sidenf of tfe Jxa//fy 3Ojear3 ana 'fy/rr///ar urM 'fs /bnd fmnsfers 
 
 ondoccu/xirK 
 
 'Hasp 
 
 Kent ancfiays ffotxaf/orr tyrges as near as />e Anom *r//tt fAf un- 
 
 derstendiiy o 
 
 'ttteol. 
 
 i^orf/es and facts of/x>ixssn>/r. /.ocaf/oa, ffterefore.food The 
 
 \uBMft */ 
 
 ineino 
 
 -Aedonffa Sittr Surtr/ed"c.L Co /3O7 "and a/so Hifft myimfiafs
 
 COMPUTATION AND OFFICE WORK 31 
 
 men form a usual party for line work in the northern woods, 
 and from one to three miles a day can commonly be run 
 with it, according to the ground and growth. The usual ex- 
 pense for such work ranges between $6 and $10 per mile. 
 A reliable transit line, on the other hand, cannot be cleared 
 out and run for twice those figures. 
 
 The work of the forest surveyor may be done for the fol- 
 lowing purposes, and the party required for each sort of 
 work, outside of maintenance, is noted in connection. 
 
 1. New work, for the purpose of sale or administration. 
 Party required : compassman, two chainmen, enough men, 
 commonly three, ahead of the compass, with axes and a 
 rod, to keep the rest of the party busy. 
 
 2. Resurvey, for the sake of reestablishing lines and 
 corners, also for getting area. Party : same as above ; or 
 it may be more economical in some circumstances not to 
 employ chainmen, but for the surveyor himself, with one 
 of his party, to go back and do the chaining. 
 
 3. Careful resurvey with the compass of old lines, no 
 chainage required. Party to correspond. 
 
 4. Remarking lines where no great difficulty is expected, 
 but where the lines need freshening. The man in charge 
 and two axemen form an economical party. A small fold- 
 ing sight compass may be used as needed. 
 
 Balance in the party is one element largely influencing 
 cost. The main thing is to have sufficient axemen to give the 
 rest of the party enough to do. Subsistence is an important 
 problem in some circumstances. A chainman can carry a 
 pack on his work, and frequently chainmen are employed 
 on long jobs in the backwoods to carry a portion -of the 
 supplies or outfit. 
 
 SECTION V 
 COMPUTATION AND OFFICE WORK 
 
 1. TRAVERSE 
 
 To " traverse" a line or route is to survey it by any 
 method that ascertains direction and distance. The cir-
 
 32 A MANUAL FOR NORTHERN WOODSMEN 
 
 cuit of a farm's boundaries by compass and chain is a 
 traverse. So is the survey of a road by usual methods. 
 
 When a survey has been made in this fashion the notes 
 are for some purposes best worked up after a method 
 called " computing by traverse," the principles and appli- 
 cations of which are developed in the following paragraphs. 
 
 If a course is run out N 30 E 20 chains, a certain dis- 
 tance is made in a northerly direction, also a certain dis- 
 tance in a direction east. The distance made in the former 
 direction is called latitude ; in the latter, departure. In this 
 case it is north latitude and easterly departure. These 
 elements may be made evident on a plot by drawing a 
 meridian and base line through the starting point and 
 lines perpendicular to these from the point reached. These 
 distances are also to be obtained from traverse tables. 
 
 The same is true of a course run in any direction and 
 for any distance. Any course not run exactly east and west 
 makes northing or southing. The former is reckoned as 
 positive latitude, with the sign (+). The latter is negative 
 or ( ) latitude. Similarly, distance made in an easterly 
 direction is (+) departure; that made towards the west 
 ( ) departure. If several courses are run in succession, 
 the sum, algebraically reckoned, of their latitudes and 
 their departures gives the position of the point finally 
 attained. 
 
 This method of reckoning, using traverse tables for the 
 purpose, has a wide use in connection with land surveying. 
 The traverse table given on pages 214-219 furnishes the 
 elements for 15' courses, those usually employed in com- 
 pass work. The following is a simple problem illustrating 
 their use. 
 
 In running a section line due north, the surveyor conies 
 to a lake shore. Setting there a post, duly marked, he runs 
 round the lake near the shore by the following courses : 
 
 N 50 E 12 chains. 
 
 N 9 30' E 20 
 
 N 40 W 9 
 
 S 80 W 6.81 " 
 
 Reckoning up his courses by the traverse table, he finds
 
 COMPUTATION AND OFFICE WORK 
 
 33 
 
 that his E and W departures balance, hence he should be 
 in line. The difference between northing and southing 
 gives him the distance. He may then set a second post, 
 add the distance to his previous chainage, and proceed with 
 his survey. 
 
 COMPUTED TRAVERSE 
 
 Field Notes. 
 
 From Traverse Tables. 
 
 Bearing. 
 
 Distance. 
 
 Latitude. 
 
 Departure. 
 
 
 
 N. 
 
 S. 
 
 E. 
 
 W. 
 
 N. 50 E. 
 
 12.0 chains 
 
 7.71 
 
 
 9.19 
 
 
 N. 930'E. 
 
 20.0 
 
 19.73 
 
 . . 
 
 3.30 
 
 
 N. 40 W. 
 
 9.0 " 
 
 6.89 
 
 . . 
 
 
 5.78 
 
 S. 80 W. 
 
 6.81 
 
 
 1.18 
 
 ... 
 
 6.71 
 
 
 34.33 
 
 1.18 
 
 12.49 12.49 
 
 
 1.18 
 
 
 
 Distance due north 
 
 33.15 chains 
 
 Balance 
 
 When a closed survey is made, that is to say, when a sur- 
 veyor starts and finishes at the same point, it is evident that 
 its (+) and ( ) departures should be equal, also its (+) 
 and ( ) latitudes. Owing to the errors unavoidable in 
 survey work it is very seldom that they do so reckon up 
 exactly. The amount by which the two ends fail to meet, 
 whether plotted or reckoned, is the error of closure, and the 
 percentage of error is the ratio of this distance to the total 
 length of the survey. A certain percentage of this error, 
 say 1 in 500 or 1 in 300, may be allowable in an ordinary 
 woods survey. For plotting and for area, however, it may 
 be desirable to distribute the error through the different 
 courses, and this, when the traverse has been reckoned out, 
 is readily done. The error in both latitude and departure 
 is usually distributed to the different courses in proportion 
 to the length of each, but if any course was more difficult of 
 chainage than the others, it may be given extra weight in
 
 34 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 the distribution. In any case the correction is applied so 
 as to help close the survey and not the reverse. This pro- 
 cess is called Balancing a Survey. 
 
 The field notes of a closed survey, the latitudes and de- 
 partures as they reckon out, and the same balanced, are 
 given herewith. The reckoning is also given, and all is in 
 convenient arrangement. The latitudes and departures 
 
 COMPUTING LATITUDES AND DEPARTURES 
 
 
 Course. 
 
 Course. 
 
 Course. 
 
 Course. 
 
 Course. 
 
 
 A B 
 
 B C 
 
 C D 
 
 D E 
 
 E A 
 
 log sin 
 
 9.9386 
 
 9.7604 
 
 9.5340 
 
 9.9555 
 
 9.5163 
 
 log dist. = 
 
 1.3010 
 
 1.1790 
 
 1.0910 
 
 1.2109 
 
 1.3444 
 
 log dep. = 
 
 1.2396 
 
 0.9394 
 
 0.6250 
 
 1.1664 
 
 0.8607 
 
 Departure = 
 
 17.36 
 
 8.70 
 
 4.22 
 
 14.67 
 
 7.26 
 
 log cos = 
 
 9.6957 
 
 9.9125 
 
 9.9730 
 
 9.6340 
 
 9.9752 
 
 log dist, = 
 
 1.3010 
 
 1.1790 
 
 1.0910 
 
 1.2109 
 
 1.3444 
 
 log lat. 
 
 0.9967 
 
 1.0915 
 
 1.0640 
 
 0.8449 
 
 1.3196 
 
 Latitude = 
 
 9.92 
 
 12.35 
 
 11.59 
 
 7.00 
 
 20.87 
 
 in this case have been reckoned out not from the traverse 
 table, but from the table of logarithmic sines and cosines. 
 A little consideration, shows that the latitude of a course is 
 the cosine of its bearing multiplied by its distance, while 
 the departure is the product of the sine multiplied by the 
 distance. Now a table of sines and cosines gives values 
 to single minutes instead of for 15' bearings. Logarithmic 
 computation, too, shortens the process. This is, therefore, 
 the more convenient way of reckoning for transit work, or 
 for accurate compass surveying. 
 
 When all but the final course has been run, it is in 
 some circumstances desirable to ascertain what course 
 to set in order to hit the starting point. This, too, may 
 readily be done by means of the figured latitudes and 
 departures. 
 
 Thus, suppose that four courses of the above survey have
 
 COMPUTATION AND OFFICE WORK 
 
 * 
 
 S S 
 8 8 
 
 8 2 3 8 2 
 
 o Q w
 
 36 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 been run out and the latitude and departure computed, as 
 given. The result shows that the point reached is north 
 
 FIGURED LATITUDES AND DEPARTURES 
 
 
 Latitude. 
 
 Departure. 
 
 
 N. 
 
 S. 
 
 E. 
 
 W. 
 
 A B 
 
 
 9.92 
 
 17.36 
 
 
 B C 
 
 12.35 
 
 
 8.70 
 
 
 C D 
 
 11.59 
 
 
 
 4.22 
 
 D E 
 
 7.00 
 
 
 
 14.67 
 
 
 30.94 
 
 9.92 
 
 26.06 
 
 18.89 
 
 
 9.92 
 
 
 18.89 
 
 
 
 21.02 
 
 
 7.17 
 
 
 and east of the starting point, much further north than 
 east; hence a course somewhat west of south 
 must be set to reach it. In the figure E X 
 represents the latitude reached and A X the 
 departure. 
 
 Now to find the bearing of E A we have 
 
 tan. A E X = 
 
 .3411. 
 
 AX 7.17 
 WX~ 21.02 
 
 A E X from the table of tangents =18 50'. 
 S 18 50' W is therefore the bearing required. 
 S The length of E A may also be found, since 
 it is the hypothenuse of a right angled tri- 
 angle whose base and altitude are the latitude and de- 
 parture given. 
 
 22.21, 
 
 the distance required. That this value and that for the 
 angle differ somewhat from the true ones is due to the 
 errors of compass surveying. 
 
 In a similar way the course and distance of an inacces- 
 sible line may be computed or omissions supplied in notes.
 
 COMPUTATION AND OFFICE WORK 37 
 
 That is a very undesirable thing to do, however, as it in- 
 fringes on the tests which serve to verify the work. 
 
 Rectangles. The woodsman in his land work has 
 most frequently to do with rectangular figures, and com- 
 putation of area is simple. If the average of the chained 
 east and west sides of a rectangular piece of land is 201 
 rods or 50.25 chains, and the north and south dimension 
 40 chains, the area equals 50.25 X 40 -r- 10 (the number of 
 square chains in an acre), or 201 acres. So with a rect- 
 angular piece of any dimensions. 
 
 Area by Triangles. The area of a triangle of known 
 base and altitude is half the product of these dimensions, 
 and an irregular figure when plotted may be cut into tri- 
 angles, the dimensions of each measured, and the areas 
 computed. The same process in case of necessity may 
 be performed on the ground. 
 
 When, as is frequently the case, it is easier to obtain the 
 three sides of a triangle than the base and altitude, the area 
 may be obtained from the formula 
 
 Area = V*(s ) (* 6) (* c), 
 where a, 6, and c are the three sides and s is half their sum. 
 
 Or, lastly, an irregular figure when plotted may be re- 
 duced graphically to the triangular form and the area ob- 
 tained at one computation by either of the methods just 
 given. 
 
 The relations between units of distance and of area are 
 given on page 19. 
 
 By Offsets. In surveying around the borders of a body 
 of water, and in some cases when the exact border of a 
 property presents great difficulties, it is customary to run 
 as near the border as is practicable and to take rectangu- 
 lar offsets to it at selected intervals along the line. These 
 offsets should be measured to angles in the border, or 
 placed near enough together so that the border between 
 offsets may be considered a straight line. The area of 
 the figure between each two offsets may then be computed 
 by multiplying the distance along the base by half the 
 sum of the two offsets.
 
 38 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 Another way is to take the offsets at regular distances 
 along the base, 10 rods apart for instance. In that 
 case the rule for the area is : Add together all the in- 
 termediate offsets and half the end offsets, and multiply 
 the sum by the constant interval between them. 
 
 By Cross Sectioning. The method of ruling off an area 
 on a map into squares of equal and known size is very 
 convenient, especially for irregular areas like bodies of 
 water. The whole squares can be counted up and the 
 fractions of squares estimated. In such cases it may be 
 best to do the ruling not on the map itself but on a de- 
 tached piece of tracing cloth or of paper. If the map is 
 opaque, the ruled tracing cloth may be laid over it and 
 held firmly till the work is done. If it is transparent, the 
 ruled sheet may be laid underneath. 
 
 By Planimeter. The area of any surface may be 
 quickly and accurately ascertained by an instrument called 
 the planimeter. That instrument is not, however, in the 
 hands of most woodsmen. 
 
 From Traverse. The area 
 enclosed by a balanced sur- 
 vey may be accurately com- 
 puted from the latitude and 
 departure of its courses. 
 The general scheme will be 
 grasped at once from the 
 figure, in which ABODE 
 represents the survey whose 
 notes are given on page 35, 
 e b is a meridian through its' 
 most westerly point, bB,cC, 
 d D, and e E are lines drawn 
 vertical to it from the angles, 
 and B m, D n, and E o are 
 parallel to it or vertical to c C 
 and d D. In this figure it is 
 evident in the first place that 
 the area of the figure b B C D E e minus the area of the 
 two triangles A E e and A B b equals the area of A B C D 
 E, and secondly that the figure b B C D E e is made up of
 
 COMPUTATION AND OFFICE WORK 39 
 
 the three trapezoids b B C c, c C D d, and d D E e. 
 The area of these trapezoids and triangles is easily com- 
 puted from their dimensions. All that is necessary is to 
 express those dimensions clearly in terms of latitude and 
 departure. 
 
 One dimension of these figures, the altitude, is the lati- 
 tude of the course in question. Thus for the triangle A B b, 
 the altitude A b is the latitude of the course A B, and in 
 the same way e A, the altitude of the triangle A E e, is the 
 latitude of E A. These latitudes, it is to be noted, are 
 negative and, to correspond, the areas of A B b and of 
 E A e are to be deducted from b B C D E e to give the area 
 of A B C D E which we are after. B m, the altitude of 
 the trapezoid b B C c, is the latitude of the course B C and 
 is positive. D n and E o have the same relation to the two 
 succeeding courses. 
 
 The bases of these triangles and trapezoids are clearly 
 related to departure, b B is the departure of the course 
 A B, and A b Xb B = twice the area of A B b. b B + 
 c C, the two bases of the trapezoid b B C c, = twice the 
 departure of A B + the departure of B C. c C + d D 
 = the same expression as the last + the departure of B C 
 + the departure of C D, which last, however, being west- 
 erly, is reckoned negatively. Now a general expression 
 for these values is double meridian distance, meridian dis- 
 tance being perpendicular distance from the meridian. 
 The D. M. D. of a course is the sum of the meridian dis- 
 tances of its two ends. For a course starting on the me- 
 ridian it equals the departure of the course. For any 
 succeeding course it equals the D. M. D. of the preceding 
 course plus the departure of that course plus the departure 
 of the new course, easterly departures being reckoned as 
 positive and westerly departures as negative. 
 
 A check on the reckoning of the D. M. D.'s is in the 
 last one, which should be numerically equal to the de- 
 parture of the last course. 
 
 These elements for convenient working out of the area 
 surrounded by a closed survey are embodied in the follow- 
 ing rule : Twice the area of the figure enclosed by a sur- 
 vey is equal to the algebraic sum of the products of the
 
 40 
 
 A MANUAL FOB NORTHERN WOODSMEN 
 
 D. M. D.'s of the several courses multiplied by the corre- 
 sponding latitudes, north latitudes being reckoned posi- 
 tively and south latitudes negatively. If the tract is kept 
 on the right in the course of the survey, the result comes 
 out with a minus sign. 
 
 An operation of this kind, starting with the balanced 
 latitudes and departures, may be conveniently arranged 
 as follows : 
 
 Course. 
 
 Lat. 
 
 Dep. 
 
 D. M. D. 
 
 + 
 Area. 
 
 Area. 
 
 A B 
 
 9.95 
 
 + 17.38 
 
 17.38 
 
 
 172.93 
 
 B C 
 
 + 12.32 
 
 + 8.72 
 
 43.48 
 
 535.67 
 
 ... 
 
 C D 
 
 + 11.57 
 
 4.21 
 
 47.99 
 
 555.24 
 
 
 D E 
 
 + 6.97 
 
 14.65 
 
 29.13 
 
 203.04 
 
 ... 
 
 E A 
 
 20.91 
 
 - 7.24 
 
 7.24 
 
 
 151.39 
 
 
 1293.95 1 324.32 
 324.32 1 
 
 2)969.63 
 
 484.81 sq. ch. 
 Area = 48.48 acres. 
 
 3. PLOTTING 
 
 The computation of traverse, if it aids in testing the 
 accuracy of a survey, gives also data for plotting it with 
 ease and accuracy. Taking the initial point of the survey 
 as the starting point for a meridian and a base line vertical 
 to it, the position of the second point of the survey may be 
 fixed by measuring off its latitude on the vertical line, its 
 departure on the horizontal, and from these points drawing 
 lines parallel to the base and the meridian until they inter- 
 sect. The latitude of the second course may then be added 
 to that of the first and the two departures also added to- 
 gether, when the third point of the survey may be fixed in 
 the same way as before, and so on until the survey is 
 finished. The points thus fixed may then be joined by 
 lines representing the courses. The position of the points 
 in the above survey as taken from the balanced figures on
 
 COMPUTATION AND OFFICE WORK 
 
 41 
 
 page 35 is given in the table, and below is a diagram 
 showing the method of plotting. 
 
 Point. 
 
 N. 
 
 s.. 
 
 E. 
 
 W. 
 
 A 
 
 
 
 
 
 B 
 
 
 9.95 
 
 17.38 
 
 
 C 
 
 2.37 
 
 
 26.10 
 
 
 D 
 
 13.94 
 
 
 21.89 
 
 
 E 
 
 20.91 
 
 
 7.24 
 
 
 It is not, however, the most common practice to plot a 
 survey after this fashion. The more usual way is to 
 plot the angles and distances directly from the notes. To 
 do this select a point on the paper for the initial point of 
 the survey and draw a meridian through it in pencil. Then 
 by means of a protractor mark the bearing of the first 
 
 METHODS OP PLOTTING A SURVEY. 
 FIG. 1 BY LATITUDES AND DEPARTURES. FIG. 2 BY COURSES AND DISTANCES. 
 
 course and draw a line of indefinite length through it. On 
 this line lay off to scale the length of the course, thus
 
 42 A MANUAL FOR NORTHERN WOODSMEN ' 
 
 establishing the second corner. Through this draw another 
 meridian in pencil and proceed as before. If the survey 
 and the plotting are both perfect, the last course should 
 hit the initial point. If it does not so hit, there is error in 
 one or the other. 
 
 To plot one course from another by means of the figured 
 angles between them is not good practice, because by that 
 method errors accumulate. 
 
 THE ESSENTIAL INSTRUMENTS FOR PLOTTING 
 
 A straight edge, a scale, a protractor, a pair of dividers, 
 and a parallel ruler or a pair of triangles are the essentials 
 for ordinary plotting. 
 
 The lettering on a woodsman's map ought to be plain. 
 The size of the letters should be varied according to the 
 importance of the object designated. It is a good rule to 
 use erect letters in general, and slant capitals and italics in 
 connection with water. 
 
 The usual practice is to represent waters and swamps 
 with blue ink, contours with brown, and all other objects 
 with black. Common brown and blue inks, however, do 
 not blueprint well, so black is ordinarily used for tracings. 
 
 Various systems have been devised for representing the 
 character and density of timber growth. A system of that 
 kind, if one is required, is best devised for each forest 
 region or property. 
 
 Maps may be rendered plainer by the judicious use of
 
 ON THE BEARING OF LINES 43 
 
 topographic symbols. A number that are in common use 
 and generally agreed upon are given herewith. 
 
 Railroad 
 
 Highway 
 
 Wood Road. . . 
 Trail . 
 
 Stone Wall ooo333coxxoocaxcxx)0 
 
 Fence 
 
 Telephone Line ,,.,.,,,. 
 
 Field or Prairie - 
 
 Open Swamp 
 
 Dam . , . . 
 
 TOPOGRAPHIC SYMBOLS 
 
 SECTION VI , 
 ON THE BEARING OF LINES 
 
 The surveying work of the woodsman of the present day 
 is mostly of the nature of resurveys, or the subdivision 
 of tracts whose boundary lines are on the ground. To 
 ascertain correctly the present bearing of old lines is there- 
 fore a problem of great importance and one very fre- 
 quently met with. 
 
 1. Bearing Directly Observed. The best and surest 
 way to find that direction is the direct one of running a 
 piece of the line. For example, suppose a section of land 
 was run out in 1845 with lines stated to run north, east, 
 south, and west by the true meridian. The surveyor com- 
 ing on to retrace it in 1915 may pay no attention to the 
 north star or reference meridians, but finding the southwest 
 corner of the tract plain and running northerly find by trial
 
 44 A MANUAL FOR NORTHERN WOODSMEN 
 
 that N 4 20' E runs through the old spots. He figures 
 now that the courses he will have to run in order to repro- 
 duce the lines of the square are N 4 20' E, S 85 40' E, 
 S 4 20' W, and N 85 40' W. He may run them so or 
 turn the vernier of his compass 4 20', so as to read N, E, 
 S, and W, like the compass of the original surveyor. In any 
 case he will not be able to reproduce the old line all around 
 exactly. Even if no errors are made in either survey the 
 daily variation of the needle will be pretty sure to cause 
 some divergence. In remarking the line he will follow as 
 closely as possible the marks of the old surveyor. 
 
 2. By Reference Meridian. The change in bearing of 
 old lines may often be ascertained by reading on a refer- 
 ence meridian. If the compass in use be so tested and if 
 the compass which did the work to be reviewed was tested 
 on the same marks at the time of the original survey, then 
 the difference in the two bearings will hold closely for a 
 considerable region around. 
 
 Example: On a county meridian in Pennsylvania in 
 1850 a surveyor's compass read N 2 30' E and in the 
 neighborhood a line was run bearing S 55 E. In 1905 
 another compass on the meridian reads N 6 20' E, show- 
 ing a change of 3 50' in the time elapsed. Then S 51 W 
 E ought to reproduce the line. 
 
 3. By Tables. The following tables, derived from 
 publications of the United States Coast and Geodetic 
 Survey, are very convenient for determining change in 
 decimation. They give for many localities well distrib- 
 uted throughout the United States declination at ten- 
 year intervals as far back as it has been recorded. The 
 change found to have taken place at a given locality 
 between any two dates may then be applied through a con- 
 siderable region around it. It should be understood, how- 
 ever, that this means of determination does not obviate 
 the chances of error due to difference between instru- 
 ments. It is well known that two compasses on the 
 same line at the same time may not read exactly alike. 
 
 Example: A land line in the Adirondacks was run out 
 in 1800 on the magnetic meridian. What course should 
 be set in 1910 to reproduce it ?
 
 ON THE BEARING OF LINES 
 
 45 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC- 
 LINATION IN THE UNITED STATES 
 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 Year Maine Maine 
 
 (Jan. 1) j N'theast ! S'thwest 
 
 New 
 Hamp. 
 
 Ver- 
 mont 
 
 Mass. 
 
 East 
 
 a 
 
 1750 
 
 12 05 W 
 
 8 34W 
 
 8 02W 
 
 7 43W 
 
 7 46W 
 
 6 21W 
 
 1760 
 
 11 53 
 
 8 15 
 
 7 28 
 
 7 09 
 
 7 19 
 
 5 52 
 
 1770 11 53 
 
 8 10 
 
 7 03 
 
 6 44 
 
 7 00 
 
 5 31 
 
 1780 
 
 12 05 
 
 8 10 
 
 6 47 
 
 6 28 
 
 6 50 
 
 5 19 
 
 1790 
 
 12 26 
 
 8 15 
 
 6 42 
 
 6 23 
 
 6 50 
 
 5 17 
 
 1800 
 
 12 58 
 
 8 34 
 
 6 49 
 
 6 30 
 
 7 01 
 
 5 25 
 
 1810 
 
 13 38 
 
 9 02 
 
 7 06 
 
 6 47 
 
 7 20 
 
 5 54 
 
 1820 
 
 14 23 
 
 9 38 
 
 7 32 
 
 7 13 
 
 7 47 
 
 6 08 
 
 1830 
 
 15 12 
 
 10 18 
 
 8 11 
 
 7 48 
 
 8 22 
 
 6 41 
 
 1840 
 
 16 02 
 
 10 57 
 
 8 56 
 
 8 29 
 
 9 04 
 
 7 21 
 
 1850 
 
 16 58 
 
 11 38 
 
 9 46 
 
 9 13 
 
 9 48 
 
 8 05 
 
 1860 
 
 17 43 
 
 12 18 
 
 10 31 
 
 9 59 
 
 10 28 
 
 8 43 
 
 1870 
 
 18 13 
 
 12 48 
 
 11 08 
 
 10 39 
 
 11 01 
 
 9 17 
 
 1880 
 
 18 34 
 
 13 22 
 
 11 38 
 
 11 14 
 
 11 32 
 
 9 58 
 
 1890 
 
 18 44 
 
 13 51 
 
 12 03 
 
 11 39 
 
 12 02 
 
 10 25 
 
 1900 
 1910 
 
 19 02 
 19 45W 
 
 14 21 
 15 06 W 
 
 12 31 
 13 16W 
 
 12 08 
 12 57W 
 
 12 34 
 13 21W 
 
 10 59 
 11 42W 
 
 Year 
 
 (Jan. 1) 
 
 Rhode 
 Island 
 
 Conn. 
 
 N. Y. 
 
 East. 
 
 N. Y. 
 West 
 
 Penn. 
 
 East 
 
 Penn. 
 West 
 
 1750 
 
 7 04W 
 
 5 47W 
 
 7 35W 
 
 4 40W 
 
 4 47W 
 
 
 1760 
 
 6 37 
 
 5 18 
 
 6 53 
 
 3 57 
 
 4 01 
 
 
 1770 
 
 6 18 
 
 4 57 
 
 6 17 
 
 3 18 
 
 3 19 
 
 
 1780 
 
 6 08 
 
 4 45 
 
 5 50 
 
 2 46 
 
 2 44 
 
 1 16W 
 
 1790 
 
 6 08 
 
 4 43 
 
 5 34 
 
 2 24 
 
 2 21 
 
 52 
 
 1800 
 
 6 19 
 
 4 51 
 
 5 28 
 
 2 13 
 
 2 08 
 
 37 
 
 1810 
 
 6 38 
 
 5 08 
 
 5 34 
 
 2 13 
 
 2 09 
 
 31 
 
 1820 
 
 7 05 
 
 5 34 
 
 5 50 
 
 2 24 
 
 2 22 
 
 37 
 
 1830 
 
 7 40 
 
 6 07 
 
 6 17 
 
 2 46 
 
 2 47 
 
 52 
 
 1840 
 
 8 22 
 
 6 47 
 
 6 53 
 
 3 18 
 
 3 21 
 
 1 16 
 
 1850 
 
 9 06 
 
 7 31 
 
 7 39 
 
 3 57 
 
 4 04 
 
 1 48 
 
 1860 
 
 9 46 
 
 8 09 
 
 8 25 
 
 4 46 
 
 4 46 
 
 2 26 
 
 1870 
 
 10 19 
 
 8 43 
 
 9 04 
 
 5 23 
 
 5 32 
 
 3 06 
 
 1880 
 
 10 50 
 
 9 24 
 
 9 51 
 
 6 16 
 
 6 16 
 
 3 50 
 
 1890 
 
 11 20 
 
 9 51 
 
 10 14 
 
 6 57 
 
 6 50 
 
 4 28 
 
 1900 
 
 11 52 
 
 10 25 
 
 10 48 
 
 7 37 
 
 7 25 
 
 5 07 
 
 1910 
 
 12 40W 
 
 11 11W 
 
 11 31W 
 
 8 12W 
 
 8 07W 
 
 5 45\V
 
 46 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC- 
 LINATION IN THE UNITED STATES 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 Year 
 (Jan. 1) 
 
 New 
 Jersey 
 
 Ohio 
 
 Indiana 
 
 Illinois 
 
 Iowa 
 
 Mich. 
 North 
 
 1750 
 
 4 43W 
 
 
 
 
 
 
 1760 
 
 4 04 
 
 
 
 
 
 
 1770 
 
 3 31 
 
 
 
 
 
 
 1780 
 
 3 06 
 
 
 
 
 
 
 1790 
 
 2 50 
 
 
 
 
 
 
 1800 
 
 2 45 
 
 3 13E 
 
 4 44E 
 
 5 54E 
 
 
 
 1810 
 
 2 fO 
 
 3 22 
 
 4 59 
 
 6 18 
 
 
 
 1820 
 
 3 06 
 
 3 22 
 
 5 04 
 
 6 33 
 
 10 09E 
 
 6 42E 
 
 1830 
 
 3 31 
 
 3 13 
 
 4 59 
 
 6 37 
 
 10 24 
 
 6 42 
 
 1840 
 
 4 04 
 
 2 53 
 
 4 44 
 
 6 33 
 
 10 30 
 
 6 28 
 
 1850 
 
 4 43 
 
 2 24 
 
 4 21 
 
 6 18 
 
 10 24 
 
 6 02 
 
 1860 
 
 5 22 
 
 1 50 
 
 3 50 
 
 5 54 
 
 10 09 
 
 5 25 
 
 1870 
 
 6 01 
 
 1 14 
 
 3 13 
 
 5 26 
 
 9 44 
 
 4 38 
 
 1880 
 
 6 41 
 
 37E 
 
 2 35 
 
 4 44 
 
 9 06 
 
 3 47 
 
 1890 
 
 7 14 
 
 02W 
 
 1 57 
 
 4 05 
 
 8 21 
 
 2 58 
 
 1900 
 
 7 49 
 
 42 
 
 1 24 
 
 3 36 
 
 7 52 
 
 2 20 
 
 1910 
 
 8 33W 
 
 HOW 
 
 1 08E 
 
 3 25E 
 
 7 57E 
 
 2 05E 
 
 Year 
 (Jan. 1) 
 
 Michigan 
 South 
 
 Wisconsin 
 
 Minnesota 
 
 North 
 
 Minnesota 
 
 South 
 
 1750 
 
 , 
 
 , 
 
 / 
 
 / 
 
 1760 
 
 
 
 
 
 1770 
 
 
 
 
 
 1780 
 
 
 
 
 
 1790 
 
 
 
 
 
 1800 
 
 
 
 
 
 1810 
 
 
 
 
 
 1820 
 
 4 10E 
 
 8 34 E 
 
 10 27E 
 
 11 20E 
 
 1830 
 
 4 04 
 
 8 40 
 
 10 44 
 
 11 36 
 
 1840 
 
 3 46 
 
 8 34 
 
 10 50 
 
 11 42 
 
 1850 
 
 3 20 
 
 8 16 
 
 10 44 
 
 11 36 
 
 1860 
 
 2 46 
 
 7 49 
 
 10 27 
 
 11 20 
 
 1870 
 
 2 04 
 
 7 14 
 
 9 59 
 
 10 54 
 
 1880 
 
 1 17 
 
 6 25 
 
 9 17 
 
 10 22 
 
 1890 
 
 32E 
 
 5 36 
 
 8 33 
 
 9 32 
 
 1900 
 
 02W 
 
 5 01 
 
 7 58 
 
 8 57 
 
 1910 
 
 27W 
 
 4 51E 
 
 8 03E 
 
 9 OOE
 
 ON THE BEARING OF LINES 
 
 47 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
 TION IN THE UNITED STATES 
 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 ll 
 
 Washington 
 D.C. 
 
 Maryland 
 (Baltimore) 
 
 Virginia 
 East 
 (Richmond) 
 
 Virginia 
 West 
 (Lynchburg) 
 
 .S| 
 
 8-1 8 
 
 *3 
 
 o 
 
 North Caro- 
 lina East 
 (Newbern) 
 
 North Caro- 
 lina West 
 (Salisbury) 
 
 1750 
 
 141W 
 
 305W 
 
 1 13W 
 
 / 
 
 o / 4 
 
 18W 
 
 1 31E 
 
 1760 
 
 1 02 
 
 2 26 
 
 037 
 
 008E 
 
 
 18E 
 
 208 
 
 1770 
 
 028 
 
 1 52 
 
 005W 
 
 42 
 
 
 50 
 
 2 42 
 
 1780 
 
 001W 
 
 1 25 
 
 20E 
 
 1 11 
 
 
 1 17 
 
 3 12 
 
 1790 
 
 19E 
 
 1 05 
 
 038 
 
 33 
 
 200E 
 
 135 
 
 3 34 
 
 1800 
 
 028 
 
 56 
 
 047 
 
 46 
 
 215 
 
 1 44 
 
 348 
 
 1810 
 
 028 
 
 56 
 
 47 
 
 51 
 
 2 20 
 
 1 44 
 
 3 52 
 
 1820 
 
 19E 
 
 1 05 
 
 038 
 
 46 
 
 2 15 
 
 1 35 
 
 3 48 
 
 1830 
 1840 
 
 001W 
 028 
 
 1 25 
 1 52 
 
 005W 
 
 33 
 11 
 
 200 
 137 
 
 1 16 
 50 
 
 3 33 
 3 10 
 
 1850 
 
 1 02 
 
 226 
 
 036 
 
 045 
 
 105 
 
 17E 
 
 240 
 
 1860 
 
 1 41 
 
 305 
 
 1 12 
 
 10E 
 
 030E 
 
 19W 
 
 206 
 
 1870 
 
 2 21 
 
 3 45 
 
 1 51 
 
 29W 
 
 12W 
 
 058 
 
 1 29 
 
 1880 
 
 3 00 
 
 4 24 
 
 2 29 
 
 1 09 
 
 51 
 
 1 35 
 
 51 
 
 1890 
 
 336 
 
 500 
 
 306 
 
 146 
 
 1 28 
 
 2 14 
 
 013E 
 
 1900 
 
 4 11 
 
 535 
 
 3 40 
 
 222 
 
 206 
 
 2 51 
 
 023W 
 
 1910 
 
 4 51W 
 
 6 15W 
 
 4 13W 
 
 2 53W 
 
 2 39W 
 
 3 25W 
 
 47W 
 
 ^ 
 
 .aSl 
 
 ""fl 
 
 ijl 
 
 a ^"3 
 
 J3 '* 
 
 || 
 
 |fg 
 
 ll 
 
 111 
 
 M 55 
 
 fl 
 
 M 
 
 5 
 
 fa fe 
 
 PI 
 
 <j*| 
 
 
 1750 
 
 204E 
 
 3 16E 
 
 2 27E 
 
 500E 
 
 500E 
 
 2 52E 
 
 / 
 
 1760 
 
 2 41 
 
 353 
 
 304 
 
 537 
 
 530 
 
 3 28 
 
 
 1770 
 
 3 15 
 
 4 29 
 
 340 
 
 6 13 
 
 555 
 
 403 
 
 
 1780 
 
 3 44 
 
 501 
 
 4 12 
 
 6 44 
 
 6 15 
 
 434 
 
 
 1790 
 
 406 
 
 526 
 
 437 
 
 7 11 
 
 6 26 
 
 502 
 
 
 1800 
 
 4 19 
 
 544 
 
 455 
 
 732 
 
 6 30 
 
 524 
 
 754E 
 
 1810 
 
 424 
 
 553 
 
 504 
 
 745 
 
 626 
 
 539 
 
 813 
 
 1820 
 
 4 19 
 
 553 
 
 504 
 
 7 50 
 
 6 15 
 
 547 
 
 824 
 
 1830 
 
 406 
 
 544 
 
 4 55 
 
 7 45 
 
 555 
 
 5 46 
 
 828 
 
 1840 
 
 3 44 
 
 526 
 
 437 
 
 731 
 
 530 
 
 5 38 
 
 8 24 
 
 1850 
 
 315 
 
 501 
 
 4 12 
 
 7 12 
 
 500 
 
 522 
 
 8 13 
 
 1860 
 
 2 41 
 
 4 29 
 
 3 40 
 
 6 45 
 
 4 28 
 
 500 
 
 757 
 
 1870 
 
 203 
 
 3 53 
 
 304 
 
 6 13 
 
 3 53 
 
 432 
 
 731 
 
 1880 
 
 1 25 
 
 3 14 
 
 225 
 
 534 
 
 3 16 
 
 354 
 
 6 55 
 
 1890 
 
 047 
 
 239 
 
 1 50 
 
 4 57 
 
 2 48 
 
 315 
 
 6 21 
 
 1900 
 
 HE 
 
 208 
 
 1 19 
 
 4 29 
 
 2 19 
 
 249 
 
 558 
 
 1910 
 
 12W 
 
 1 52E 
 
 1 05E 
 
 4 22E 
 
 2 06E 
 
 2 45E 
 
 6 08E
 
 48 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
 TION IN THE UNITED STATES 
 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 Sd 
 
 ^ 
 
 Tennessee 
 East (Chat- 
 tanooga) 
 
 Tennessee 
 West (Hun- 
 tingdon) 
 
 Kentucky 
 East 
 (Lexington ) 
 
 Kentucky 
 West 
 (Princeton) 
 
 Louisiana 
 
 (Alexandria) 
 
 Texas East 
 (Houston) 
 
 Texas Mid- 
 1 die (San 
 Antonio) 
 
 1750 
 
 / 
 
 1 
 
 
 
 
 
 
 1760 
 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 
 1780 
 
 
 
 
 
 
 
 
 1790 
 
 
 
 
 
 
 
 
 1800 
 
 507E 
 
 
 4 22E 
 
 6 32E 
 
 804E 
 
 
 
 1810 
 
 5 16 
 
 
 431 
 
 6 50 
 
 825 
 
 
 
 1820 
 
 516 
 
 7 24E 
 
 431 
 
 6 59 
 
 841 
 
 855E 
 
 
 1830 
 
 507 
 
 7 24 
 
 4 22 
 
 659 
 
 849 
 
 9 10 
 
 9 37E 
 
 1840 
 
 4 49 
 
 7 16 
 
 404 
 
 6 50 
 
 8 48 
 
 9 19 
 
 9 48 
 
 1850 " 
 
 424 
 
 659 
 
 339 
 
 632 
 
 840 
 
 9 19 
 
 9 53 
 
 1860 
 
 3 52 
 
 635 
 
 307 
 
 607 
 
 824 
 
 9 12 
 
 948 
 
 1870 
 
 3 16 
 
 605 
 
 231 
 
 537 
 
 802 
 
 856 
 
 937 
 
 1880 
 
 236 
 
 5 29 
 
 1 53 
 
 457 
 
 7 26 
 
 8 29 
 
 9 19 
 
 1890 
 
 201 
 
 4 53 
 
 1 15 
 
 420 
 
 6 53 
 
 7 56 
 
 852 
 
 1900 
 
 1 30 
 
 424 
 
 041 
 
 3 51 
 
 633 
 
 7 44 
 
 8 43 
 
 1910 
 
 1 12E 
 
 4 18E 
 
 19E 
 
 3 36E 
 
 6 50E 
 
 8 05E 
 
 9 09E 
 
 & 
 
 Sf| 
 
 11 
 
 klahoma 
 kmulgee) 
 
 I 
 
 nsas East 
 Imporia) 
 
 Ik 
 
 I S 
 
 111 
 
 s w 
 
 
 
 3 
 
 00 
 
 ss 
 
 H 
 
 fc 
 
 & a 
 
 1750 
 
 
 
 
 
 
 
 
 1760 
 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 
 1780 
 
 
 
 
 
 
 
 
 1790 
 
 
 
 
 
 
 
 
 1800 
 
 
 813E 
 
 
 
 
 
 
 1810 
 
 
 8 36 
 
 
 
 
 
 
 1820 
 
 
 8 51 
 
 
 1003E 
 
 
 
 11 39E 
 
 1830 
 
 1046E 
 
 900 
 
 
 10 13 
 
 
 
 11 57 
 
 1840 
 
 11 00 
 
 859 
 
 
 10 13 
 
 
 
 1207 
 
 1850 
 
 11 08 
 
 851 
 
 10 15E 
 
 1004 
 
 11 34E 
 
 12 24E 
 
 12 07 
 
 1860 
 
 11 07 
 
 834 
 
 1006 
 
 9 46 
 
 11 28 
 
 1223 
 
 11 59 
 
 1870 
 
 11 00 
 
 8 14 
 
 951 
 
 9 24 
 
 11 12 
 
 12 12 
 
 11 41 
 
 1880 
 
 1048 
 
 738 - 
 
 9 33 
 
 844 
 
 10 45 
 
 11 54 
 
 11 10 
 
 1890 
 
 10 24 
 
 701 
 
 9 07 
 
 802 
 
 1007 
 
 11 21 
 
 1031 
 
 1900 
 1910 
 
 10 18 
 10 50E 
 
 638 
 6 49E 
 
 8 42 
 
 855E 
 
 738 
 
 7 46E 
 
 9 50 
 10 08E 
 
 11 08 
 11 27E 
 
 10 14 
 
 10 28E
 
 ON THE BEARING OF LINES 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
 TION IN THE UNITED STATES 
 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 ll 
 
 Nebraska 
 West 
 (Alliance) 
 
 South Da- 
 kota East 
 (Huron) 
 
 South Da- 
 kota West 
 (Rapid City) 
 
 North Da- 
 kota East 
 (Jamestown) 
 
 North Da- 
 kota West 
 (Dickinson) 
 
 Montana 
 East 
 (Forsyth) 
 
 Montana 
 West 
 (Helena) 
 
 1750 
 
 / 
 
 , 
 
 , 
 
 / 
 
 ' 
 
 
 
 / 
 
 1760 
 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 
 1780 
 
 
 
 
 
 
 
 
 1790 
 
 
 
 
 
 
 
 
 1800 
 
 
 
 
 
 
 
 
 1810 
 
 
 
 
 
 
 
 
 1820 
 
 
 
 
 
 
 
 
 1830 
 
 
 
 
 
 
 
 
 1840 
 
 
 1306E 
 
 
 
 
 1809E 
 
 18 53E 
 
 1850 
 
 1527E 
 
 1306 
 
 16 26E 
 
 1431E 
 
 1737E 
 
 18 27 
 
 19 18 
 
 1860 
 
 15 27 
 
 12 57 
 
 16 26 
 
 14 21 
 
 17 37 
 
 1836 
 
 1936 
 
 1870 
 
 15 18 
 
 12 39 
 
 16 16 
 
 1402 
 
 17 27 
 
 18 36 
 
 19 45 
 
 1880 
 
 14 50 
 
 1207 
 
 1550 
 
 13 31 
 
 1700 
 
 1821 
 
 1934 
 
 1890 
 
 14 20 
 
 11 25 
 
 15 17 
 
 12 43 
 
 16 21 
 
 17 53 
 
 19 23 
 
 1900 
 
 14 10 
 
 11 07 
 
 1507 
 
 1224 
 
 16 10 
 
 17 50 
 
 1931 
 
 1910 
 
 14 31E 
 
 11 28E 
 
 15 27E 
 
 12 44E 
 
 .16 36E 
 
 1817E 
 
 20 02E 
 
 -J 
 
 JLl 
 
 fj 
 
 s'* 
 
 y* 
 
 Ls 
 
 ll 
 
 |* 
 
 * s 
 
 II! 
 
 S $W 
 
 || 
 
 IS? 
 
 2 * =5 
 
 c g* 
 
 1 
 
 5 
 
 > w 
 
 ^ 
 
 MM 
 
 S 
 
 | * 
 
 a? ^ 
 
 8 
 
 
 1750 
 
 o / 
 
 / 
 
 / 
 
 o , 
 
 / 
 
 / 
 
 / 
 
 1760 
 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 
 1780 
 
 
 
 
 
 17 19E 
 
 
 
 1790 
 
 
 
 
 
 1752 
 
 
 
 1800 
 
 
 
 
 
 18 27 
 
 
 1605E 
 
 1810 
 
 
 
 
 
 1904 
 
 
 16 43 
 
 1820 
 
 
 
 
 
 1941 
 
 
 17 22 
 
 1830 
 
 
 
 
 
 2016 
 
 
 1801 
 
 1840 
 
 
 
 
 
 2049 
 
 
 1838 
 
 1850 
 
 15 51E 
 
 16 45E 
 
 18 OOE 
 
 21 16E 
 
 21 19 
 
 19 15E 
 
 19 12 
 
 1860 
 
 1559 
 
 16 58 
 
 18 30 
 
 21 37 
 
 21 45 
 
 19 40 
 
 19 41 
 
 1870 
 
 1559 
 
 17 02 
 
 18 45 
 
 21 52 
 
 2206 
 
 19 58 
 
 2006 
 
 1880 
 1890 
 
 15 47 
 1524 
 
 16 54 
 1636 
 
 18 45 
 
 18 39 
 
 21 56 
 2206 
 
 22 19 
 2238 
 
 2009 
 20 11 
 
 20 24 
 2032 
 
 1900 
 1910 
 
 15 19 
 1543E 
 
 1637 
 17 08E 
 
 1851 
 1931E 
 
 22 22 
 23 OOE 
 
 22 58 
 23 40E 
 
 2026 
 21 07E 
 
 20 50 
 2133E
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
 TION IN THE UNITED STATES 
 
 (From U. S. Coast and Geodetic Survey Reports) 
 
 K 
 
 PM^ 
 
 California 
 South (Los 
 Angeles) 
 
 California 
 Middle 
 (San Jose) 
 
 California 
 North 
 (Redding) 
 
 III 
 
 Sgg 
 
 Nevada 
 West (Haw- 
 thorne) 
 
 Utah 
 (Salt Lake) 
 
 1750 
 
 / 
 
 
 
 
 
 
 1760 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 1780 
 
 1024E 
 
 13 37E 
 
 1407E 
 
 
 
 
 1790 
 
 1058 
 
 1403 
 
 14 35 
 
 
 
 
 1800 
 
 11 32 
 
 1432 
 
 1504 
 
 
 
 
 1810 
 
 1207 
 
 15 01 
 
 1534 
 
 
 
 
 1820 
 
 1239 
 
 1530 
 
 1604 
 
 
 
 
 1830 
 
 1309 
 
 1557 
 
 1633 
 
 
 
 
 1840 
 
 13 36 
 
 16 22 
 
 1701 
 
 
 
 
 1850 
 
 13 57 
 
 1645 
 
 17 26 
 
 17 20E 
 
 16 16E 
 
 16 25E 
 
 1860 
 
 14 13 
 
 1705 
 
 17 47 
 
 1736 
 
 1637 
 
 16 30 
 
 1870 
 
 14 24 
 
 17 20 
 
 1806 
 
 17 41 
 
 1652 
 
 16 40 
 
 1880 
 
 14 33 
 
 17 28 
 
 18 15 
 
 1744 
 
 1700 
 
 16 30 
 
 1890 
 
 1436 
 
 1732 
 
 1820 
 
 1738 
 
 1702 
 
 16 20 
 
 1900 
 
 1452 
 
 17 51 
 
 1839 
 
 17 49 
 
 17 17 
 
 16 28 
 
 1910 
 
 15 35E 
 
 1832E 
 
 19 22E 
 
 18 27E 
 
 17 58E 
 
 17 03E 
 
 Ij 
 
 w 
 
 Colorado 
 West (Glen- 
 wood 
 
 Springs) 
 
 New Mexico 
 East 
 (Santa Rosa) 
 
 8 ~ 
 
 '?' - 
 
 fl 
 
 'A 
 
 111 
 
 1750 
 
 
 
 
 
 
 
 1760 
 
 
 
 
 
 
 
 1770 
 
 
 
 
 
 
 
 1780 
 
 
 
 
 
 
 
 1790 
 
 
 
 
 
 
 
 1800 
 1810 
 
 
 
 
 
 
 
 1820 
 
 
 
 
 
 
 
 1830 
 
 
 
 
 
 
 
 1840 
 
 
 
 
 
 
 
 1850 
 
 13 47E 
 
 1607E 
 
 1243E 
 
 13 26E 
 
 13 33E 
 
 13 19E 
 
 1860 
 
 13 50 
 
 16 15 
 
 1247 
 
 13 33 
 
 13 44 
 
 1233 
 
 1870 
 
 13 46 
 
 16 16 
 
 12 43 
 
 13 34 
 
 13 47 
 
 13 40 
 
 1880 
 
 1331 
 
 1604 
 
 12 29 
 
 13 22 
 
 13 40 
 
 13 36 
 
 1890 
 
 1300 
 
 15 40 
 
 1203 
 
 1302 
 
 13 25 
 
 13 32 
 
 1900 
 1910 
 
 12 53 
 13 19E 
 
 1539 
 16 10E 
 
 11 59 
 12 29E 
 
 1302 
 13 36E 
 
 13 29 
 
 U 05E 
 
 13 44 
 14 25E
 
 ON OBTAINING THE MERIDIAN 51 
 
 From the table for change of declination, and for the 
 locality eastern New York, the values 5 28' and 11 31' 
 are obtained, showing that the needle in the 110 years 
 swung 6 03' to the westward. The desired bearing 
 therefore should prove to be N 6 E nearly. 
 
 SECTION VII 
 ON OBTAINING THE MERIDIAN 
 
 When for any reason it is necessary to determine a true 
 meridian, that is best obtained from the north star. This 
 star, easily identified by the range of the " pointers," is nol 
 exactly at the pole of the heavens, but in 1908 was 1 11' 4" 
 from it. This angle is called the " polar distance" of the 
 star. It is decreasing at the rate of about one third of a 
 minute yearly. 
 
 The north star, like other stars, is thus circling around 
 the pole once in about 24 hours. When directly over or 
 under the pole it is said to be in culmination, upper or 
 lower as the case may be. The star is then in the meridian, 
 and bringing it down with plumb line or transit gives the 
 meridian directly. 
 
 When the north star is farthest from the meridian 'it is 
 said to be in elongation, east when the star is east of the 
 meridian, west when on the opposite side. A plane through 
 the observer, the zenith, and the north star when at elonga- 
 tion, prolonged downward to the horizon, makes an angle 
 with the meridian which is called the azimuth of the star 
 at that time. This angle may be obtained for any time and 
 position from tables, and setting off the angle, the true 
 meridian is found. Upon this meridian the needle can be 
 read or marks can be left for reference at any future time. 
 
 The operation of bringing down the star may be per- 
 formed either with the plumb line or, more accurately and 
 conveniently, with a well-adjusted transit. When the 
 transit is used it is necessary to illuminate the cross wires. 
 This may often be done by holding a lantern or candle 
 in front of the transit tube and a little to one side, when 
 the field should appear light with the cross hairs show-
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 REFLECTOR 
 
 ing as dark lines. If light enough is not so obtained, 
 a tin reflector may be made of the design shown, or a 
 piece of tracing cloth or greased paper, 
 with a hole cut in it may be bound bell- 
 shape over the front of the instrument 
 with a string or rubber band. 
 
 Directions for obtaining the true merid- 
 ian which involve an accurate knowledge 
 of time are not adapted to the use of the 
 woodsman. The following directions do 
 not impose that very difficult requirement. 
 (From United States " Manual of Instructions for Sur- 
 vey of the Public Lands.") 
 
 To OBTAIN A MERIDIAN AT CULMINATION OF POLARIS 
 
 A very close approximation to a meridian may be had by re- 
 membering that Polaris very nearly reaches the meridian when 
 it is in the same vertical plane with the star Delta (5) in the con- 
 stellation Cassiopeia. The vertical 
 wire of the transit should be fixed 
 upon Polaris, and occasionally brought * 
 
 down to the star Delta, to observe its 
 approach to the same vertical line. * 
 When both stars are seen upon the 
 wire, Polaris is very near the meridian. 
 A small interval of time (as 6 min. in 
 1908) will then be allowed to pass, 
 while Delta moves rapidly east and 
 Polaris slightly east to the actual me- 
 ridian. At that moment the cross wire 
 should be placed upon Polaris, and the 
 meridian firmly marked by stakes and 
 tack-heads. 
 
 This method is practicable only 
 when the star Delta is below the pole 
 during the night; when it passes the 
 meridian above the pole, it is too near 
 the zenith to be of service, in which 
 case the star Zeta (f), the last star but 
 one in the tail of the Great Bear, may 
 be used instead. 
 
 Delta (5) Cassiopeia; is on the me- 
 ridian below Polaris and the pole, at Cassio 
 midnight about April 10, and is, there- 
 fore, the proper star to use at that date and for some two or 
 three months before and after. 
 
 North Pole 
 
 peia
 
 ON OBTAINING THE MERIDIAN 53 
 
 Six months later the star Zeta (fl, in the tail of the Great Bear, 
 will supply its place, and will be used in precisely the same manner. 
 
 The diagram, drawn to scale, exhibits the principal stars of 
 the constellations Cassiopeia and Great Bear, with Delta (5) Cas- 
 siopeiae, Zeta (f) Ursse Majoris (also called Mizar), and Polaris 
 on the meridian, represented by the straight Line; Polaris being 
 at lower culmination. 
 
 In the above process, the interval of waiting time may 
 be found for the proper year from the following data : 
 
 (1910 . 
 
 * For Zeta Urs. Maj. { 1920 . 
 (1930 . 
 
 1910 . 
 
 For Delta Cass. 
 
 !1930 
 
 6.5 min. ( annual 
 
 10.6 ' < increase 
 
 14.7 " ( .41 min. 
 
 7.1 min. ( annual 
 
 11.0 " < increase 
 
 14.9 " ( .39 min. 
 
 * Data furnished by Prof. Robt. W. Willson. 
 
 Instead of the transit the plumb line may be used for 
 this observation in much the manner described later on. 
 
 At certain times of year it is inconvenient to observe 
 Polaris at culmination, and for other reasons as well it is 
 more usual to observe the star at elongation. The Land 
 Office instructions follow, and the table for azimuths of 
 the star and for time of elongation which are required. 
 
 To ESTABLISH A MERIDIAN AT ELONGATION BY TELESCOPIC 
 INSTRUMENT 
 
 Set a stone, or drive a wooden peg, firmly in the ground, and 
 upon the top thereof make a small, distinct mark. 
 
 About thirty minutes before the time of the eastern or western 
 elongation of Polaris, obtained from the table, set up the transit 
 firmly, with its vertical axis exactly over the mark, and carefully 
 level the instrument. 
 
 Illuminate the cross wires by the light from a suitable lantern, 
 the rays being directed into the object end of the telescope by an 
 assistant; while great care will be taken, by perfect leveling, to 
 insure that the line of collimation describe a truly vertical plane. 
 
 Place the vertical wire upon the star, which, if it has not reached 
 its elongation, will move to the right for eastern, or to the left for 
 western elongation. 
 
 While the star moves toward its point of elongation, by means of 
 the tangent screw of the vernier plate it will be repeatedly covered 
 by the vertical wire, until a point is reached where it will appear to 
 remain on the wire for some time, then leave it in a direction con- 
 trary to its former motion ; thus indicating the tune of elongation. 
 
 Then while the star appears to thread the vertical wire, depress
 
 54 A MANUAL FOR NORTHERN WOODSMEN 
 
 the telescope to a horizontal position; five chains north of the 
 place of observation set a stone or drive a firm peg, upon which 
 by a strongly illuminated pencil or other slender object, exactly 
 coincident with the vertical wire, mark a point and drive a tack 
 in the line of sight thus determined; then, to eliminate possible 
 errors of collimation or imperfect verticality of the motion of the 
 telescope, quickly revolve the vernier plate 180, direct the glass 
 at Polaris and repeat the observation ; if it gives a different result 
 find and mark the middle point between the two results. This 
 middle point, with the point marked by the plumb bob of the 
 transit, will define the trace of the vertical plane through Polaris 
 at its eastern or western elongation, as the case may be. 
 
 By daylight lay off to the east or west, as the case may require, 
 the proper azimuth taken from the following table (page 56) ; the 
 instrument will then define the meridian. The needle may be 
 read then, giving the magnetic declination, east or west as the case 
 may be. Or the line may be permanently marked for reference 
 at another time or with another instrument. 
 
 To DETERMINE A MERIDIAN WITHOUT A TELESCOPE 
 
 Attach a plumb line to a support situated as far above the 
 ground as practicable, such as the limb of a tree, a piece of board 
 nailed or otherwise fastened to a telegraph pole, a house, barn, 
 or other building, affording a clear view north and south. 
 
 The plumb bob may consist of some weighty material, such as 
 a brick, a piece of iron or stone, weighing four to five pounds, 
 which will hold the plumb line vertical, fully as well as one of 
 finished metal. 
 
 Strongly illuminate the plumb line just below its support by a 
 lamp or candle, care being taken to obscure the source of light 
 from the view of the observer by a screen. 
 
 For a peep sight, cut a slot about one-sixteenth of an inch wide 
 in a thin piece of board, or nail two strips of tin, with straight 
 edges, to a square block of woqd, so arranged that they will stand 
 vertical when the block is placed flat on its base upon a smooth 
 horizontal rest, which will be placed at a convenient height south 
 of the plumb line and firmly secured in an east and west direction, 
 in such a position that, when viewed through the peep sight, Po- 
 laris will appear about a foot below the support of the plumb line. 
 
 The position may be practically determined by trial the night 
 preceding that set for the observation. 
 
 About thirty minutes before the time of elongation, as obtained 
 from the table, bring the peep sight into the same line of sight with 
 the plumb line and Polaris. 
 
 To reach elongation, the star will move off the plumb line to 
 the east for eastern elongation, or to the west for western elonga- 
 tion ; therefore by moving the peep sight in the proper direction, 
 east or west, as the case may be, keep the star on the plumb line 
 until it appears to remain stationary, thus indicating that it has 
 reached its point of elongation.
 
 ON OBTAINING THE MERIDIAN 55 
 
 The peep sight will now be secured in place by a clamp or 
 weight with its exact position marked on the rest, and all further 
 operations will be deferred until the next morning. 
 
 By daylight, place a slender rod at a distance of two or three 
 hundred feet from the peep sight, and exactly in range with it and 
 the plumb line ; carefully measure this distance. 
 
 Take from the table on page 56 the azimuth of Polaris cor- 
 responding to the latitude of the station and year of observation ; 
 find the natural tangent of said -azimuth and multiply it by the 
 distance from the peep sight to the rod ; the product will express 
 the distance to be laid off from the rod exactly at right angles to 
 the direction already determined (to the west for eastern elonga- 
 tion or to the east for western elongation), to a point, which with 
 the peep sight, will define the direction of the meridian with suffi- 
 cient accuracy for the needs of local surveyors. 
 
 Example: Sept. 10, 1915, in latitude 45 N, longitude 
 71 W, it is desired to obtain the declination of the needle. 
 
 From the table giving times of elongation it is found that 
 Polaris is at eastern elongation on Sept. 1st at 53.2 minutes past 
 8 P.M. 
 
 Correction A is not required in this case. 
 
 Correction B, for the 9 days elapsed since Sept. 1st, is 35.3 rain., 
 to be subtracted. 
 
 Correction C, for 71 longitude, is 16 min., to be subtracted. 
 
 Correction D, for 45 latitude, is 0.85 min., to be added. 
 
 Correction E is 0.2 min., to be added. 
 
 8 hrs. 53.2 min. 35.3 min. 16 min. + .85 min. + .2 min. 
 = 8 hrs. 3 min., time of elongation by the watch. 
 
 The star having been observed at the time indicated and brought 
 down to the horizon, its azimuth is ascertained from the table of 
 azimuths. For 1915 and latitude 45, this value is 1 37.4' and 
 there is no appreciable correction for apparent place. The merid- 
 ian then is that much to the west of the line determined. In this 
 case, with the instrument on the azimuth line the needle was 
 allowed to settle and a reading of N 17 50' E obtained. 17 50' 
 1 37.4' = 16 12.6'. 16 12.6' is therefore the magnetic declination 
 for the place and time, or 16 15' as near as a needle can be 
 read. 
 
 In practice corrections D and E may usually be neglected. 
 Using the table for time of elongation with corrections A, B, and C 
 applied to it, the surveyor will ascertain when to be on hand for 
 the observation. Then, watching the star, when satisfied by its 
 motion that it has reached elongation he will bring his instrument 
 down without regard to time. In fact, Polaris traverses less than 
 4' of azimuth in the hour before and the hour after elongation.
 
 56 A MANUAL FOR NORTHERN WOODSMEN 
 
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 SSrf^o dSS2 d-S^5 S^S2 S^doid S 
 
 coro-*^u" 
 
 coojtqwq t-iocoiNrH -HrHNcijio t^q^oq-* qO'ttos 
 
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 rtrtrtrtrt ^ rt _i rt(N MINMNIN IMNMCOM WWTITI ^ 
 * -* iO to |^ 
 
 t-H 
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 31 
 
 Si 
 
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 * I 
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 2 
 
 2
 
 ON OBTAINING THE MERIDIAN 
 
 57 
 
 The table on the preceding page was computed with 
 mean declination of Polaris for each year. A more ac- 
 curate result will be had by applying to the tabular values 
 the following correction, which depends on the difference 
 of the mean and the apparent place of the star. The 
 deduced azimuth will in general be correct within 0.3'. 
 
 For Middle of 
 
 Correction 
 
 For Middle of 
 
 Correction 
 
 January 
 February 
 March 
 April 
 May 
 June 
 
 0.5 
 
 0.4 
 
 =8:o 3 
 tti 
 
 July 
 August 
 September 
 October 
 November 
 December 
 
 + 0.2 
 + 0.1 
 0.1 
 0.4 
 0.6 
 0.8 
 
 LOCAL CIVIL (NOT STANDARD) TIME OF THE ELONGATIONS 
 OF POLARIS IN THE YEAR 1915. (COMPUTED FOR LATI- 
 TUDE 40o NORTH AND LONGITUDE 90 OR 6h WEST 
 
 OF GREENWICH) 
 (From United States Coast and Geodetic Survey) 
 
 Date 
 
 Eastern Elongation 
 
 Western Elongation 
 
 1915 
 
 h. 
 
 m. 
 
 h. 
 
 m. 
 
 January 1 
 
 
 
 51.7 P. M. 
 
 
 
 46.0 P. M. 
 
 January 15 
 
 11 
 
 56.4 A. M. 
 
 11 
 
 46.8 P. M. 
 
 February 1 
 
 10 
 
 49.2 A. M. 
 
 10 
 
 39.7 P. M. 
 
 February 15 
 March 1 
 
 8 
 
 54.0 A. M. 
 58.7 A. M. 
 
 9 
 
 8 
 
 44.4 P. M. 
 49.2 P. M. 
 
 March 15 
 
 8 
 
 3.5 A. M. 
 
 7 
 
 54.0 P. M. 
 
 April 1 
 
 6 
 
 56.6 A. M. 
 
 6 
 
 47.1 P. M. . 
 
 April 15 
 
 6 
 
 1.6 A. M. 
 
 5 
 
 52.0 P. M. 
 
 May 1 
 
 4 
 
 58.7 A. M. 
 
 4 
 
 49.2 P. M. 
 
 May 15 
 
 4 
 
 3.8 A. M. 
 
 3 
 
 54.2 P. M. 
 
 June 1 
 
 2 
 
 57.2 A. M. 
 
 2 
 
 47.6 P. M. 
 
 June 15 
 
 2 
 
 2.4 A. M. 
 
 1 
 
 52.8 P. M. 
 
 July 1 
 
 
 
 59.8 A. M. 
 
 
 
 50.2 P. M. 
 
 July 15 
 
 
 
 5.0 A. M. 
 
 11 
 
 55.4 A. M. 
 
 August 1 
 
 10 
 
 54.5 P. M. 
 
 10 
 
 48.8 A. M. 
 
 August 15 
 
 9 
 
 59.8 P. M. 
 
 9 
 
 54.1 A. M. 
 
 September 1 
 
 8 
 
 53.2 P. M. 
 
 8 
 
 47.5 A. M. 
 
 September 15 
 October 1 
 
 7 
 6 
 
 58.3 P. M. 
 55.5 P. M. 
 
 7 
 6 
 
 52.6 A. M. 
 49.8 A. M. 
 
 October 15 
 
 6 
 
 00.6 P. M. 
 
 5 
 
 54.9 A. M. 
 
 November 1 
 
 4 
 
 53.7 P. M. 
 
 4 
 
 48.0 A. M. 
 
 November 15 
 
 3 
 
 58.6 P. M. 
 
 3 
 
 52.9 A. M. 
 
 December 1 
 
 2 
 
 55.6 P. M. 
 
 2 
 
 49.9 A. M. 
 
 December 15 
 
 2 
 
 00.4 P. M. 
 
 1 
 
 54.7 A. M.
 
 58 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 A. To refer the above tabular quantities to years subse- 
 quent to 1915: 
 
 For year 1917 
 
 subtract 
 
 0.7 minute 
 
 
 1918 
 
 add 
 
 0.9 minute 
 
 
 1919 
 
 add 
 
 2.5 minutes 
 
 
 1920 
 
 
 4.0 minutes 
 0.1 minute 
 
 up to March 1 
 on and after March 1 
 
 1921 
 
 add 
 
 1.6 minutes 
 
 
 1922 
 
 add 
 
 3.1 minutes 
 
 
 1923 
 
 add 
 
 4.5 minutes 
 
 
 
 
 5.9 minutes 
 
 up to March 1 
 
 1924 
 
 1 add 
 
 2.0 minutes 
 
 on and after March 1 
 
 1925 
 
 add 
 
 3.3 minutes 
 
 
 1926 
 
 add 
 
 4.6 minutes 
 
 
 1927 
 
 add 
 
 5.9 minutes 
 
 
 1928 
 
 /add 
 add 
 
 7.2 minutes 
 3.3 minutes 
 
 up to March 1 
 on and after March 1 
 
 B. To refer to any calendar day other than the first and 
 fifteenth of each month, subtract the quantities below from 
 the tabular quantity for the preceding date. 
 
 Day of Month 
 
 Minutes 
 
 No. of Days Elapsed 
 
 2 or 16 
 
 3.9 
 
 1 
 
 3 or 17 
 
 7.8 
 
 2 
 
 4 or 18 
 
 11.8 
 
 3 
 
 5 or 19 
 
 15.7 
 
 4 
 
 6 or 20 
 
 19.6 
 
 5 
 
 7 or 21 
 
 23.5 
 
 6 
 
 8 or 22 
 
 27.4 
 
 7 
 
 9 or 23 
 
 31.4 
 
 8 
 
 10 or 24 
 
 35.3 
 
 9 
 
 11 or 25 
 
 39.2 
 
 10 
 
 12 or 26 
 
 43.1 
 
 11 
 
 13 or 27 
 
 47.0 
 
 12 
 
 14 or 28 
 
 51.0 
 
 13 
 
 29 
 
 54.9 
 
 14 
 
 30 
 
 58.8 
 
 15 
 
 31 
 
 62.7 
 
 16 
 
 For the tabular year, two eastern elongations occur on 
 January 14, and two western elongations on July 13. 
 
 C. To refer the table to standard time: Add to the tab- 
 ular quantities four minutes for every degree of longitude 
 the place is west of the standard meridian and subtract 
 when the place is east of the standard meridian. 
 
 D. To refer to any other than the tabular latitude between 
 the limits of 25 and 50 North: Add to the time of west 
 elongation 0.10 min. for every degree south of 40 and
 
 ON OBTAINING THE MERIDIAN 59 
 
 subtract from the time of west elongation 0.16 min. for 
 every degree north of 40. For eastern elongations sub- 
 tract 0.10 min. for every degree south of 40, and add 0.16 
 min. for every degree north of 40. 
 
 E. To refer to any other than the tabular longitude : Add 
 0.16 min.for each 15 east of the ninetieth meridian and sub- 
 tract 0.16 min. for each 15 west of the ninetieth meridian. 
 
 The deduced time of elongation will seldom be in error 
 more than 0.3 min. 
 
 For Evening Observation. Study of the tables will 
 show that at certain times of the year a choice of methods 
 is offered. Since, however, evening observation is usually 
 most convenient, the following directions have been ar- 
 ranged with that in view. The time limits for these 
 observations, it will be understood, vary somewhat with 
 the latitude. 
 
 On the tenth of January observe western elongation 
 at midnight and for each fifteen days thereafter earlier 
 by one hour. This may be done until late March. 
 
 From late March to early June, use lower culmination 
 with the help of Delta of Cassiopeia. On April 1st the 
 culmination occurs at 12.37 and after that for each fifteen 
 days earlier by one hour. 
 
 From early June to early October use eastern elonga- 
 tion. On June 15th it occurs at 2 A. M. 
 
 From early October to middle January use upper cul- 
 mination with Zeta of the Great Bear.
 
 60 A MANUAL FOR NORTHERN WOODSMEN 
 
 SECTION VHI 
 THE UNITED STATES PUBIJC LAND SURVEYS 
 
 In the original States there is a great variety of system, 
 or lack of system, in the division of land for ownership. 
 Land which has ever been a part of the Public Domain of 
 the United States and that embraces in general the 
 territory north of the Ohio River and from the Mississippi 
 River west to the Pacific coast has been surveyed, with 
 small exceptions, under a common system, the so-called 
 " System of Rectangular Surveying." An account of this, 
 so far as it concerns the woodsman, follows. 
 
 Chapter III of the Public Land Laws contains the fol- 
 lowing sections: 
 
 SEC. 99. The public lands shall be divided by north and south 
 lines run according to the true meridian, and by others crossing 
 them at right angles, so as to form townships of six miles square, 
 unless where the line of an Indian reservation, or of tracts of land 
 heretofore sun-eyed or patented, or the course of navigable rivers, 
 may render this impracticable; and in that case this rule must 
 be departed from no further than such particular circumstances 
 require. 
 
 Second. The corners of the townships must be marked with 
 progressive numbers from the beginning ; each distance of a mile 
 between such corners must be also distinctly marked with marks 
 different from those of the corners. 
 
 Third. The township shall be subdivided into sections, con- 
 taining, as nearly as may be, six hundred and forty acres each, 
 by running through the same, each way, parallel lines at the end 
 of every two miles ; and by making a corner on each of such lines 
 at the end of every mile. The sections shall be numbered, re- 
 spectively, beginning with the number one in the northeast section, 
 and proceeding west and east alternately through the township 
 with progressive numbers till the thirty-six be completed. 
 
 Fourth. The deputy surveyors, respectively, shall cause to 
 be marked on a tree near each corner established in the manner 
 described, and within the section, the number of such section 
 and over it the number of the township within which such section 
 may be. 
 
 Fifth. Where the exterior lines of the townships which may 
 be subdivided into sections or half-sections exceed or do not ex- 
 tend six miles, the excess or deficiency shall be specially noted
 
 UNITED STATES PUBLIC LAND SURVEYS 61 
 
 and added to or deducted from the western and northern ranges 
 of sections or half-sections in such townships, according as the 
 error may be in running the lines from east to west, or from north 
 to south ; the sections and half -sections bounded on the northern 
 and western lines of such townships shall be sold as containing 
 only the quantity expressed in the returns and plats, respectively, 
 and all others as containing the complete legal quantity. 
 
 Sixth. All lines shall be plainly marked upon trees, and meas- 
 ured with chains, containing two perches of sixteen and one-half 
 feet each, subdivided into twenty-five equal links ; and the chain 
 shall be adjusted to a standard to be kept for that purpose. 
 
 SEC. 100. The boundaries and contents of the several sections, 
 half-sections, and quarter-sections of the public lands shall be as- 
 certained in conformity with the following principles: 
 
 First. All the corners marked in the surveys returned by the 
 surveyor-general shall be established as the proper corners of 
 sections, or subdivisions of sections, which they were intended to 
 designate, and the corners of half and quarter-sections, not marked 
 on the surveys, shall be placed as nearly as possible equidistant 
 from two corners which stand on the same line. 
 
 Second. The boundary lines, actually run and marked in the 
 surveys returned by the surveyor-general, shall be established as 
 the proper boundary lines of the sections or subdivisions for which 
 they were intended, and the length of such lines as returned shall 
 be held and considered as the true length thereof. And the 
 boundary lines which have not been actually run and marked 
 shall be ascertained by running straight lines from the established 
 corners to the opposite corresponding corners; but in those por- 
 tions of the fractional townships, where no such opposite corre- 
 sponding corners have been or can be fixed, the boundary lines 
 shall be ascertained by running from the established corners due 
 north and south or east and west lines, as the case may be, to the 
 water-course, Indian boundary line, or other external boundary 
 of such fractional township. 
 
 Third. Each section or subdivision of section, the contents 
 whereof have been returned by the surveyor-general, shall be 
 held and considered as containing the exact quantity expressed 
 in such return; and the half -sections and quarter-sections, the 
 contents whereof shall not have been thus returned, shall be held 
 and considered as containing the one-half or the one-fourth part, 
 respectively, of the returned contents of the section of which they 
 may make part. (Act of Feb. 11, 1805, and R. S., 2396.) 
 
 SEC. 101. In every case of the division of a quarter-section 
 the line for the division thereof shall run north and south, and the 
 corners and contents of half-quarter-sections which may there- 
 after be sold shall be ascertained in the manner and on the prin- 
 ciples directed and prescribed by the section preceding.
 
 62 A MANUAL FOR NORTHERN WOODSMEN 
 
 In elaboration of the law are the following rules laid 
 down by the Federal Land Office: 
 
 24. Existing law requires that in general the public lands of 
 the United States "shall be divided by north and south lines run 
 according to the true meridian, and by others crossing them at 
 right angles so as to form townships six miles square," and that 
 the corners of the townships thus surveyed "must be marked with 
 progressive numbers from the beginning." 
 
 Also, that the townships shall be subdivided into thirty-six sec- 
 tions, each of which shall contain 640 acres, as nearly as may be, 
 by a system of two sets of parallel lines, one governed by true 
 meridians and the other by parallels of latitude, the latter inter- 
 secting the former at right angles, at intervals of a mile. 
 
 25. In the execution of the public surveys under existing law, 
 it is apparent that the requirements that the lines of survey shall 
 conform to true meridians, and that the townships shall be six miles 
 square, taken together, involve a mathematical impossibility due 
 to the convergency of the meridians. 
 
 Therefore, to conform the meridional township lines to the 
 true meridians produces townships of a trapezoidal form which 
 do not contain the precise area of 23,040 acres required by law, 
 and which discrepancy increases with the increase in the con- 
 vergency of the meridians as the surveys attain the higher latitudes. 
 
 26. In view of these facts, and under the provisions of Sec- 
 tion 2 of the Act of May 18, 1796, that sections of a mile square 
 shall contain 640 acres, as nearly as may be, and also under those 
 of Section 3 of the Act of May 10, 1800, that "in all cases where the 
 exterior lines of the townships, thus to be subdivided into sections 
 and half-sections, shall exceed, or shall not extend six miles, the 
 excess or deficiency shall be specially noted, and added to or de- 
 ducted from the western or northern ranges of sections or half- 
 sections in such township, according as the error may be in run- 
 ning lines from east to west, or from south to north ; the sections 
 and half-sections bounded on the northern and western lines of 
 such townships shall be sold as containing only the quantity ex- 
 pressed in the returns and plats, respectively, and all others as 
 containing the complete legal quantity," the public lands of the 
 United States shall be surveyed under the methods of the system 
 of rectangular surveying, which harmonizes the incompatibilities 
 of the requirements of law and practice, as follows: 
 
 First. The establishment of a principal meridian conforming 
 to the true meridian, and, at right angles to it, a base line conform- 
 ing to a parallel of latitude. 
 
 Second. The establishment of standard parallels conforming 
 to parallels of latitude, initiated from the principal meridian at 
 intervals of 24 miles and extended east and west of the same. 
 
 Third. The establishment of guide meridians conforming to 
 true meridians, initiated upon the base line and successive standard
 
 UNITED STATES PUBLIC LAND SURVEYS 63 
 
 parallels at intervals of twenty-four miles, resulting in tracts of land 
 twenty-four miles square, as nearly as may be, which shall be sub- 
 sequently divided into tracts of land six miles square by two sets 
 of lines, one conforming to true meridians, crossed by others con- 
 forming to parallels of latitude at intervals of six miles, containing 
 23,040 acres, as nearly as may be, and designated townships. 
 
 Such townships shall be subdivided into thirty-six tracts, called 
 sections, each of which shall contain 640 acres, as nearly as may 
 be, by two sets of parallel lines, one set parallel to a true meridian 
 and the other conforming to parallels of latitude, mutually inter- 
 secting at intervals of one mile and at right angles, as nearly as 
 may be. 
 
 27. Any series of contiguous townships or sections situated 
 north and south of each other constitutes a RANGE, while such a 
 series situated in an east and west direction constitutes a TIER. 
 
 28. By the terms of the original law and by general practice, 
 section lines were surveyed from south to north and from east to 
 west, in order to uniformly place excess or deficiency of measure- 
 ment on the north and west sides of the townships. But under 
 modern conditions many cases arise in which a departure from 
 this method is necessary. Where the west or the north boundary 
 is sufficiently correct as to course, to serve as a basis for rectangular 
 subdivision, and the opposite line is defective, the section lines 
 should be run by a reversed method. 
 
 For convenience the well-surveyed lines on which subdivi- 
 sions are to be based will be called governing boundaries of the 
 township. 
 
 29. The tiers of townships will be numbered, to the north or 
 south commencing with No. 1, at the base line; and the ranges 
 of the townships, to the east or west, beginning with No. 1, at the 
 principal meridian of the system. 
 
 30. The thirty-six sections into which a township is subdi- 
 vided are numbered, commencing with No. 1 at the north- 
 east angle of the township, and proceeding west to number six, 
 and thence proceeding east to number twelve, and so on, alter- 
 nately, to number thirty-six in the southeast angle. In all cases 
 of surveys of fractional townships, the sections will bear the same 
 numbers they would have if the township was full; and where 
 doubt arises as to which section numbers should be omitted, the 
 proper section numbers will be used on the side or sides which 
 are governing boundaries, leaving any deficiency to fall on the 
 opposite sides. 
 
 31. Standard parallels (formerly called correction lines) shall 
 be established at intervals of twenty-four miles, north and south of 
 the base line, and guide meridians at intervals of twenty-four miles, 
 east and west of the principal meridian ; thus confining the errors 
 resulting from convergence of meridians and inaccuracies in meas- 
 urement within comparatively small areas.
 
 64 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 In pursuit of this system, during the course of the pub- 
 lic land surveys twenty-four initial points have been 
 established, a principal meridian has been run due north 
 and south from each of these, and a base line east and 
 west. Each twenty-four miles north and south of the 
 initial point standard parallels or correction lines have 
 been started on which, as they were run east and west, 
 marks have been left each six miles for the starting of 
 township lines. These are run due north to the next 
 standard parallel; each fourth one being run first and 
 
 Standard 
 
 Parall 
 
 el 
 
 
 
 
 
 1 
 
 f 
 
 i 
 
 I 
 
 i 
 i 
 
 E 
 
 E 
 
 j 
 
 \ 
 
 I 
 
 1 
 
 
 
 
 
 \ 
 
 FIHST SUBDIVISION op LAND 
 
 Standard Parallel 
 
 DIVISION INTO TOWNSHIPS 
 
 most accurately as a guide meridian. On the north and 
 south lines township corners are fixed each six miles by 
 measurement, and each pair of corners is later connected. 
 A township corner is common to four townships except on a 
 standard parallel. There, owing to convergence of merid- 
 ians, the corners of the townships north are farther from the 
 principal meridian than those of the townships south ; farther 
 east or west, as the case may be. The ranges of townships 
 connected with any given initial point are numbered east 
 and west from the principal meridian, and the townships 
 themselves are numbered north and south from the base 
 line. Thus the sixth township north of a base line in the 
 fourth range east of a principal meridian is designated as 
 township 6 north, range 4 east. Each township contains
 
 UNITED STATES PUBLIC LAND SURVEYS 
 
 65 
 
 thirty-six square miles or 23,040 acres, neglecting the nar- 
 rowing effect of the convergence of the meridians. These 
 relations are indicated clearly in the diagrams. 
 
 As the township lines are run, corner marks are left each 
 mile, and the township is divided into thirty-six sections by 
 beginning on the south side at each mile mark and running 
 north, marking each mile or section corner, also each half 
 mile or quarter-section corner. At the north end these 
 lines are made to close on the mile marks left in surveying 
 the north line of the township, with the exception of those 
 on a standard parallel. Here the section lines are run 
 straight out to the parallel, which thus serves as a "cor- 
 rection-line" for the sections as well as for the townships. 
 
 N 
 
 G 
 
 5 
 
 4 
 
 3 
 
 2 
 
 1 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11* 
 
 12 
 
 18 
 
 17 
 
 16 
 
 . 15 
 
 14 
 
 13 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 30 
 
 29 
 
 28 
 
 27 
 
 26 
 
 25 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 X. W. % 
 160 acres 
 
 N. E. M 
 100 acres 
 
 Yf T/ 
 
 ofS.W. 
 
 80 acres 
 
 ofS.W. 
 
 N.W. J^ 
 ofS.E. 
 54 
 
 40 acres 
 
 40 acres 
 
 S.E.Ji 
 ofS.E. 
 
 SECTIONS IN A TOWNSHIP 
 
 SUBDIVISION OF A SECTION 
 
 The east and west section lines are run between corre- 
 sponding corners on the north and south lines, always 
 marking the half-mile or quarter-section point. The 
 effect on area of convergence of meridians is localized in 
 the case of sections, in the first place by chaining the 
 latitudinal township lines always from the east end, thus 
 confining any deficiency of width to the westerly board 
 of sections; in the second place by running the north and 
 south lines not due north exactly, but with a westerly 
 bearing sufficient at one, two, three, four, and five miles 
 from the east line to keep them at equal distances apart 
 throughout their length. Short area is thus confined to
 
 66 A MANUAL FOR NORTHERN WOODSMEN 
 
 the westerly board of sections in each township when 
 surveys are accurately made. For the same purpose, 
 reduction in the number of irregular units, quarter corners 
 for the north and west tiers of sections are placed exactly 
 forty chains from the interior corners, not at the middle 
 point of the section lines. 
 
 The Land Office instructions to surveyors contain 
 several articles on the marking of lines, of which those of 
 interest to the woodsman are quoted on page 24 of this 
 work. Instructions for establishing corners and erecting 
 monuments are also given, but are far too elaborate to be 
 here quoted in full. Corner monuments consist of an ob- 
 ject marking the corner itself and its accessories. They 
 are to be set up at the intersection of all the lines noted 
 in the instructions quoted above and at some other points 
 to be mentioned hereafter. Several approved forms of 
 corner monuments are described below. Any one may 
 be used for a township, a section, or a quarter-section 
 corner, the marks upon it indicating what the corner is. 
 
 1. Stone with pits and mound of earth. 
 
 2. Stone with mound of stone. 
 
 3. Stone with bearing trees. 
 
 4. Post with pits and mound of earth. 
 
 5. Post with bearing trees. 
 
 6. Mound of earth, with marked stone or charcoal de- 
 posited inside, and stake in pit. 
 
 7. Tree with pit and mound of stone. 
 
 8. Tree with bearing trees. 
 
 Posts of wood and stone and bearing trees have been 
 employed largely as corner monuments in timbered 
 country. The post is set not to exceed one foot out of the 
 ground. At a standard, closing, or quarter corner it is set 
 facing cardinal directions, diagonally at a corner common 
 to four townships or sections. Plain figures and initial 
 letters inscribed on the faces give the location, and this in 
 the case of section corners is also indicated by notches cut 
 in the edges or by grooves on faces. These notches, on 
 account of their durability, are of much service in identi-
 
 UNITED STATES PUBLIC LAND SURVEYS 67 
 
 fication of section corners. They are placed on the south 
 and east angles of the posts, one for each mile to the town- 
 ship boundary in the given direction. Quarter corners are 
 not notched; township corners are cut six times on each 
 face or angle. 
 
 Equally serviceable are the bearing trees. These are 
 blazed rather close to the ground so that the stump can 
 be identified if the tree is cut down. The blazes face the 
 corner, and that on each tree at township or section corners 
 is plainly scribed with the township number and range and 
 that of the section in which it stands. Thus, T 10 S R 
 6 E S 24 B T (B T for bearing tree). 
 
 There are several exceptions to the system of rectan- 
 gular surveying and the regular scheme of monuments 
 resulting therefrom, which it is necessary for the woodsman 
 to understand. 
 
 1. Toimship and Section Corners on Standard Parallels. 
 
 It will be noted after careful reading of the above that 
 township or section corners are common to four townships 
 or sections, with the exception of those on the standard 
 parallels which are four townships apart. Here the corners 
 for the townships north of the parallel are not the same as 
 for those south, but are further from the principal me- 
 ridian. The former are called "standard corners" and are 
 marked S C in addition to other marks placed on them for 
 their identification. In a similar way the corners relating 
 to land subdivisions lying south of the parallel are marked 
 C C, "closing corner." This last term is also applied in 
 other connections, as when a rectangular survey closes on 
 the boundary of a state, a reservation, or a previous land 
 claim, while occasions for its application have often been 
 found in connection with errors or departures from instruc- 
 tions in the system of surveying. 
 
 2. Meander Lines and Corners. 
 
 Ownership of considerable streams or lakes, with the 
 exception of certain "riparian rights," is not conveyed 
 with a land title, the legal limit being high-water mark, or 
 the line at which continuous vegetation ends and the sandy
 
 68 A MANUAL FOB NORTHERN WOODSMEN 
 
 or muddy shore begins. This line is surveyed in connec- 
 tion with a United States land survey, the process being 
 called " meandering." 
 
 At every point where a standard, township, or section 
 line intersects the bank of a navigable stream or other 
 meanderable body of water, corners are established at the 
 time of running these lines. These are called " meander 
 corners." They are always marked M C in addition to any 
 other marks left for their identification. 
 
 In the same way, when a line subdividing a section runs 
 into a considerable body of water, a " special meander 
 corner" is established and marked in the same way. 
 
 3. Witness Carriers and Witness Points. 
 
 A key to the location and meaning of these will be found 
 in the following sections from the " Instructions." 
 
 49. Under circumstances where the survey of a township or 
 section line is obstructed by an impassable obstacle, such as a 
 pond, swamp, or marsh (not meanderable), the line will be pro- 
 longed across such obstruction by making the necessary right- 
 angle offsets; or, if such proceeding be impracticable, a traverse 
 line will be run, or some proper trigonometrical operation em- 
 ployed to locate the line on the opposite side of the obstruction ; 
 and in case the line, either meridional or latitudinal, thus regained, 
 is recovered beyond the intervening obstacle, said line will be sur- 
 veyed back to the margin of the obstruction. 
 
 50. As a guide in alignment and measurement, at each point 
 where the line intersects the margin of an obstacle a witness point 
 will be established, except when such point is less than twenty 
 chains distant from the true point for a legal corner which falls in 
 the obstruction, in which case a witness corner will be established 
 at the intersection. 
 
 51. In a case where all the points of intersection with the ob- 
 stacle to measurement fall more than twenty chains from the proper 
 place for a legal corner in the obstruction, and a witness corner 
 can be placed on the offset line within twenty chains of the inac- 
 cessible corner point, such witness corner will be established. 
 
 97. The point for a corner falling on a railroad, street, or 
 wagon road, will \>e perpetuated by a marked stone (charred stake 
 or quart of charcoal), deposited twenty-four inches in the ground, 
 and witnessed by two witness corners, one of which will be estab- 
 lished on each limiting line of the highway. 
 
 In case the point for any regular corner falls at the intersection 
 of two or more streets or roads, it will be perpetuated by a marked 
 stone (charred stake or quart of charcoal), deposited twenty-four 
 inches in the ground, and witnessed by two witness corners estab-
 
 UNITED STATES PUBLIC LAND SURVEYS 69 
 
 lished on opposite sides of the corner point, and at the mutual in- 
 tersections of the lines limiting the roads or streets, as the case 
 may be. 
 
 94. When the true point for any corner described in these 
 instructions falls where prevailing conditions would insure its 
 destruction by natural causes, a witness corner will be established 
 in a secure position, on a surveyed line if possible, and within 
 twenty chains of the corner point thus witnessed. 
 
 95. A witness corner will bear the same marks that would be 
 placed upon the corner for which it is a witness, and in addition, 
 will have the letters W C (for witness corner) conspicuously dis- 
 played above the regular markings on the NE. face when witness- 
 ing in township or section corner; such witness corners will be 
 established, in all other respects, like a regular corner, marking 
 bearing trees with the proper numbers for the sections in which 
 they stand. 
 
 W C will also be cut into the wood of each bearing tree above 
 the other markings. 
 
 98. Witness points will be perpetuated by corners similar to 
 those described for quarter-section corners, with the marking W P 
 (for witness point), in place of J, or J S, as the case may be. 
 
 If bearing trees are available as accessories to witness points, 
 each tree wUl be marked W P B T. 
 
 4. Fractional Sections, Lots, etc. 
 
 A section or quarter-section made of less than full size by 
 water is called "fractional," and in some cases is subdivided 
 according to special rules laid down by the Land Office. 
 The sections on the westerly board of a township, into 
 which, under the plan of survey, shrinkage of area due to 
 convergence of township lines toward the north is crowded, 
 are called fractional as well. Within these sections again, 
 the westerly quarters and forties will be fractional for the 
 same reason. The final subdivisions of irregular area 
 the system is followed next the north as well as the west 
 line of the townships are called "lots." In a regular 
 township there are four to each section, numbered from 
 1 to 4 for each, beginning with the east or north, with seven 
 lots for Section 6. In timbered country, however, they 
 are seldom run out on the ground. 
 
 While the above are usual features of the public land 
 surveys, numerous exceptions were made, as for instance 
 in case of a defective east or south boundary in a township,
 
 70 A MANUAL FOR NORTHERN WOODSMEN 
 
 when subdivision was begun from the opposite side. 
 Somewhat different rules also were in force during the 
 very early surveys. Then hi addition irregularities due 
 to the errors of surveying, and these sometimes of an 
 extreme nature, are sometimes found.
 
 PART II 
 FOREST MAPS
 
 PART II. FOREST MAPS 
 
 SECTION I. . THE TRANSIT 73 
 
 1. Adjustments 73 
 
 2. Care of the Transit 77 
 
 3. Stadia Measurement 77 
 
 4. Uses of the Transit 80 
 
 5. Summary . . . 87 
 
 SECTION II. THE LEVEL 87 
 
 1. Adjustments 88 
 
 2. Uses of the level 90 
 
 SECTION III. THE HAND LEVEL AND CLINOMETER . . 93 
 
 SECTION IV. COMPASS AND PACING 94 
 
 SECTION V. THE TRAVERSE BOARD 98 
 
 SECTION VI. THE ANEROID BAROMETER 103 
 
 SECTION VII. METHODS OF MAP MAKING 113 
 
 1. Introductory 113 
 
 2. Small Tracts 117 
 
 3. Large Tracts 121 
 
 A. With Land already subdivided 121 
 
 B. Based on Survey of Roads or Streams . . . 121 
 
 C. Subdivision and Survey combined 123 
 
 D. Western Topography. Use of the Clinometer 129 
 SECTION VIII. ADVANTAGES OF A MAP SYSTEM 133
 
 PART II. FOREST MAPS 
 
 SECTION I 
 THE TRANSIT 
 
 THE transit in general engineering work is the most 
 useful and most frequently employed of surveying instru- 
 ments. It is commonly used to measure horizontal and 
 vertical angles, but, having a magnetic needle, it may be 
 used to take bearings, and, when provided with stadia 
 wires, to measure distances. It may also be used as a 
 levelling instrument. A cut of a transit is shown here- 
 with, also a sectional view through the axis of the same 
 instrument. 
 
 The essential parts of an engineer's transit are described 
 below. The telescope is attached by means of a hori- 
 zontal axis and standards to the upper of two circular 
 plates. The two plates move freely on one another, the 
 lower being graduated, while the upper has a vernier 
 which allows readings to be made with accuracy. A 
 compass circle is also attached to the upper plate. A 
 clamp fixes the upper to the lower plate, and a tangent 
 screw secures a slow adjusting movement between the 
 two. A similar arrangement is placed between the lower 
 plate and the head of the instrument. 
 
 The whole instrument is supported on a tripod ; levelling 
 screws serve with the aid of cross levels to fix the plates in 
 a horizontal position ; and a finely turned spindle and socket 
 arrangement guides the plates in their movement on one 
 another. By means of a plumb line attached to the lower 
 end of the spindle the instrument may be set with its axis 
 exactly over any desired point. 
 
 1. ADJUSTMENTS OF THE TRANSIT 
 
 The object of these adjustments is to cause (1) the 
 instrument to revolve in a horizontal plane; (2) the line 
 of sight to generate a vertical plane when the telescope is 
 73
 
 74 
 
 A MANUAL FOB NORTHERN WOODSMEN 
 
 revolved on its axis; (3) the axis of the telescope bubble 
 to be parallel to the line of sight, thus enabling the instru- 
 ment to be used as a level ; (4) the vernier on the vertical 
 
 THE TRANSIT 
 
 circle to be so adjusted as to give the true altitude of the 
 line of sight. These results may be secured as follows: 
 a. To adjust the plate levels so that each is in a plane
 
 THE TRANSIT 
 
 75 
 
 perpendicular to the vertical axis of the instrument. Set 
 up the transit and bring the bubbles to the center of their 
 respective tubes. Turn the plate 180 about its vertical 
 axis, and see if the bubbles remain in the center. If they 
 move from the center, turn the capstan-headed screws on 
 the bubble tube until the bubble moves half-way back to 
 the center, or as nearly so as this can be estimated. Each 
 bubble must be adjusted independently. The adjust- 
 ment should be tested again by relevelling and reversing 
 as before, and the process continued until the bubbles re- 
 main in the center when reversed. When both -levels are 
 adjusted, the bubbles should remain. in the center during 
 the entire revolution about the vertical axis. 
 
 
 CROSS-SECTION OF THE TRANSIT HEAD 
 
 b. To make the line of sight perpendicular to the hori- 
 zontal axis so that the telescope when revolved will 
 generate a plane. To do this choose open and nearly level 
 ground. Set up the transit carefully over a point A, sight 
 accurately at a point B at about the same level and 200 or 
 300 feet away, and clamp both plates. Revolve the tele- 
 scope and set C in line with the vertical cross-hair at about 
 the same distance and elevation. B, A, and C should then 
 be in a straight line. To test this, turn the instrument
 
 76 A MANUAL FOR NORTHERN WOODSMEN 
 
 about the vertical axis until B is again sighted. Clamp the 
 plate, revolve the telescope, and observe if point C is in 
 line. If not, set a third point D in the new line. Then, 
 to adjust, the cross-hair ring must be moved until the 
 vertical hair appears to have moved to the point E, one- 
 fourth the distance from D toward C, since, in this case, 
 a double reversal has been made. 
 
 The cross-hair ring is moved by loosening one of the 
 screws which hold it in the telescope tube and tightening 
 the opposite screw. The process of reversal should be 
 repeated until no further adjustment is required. \Yhen 
 finally adjusted, the screws should hold the ring firmly but 
 without straining it. 
 
 c. To make the horizontal axis of the telescope per- 
 pendicular to the vertical axis of the instrument, so that 
 the telescope in its revolution will generate a vertical 
 plane. Set up the instrument and level it carefully. Sus- 
 pend a fine, smooth plumb line twenty or thirty feet long 
 some twenty feet away from the instrument with a weight 
 on the lower end hanging freely in a pail of water. Set the 
 line of sight carefully on the cord at its upper end. Clamp 
 both plates and bring the telescope down until it reads on 
 the lower end of the cord. If the line of sight does not cut 
 the cord, raise or lower the adjustable end of the horizon- 
 tal axis until the line of sight does revolve in a vertical 
 plane. Constant attention must be given to the plate 
 bubbles to see that they do not indicate an inclined verti- 
 cal axis. 
 
 If more convenient two points in a vertical line may be 
 used, as points on a building. Set on the top point and turn 
 down to the bottom one, marking it carefully. Revolve 
 both plate and telescope 180 and set again on the bottom 
 point. Raise the telescope again and read on the top point. 
 The second pointing at the top point should correspond 
 with the first. If it does not, adjust as above for half the 
 difference. 
 
 d. To make the telescope bubble parallel to the line of 
 sight. This adjustment is performed in the same way as 
 for a level, as explained on pages 89 and 90. 
 
 e. To make the vernier of the vertical circle read zero
 
 THE TRANSIT 77 
 
 when the line of sight is horizontal. Having made the 
 axis of the telescope bubble parallel to the line of sight, 
 bring the bubble into the center of the tube and adjust the 
 vernier of the vertical circle until it reads zero on the limb. 
 If the vernier is not adjustable, the reading in this position 
 is its index error, to be applied to all readings. 
 
 2. CARE OF THE TRANSIT 
 
 The transit should be protected from wet and dust as 
 much as possible, a waterproof bag to cover it being useful 
 for that purpose. The tripod legs should move freely, but 
 not too freely; there should be no lost motion about their 
 shoes or elsewhere. Dust or water should be removed from 
 the glasses by a camel's hair brush or the gentle use of a 
 clean handkerchief; grease may be removed by alcohol. 
 Care should be taken not to strain the parts of the instru- 
 ment by too great pressure on the screws when using or 
 adjusting it. Before the transit is picked up, the levelling 
 screws should be brought approximately to their mid po- 
 sition, the telescope should be turned vertically and lightly 
 clamped, and the clamp of the lower plate should be loos- 
 ened. Then, if the instrument strikes anything while being- 
 carried from point to point, some part will move easily and 
 severe shock will be avoided. 
 
 3. STADIA MEASUREMENT 
 
 Measurement of distance by stadia is secured by simply 
 sighting with a transit at a graduated rod held on any de- 
 sired point and noting the space on the rod included 
 between two special cross-hairs set in the focus of the in- 
 strument. This is a very rapid method of measurement, 
 being especially handy and effective over broken land; it 
 gives a degree of accuracy sufficient for very many pur- 
 poses ; it allows the computation of the difference in ele- 
 vation between two points. Thus for many purposes it is 
 the most effective method of survey, and it is coming 
 into general use. 
 
 The Instrument. A transit intended for stadia work is
 
 78 A MANUAL FOR NORTHERN WOODSMEN 
 
 provided with two additional horizontal hairs, usually fas- 
 tened to the same diaphragm as the ordinary cross-hairs, 
 and placed at a known distance apart. The space be- 
 tween these two extra hairs is preferably fixed, but in 
 some transits the diaphragm is so arranged that it can be 
 adjusted. The instrument must also be provided with a 
 level on the telescope and a circle or arc for measuring 
 vertical angles, since the telescope is seldom level when 
 measurements are taken. 
 
 Stadia rods are usually 10 or 12 feet long. They are 
 plainly painted in such a design as to be read at long dis- 
 tances. Engineers generally use rods graduated to feet 
 and tenths, the hairs cutting off one foot on the rod at a 
 distance of 100 feet. Hundredths of a foot are generally 
 estimated. For use in connection with a land survey it may 
 be more convenient to graduate the rod or adjust the hairs 
 so that one unit will be cut off at a distance of 66 feet or 
 one chain. 
 
 Inclined Sights. The distance between instrument and 
 rod is measured directly if the sight is taken horizontally, 
 and a vertical angle between them of 5 or less does not so 
 affect the sight as to matter particularly in many kinds of 
 work. If, however, a sight of greater inclination is taken, 
 a reading is obtained that represents a greater distance 
 than the horizontal one between instrument and rod. If 
 for an inclined reading the rod is also inclined, so as to be 
 perpendicular to the line of sight, the reading represents 
 the inclined distance, and the horizontal distance is the 
 cosine of the angle of inclination multiplied by the inclined 
 distance. Similarly, the difference in elevation is the in- 
 clined distance multiplied by the sine of the angle. 
 
 It is usual, however, and better, to hold the rod plumb, 
 and here the computation of horizontal and vertical ele- 
 ments is not so simple. Tables, however, have been com- 
 puted which give these elements, horizontal distance and 
 difference of elevation, directly. A compact stadia table 
 will be found on page 211 of this work and an example 
 showing the method of its use is given on page 80. 
 
 What has been written above needs, however, one 
 qualification. Stadia wires to read truly at all distances
 
 THE TRANSIT 79 
 
 must cut off the unit distance on the rod not at a distance 
 of 100 or of 66 feet, but at a greater distance equal to the 
 distance from the center of the instrument to the objective 
 lens + the distance from the cross-wires to the same lens 
 when focused on a distant object. This correction, (/ + c) 
 as it is called, is about 1 foot in common transits. 
 
 In testing the instrument on measured bases, therefore, 
 these should be measured out from the plumb line or 
 center of instrument to the required distance + the 
 constant above described, and for accurate determina- 
 tion of distance the constant should be added to the 
 distance observed. In working out inclined sights from 
 the table this constant may be added to the rod reading 
 before the reductions for horizontal distance and elevation 
 are made. 
 
 In the practice of woodsmen, however, work will generally 
 be accurate enough if this constant is neglected, all the 
 more so since this error tends to be compensated by that 
 arising from neglect of the small vertical angles noted above. 
 There are, indeed, a few transits so constructed that no 
 such constant correction as that above stated has to be 
 considered. 
 
 Accuracy. The accuracy of stadia measurement de- 
 pends largely on the state of the atmosphere. If that is 
 hazy, or unsteady from the effects of heat, long shots can- 
 not be taken and measurements on shorter distances 
 cannot be accurately obtained. There is furthermore the 
 possibility that the line of sight by the lower hair when 
 passing over very hot ground may be refracted more than 
 the other and thereby give too small a reading. Other- 
 wise than here and above stated the only sources of in- 
 accuracy are due to errors in rod readings which for small 
 errors are as apt to be + as and so mainly balance one 
 another. Thus while on single shots stadia measurement 
 may be appreciably inaccurate, the relative error decreases 
 with the length of the line run. 
 
 In general it may be said that stadia measurement gives 
 satisfactory results for very many purposes, and that it has 
 great advantages in the way of rapidity and cheapness. 
 With good instruments and clear air it can be employed
 
 80 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 on distances from one quarter to one third of a mile, giving 
 results which are accurate to within a few feet. 
 
 Example and Reduction of Readings. 1' on rod cut off 
 at distance of 100'. In computation, correction made for 
 1' instrumental constant. True horizontal distance and 
 difference of elevation between points both worked out. 
 Height of instrument over station obtained at each setting 
 and center hair for vertical angle read at same height on 
 rod. 
 
 Observed 
 
 Computed 
 
 Bearing 
 
 Rod 
 Reading 
 
 Vert. 
 Angle 
 
 Distance 
 
 Diflf. 
 
 Elev. 
 
 Elev. 
 
 N. 5 E. 
 
 2.00' 
 
 + 1 30' 
 
 200.86' 
 
 + 5.27' 
 
 5.27' 
 
 N. 5 E. 
 
 1.80' 
 
 + 4 10' 
 
 179.84' 
 
 + 13.12' 
 
 18.39' 
 
 N. 5 E. 
 
 1.05' 
 
 + 8 
 
 103.94' 
 
 + 14.61' 
 
 33.00' 
 
 N. 5 E. 
 
 1.50' 
 
 30' 
 
 150.98' 
 
 1.31' 
 
 31.69' 
 
 
 
 
 635.62' 
 
 
 31.69' 
 
 Computation. First shot, with v. a. of 1 30', rod reading 2.00'. 
 Add .01' for instrument constant, making 2.01', for corrected rod 
 reading. From table the horizontal distance fof 1' rod reading is 
 found to be 99.93' the difference of elevation 2.62'. For 2.01' rod 
 reading the elements are 99.93 X 2.01 and 2.62 X 2.01 or 200.86' 
 and 5.27', as above. 
 
 Second shot, 1.80 + .01, = 1.81, corrected rod reading. 
 
 For v. a. 4 10' and rod reading 1', horizontal distance 99.47 
 and diff. elev. 7.25 are found in the tables. 99.47 X 1.81 and 
 7.25 X 1.81 = 179.84 and 13.12. 
 
 Similarly for succeeding shots 
 
 4. USES OF THE TRANSIT 
 
 To Take the Bearing of a Line. Set up over the first 
 point, level the instrument, free the needle, and turn the 
 telescope toward the other point. Read the bearing in the 
 same way as with a compass. 
 
 When set up on the forward one of two points, exactly 
 the same bearing may be read as if the instrument were
 
 THE TRANSIT 81 
 
 set up on the rear point, if the telescope is revolved before 
 the pointing is made and the bearing taken. 
 
 To Measure a Horizontal Angle. Set up the instru- 
 ment, center it by means of the plumb line over the vertex 
 of the angle required, set the zeros of the two plates to- 
 gether, clamp them, and turn the telescope toward one of 
 the points, making the final adjustment by means of the 
 lower tangent screw. Then loosen the upper clamp, turn 
 toward the other point, clamp again, and set finally by the 
 upper tangent screw. Read the angle turned by means of 
 the vernier. If the instrument has two verniers, both may 
 be read and the average taken. 
 
 Measurement by Repetition. A more accurate meas- 
 urement may be had by turning the angle several times, tak- 
 ing the final reading, and dividing it by the number of 
 times the angle has been turned. If the final reading is 
 about 360, possible errors in the graduation of the instru- 
 ment will have no effect on the angle read, and if later the 
 telescope is inverted and the angle turned in the opposite 
 direction from the first turning, other sources of error will 
 have been eliminated. The exact program for an obser- 
 vation of this kind is as follows : 
 
 a. Telescope direct. 1 
 
 1. Clamp plates on zeros, and set on left station. Clamp 
 below. 
 
 2. Unclamp above and set on right station. 
 
 3. Unclamp below and set on left station. 
 
 4. Unclamp above and set on right station. 
 Continue until the desired number of turnings have been 
 
 made, when the final reading may be taken. 
 
 b. Telescope inverted. 
 
 1. Clamp plates on zeros and set on right station. 
 Clamp below. 
 
 2. Unclamp above and set on left station. 
 
 3. Unclamp below and set on right station. 
 
 4. Unclamp above and set on left station. 
 
 Continue for the same number of turnings as before 
 
 1 That is, with the level tube underneath the telescope.
 
 82 A MANUAL FOR NORTHERN WOODSMEN 
 
 and read the final angle. If the instrument has two ver- 
 niers both should be read. It is customary to record the 
 reading after turning the angle once, as a check on 
 the repeated reading. The true reading is the average of 
 the values obtained for the angle with telescope direct 
 and telescope inverted. 
 
 To Prolong a Straight Line. Set up the instrument over 
 the forward point and sight the telescope on. the rear one. 
 Set both clamps, revolve the telescope on its axis, and set a 
 new point as far ahead as convenient or desired. 
 
 More Accurately. With the telescope in its natural 
 position, turn on the rear point, clamp, revolve the tele- 
 scope as above, and set a stake and tack at the forward 
 pointing. Then, leaving the telescope inverted as it is, 
 swing the plates around half a circle and set on the rear 
 point again. Revolve the telescope, and again sight at 
 the forward point. If the two pointings ahead do not 
 coincide, set a tack half-way between the two and it will 
 be in the line desired. 
 
 To Measure a Vertical Angle. For this purpose the ver- 
 tical circle must be adjusted so as to read zero when the 
 telescope is level, or, if it is not adjustable, the error of its 
 reading must be obtained, as explained under adjustments 
 of the transit. Then the angle of elevation or depression 
 to any point may be measured by sighting the telescope 
 upon it and reading the vertical angle by means of the 
 vertical circle and its vernier. 
 
 To Survey a Piece of Ground with the Transit. Set 
 up on the initial point of the survey, turn to the second 
 point, read the bearing of the line, recording it for a check 
 on later angles, and measure the line. Set up over the 
 second point, set the two plates to read zero, and clamp 
 them together; then turn the telescope at a rod held ver- 
 tical and carefully centered over the first point. Set the 
 lower clamp and loosen the upper one, swing the tele- 
 scope with the upper plate around until the third point is 
 sighted, and read the angle so turned. Head the bearing 
 for a check, and measure the line. Proceed in this way 
 until all the angles have been turned and all the sides 
 measured. Interior angles should always be read, though
 
 THE TRANSIT 83 
 
 they may be more than 180. The magnetic bearings 
 may be used to figure out the angles as a check on 
 measurement; they also help to locate an error if one 
 exists, but a more accurate check is the sum of all the 
 angles which should equal twice as many right angles 
 less four as the figure has sides. 
 
 Computed bearings are worked out by applying the 
 angle measurements to the bearing of the first line. Com- 
 puted, not observed, bearings should be used for plotting 
 or for computing traverse. Notes may be kept as follows: 
 
 
 /Votes of -Survey of F/e/cf 
 
 Sfa. 
 
 Inf. Any /e 
 
 Oiserux/ 
 ffear/ny 
 
 Computed 
 Bear/ry 
 
 D/sfance. 
 
 
 o 
 
 
 N8/ 
 
 M8I 
 
 JJ8.63fh 
 
 
 1 
 
 aea" /9' 
 
 A/8'JS'W 
 
 /V8"/9'W 
 
 48 J3 " 
 
 
 a 
 
 af32' 
 
 N7S45E 
 
 /V7549' 
 
 300.53" 
 
 
 3 
 
 85 /Z' 
 
 S930'E 
 
 S923'E 
 
 183.60 " 
 
 
 4 
 
 eras' 
 
 S79/JW 
 
 S799W 
 
 813.96" 
 
 
 J 
 
 86J6' 
 
 A/7"4S'W 
 
 A/7*47'W 
 
 134.85" 
 
 
 
 
 9l/3' 
 
 M8/ 
 
 
 
 
 48.19' 
 
 819.96' 
 
 SKETCH OP SURVEY 
 
 Instead of interior angles, deflection angles may be 
 read, a deflection angle being the angle which any course 
 makes with the prolongation of the one preceding. To 
 get this, after the instrument has been turned on the rear 
 point, revolve the telescope on its axis and turn to the point 
 ahead. The deflection must be recorded as right or left,
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 along with the amount of the deflection. Notes may be 
 kept as follows: 
 
 Instr. 
 
 at 
 
 Deflection 
 Angle 
 
 Observed 
 Bearing 
 
 Computed 
 Bearing 
 
 Distance 
 
 
 
 
 N. 81 E. 
 
 K.WE. 
 
 518.63 ft. 
 
 1 
 
 89 l^L. 
 
 N. 8 15' W. 
 
 N. 8 19' W. 
 
 48.19 ft, 
 
 2 
 
 84 8'R. 
 
 N. 75 45' E. 
 
 N. 75 49' E. 
 
 300.53 ft. 
 
 In any case, a sketch kept on the right-hand page of the 
 note book will be an aid to clearness. The whole survey, 
 indeed, may be recorded in that form. 
 
 A Survey or Traverse by Azimuths. Azimuth is the 
 angle which a line forms with the meridian, or with any 
 other line which is selected as a basis. It is similar to bear- 
 ing, but is measured in one direction, commonly from 
 south around through west, north, and east up to 360, and 
 transits are commonly graduated so as to be read directly 
 in this way. The method of work is as follows : 
 
 Set up on the initial point of the survey, set the zeros of 
 the two plates together, clamp them, and turn until the 
 telescope points south, as shown by the needle. Clamp 
 below, loosen above, and point the telescope at the second 
 point of the survey, recording the angular reading, and the 
 bearing for a check upon it. Clamp above and loosen 
 below. Measure the line. 
 
 Set up over the second point, revolve the telescope, and 
 turn on the first point, making sure not to start the upper 
 clamp at any time during the process. Clamp below ; then 
 revolve the telescope into its natural position, loosen above, 
 and turn on the third point of the survey. The azimuth of 
 this line may now be read off the plate and bearing by the 
 needle for a check. Measure the second line. Proceed in 
 this way until the survey is completed. If the survey is a 
 closed one, when the transit is finally set up again at the 
 initial point, the azimuth of the first line should be the 
 same as it was at the beginning.
 
 THE TRANSIT 
 Notes may be kept as follows: 
 
 85 
 
 Line 
 
 Azimuth 
 
 Bearing 
 
 Distance 
 
 A B 
 
 162 12' 30" 
 
 N. 17 45' W. 
 
 6.40 ch. 
 
 B C 
 
 223 30' 
 
 N. 43 30' E. 
 
 7.25 ch. 
 
 C D 
 
 280 25' 
 
 S. 79 30' E. 
 
 4.92 ch. 
 
 D E 
 
 5 43' 30" 
 
 S. 5 45' W. 
 
 6.10 ch. 
 
 Caution. In transit surveying, where angles are read, 
 each line is referred to the one that goes before, and in 
 consequence an error in reading one angle is perpetuated 
 throughout the survey. Further than that, some of the 
 errors arising from lack of adjustment of the instrument 
 are multiplying errors, increasing as the work proceeds, 
 and unless every precaution is taken they may, though 
 individually small, mount up to a very considerable size 
 in the course of a survey. 
 
 With compass surveying, on the other hand, though 
 bearings cannot be read with great exactness and single 
 angles are not so accurately determined as with the transit, 
 yet errors have not the same opportunity to accumulate 
 because each course in the survey is referred anew to the 
 meridian. 
 
 The man who is not in constant practice, therefore, will 
 be likely to find that he attains better results with the 
 needle than by turning angles, and in that case, unless the 
 telescope is wanted for stadia measurements, the compass 
 is the instrument to use. The matter of cost is, in woods 
 conditions, strongly on the side of the compass, for it is 
 usually expensive to cut away for the long, clear sights 
 requisite to the running of a reliable transit line. 
 
 Typical examples of stadia surveys such as the woods- 
 man may have occasion to perform are as follows: 
 
 Stadia Survey of a Pond as carried out on the ice. 
 The needle was relied on in this case, but it will readily be 
 understood that angles might be read instead of bearings 
 and the survey so rendered independent of the magnetic 
 needle. If the survey were to be made in summer, points
 
 86 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 and islands would have to be used for observing stations, 
 and it might be necessary to do a good deal of traversing 
 of the shore. 
 
 Base lines read on fore and 
 
 back sight for check 
 
 Shots to locate shore 
 
 Stadia Survey of Road. 1 foot on rod cut off at dis- 
 tance of one chain. Instrument set up at alternate stations 
 only, except where a check on local attraction of the needle 
 is desired. Vertical angles of less than 5 neglected as hav- 
 ing no material effect on horizontal distance. 
 
 Bear/^g 
 
 Oist 
 
 RemarAs 
 
 o-l 
 
 1-0 
 
 3-2. 
 3-4- 
 S-4- 
 S-6 
 7-6 
 7-8 
 3-8 
 9-JO 
 10-3 
 
 57830 
 
 Z.30 
 2..30 
 6./6 
 
 /JO 
 6.S2 
 S.30 
 6./O 
 
 e.& 
 
 3.SO 
 9. SO 
 
 ZAOch 
 
 tffi,rOH!A 
 ' t>< eaf/e. 
 
 -2' 
 
 6./0" 
 8./S' 
 3.60' 
 9.50" 
 
 Sfa. O 0/7 WsssA///7 offrocf /mf/e. 
 
 J~6. S c/ra/rrs So. on // as S/roiv/r t>y 
 Surrey of 6>ot//fafary 
 These courses a/o/y Sotr/& stye 
 onfo shoulder com/ry fron N 
 
 2.4S on this course t>n*>A crosses 
 
 Test of sreecf/e.
 
 THE LEVEL 87 
 
 5. SUMMARY 
 
 The transit of late years has gained a considerable field 
 of use among working foresters for map making and other 
 purposes. The instrument has for woods work great 
 advantages over the plane table in that it is more portable, 
 is less liable to accident, and is not so easily driven off the 
 field by bad weather. 
 
 The uses for it, present and prospective, are as follows: 
 
 (1) It is the instrument for land surveys when great ac- 
 curacy is required or the needle is seriously disturbed. 
 When it is so employed the stadia wires in some cases 
 afford the most effective means of distance measurement. 
 
 (2) It may be used as a level in dam and road building 
 or for topographic purposes. 
 
 (3) Two men using transit and stadia can traverse roads, 
 streams, or lake shores very rapidly, using the needle and, 
 except for a check on local attraction, setting up the instru- 
 ment on alternate points only. 
 
 (4) Uses (2) and (3) may be combined, allowing a 
 traverse and a profile to be run at the same time by the 
 same party. 
 
 (5) A skeleton of accurately run lines, embracing both 
 horizontal and vertical angles, may be made the basis of 
 topographic surveys, and the method is in fact highly 
 serviceable in some kinds of country. 
 
 (6) With its various capacities again utilized, the 
 transit is sometimes employed to work out the detail 
 of small tracts requiring great accuracy. 
 
 SECTION II 
 THE LEVEL 
 
 The engineer's level consists of a telescopic line of sight 
 joined to a spirit level, the whole properly supported, and 
 revolving on a vertical axis. The outside parts of the frame 
 which support the telescope are called the wyes, and the
 
 88 A MANUAL FOR NORTHERN WOODSMEN 
 
 corresponding bearings on the telescope tube, the pivot 
 rings. The telescope can be lifted out of the wyes by lift- 
 ing up the clips over the rings. The attached bubble 
 enables the line of sight in the telescope to be brought 
 into a horizontal position. 
 
 THE LEVEL 
 
 1. ADJUSTMENTS OF THE LEVEL 
 
 (a.) Make the line of sight coincide with the axis of 
 the pivot rings. Pull out the pins which hold the clips on 
 the telescope and turn the clips back so that the telescope 
 is free to turn in the wyes. Sight the intersection of the 
 cross-hairs at some well-defined point. Then rotate the 
 telescope 180 in the wyes, so that the bubble tube is above 
 the telescope. The intersection of the cross-hairs should 
 still be on the point. If not, move the horizontal cross- 
 hair half-way back to its first position by means of the 
 upper and lower adjusting screws of the cross-hair ring. 
 Then move the vertical cross-hair half-way back to its 
 first position by the other pair of screws. Repeat the test 
 until the adjustment is perfect. 
 
 (b.) Place the line of sight and the bubble in the same 
 vertical plane. Bring the bubble to the center of the tube. 
 Revolve the telescope a few degrees in the wyes and note 
 the action of the bubble. If it runs to one end, bring the 
 tube under the axis of the telescope by means of the lateral
 
 THE LEVEL OV 
 
 adjusting screws. When the two axes are in the same 
 plane, the bubble will remain in the center while the 
 telescope is revolving. 
 
 (c.) Make the level tube parallel to the line of sight. 
 This may be done in two ways. The first or indirect 
 method is as follows : 
 
 Clamp the instrument over a pair of levelling screws ; 
 then bring the bubble to the center of the tube, lift the tele- 
 scope out of the wyes, turn it end for end, and set it down 
 in the wyes again. The eye end now is where the objective 
 was originally. This operation must be performed with 
 the greatest care, as the slightest jar of the instrument will 
 vitiate the result. If the bubble returns to the center of the 
 tube the axis of the tube is in the correct position. If it does 
 not return to the center, the end of the tube provided with 
 the vertical adjustment should be moved until the bubble 
 moves half-way back to the center. This test must be 
 repeated to make sure that the movement is due to defec- 
 tive adjustment and not to the jarring of the instrument. 
 
 For the second, the direct or peg adjustment, select the 
 points A and B, say 200 feet apart. The distance need not 
 be measured. Set up the level close to A so that when the 
 rod is held upon it the eyepiece of the telescope will swing 
 within about half an inch of its face. Bring the bubble to 
 the middle of the tube and looking through the telescope 
 wrong end to, put a pencil mark on the rod at the center 
 of the small field of view. Note the rod reading thus ob- 
 tained. Then turn the telescope toward B and take a rod 
 reading in the usual way, making sure that the bubble is 
 in the middle of the tube. The difference between these 
 two rod readings is the difference in elevation of the two 
 points + or the error of adjustment. Next take the 
 level to B and repeat the above operation. The result here 
 gained is the difference in elevation or + the error 
 of adjustment, and the mean of the two results is the differ- 
 ence of elevation between points A and B. Now, knowing 
 the difference between A and B and the height of the in- 
 strument above B, the rod reading at A which will bring 
 the target on the same level as the instrument may be com- 
 puted. With the horizontal cross-hair on the target, the
 
 90 A MANUAL FOR NORTHERN WOODSMEN 
 
 adjustable end of the level tube is raised or lowered by 
 means of the adjusting screws until the bubble is in the 
 middle. The adjustment should then be correct, but it 
 will be well to test it. 
 
 EXAMPLE 
 Instrument at A 
 
 Rod reading on A = 4.062 
 
 Rod reading on B = 5.129 
 
 Diff. elev. of A and B = 1.067 
 
 Instrument at B 
 
 Rod reading on B = 5.076 
 
 Rod reading on A = 4.127 
 
 Diff. elev. of B and A = 0.949 
 Mean of the two results = 1.067 +0.949 = 1.008, true diff. in elev. 
 
 2 
 
 Instrument is now 5.076 above B. 
 
 Rod reading at A should be 5.076 1.008 = 4.068 to give a level 
 sight. 
 
 This method of adjustment may be used for the transit 
 with this difference that instead of adjusting the level 
 tube to the line of sight, the level tube is first made hori- 
 zontal and then the line of sight is made parallel with it 
 by adjusting the cross-hair. The same is true of a dumpy- 
 level. 
 
 (d.) Make the axis of the level tube perpendicular to 
 the vertical axis of the instrument. 
 
 Bring the two clips down over the telescope and fasten 
 them. Level the instrument, bring the bubble precisely to 
 the middle of the tube over one set of levelling screws, and 
 then turn the telescope 180 about the vertical axis. If 
 the 'bubble moves from the center, bring it half-way back 
 by means of the adjusting screws at the foot of one of the 
 wye supports. 
 
 Since the bubble is brought to the center of the tube each 
 time a rod reading is taken, this last adjustment in no way 
 affects the accuracy of levelling work, but it is a con- 
 venience and a saving of time. 
 
 2. USE OF THE LEVEL 
 
 Levelling is employed to get the difference in elevation 
 between points. With the level set up and the rod held on
 
 THE LEVEL 
 
 91 
 
 a point whose elevation is known or assumed, the reading 
 that is obtained is called a (+) or backsight. Similarly, 
 a reading on a point ahead or unknown is called a ( ) or 
 foresight. A point occupied by the rod in this way, but 
 not recorded or used further, is called a turning-point. 
 When two points have been connected by a series of read- 
 ings of this kind, the sum of the backsights minus the sum 
 of the foresights gives the difference in elevation. If the 
 backsights are greater, the second point is the higher of the 
 two. If the foresights are greater, it is the lower. A brief 
 set of notes is given and worked out illustrating this 
 matter. Work of this kind is called differential levelling. 
 
 B.S. 
 
 F.S. 
 
 Remarks 
 
 9.52' 
 10.12' 
 
 4.45' 
 3.27' 
 
 .B.S. onto B.M. of previous 
 survey. 
 
 8.56' 
 
 1.01' 
 
 
 7.40' 
 
 5.71' 
 
 
 3.65' 
 
 8.62' 
 
 F.S. to pond level required. 
 Pond is above B. M. 
 
 39.25' 
 23.06' 
 
 23.06' 
 
 16.19' 
 
 When levelling is employed to get the elevation of a 
 large number of points in a region, several or many fore- 
 sights may be taken from one position of the instrument. 
 It is customary then to note the height of instrument, and 
 the elevation of any point observed will be that height 
 less the foresight to the point. 
 
 A benchmark is a point whose elevation has been deter- 
 mined and which is marked and left for reference. It is 
 noted B. M. in level notes. 
 
 The following set of notes illustrates those commonly 
 kept in running profiles of a road or railway. The form 
 may be easily modified for any other class of work. 
 
 Summary. Levelling is comparatively simple work. 
 Even though a level is somewhat out of adjustment, accu-
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 rate results may nevertheless be had by taking backward 
 and forward sights of equal length, and this check it is easy 
 
 /^ Profile offbrtftoac/ 
 
 S e/ >f /V/907. {%?%5>o*^\ 
 
 3*7 
 
 ff.S. 
 
 H.I. 
 
 /vS. 
 
 /ev. 
 
 w. 
 
 )&scr//yfr'o/r 
 
 /% 
 
 /z.23 
 
 3438 
 
 
 
 azjs 
 
 
 O 
 
 
 
 38 
 
 2S.2 
 
 
 
 1 
 
 
 
 6.6 
 
 28.4 
 
 
 
 
 
 
 
 3.0 
 
 32.0 
 
 
 
 7-/P, 
 
 
 
 /.43 
 
 
 33.J5 
 
 O/f sfumjo 
 
 // 
 
 //./# 
 
 44.73 
 
 
 
 
 
 3 
 
 
 
 6./ 
 
 38.6 
 
 
 
 +66' 
 
 
 
 2.7 
 
 42.0 
 
 
 
 4 
 
 
 
 3.7 
 
 410 
 
 
 
 S 
 
 
 
 S.2 
 
 39.S 
 
 
 
 6 
 
 
 
 //a 
 
 33.S 
 
 
 
 TP Z 
 
 
 
 J.62 
 
 
 39.// 
 
 Boulder 
 
 " 
 
 3.48 
 
 4e.J9 
 
 
 
 
 
 7 
 
 
 
 /02 
 
 32.4 
 
 
 
 \^ 
 
 
 
 
 
 
 j 
 
 to secure by pacing. It is important that the rod should 
 be held plumb during the levelling operation. This position 
 is secured by careful attention on the part of the rodman 
 and by waving the rod slightly. The length of sight varies 
 with the instrument, the condition of the air, and the ac- 
 curacy desired. About 300 feet is stated to be in general 
 the best length on the score of accuracy, but speed will 
 often require that much longer shots be taken. In accu- 
 rate work, it should be remembered that error may be 
 introduced by the slightest causes, such as disturbance of 
 the tripod. 
 
 Levelling is employed by woodsmen in constructing 
 dams and ascertaining the area of flowage, in laying out 
 roads and railroads, and for the basis of topographic work.
 
 COMBINED HAND LEVEL AND CLINOMETER 93 
 
 For these uses a light and cheap form of the level, some- 
 times called the architect's level, costing about half as 
 much as one adapted to railway work, is commonly 
 sufficient. 
 
 SECTION III 
 COMBINED HAND LEVEL AND CLINOMETER 
 
 A pocket instrument capable of a great variety of uses 
 is shown in the accompanying figure. The eye is placed 
 at a peep hole at the right end (a) of the main tube. 
 The cross-wire is over (6) in the figure, and beside it, 
 occupying half the orifice of the tube, is a mirror set at 
 
 an angle of 45. Directly over the wire and mirror is a 
 spirit tube (c), shown inclined in the figure. It is fixed to 
 the milled wheel (d) which turns it, and the graduated 
 arm (e), which serves to set the bubble parallel to the 
 line of sight of the instrument, or to read the angle of 
 inclination between them. When the bubble is in the 
 center of the tube, the mirror below reflects it side by 
 side with the cross-wire back through the peep hole. 
 
 This instrument is largely used by northwestern lum- 
 bermen in laying out roads, locating dams, etc., and it 
 ought to be in the outfit of every woodsman. To use it 
 as a hand level the zeros of the graduated arm and the 
 scale must first be set together. The observer then sights 
 an object through the tube, which he brings to a level 
 by the bubble reflected in the mirror. He may then place 
 himself on a level with the object by sighting at it directly,
 
 94 A MANUAL FOR NORTHERN WOODSMEN 
 
 or, if difference in elevation is required, a pole or level rod 
 may be used to measure the amount. 
 
 The instrument may be used to find the difference in 
 elevation between any two points without the use of a 
 level rod. To 'do this the observer begins at the lower 
 point, and, after levelling the instrument, sights in the 
 desired direction and notes the point on the ground ahead 
 intersected by the cross-wire. He then advances to that 
 point and repeats the operation, and so moves on up the 
 grade until the upper point is reached. As between every 
 two observations he has advanced to a height equal to the 
 distance from the ground to his eye, the height of the hill 
 will be the product of that distance by the number of 
 sights taken. 
 
 The instrument may also be used as a clinometer to 
 measure slope. To do this the observer sights along the 
 slope parallel to the ground, and then uses the hand wheel 
 to turn the level tube until the bubble shows it is level. 
 The measuring arm, turning with the wheel and the level, 
 sweeps the scale and indicates the slope in degrees, or in 
 per cents, according as the instrument is graduated. 
 
 In the same way, and with the aid of a table of tangents, 
 one may use the instrument to obtain the height of a tree 
 or a hill. This process is explained and illustrated on 
 page 166. 
 
 For an improved form and more complicated use of 
 the instrument, see pages 130-131. 
 
 SECTION IV 
 COMPASS AND PACING 
 
 The staff compass, with folding sights, cross levels, and 
 a needle from 2| to 4 inches long, is familiar to most 
 woodsmen. It is a very compact and practical instrument, 
 has long been employed for retracing lines, and of late 
 years, as forest lands have come to be handled more 
 systematically, has attained a great extent and variety of 
 uses. It has also been constructed in a variety of forms, 
 combined with other instruments in some cases. The form
 
 COMPASS AND PACING 95 
 
 shown in illustration is the pattern of the U. S. Forest 
 Service. The base is flat so that the instrument may be 
 used to orient a plane table it is square also and gradu- 
 ated on its edges with a protractor and two scales for draft- 
 ing purposes; declination can be set off by means of a 
 vernier; inside the box a pendulum is fitted and the staff 
 mountings permit of turning the instrument and holding 
 it edgewise while employed as a level or clinometer. 
 
 STAFF COMPASS 
 
 A main use for the staff compass in topographical and 
 timber work is for making foot traverses, a purpose for 
 which it is thoroughly adapted. The common pocket 
 compass with needle If to 2 inches long, indeed, may be 
 used for the same purpose, and when it .enables a man to 
 travel a mile with only 1 or 2 of angular swing, as it 
 will do if carefully used, it deserves to be called a surveying 
 instrument. 
 
 Pacing. The pace has been long used as a check on 
 short distances, but the real capacity of pacing as a method 
 of measurement has only recently been developed. It 
 is of special value to woodsmen who must travel their 
 country over in any case, and who by a little extra pains 
 taken in this direction can bring out much valuable infor-
 
 96 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 mation. As against chaining, pacing has the advantage 
 of cheapness, it can be done by one man alone, and its 
 accuracy is frequently quite sufficient. 
 
 The natural gait of the woodsman should be tested on 
 measured lines and in pacing for distance he should always 
 walk at his natural gait, not try to take a three-foot stride. 
 The slope of the ground, if it is considerable, affects the 
 length of step ; the step is shortened whether one goes up 
 or down hill. 
 
 This matter has been investigated accurately and the 
 results of one extensive test are given in the table below, 
 
 INFLUENCE OF SLOPE ON LENGTH OF PACE AS TESTED 
 Otf MOUNTAIN TRAILS 
 
 Slope 
 
 Length of step ascending 
 
 Length of step descending 
 
 
 
 2.53 
 
 2.53 
 
 5 
 
 2.30 
 
 2.43 
 
 10 
 
 2.03 
 
 2.36 
 
 15 
 
 1.84 
 
 2.30 
 
 20 
 
 1.64 
 
 2.20 
 
 25 
 
 1.48 
 
 1.97 
 
 30 
 
 1.25 
 
 1.64 
 
 but for practical work it is better for each man to train 
 himself on measured distances and learn to discount on 
 slopes by experience and the sense that he develops. Sim- 
 ilarly, rough bottom and bushes have an effect on the pace. 
 This is best dealt with in the same way. 
 
 Harder perhaps to allow for, are the errors arising from 
 a man's own condition. A man steps shorter when trav- 
 elling slowly than when going at a good rate; he steps 
 shorter when tired unless he forces himself to the work; 
 he is not sure of himself in the morning or after a longer 
 rest until he gets " into his gait " ; he has his " off times " 
 when nothing seems to go right. Keeping the count also 
 is a source of frequent error. Woods travel is too uneven
 
 COMPASS AND PACING 97 
 
 as a rule to allow a pedometer to be employed. Some 
 men register double paces. Others count up to a hundred 
 in the head and take down the hundreds on a "clicker," 
 in a note book, or by breaking an elbow in a tough twig 
 carried in the teeth or hand. 
 
 Accuracy. With all its limitations, pacing is a very ser- 
 viceable means of measurement and a man who has duly 
 trained himself can get very good results. Johnson's 
 " Surveying " says, that when a man's gait has been stand- 
 ardized and on the work he walks at a constant rate, " dis- 
 tances can be determined by pedometer or by counting the 
 paces to within 2 per cent of the truth." That refers, 
 without doubt, to open land. In woods work too there 
 
 Section Lines 
 
 Compass Bearings 
 
 Pacing Traverses . 
 
 POND SURVEYED FROM SECTION LINES BY CROSS BEARINGS AND THE 
 COMPASS AND PACING METHOD 
 
 are many men who can be depended on for results as clbse 
 as that, but errors up to 5 per cent in a straight mile on 
 uneven land is for the writer the usual standard of work. 
 This is not serious. When the error is distributed over the 
 mile by plotting, the utmost probable error in the location 
 of any point is not over 25 yards. 
 
 Uses of the Method. (1) The staff compass is largely 
 used in retracing old lines. Pacing may well be employed 
 with it as a means of finding blind marks and corners, for 
 this purpose replacing the chain.
 
 98 A MANUAL FOR NORTHERN WOODSMEN 
 
 (2) In timber estimating, the area of waste lands, heavy 
 bodies of timber, etc., can often be obtained quickly and 
 with a fair degree of accuracy by this method, and these 
 facts often furnish very great help in securing a close 
 estimate. 
 
 (3) The compass and pacing method is the cheapest for 
 mapping roads, streams, ponds, and other topographic 
 details in wooded country. For a real map, however, 
 this method of survey should not cover too long distances, 
 but should tie into more accurate work. 
 
 (4) Compass and pacing may be used to get a recon- 
 noissance map of a region of any size, using a road or any 
 other avenue of travel that passes through it. Not only 
 the line of travel may be mapped, but the hills and other 
 features of the country that can be seen. Cross bearings 
 with the compass will locate them in the horizontal posi- 
 tion, and the clinometer will serve to get their height. 
 
 Specimen notes illustrating this method of work com- 
 bined with the use of the aneroid barometer for determin- 
 ing height, and a diagram showing how it is made to 
 contribute to the production of a topographic map will 
 be found on pages 130-132. 
 
 SECTION V 
 THE TRAVERSE BOARD 
 
 The plane table in its simplest form is called a traverse 
 board, and consists of a square board without levels 
 mounted on a tripod. On this board a sheet of paper 
 is pinned, and the map is developed in the field. A 
 compass needle set into the edge of the board serves to 
 " orient " it, or, in other words, to fix one edge always in 
 the north and south position. A brass ruler with vertical 
 sights attached serves both to sight with and to draw lines 
 and scale off distances on the map. It is called an 
 alidade. 
 
 A simple use for the board is to traverse a road, a 
 stream, or the shore of a pond. Suppose, for instance, it is 
 desired to survey a stream on the ice in winter, and a point
 
 THE TRAVERSE BOARD 
 
 99 
 
 on it is known by the crossing of a section line. The 
 instrument should be set up at the known point, with one 
 edge of the board set north and south as shown by the 
 needle. A point is then chosen on the sheet to represent 
 the one occupied on the ground, the edge of the ruler is 
 swung about it until the sights range- toward the second 
 point to be occupied, say the next turn of the stream, and 
 
 TRAVERSE BOARD 
 
 a line is drawn in its direction. The distance between the 
 two points is then chained or paced, and when this has 
 been scaled off a second point on the map is obtained. 
 The board must then be set up at the new point and 
 oriented as before, when, the ruler being swung about the 
 new point, a ray may be drawn from it to a third, and 
 so on. Little difficulty will be experienced by one who 
 understands compass surveying in working this instru- 
 ment. A point on the sheet always represents the point 
 occupied, and that is always the point to work from. 
 The map is carried to completion right in the field and 
 that, as regards both cost and accuracy, constitutes the 
 advantage of the method.
 
 100 A MANUAL FOR NORTHERN WOODSMEN 
 
 Another method of working is by intersections. For 
 this, it is necessary to have two known points or a measured 
 base. The instrument is set up at one of the known 
 points, and, the alidade being pointed at the other, a line 
 
 Plane Table Map 
 
 ROUND LAKE 
 
 Washington Co. 
 
 Maine 
 C. A. Gary 1907 
 
 Area 343 Acres 
 . Scale of Feet 
 
 1500 2000 2500 
 
 is drawn and the known distance scaled off upon it. 
 Then, from that end of the base line representing the 
 point occupied, rays are drawn in the direction of other 
 well-defined objects on the shore which it will be desir- 
 able to locate. Flags may be used to define them, but 
 natural objects will often suffice. The instrument is then
 
 THE TRAVERSE BOARD 
 
 101 
 
 taken to the other known point, and set up by the range 
 back to the first. Then swinging the ruler about the 
 second point located on the sheet, the surveyor draws 
 rays from this to the same objects as before. The in- 
 tersection of pairs of rays directed toward the same object 
 in the field fixes that point upon the map. This is done 
 directly and graphically, no computation or reduction 
 being required. 
 
 More complicated forms of the instrument, telescopic 
 alidades, the application of the vertical angle, etc., need 
 not be here discussed, as they are hardly likely to be em- 
 ployed by other than specialists. It seems likely, how- 
 ever, that among a large class of foresters and woodsmen 
 this simple form of the plane table will find general use. 
 
 The following survey of a small lake made with the 
 traverse board involves a somewhat . more complicated 
 use of the instrument than that described above. This 
 particular piece of work took the time of two men for two 
 days, but on the ice it could have been done more quickly. 
 The steps in making, the survey were as follows : 
 
 1. Base line A B measured, the longest straight line 
 that could be had on the shore and in wading depth of 
 water. Flags set up at its ends and at C, D, E, F, and G, 
 prominent points on the shore visible from both ends of 
 the base line. 
 
 2. Plane table set up at A as oriented by the needle. 
 Point a selected on the paper, line drawn from it in direc- 
 tion of B and a b measured to scale. Rays a c, a d, a e, a f, 
 a g drawn in direction of C, D, E, F, and G. 
 
 Board at A Board at B 
 
 3. Table set up at B, oriented by ranging b a at A and 
 checked by the needle. Rays drawn from b toward C and
 
 102 A MANUAL FOR NORTHERN WOODSMEN 
 
 D. These where they intersect corresponding rays from 
 a fix points c and d. Rays also drawn toward E, F, and 
 G, but the angles made with the corresponding rays from a 
 are so small that these points are not given a good location. 
 4. Board taken to C and oriented by A and B. Check 
 ray drawn to d. Rays toward E, F, and G, intersecting 
 similar rays from a, fix e, /, and g. 
 
 Board at C 
 
 Board at D 
 
 5. Board taken to D and similar process performed for 
 a check. E, F, and G may also be checked with one 
 another. 
 
 6. Fix other points on the shore such as prominent 
 rocks or trees. 
 
 (a) By intersecting rays from any two of the primary 
 points in the same manner as these were fixed. 
 
 (6) By drawing a ray from one of the primary points as 
 c toward any object as X, setting up at X, using c x to 
 orient by, and then fixing a; by a ray brought back in the 
 range A a until it cuts c x. 
 
 Board at X 
 
 Board at Y 
 
 (c) By setting up the board on any desired point on the 
 shore as Y, oriented by the needle, and ranging back from
 
 THE ANEROID BAROMETER 
 
 103 
 
 any two flags or fixed points, through the corresponding 
 points on paper, to an intersection which will fix the 
 point occupied. 
 
 7. Fill in the shore line as the other work progresses, 
 whatever at the time is nearest the instrument, by traverses, 
 sketching, etc. 
 
 SECTION VI 
 THE ANEROID BAROMETER 
 
 The aneroid barometer is a cheap and handy instrument 
 which, when carried from one point to another, will tell 
 approximately their difference in height. This it does by 
 measuring the pressure of the air, varying as that does 
 when one goes up or 
 down hill. . 
 
 The essential parts 
 of an aneroid bar- 
 ometer are out of 
 sight. The instru- 
 ment consists of a 
 vacuum box with one 
 very flexible and sen- 
 sitive side, which 
 works in and out 
 with varying pres- 
 sure of the air. This 
 slight movement is 
 multiplied, and con- 
 verted into the cir- 
 cular motion of the 
 pointing hand seen 
 on the face of the 
 instrument. At sea 
 level the hand points 
 to one part of the ANEROID BAROMETER 
 
 dial. As the instru- 
 ment is carried up a hill or mountain the hand, worked by 
 expansion of the box within, turns round to the left. The
 
 104 A MANUAL FOR NORTHERN WOODSMEN 
 
 face is graduated to correspond with the height of column of 
 a mercurial barometer, 30, 29, 28, etc., inches, these even 
 inches being divided into fractional parts. 
 
 This change in pressure corresponds with definite change 
 in altitude. One inch on the scale means roughly 900 feet 
 in altitude; a half inch means 450 feet, and so on. As 
 a matter of fact, there is a foot scale on most aneroids 
 outside the inch scale, movable and graduated from zero 
 up to the capacity of the instrument. Thus, if one knows 
 how high he is above sea level, he may turn the foot scale 
 of his instrument until the registering hand points to that 
 height, and, going either up or down hill, read directly the 
 elevation of any station which he may occupy. 
 
 Just this process answers many purposes, but when best 
 results are sought for, the operation is not quite so simple. 
 First, there is the Correction fer the Temperature of the 
 Air. An inch difference in pressure at a tejnperature of 
 32, for instance, converted into height, means one thing; 
 at 70 it means a good deal more. In order to get accu- 
 rate results, therefore, on considerable elevations, it is 
 necessary to read the inner or inch scale of the instrument, 
 take the temperature of the air at the two points, and 
 obtain the elevation from tables. Such tables will be 
 found on pages 111 and 112 and full directions for their 
 use accompany them. 
 
 Correction for Weather Change. The other liability to 
 error arises from the fact that the air pressure is frequently 
 changing with the weather. This does not hamper work 
 seriously in the western country where the weather and 
 pressure remain steady for long periods at a time, but diffi- 
 culty does arise from this source throughout the East. 
 With an approaching storm the air grows lighter, and the 
 reverse in clearing weather. This effect is best seen on a 
 stationary barometer, but it has a like effect on one that 
 is in motion. Thus, if an explorer starts at a lake of known 
 elevation and takes two hours in going to the top of a hill, 
 the air pressure meanwhile may have changed so as to 
 throw his height readings off materially. 
 
 There are three ways of obviating this, outside the evi- 
 dent one of working only in steady weather. One is to
 
 THE ANEROID BAROMETER 
 
 105 
 
 return to the lake and take a second reading, using the 
 average of the two to compare with that observed at the 
 summit. A second, often available in cruising timber, is 
 to read on the same point two or more times during the 
 day and so ascertain the course of the barometer. The 
 third method of correction is by means of another instru- 
 ment which is left at the base station or some other 
 convenient point, and read by another person every hour 
 or half hour while the observer is in the field. Since in 
 ordinary weather the air changes are the same over large 
 areas, this arrangement tells what the field barometer 
 would have read on the base station at any hour during 
 the day. Better than this, however, is a self-recording 
 barometer, or barograph, which makes a continuous record 
 of pressure. The explorer compares his pocket instru- 
 
 AROGRAPH 
 
 ment with this as he starts out on his work, and again 
 when he comes in. If these comparisons are satisfactory, 
 he has the means of telling what his field instrument would 
 have read on the base station at any time while he was 
 gone, and so obtains the correct figure for comparison 
 with any given field observation. This arrangement en- 
 ables him to stay away from known elevations half a day
 
 106 A MANUAL FOR NORTHERN WOODSMEN 
 
 or a day at a time and still make fairly satisfactory height 
 determinations. 
 
 This is all good in theory, but it must be said that in 
 practice it does not always work out to one's entire sat- 
 isfaction. The air, in the first place, is not the homoge- 
 neous fluid that it has been considered, but varies more or 
 less from point to point. Then aneroids are not sure in 
 their workings. Different instruments of the same make 
 and cost vary greatly in reliability, and the observer needs 
 to watch the best of them to see that they do not get out 
 of order or play some kind of a trick. Barographs, again, 
 are not thoroughly reliable. In particular, some of them 
 do not follow the changes in pressure as fast as the port- 
 able instrument. Nevertheless, trial has shown that by 
 the methods outlined sufficiently accurate results for many 
 purposes can be obtained. In general it may be said of 
 aneroid work that, while it cannot be counted on for re- 
 fined accuracy, there is a large field open to it of good, 
 useful work which no other instrument, on account of con- 
 siderations of cost, can do. It is particularly serviceable in 
 a timbered country where it is difficult to see from point to 
 point, having there the same sort of advantage that the 
 compass possesses in the same field. 
 
 Aneroids for ordinary work should be 2$ to 3 inches in 
 diameter, graduated to the equivalent of 20 feet, and have 
 as open a scale as may be. Such instruments cost from 
 $20 to $35. For the finer class of work it may be advisable 
 to employ a larger and more delicate instrument furnished 
 with a vernier. A barograph costs from $40 to $50. Ther- 
 mometers suitable for the work, in a nickel or rubber case 
 about the size of a lead pencil, can be had for $.50 to $1 
 each. 
 
 The following Working Rules have grown out of the 
 experience of the writer and others : 
 
 1. Each instrument should be tested not only under 
 the air pump but for general behavior in the field. 
 
 2. The best place to carry an aneroid while at woods 
 work is in a leather case hung on the belt. The case serves 
 to protect it trom damage, also from extreme heat and 
 rapid changes of tempera turfc.
 
 THE ANEROID BAROMETER 107 
 
 3. Any considerable blow is likely to throw the instru- 
 ment out of order for the time being, if not permanently. 
 Two instruments carried are a considerable insurance. 
 
 4. The aneroid should always be held in the same posi- 
 tion when read, and be given a little time to adjust itself. 
 By gentle tapping on the face the observer should assure 
 himself that its various parts are all free and in working 
 order. 
 
 5. In starting out for work it is well to carry the instru- 
 ment a while, so as to get it into its regular field working 
 order, before reading on the base station. 
 
 6. One should check on points of known elevation as 
 often as possible, and, if there is a choice of readings to 
 refer to, he should depend on that which is nearer, time 
 and elevation both considered. 
 
 7. A general caution may be needed that the proper 
 use of the instrument is to obtain relative elevation of 
 points by means of readings on the two. One must not 
 expect by one reading to obtain his height above sea 
 level. 
 
 REDUCTION OF ANEROID READINGS BY USE OF THE 
 TABLES AND WITH CORRECTION FOR TEMPERATURE 
 AND WEATHER CHANGES 
 
 (See tables on pages 111 and 112) 
 
 PROBLEM I. Given barometric readings on two stations 
 and temperature at each, to find the difference in elevation 
 of the two points. 
 
 Rule. Enter the first column of Table I with the read- 
 ings of the barometer on the two stations, and take out the 
 corresponding numbers from column 2 (column 3 is for 
 help in interpolating). Take the difference between these 
 two figures. Call this result for the present a. 
 
 Add the two temperatures together (or if the tempera- 
 tures of the two stations do not differ materially, multiply 
 that of the region by two). With this enter Table II, that 
 for temperature correction, and find in dolumn 1 the near- 
 est number of degrees given. Take out of column 2 the 
 number corresponding, noting the + or sign, and
 
 108 A MANUAL FOR NORTHERN WOODSMEN 
 
 multiply a above by this percentage. Let us call this b. 
 If b has a plus sign, add it to a; if a minus sign, subtract 
 from a. The result will be the desired elevation. 
 
 Example. The barometric reading on a lake of known 
 elevation is 29.500 inches, and the temperature there 72 F. 
 Shortly after, the reading on a hill not far away is found to 
 be 28.760 and the temperature 63. How high is the 
 hilltop above the lake ? 
 
 From Table I we have 
 
 Barometric elevation of hill 1150 feet 
 Barometric elevation of lake 458 feet 
 
 Difference (a above) 692 feet 
 
 From Table II we have for t + t' = 135, C = + .042. 
 6 therefore = 692 X .042, is = 29 feet. This must be 
 added to a, since the sign of the factor is +, and the 
 result (692 +29= 721) gives 721 feet as the required 
 answer. 
 
 A short cut to the same result, which is accurate enough 
 and which will save much labor in reducing a number of 
 readings referred to the same base station, is as follows: 
 Between 29.500 and 28.760 inches the difference of eleva- 
 tion corresponding to .1 inch pressure is 94 feet. This 
 is obtained instantly by inspection of column 3 of Table 
 I. Stated another way, the difference of elevation in feet 
 is 6 per cent less than the difference between barometric 
 readings expressed in thousandths of an inch. But the 
 temperature correction for the conditions is + 4 per cent, 
 leaving a net loss of 2 per cent on the difference in the 
 barometric readings. 
 
 Now 29.500- 28.760= .740, and 740- 2 per cent = 
 725. Answer, 725 feet. 
 
 PROBLEM II. To correct for changes of pressure due 
 to the weather, as shown by regular readings on a station 
 barometer or the record of a barograph. 
 
 The barograph sheet reproduced herewith shows for 
 the working hours of that Friday a steady fall of pressure. 
 At 6.30 in the morning when the party left camp the 
 indicated pressure was 29.250 inches. When they got in
 
 THE ANEROID BAROMETER 
 
 109 
 
 at 5 P. M. it was 29.160. That difference in pressure 
 corresponds to nearly 150 feet in elevation, and height 
 observations made during the day would be uncertain to 
 very wide limits if the change could not be allowed for. 
 
 THURSDA Y FRIDA Y 
 
 8 1,0 y T 2 4 6 8 10 XII 2468 10/jf T 2 468 10 XII 2 4 6 8 1.0O T 2 
 7/7 ////////// / / ////////////// 
 
 
 
 \\\\\\\\ 
 
 The possibility of correction rests in two suppositions: 
 (1) that at any moment of time the air pressure is constant 
 over a considerable horizontal area, and (2) that the field 
 barometer and the station barometer work together, and 
 that they both follow exactly and quickly the change of air 
 pressure. The latter point may be expressed in this way 
 that the field barometer, if left at the base station, would 
 have followed the same course as did the instrument which 
 in fact was left there. 
 
 The field barometer may not read the same as the 
 barograph when they are brought together, but that 
 " index error," as it is called, does not matter if the differ- 
 ence between the two remains constant. In this case the 
 field barometer at camp in the morning read 29.350 and at 
 night 29.200, .1 inch higher than the barograph. One 
 may, therefore, when he gets to computing, draw on the
 
 110 ' A MANUAL FOR NORTHERN WOODSMEN 
 
 barograph sheet a curve through these two new points 
 and parallel to the one made by the barograph pen. 
 From this curve he may take off the reading for any hour 
 in the day to compare with a field reading taken at the 
 same time. Such a supplementing curve is shown on the 
 sheet illustrated. 
 
 Example. At 11 A. M. on the day in question at a 
 point two miles away from camp the field barometer 
 read 29.270. What was the elevation relative to the base 
 station ? 
 
 The field reading can not be compared with the morning 
 reading at camp because the barometric pressure is known 
 to have been changing. Neither can it be compared with 
 the night reading, for the same reason. The short curve 
 on the sheet, however, does tell what the field instrument 
 would presumably have read at camp at any hour in the 
 day. The curve at 11 A. M. is at 29.270, and the two points, 
 therefore, are of equal elevation. 
 
 In view of the low accuracy of aneroid work, different 
 users of the instrument have devised schemes for shorten- 
 ing or obviating the labor of computation. One that is 
 serviceable where temperature at different seasons shows 
 wide variation is as follows: 
 
 On the foot scale of most instruments 1000 feet at the 
 higher elevations will be found to occupy a smaller sector 
 on the scale than 1000 feet at low elevations as 5000- 
 6000 as against 0-1000. This can be tested by comparing 
 against identical marks on the inner scale. 
 
 Now, being at a known or assumed elevation, set the 
 corresponding graduation against the movable hand and 
 observe where the thousand-foot marks above and below 
 cut the inner or inch scale; next, take the values so ob- 
 tained and compute difference of elevation accurately, 
 correcting for temperature. If the result obtained varies 
 seriously from 1000 feet, shift the foot scale by even 
 thousands until a portion is found so graduated that it 
 does correspond. With a constant correction of even 
 thousands, elevations may now be had directly. Correc- 
 tion is not thus made for weather changes, however.
 
 THE ANEROID BAROMETER 
 
 111 
 
 TABLES FOR REDUCING READINGS OF THE ANEROID 
 BAROMETER 1 
 
 I Barometric Elevation 
 
 Reading 
 Inches 
 
 Elevation 
 Feet 
 
 Difference 
 for .01 inch 
 Feet 
 
 Reading 
 Inches 
 
 Elevation 
 Feet 
 
 Difference 
 for .01 inch 
 Feet 
 
 20.0 
 20.1 
 
 11047 
 10911 
 
 -13.6 
 
 23.4 
 23.5 
 
 6770 
 6654 
 
 11.7 
 11.6 
 
 20.2 
 20.3 
 
 10776 
 10642 
 
 13.5 
 13.4 
 
 23.6 
 23.7 
 
 6538 
 6423 
 
 -11.6 
 11.5 
 
 20.4 
 
 10508 
 
 13.4 
 
 23.8 
 
 6308 
 
 11.5 
 
 20.5 
 
 10375 
 
 13.3 
 
 23.9 
 
 6194 
 
 11.4 
 
 20.6 
 20.7 
 
 10242 
 10110 
 
 13.3 
 -13.2 
 
 24.0 
 24.1 
 
 6080 
 5967 
 
 11.4 
 11.3 
 
 20.8 
 20.9 
 
 9979 
 9848 
 
 13.1 
 -13.1 
 
 24.2 
 24.3 
 
 5854 
 5741 
 
 11.3 
 -11.3 
 
 21.0 
 
 9718 
 
 -13.0 
 
 24.4 
 
 5629 
 
 11.2 
 
 21.1 
 
 9589 
 
 -12.9 
 
 24.5 
 
 5518 
 
 11.1 
 
 21.2 
 
 9460 
 
 12.9 
 
 24.6 
 
 5407 
 
 11.1 
 
 21.3 
 
 9332 
 
 12.8 
 
 24.7 
 
 5296 
 
 -11.1 
 
 21.4 
 
 9204 
 
 -12.8 
 
 24.8 
 
 5186 
 
 11.0 
 
 21.5 
 21.6 
 
 9077 
 8951 
 
 12.7 
 -12.6 
 
 24.9 
 25.0 
 
 5077 
 4968 
 
 10.9 
 10.9 
 
 21.7 
 
 8825 
 
 12.6 
 
 25.1 
 
 4859 
 
 10.9 
 
 21.8 
 
 8700 
 
 12.5 
 
 25.2 
 
 4751 
 
 10.8 
 
 21.9 
 
 8575 
 
 -12.5 
 
 25.3 
 
 4643 
 
 10.8 
 
 22.0 
 
 8451 
 
 12.4 
 
 25.4 
 
 4535 
 
 10.7 
 
 22.1 
 22.2 
 
 8327 
 8204 
 
 12.4 
 -12.3 
 
 25.5 
 25.6 
 
 4428 
 4321 
 
 10.7 
 10.6 
 
 22.3 
 
 8082 
 
 -12.2 
 
 25.7 
 
 4215 
 
 10.6 
 
 22.4 
 
 7960 
 
 12.2 
 
 25.8 
 
 4109 
 
 -10.5 
 
 22.5 
 22.6 
 
 7838 
 7717 
 
 12.2 
 12.1 
 
 25.9 
 26.0 
 
 4004 
 3899 
 
 10.5 
 10.5 
 
 22.7 
 22.8 
 
 7597 
 7477 
 
 12.0 
 12.0 
 
 26.1 
 26.2 
 
 3794 
 3690 
 
 10.4 
 10.4 
 
 22.9 
 23.0 
 23.1 
 
 7358 
 7239 
 7121 
 
 11.9 
 11.9 
 -11.8 
 
 26.3 
 26.4 
 26.5 
 
 3586 
 3483 
 3380 
 
 10.3 
 10.3 
 -10.3 
 
 23.2 
 23.3 
 
 7004 
 
 6887 
 
 11.7 
 11.7 
 
 26.6 
 26.7 
 
 3277 
 3175 
 
 10.2 
 10.2 
 
 t Taken from Johnson's "Surveying " and Report of U. S. Coast and 
 Geodetic Survey for 1881.
 
 A MANtTAL FOR NORTHERN WOODSMEN 
 
 I Barometer Elevation continued. 
 
 Reading 
 Inches 
 
 Elevation 
 Feet 
 
 Difference 
 for .01 inch 
 Feet 
 
 Reading 
 Inches 
 
 Elevation 
 Feet 
 
 Difference 
 for .01 inch 
 Feet 
 
 26.8 
 
 3073 
 
 -10.1 
 
 28.7 
 
 1207 
 
 -9.5 
 
 26.9 
 
 2972 
 
 10.1 
 
 28.8 
 
 1112 
 
 9.4 
 
 27.0 
 
 2871 
 
 10.1 
 
 28.9 
 
 1018 
 
 9.4 
 
 27.1 
 
 2770 
 
 10.0 
 
 29.0 
 
 924 
 
 9.4 
 
 27.2 
 
 2670 
 
 10.0 
 
 29.1 
 
 830 
 
 9.4 
 
 27.3 
 
 2570 
 
 10.0 
 
 29.2 
 
 736 
 
 9.3 
 
 27.4 
 
 2470 
 
 -9.9 
 
 29.3 
 
 643 
 
 9.3 
 
 27.5 
 
 2371 
 
 9.9 
 
 29.4 
 
 550 
 
 -9.2 
 
 27.6 
 
 2272 
 
 9.9 
 
 29.5 
 
 458 
 
 9.2 
 
 27.7 
 
 2173 
 
 9.8 
 
 29.6 
 
 366 
 
 9.2 
 
 27.8 
 
 2075 
 
 9.8 
 
 29.7 
 
 274 
 
 9.2 
 
 27.9 
 
 1977 
 
 9.7 
 
 29.8 
 
 182 
 
 9.1 
 
 28.0 
 
 1880 
 
 9.7 
 
 29.9 
 
 91 
 
 9.1 
 
 28.1 
 
 1783 
 
 9.7 
 
 30.0 
 
 00 
 
 9.1 
 
 28.2 
 
 1686 
 
 9.7 
 
 30.1 
 
 -91 
 
 9.0 
 
 28.3 
 
 1589 
 
 9.6 
 
 30.2 
 
 181 
 
 9.0 
 
 28.4 
 
 1493 
 
 9.6 
 
 30.3 
 
 271 
 
 9.0 
 
 28.5 
 
 1397 
 
 -9.5 
 
 30.4 
 
 361 
 
 9.0 
 
 28.6 
 
 1302 
 
 9.5 
 
 30.5 
 
 451 
 
 9.0 
 
 II Correction for Temperature in Degrees Fahrenheit 
 
 t + t' 
 
 C. 
 
 t+t' 
 
 C. 
 
 t+t' 
 
 C. 
 
 
 
 0.1025 
 
 60 
 
 0.0380 
 
 120 
 
 +0.0262 
 
 5 3 
 
 -0.0970 
 
 65 
 
 0.0326 
 
 125 
 
 +0.0315 
 
 10 
 
 0.0915 
 
 70 
 
 -0.0273 
 
 130 
 
 +0.0368 
 
 15 
 
 0.0860 
 
 75 
 
 -0.0220 
 
 135 
 
 + 0.0420 
 
 20 
 
 0.0806 
 
 80 
 
 0.0166 
 
 140 
 
 +0.0472 
 
 25 
 
 0.0752 
 
 85 
 
 0.0112 
 
 145 
 
 + 0.0524 
 
 30 
 
 0.0698 
 
 90 
 
 0.0058 
 
 150 
 
 + 0.0575 
 
 35 
 
 0.0645 
 
 95 
 
 0.0004 
 
 155 
 
 +0.0626 
 
 40 
 
 0.0592 
 
 100 
 
 + 0.0049 
 
 160 
 
 + 0.0677 
 
 45 
 
 0.0539 
 
 105 
 
 +0.0102 
 
 165 
 
 + 0.0728 
 
 50 
 
 0.0486 
 
 110 
 
 +0.0156 
 
 170 
 
 + 0.0779 
 
 55 
 
 0.0433 
 
 115 
 
 +0.0209 
 
 175 
 
 + 0.0829 
 
 60 
 
 -0.0380 
 
 120 
 
 + 0.0262 
 
 180 
 
 + 0.0879
 
 METHODS OF MAP MAKING 113 
 
 SECTION VII 
 METHODS OF MAP MAKING 
 
 1 . INTRODUCTORY 
 
 There is a well defined call at the present time for good 
 maps of small forest areas maps which show topo- 
 graphic features and record essential facts about timber 
 stand. With the consolidation of large forest properties 
 and their more careful and foresighted management, the 
 need is felt for good maps of these as well, and it is certain 
 that this demand will increase. 
 
 The maps of the past are of all grades of accuracy and 
 utility. A checkerboard of lot lines, with the waters 
 roughly laid down, and estimates of the stand of timber, is 
 the utmost that many lumber companies can command. 
 Some improve this by hatching to represent mountains and 
 divides, and by going more carefully into water lines and 
 areas. 
 
 Hatched Maps. The accompanying map represents part 
 of a township owned by a Maine lumber company, and is a 
 good example of a class of maps now having wide use. For 
 the purposes of the map and of administration, the township 
 was divided into sections, and as the lines were run, chain- 
 age was taken at the crossings of streams and main divides. 
 In addition, some cruising was done within the lots, 
 chiefly to ascertain the amount of timber. On this basis 
 the map was drawn. The course of streams is shown 
 approximately. Mountains and prominent ridges are 
 hatched in. Main existing roads may be put in roughly. 
 
 A map like this, with lines on the ground to correspond 
 with it, is of great service in the management of forest 
 property. Logging contracts can be let with clearly 
 defined boundaries; distance to haul is approximately 
 known ; in a rough way the nature of the ground is repre- 
 sented. It has, however, very evident limitations. Off 
 the section lines, it is all judgment or guesswork, and the 
 details of the country, such as have a very material effect
 
 114 A MANUAL FOR NORTHERN WOODSMEN 
 
 on all operations, are not shown and cannot be shown with 
 that method of representation. 
 
 The cost of such a map is very slight over and above the 
 cost of the survey work in sectioning. That in the region 
 named commonly costs from $600 to $800 per township. 
 If a region is divided into sections or quarter-sections, a 
 
 good cruiser can produce a map like this as fast as he can 
 travel over the country. 
 
 Contour Maps. The actual shape of a country is best 
 represented by contour lines. A contour line is a line of 
 equal elevation, the line a man would follow if he traveled 
 round a country keeping at a constant height, or what 
 would be the shore line could a country be submerged to 
 a given level. The base level of a map representing a 
 country near the seashore would naturally be sea level. 
 The first contour on the map might follow the line of 100
 
 METHODS OF MAP MAKING 115 
 
 feet elevation, the second run 100 feet above that, and so 
 on, one for each 100 feet. A little consideration will show 
 that the lines indicate not only direction of the slope of the 
 land, but also the rapidity of slope, for when contours are 
 close together the ground is steep, while on flat land they 
 are wide apart. Hill tops are circled by a succession of 
 contour lines. On lower land they often run in a very 
 sinuous course. 
 
 When one examines such a map and thinks of its con- 
 struction, the first idea is that a tremendous amount of 
 labor is involved. To follow out a succession of contour 
 lines with ordinary surveying methods would indeed be 
 an endless task. That is not the method of construction, 
 however. It is rather sketching, guided by the location, 
 in horizontal position and height, of a sufficient number of 
 points. If one knows how high the top of a hill is above its 
 base, that tells one at once how many contours, 100 feet 
 apart, come between the two, and a glance at the hill 
 perhaps will tell if it is of even slope. Similarly the location 
 of divides and ridge tops, and, on the other hand, of low 
 points, whether occupied by water or not, gives control 
 points which aid in representing the slope of the land. 
 The main problem of the topographer is how best to make 
 these locations most accurately and at least cost. 
 
 General Considerations. The instruments and methods 
 available for the production of topographic maps have 
 been described on previous pages. In employing them, to 
 secure practical results, very much depends, of course, on 
 their effective use and proper combination. In this rela- 
 tion, some general principles of surveying work and the 
 conditions of woods work, as distinct from those of ordinary 
 surveying, require first to be stated. 
 
 1 . A hunger for accuracy is part of the make-up of every 
 good surveyor and map-maker. At the same time, he has 
 to remember that if such work costs more than it is 
 worth to the man who pays for it, it will not be done. 
 Accuracy to a certain degree is necessary; on the other 
 hand, there are limits of cost. A proper balance between 
 the two is required. The result may be called an " 
 map.
 
 116 A MANUAL FOB NORTHERN WOODSMEN 
 
 2. In securing an efficient map, a main principle to hold 
 in mind is the relation between accurate and expensive 
 work and work of a lower degree of accuracy. If elevations 
 in a topographic survey were put in by level only, and 
 horizontal positions fixed by compass and chain, an 
 accurate result would be had, it is true, but it would be at 
 enormous cost. On the other hand, the use of barometer 
 and pacing alone might furnish a map so inaccurate as to 
 be of little account. The effort must be to construct a 
 skeleton of reliable points and lines, to which less accurate 
 and costly work may be tied to put points within reach, 
 one might say, of the weaker method or instrument. Sur- 
 veyor's compass and chain, staff compass and pacing, and 
 sketching form such a series in the horizontal determination 
 of points. The level, the aneroid, and sketching are similarly 
 related in height work. Sketching is the final term in any 
 case, and much depends on it for both accuracy and 
 appearance. In a way, it is easy, but real excellence in 
 the art depends on a combination of eye, memory, and 
 artistic sense. 
 
 3. Throughout any ordinary work of this kind, it has to 
 be understood that much detail is too fine for representa- 
 tion or is really unessential, and on that account the 
 topographer should neglect it. Makers of accurate maps 
 neglect only what does not show on the scale of the map. 
 Woodsmen will generally find it necessary to adopt a 
 more liberal rule. 
 
 The conditions under which forest mapping is done have 
 an influence on methods in the following ways. 
 
 1. Timber growth itself presents an obstacle to clear 
 sighting. That favors the compass as against the transit 
 for boundary work, and in the same way, in topographic 
 mapping, triangulation and the vertical angle are put at 
 a disadvantage as agaiast methods which can be carried 
 on under the cover of the woods. 
 
 2. Forest topography should generally be tied to 
 property boundaries, rather than to topographic promi- 
 nences. Commonly, a survey of his boundaries is the first 
 and most important work to be done for an owner who 
 wants accurate knowledge about his land. It will, there-
 
 METHODS OF MAP MAKING 117 
 
 fore, save time and money if the interior features can be 
 tied to them. 
 
 3. Topographic maps of forest property should be 
 especially clear in respect to road lines and other points of 
 importance in lumbering operations. The map-maker 
 should, therefore, understand these operations. It will, 
 also, save time and money if topography and timber can 
 be examined together, at the same time, and by the same 
 man. 
 
 With these principles in view, the following are methods 
 recommended for the production of forest maps. It is 
 well in discussion of the matter to divide the work into 
 two classes that on small tracts, where close work is 
 required, and that on larger tracts, where different methods 
 must be employed and a lower standard of accuracy may 
 be allowed. 
 
 2. MAPPING SMALL TRACTS 
 
 A tract of eighty-nine acres, well timbered and of strong 
 relief, that was surveyed by the class of 1907 in the Harvard 
 School of Forestry will serve as illustration. The following 
 steps were taken in the process. 
 
 1. Boundaries surveyed by compass and chain ; marked 
 stakes left every twenty rods ; bounding lines and corners 
 remarked. Two days' work for three men, more if there is 
 special difficulty with the old boundaries. 
 
 2. Elevation of one convenient point ascertained or 
 assumed, and levels run over the roads crossing the tract, 
 leaving bench marks plainly marked every twenty rods or 
 so. Levels, also, run down to point x. (See page 119.) 
 One half day's work for two men. 
 
 3. Outlines of tract plotted to scale on paper; this 
 pinned on traverse board with meridian of survey parallel 
 to N and S edge of board ; roads run in with the chain and 
 position of bench marks taken. One half day's work for 
 three men. 
 
 4. Sheet on the board without the tripod taken into the 
 field, a scale serving for alidade; detail mapped in by 
 short foot traverses from the known points ; elevations got 
 partly by aneroid, partly by hand level. One day's work
 
 118 A MANUAL FOR NORTHERN WOODSMEN 
 
 for one man. Any board to hold the sheet will do, a small 
 compass being used to orient it. By the time this work is 
 done, a practical man may, in addition, have learned 
 about all he wants to know regarding the timber. 
 
 Clark Lumber Go's. 
 
 "PARKER" LOT 
 
 Woodstock Mass. 
 
 Surveyed by 
 
 MO 400 300 800 100 
 
 5. Since the lot is to be operated from a portable mill set 
 near its northeast corner, go over the lot with the map in 
 hand and see that the topographic difficulties and oppor- 
 tunities are correctly represented.
 
 METHODS OF MAP MAKING 
 
 119 
 
 Alternative Methods. 1. Compass and chain may be 
 used to survey the roads and the plotting done off the field. 
 This is most convenient in wet weather, but when a traverse 
 board is at hand and can be used, it will be found the 
 quickest method of survey and the least liable to error. 
 
 Diagram showing 
 Method of Survey 
 
 Lines surveyed & chained 
 
 Points marked for refprpnna t i | i 
 
 Levelled lines 
 
 Bench marks O O O 
 
 Traverses with barometer 
 
 or hand level 
 
 2. Transit and stadia might be substituted for both 
 level and traverse board in the survey of the roads, and, 
 where the woods are open enough, in mapping the detail 
 of the topography. This method involves much comput- 
 ing, is generally cumbersome, and except in the hands of a 
 skilled and practiced man is liable to give rise to error.
 
 120 A MANUAL FOR NORTHERN WOODSMEN 
 
 3. After the boundaries are surveyed and the primary 
 point in elevation is fixed, a topographic survey and timber 
 estimate might be made together by means of the strip 
 system of survey described on page 188. For the topo- 
 graphic work, a barometer would be carried in the party 
 
 Same Tract 
 as Surveyed by 
 Strip System 
 
 and the elevation of needed points read and noted or 
 plotted down in connection with the chainage by the note- 
 keeper. If the air pressure was not steady, it would be 
 necessary for the barometer man once in a while to leave 
 the party and go back to the base for correction. The 
 combination of barometer and barograph gives rise, in a
 
 METHODS OF MAP MAKING 121 
 
 method already not too accurate, to additional errors, and 
 should not be employed except when it is the only practi- 
 cable method. 
 
 This method of survey may suffice in favorable condi- 
 tions, and where the requirements are not of the strictest. 
 Work with the level, however, is quick and sure, and in 
 general it will be found advisable to use it freely. 
 
 The Map. In plotting tracts of this size, and up to a few 
 hundred acres in extent, scales of 400 feet or 20 rods to the 
 inch are found to go well with a 10-foot contour interval, 
 and to furnish a serviceable map. A larger scale and a 
 smaller contour interval would naturally go together. 
 
 3. MAPPING LARGE TRACTS 
 
 A. With Land already Subdivided. If the region to be 
 mapped comes under the public land surveys, or if there are 
 plain and reliable lines of other origin on the ground, a 
 skeleton of level lines with barometer work tied to them is 
 the treatment indicated. Generally the level work is best 
 carried along the waters or roads. Ponds and lakes form 
 the best sort of reference points, and frequently natural 
 water levels perform a large part of the work required. 
 Section lines may, however, furnish in some cases the best 
 routes available, while on very broken land it might be 
 necessary to resort to the vertical angle. 
 
 ^How the barometer work shall be done depends on 
 circumstances. If the weather is perfectly steady, or the 
 level points are near enough together, elevations may be 
 read direct without a weather change correction. If, 
 however, the weather is shifting, and the cruiser must stay 
 away from known points many hours at a time, a station 
 barometer or barograph will have to be employed. In any 
 case, the topography can be mapped at the same time that 
 the timber is being examined. 
 
 B. Topography Based on Survey of Roads or Streams. 
 If the tract to be surveyed is an undivided township, or is in 
 any other form that is too large for accurate mapping, it may 
 be cut up by one means or another into smaller areas that 
 can be handled. The lines of easy subdivision naturally
 
 122 A MANUAL FOR NORTHERN WOODSMEN 
 
 furnished by a large timber tract are its streams. On 
 these transit and stadia furnish the most efficient means 
 of survey. If roads are available, the same method may 
 be employed, or another may be substituted. 
 
 One Mile 
 
 Surveyed bounds with chainage marks . 
 Road surveyed by stadia, reference points 
 fixed by stadia and by level - 
 
 Strip surveys with barometer. 
 
 On the tract used in illustration, the road, rather than 
 the stream, was used for the subdivision. The different 
 steps in the process of survey were as follows : 
 
 1. Outside boundaries run with compass and chain. 
 Chainage marks for reference left every quarter mile. 
 
 2. Road across the tract surveyed by transit and stadia, 
 using the needle and setting up the instrument at alternate 
 stations. Points marked at short intervals. See notes on 
 page 86. 
 
 3. Level line run along road, giving elevation of points 
 established in the stadia traverse. 
 
 4. Strip surveys run between the road and the boundary
 
 METHODS OF MAP MAKING 123 
 
 (see page 188), tying into the marks left. Elevations got 
 by aneroid, corrected by barograph. Numerous modifica- 
 tions of the rectangular system made as required. 
 
 Alternative Methods. 1. On roads the traverse board 
 with chain is undoubtedly the best instrument for making 
 a survey of fair accuracy. The compass and chain might 
 also be used. But when streams are utilized, unless on ice, 
 stadia measurement will be found to be best and quickest. 
 
 2. The level might be dispensed with, and the transit 
 used as a level on the same settings from which it is used 
 to get bearing and distance. This works best on a stream 
 with grade all one w r ay, and, in the case of a party by itself 
 in the backwoods, is probably the best means of getting 
 data of this kind. One additional man is then required 
 for maintenance. 
 
 3. Instead of the strip survey, using compass and chain, 
 compass and pacing may be employed with circular plots 
 for the timber. It may also be better or necessary to 
 discard both rectangular systems, and work out the topog- 
 raphy by means of. road lines, passes, etc., controlling 
 features in the lumbering development. 
 
 C. Subdivision and Topographic Survey Combined. 
 The following procedure has been carried out on a con- 
 siderable scale on undivided townships in New England. 
 The methods employed have been found to be cheap and 
 practical, and the maps resulting have stood the tests of 
 use and time. 
 
 1. Boundaries renewed and tract divided into sections 
 by compass and chain. Topographic notes taken ; chain- 
 age marks left every quarter mile. Two months' work for 
 a party of seven men. 
 
 2. Elevation of some point above sea level obtained, if 
 possible ; if not, datum plane assumed at or below lowest 
 point on the tract. Level lines run over roads and streams 
 to ponds, camps, and other accessible points, well distrib- 
 uted through the tract. Commonly a week's work for 
 two men. 
 
 3. Detail of topography and timber worked out together. 
 Mountain peaks located by cross bearings; streams and 
 roads by compass and pacing traverse; other features
 
 124 A MANUAL FOR NORTHERN WOODSMEN 
 
 partly by traverse, partly by straight-line travel across the 
 sections. Elevations by barometer checked by the baro- 
 graph whenever it is necessary to remain away from known 
 points a considerable time. Timber estimated and topo- 
 graphic notes obtained at same time. Cruising, reduction 
 of notes, and map making about six weeks' work for the 
 explorer, who may need a companion or camp man. 
 
 Comments. 1. Division into mile squares may look 
 expensive, like going a long way round to secure topo- 
 graphic data. These lines, however, have value on other 
 accounts; have, in fact, proved their value over and over 
 again in timber land administration. As before stated, 
 they are useful in definitely bounding logging contracts, 
 they are perfectly understood by logging foremen, and 
 are of great service to them in their timber estimates 
 and the laying out of their roads. They are, in addition, of 
 great service in keeping track of subsequent cutting or 
 other developments on the land. 
 
 On the other hand, the mile square is not so large an 
 area but that it can be mapped accurately and its timber 
 estimated according to the methods here recommended. 
 
 2. The strip survey system might, of course, be used 
 instead of the one-man system employed. The advantages 
 of each will be understood from what comes before and 
 after. 
 
 3. It may be advisable in some cases to separate entirely 
 the topographic and timber work. In general, however, 
 the thoroughly equipped man will find that travel that 
 helps him in one direction helps also in the other. 
 
 The Maps. Maps of forest property should be on a 
 large scale to allow the preservation of notes about small 
 bunches of timber, etc. Four inches to the mile for tracts of 
 large size has proved serviceable. As to contours, a fifty- 
 foot interval will serve, in the rough land of New England, 
 to represent most features of the topography. 
 
 The results of such a survey are, for business purposes, 
 best embodied in two map sheets, one showing the waters, 
 relief, and other permanent features of the country, the 
 other exhibiting all the. facts concerning the timber. 
 This last should be on tracing linen, so that it may be laid
 
 METHODS OF MAP MAKING 125 
 
 over the topographic sheet, and the two seen in relation. 
 Not only the amount of timber is thus exhibited, but the 
 steepness of the ground it stands on, and the distance it 
 must be hauled. It will appear, too, whether a valley 
 has been cut clean to a divide. On this timber sheet, cut- 
 tings and other operations of succeeding years may be 
 plotted. If it gets too complicated, it may be thrown away 
 and a new one substituted. 
 
 A sample map of this kind is reproduced on reduced 
 scale herewith. These maps may also be supplemented 
 by topographic models. Contour maps are "not read easily 
 by every person, as, for instance, by some lumbermen, 
 but a model of the land, as it lies out of doors, is imme- 
 diately grasped by all. With the aid of a blue print of 
 the map which may be cut up and used as a pattern a 
 model is cheaply built out of cardboard or veneer. With 
 such a model at hand, a contract may be let or plans 
 of work talked over in the office with the same clearness 
 as to major features as if men stood on the ground. 
 
 Following is a topographic map of a section of land as 
 derived from traverse of the boundaries, a road, and two 
 trips across it. After that come notes of the road traverse 
 and of one of the trips across it. For notes of survey of 
 south line see page 29. On the map observed elevations 
 are written in. ' Contours as seen are solid; contours in- 
 ferred are broken. 
 
 Principles of Cruising. A plan of cruising designed 
 to secure topographical and timber data every man will 
 think out for himself and a new one for each tract under- 
 taken. The following, however, are believed to be sound 
 principles for guidance in this class of work. 
 
 1. Main streams, roads, lakes, etc., should of course be 
 traversed, and they may be important enough to demand 
 some other method of survey than compass and pacing. 
 One should be very careful, too, about waste lands, burns, 
 and the boundaries of heavy bodies of timber. 
 
 2. It is generally advisable to explore the country one 
 section at a time, for in that way one comes out with the 
 clearest ideas upon it. 
 
 3. Cross country travel which locates brooks and ridge
 
 126 A MANUAL FOR NORTHERN WOODSMEN 
 
 tops by intersection may suffice for topographical purposes, 
 while it gives a juster view of the timber than could other- 
 wise be gained. Locations, too, will be more accurate 
 along such a line than where a crooked route is followed. 
 
 4. Extreme points are in general the -ones to read on 
 for height, that is to say, ridge tops, brook crossings, etc. 
 One may combine with this also a system of reading at 
 regular intervals. It will be enough to read the thermom- 
 eter half a dozen times during a day to get the course of 
 the temperature, unless extremely high points are occupied. 
 
 5. Relative heights are frequently of far more importance 
 for logging purposes, as, for instance, in connection with the 
 grade of roads, than is absolute elevation. It is often ad- 
 visable, therefore, to establish sub-centers of work and 
 determine elevations relatively around them rather than 
 refer readings always to a distant base station. On the 
 same principle, if a region is hard to get at with the level, it 
 may serve the purpose of the map to fix the height of some 
 central point in it by two or more aneroid readings, and 
 then work around that.
 
 METHODS OF MAP MAKING 
 
 127 
 
 f 
 
 St-arf/ 
 
 7? ai~6 
 
 jt//fi ///7e of 7bw/7S/7//), S~/T3ds 0/7 rtre S ///r& 
 
 ofSe 
 
 -fy'o/7 a 
 
 5 q/ife/? /'/? survey /7o/s. /evafa'o/7 37O ft 
 
 as 05 
 
 CQffa//, 
 
 ed frv/n /3O/7C/ /?ear6y dsfer/7?//?ec/ 6y /ere/. 
 
 
 
 Tfience //7^ecfib/? 2S 
 
 Searing 
 
 rbces 
 
 
 A/20 
 
 2OO 
 
 A/o/iy easy 6/o/oe r/g/rf; /ft good f/mber; 
 
 MS" 
 
 3SO 
 
 f~o syya/np 
 
 WSO'E 
 
 7S 
 
 /o sma// brooA rurtfl/nq <5. /evaf-/bfi 94o' 
 
 MJJ 
 
 2SO 
 
 ctf~ /OO ' //7/D /7/7?6es~ cryo//7 
 
 A/73E 
 
 /SO 
 
 Up s/q/oe, /o pass be,fween /7///S 
 
 #65 
 
 32S 
 
 r/ghf- & /etf- /er. /o<$o ' 
 
 V42E 
 
 /7S 
 
 on agenerti/ S/ope Easf- of a6oirf- /o% 
 
 M2S 
 
 4OO 
 
 ' fo -f/af /and and 
 
 N20 
 
 tes 
 
 /e\saf/or? 3&O ' 
 
 N 
 
 30O 
 
 f/7 f/af /and w/fh fft/cA spruce- growth 
 
 Ww 
 
 22S 
 
 to Norrh //'/7e -secfrb/? 2S- /-9O /-ods asf 
 
 
 
 on // crsg/ye/7 6>y Survey /?0r&s. 
 
 
 
 /er.880fr Greeted on 0.Af./ra/f an four fab- 
 
 
 
 
 COMPASS AND PACING TRAVERSE OF ROAD ACROSS SAME SECTION. 
 ELEVATIONS READ FROM FOOT SCALE OF BAROMETER 
 
 6. There is occasionally a locality especially critical 
 from the lumbering point of view, such, for instance, as a 
 pass which makes it possible to haul from one drainage to 
 another with a level road. The topographer ought to be 
 enough of a lumberman to recognize these points, and 
 when he does he will put special time and pains upon them. 
 
 7. Field observations may be recorded either in the form 
 of running notes, or mainly in the shape of sketches on a 
 plat of the ground. Probably a combination of the two 
 methods will be found most satisfactory. A note book 
 especially ruled for the purpose to the same scale as the final
 
 128 A MANUAL FOR NORTHERN WOODSMEN 
 
 /" 
 
 
 Bar Camp. (Eter. 6y/eve/3o;') 6A.M. 29. JSO 
 
 
 TA. 60" Barvgrapf, 6A.M. 3. 2 JO Bar. <%%%$?,_ 
 
 
 Canada road on /V. /irre section S T/me 7JO 23.3 6O 
 
 88/' 
 
 Steps 
 
 60 Wesf on -Section /i/?e 
 
 '90 
 
 i/7?i/e mart of5i/rrey. f~/af fyruce aroi/nd. 23. 36S 
 
 876 
 
 S/0 
 
 % mile mark. S/ope M. then //. 29. 29S 
 
 935 
 
 SIS 
 
 Section cor/xv: Gevf/es/o/vA/.W. A// spruce 
 
 
 timber. Bar. 7.4O 2.9.30S 
 
 920 
 
 
 Ref-urn fo /OO steps . of % m/7e /nar* and 
 
 
 go 5.7 W. /n Section. Starfaf 7.S0 A.M. 
 
 350 
 
 Genf/e S/ope MMW. S/?rvce growt/? 29.ZOS 
 
 /0/6 
 
 400 
 
 Top of A///. fa//s Sfeep/y .wdW. 3.390 
 
 1220 
 
 470 
 
 Down strong grade S.W. 7/m heron hi// mixed 
 
 
 ffrrdsnorf. ffotfom roiyh 29.I7S 
 
 IO3S 
 
 /7S 
 
 Canada nay road on easy /and 2.9. /9J 
 
 so/s 
 
 37S 
 
 Down easily w /arge /n/jred^row/'n fo edge 
 
 
 of snrampy /and Z9.26O 
 
 350 
 
 280 
 
 Town s nip ///?e 6~O sfeps Easf of %. n?i/e mart 
 
 
 Bar ass (TA . 6SJ 29 aao 
 
 930 
 
 
 Bar Camp //A. M. (TA. 6S>J 9. 28O 
 
 
 Barograpfi //, E9./7S 
 
 
 
 STRAIGHT TRAVERSE ACROSS SECTION. ELEVATIONS BY BAROMETER 
 CORRECTED BY BAROGRAPH 
 
 map will be found a great saving of labor and an aid to 
 clearness. 
 
 8. The map is best worked up on the ground. The 
 added accuracy and certainty gained in this way more than 
 pay for the cost of carrying necessary equipment around. 
 The topography may be drawn in pencil on the final 
 manuscript sheet, and an outline sketch on any kind of 
 paper will serve to gather up the timber notes temporarily.
 
 TIMBER SHEET 
 
 Explored I 900 Cutting since that date marked by section lining
 
 
 28.9$. 
 
 
 T33H8 
 
 
 
 'ttch on an
 
 PORTION OFTOWNSHIP 5 R IV OXFORD CO. MAINE 
 
 Topographical Sheet Datum Plane, Umbagog Lake 
 
 Contour Interval = 50 feet
 
 METHODS OF MAP MAKING 129 
 
 D. Western Topography. Use of the Clinometer. 
 The above described methods grew up in the East among 
 varied conditions of topography and value. Brush that 
 interferes with sighting is widely prevalent, and another 
 determining factor is the general employment of horse 
 logging, a style of operation for which close regulation of 
 grades is not essential. Conditions in the West are fre- 
 quently different from the above, in respect to one or 
 more particulars. 
 
 The aneroid barometer has not on that account yielded 
 its place entirely. Particularly in Western Washington 
 and Oregon does it still hold the field, because of the dense 
 brush widely encountered, which makes almost impossible 
 the clear sighting necessary for the employment of any 
 other height-determining instrument. On the contrary, 
 the temptation is to rely on the aneroid for work that it 
 should not be called upon to do. Where, as is the case 
 here, railroads are employed for nearly all mam transpor- 
 tation, heights with a reliable basis are essential if a 
 map is to be widely serviceable. Frequently the ground 
 lies in such a way that the routes of future railroad de- 
 velopment are evident. Levels run along these routes,, 
 with aneroid work for the rest, is then the natural treat- 
 ment. Just this method has been employed in numerous 
 cases. 
 
 Such logical and adequate treatment is not always 
 possible, however, nor is it always permissible under the 
 restrictions of the work in hand. A variety of methods is 
 in fact employed, especially for the control work. As 
 for the detail, the fact remains that when points in eleva- 
 tion have been reliably determined at distances not more 
 than from one to two miles apart, good aneroids intelli- 
 gently used will give topography sufficiently accurate for 
 general purposes, while here as elsewhere their use saves 
 expense by permitting the topographic and estimating 
 work to be done together. Complaints of the results of 
 aneroid work frequently arise from unskilled use and from 
 employment of instruments of inferior character. The 
 quality of instruments obtainable at moderate cost has 
 within a very few years greatly improved. It is not to be
 
 130 A MANUAL FOR NORTHERN WOODSMEN 
 
 denied, however, that rapid weather changes sometimes 
 make accurate work difficult. 
 
 Some interior mountain territory is characterized by 
 lightly forested ridges contrasting with great density of 
 timber and brush along the streams, while logging methods 
 are often such that accurate knowledge of grades on valley 
 lines is not essential. In circumstances such as these, 
 circuits of transit and stadia work carried over the ridges 
 have proved a satisfactory method of height control. 
 When areas concerned have never been covered by the land 
 surveys, angles have been turned and read in addition for 
 the purpose of control in the horizontal direction. 
 
 With control laid out in this way the early plans of 
 reconnaissance in such country involved, as the next step, 
 the crossing of valleys with strip surveys, the aneroid 
 being relied on for elevation. This plan of work, starting 
 from known points on the ridges and running long lines 
 independent of one another, crossing the brooks and valley 
 bottoms (where grade was most important) at a long 
 distance from known bases both horizontally and verti- 
 cally, made demands on the aneroid which it was not able 
 to meet successfully. 
 
 Height work along the stream lines was an evident 
 corrective, but a substitute scheme that at the time of 
 writing seems to be filling the requirement is the use of the 
 tape and clinometer. 1 Both instruments have, however, 
 been subjected to modification. The clinometer has been 
 made more efficient in numerous ways; in particular the 
 arc has been enlarged and so graduated that instead of 
 degree or per cent of slope it gives difference of elevation in 
 feet for the given slope and a stated distance (66 feet or one 
 chain in present practice). The tape used for the purpose 
 is 2| chains long, two chains of it marked in links as usual, 
 while the extra length or "trailer" is so graduated that 
 the inclined distance along any slope which corresponds to 
 two chains horizontal may be set directly. By these 
 devices two short cuts are accomplished : first, difference in 
 
 1 For a fuller description of this method see "The Timberman,'' 
 March, 1916, or "Engineering News," Vol. 75, No. 1, p. 24.
 
 METHODS OF MAP MAKING 131 
 
 elevation is found directly from the slope observation; 
 second, with similar directness surface chainage is con- 
 verted into horizontal distance. These two things are the 
 essentials wanted. To facilitate the work, the graduations 
 on the trailer of the tape correspond with those on the arc 
 of the clinometer. 
 
 The method will be grasped from the accompanying 
 figure and the following explanation : If a party is ascend- 
 ing the slope indicated in the figure, the man ahead (who 
 serves not only as head chainman, but runs the compass, 
 takes notes, and sketches topography), as the tape comes 
 to its end, sights with his clinometer at the height of his 
 eye on the rear man (who may be the timber cruiser as 
 well as rear chainman). The reading obtained, in this 
 case 38, is the vertical rise per 66 feet horizontal on the 
 slope between the two men. That corresponds to a vertical 
 angle of 30, but the fact, not being needed, is neglected. 
 The topographer now calls out "38" to the rear man, who 
 lets the tape run out to that mark, as a matter of fact 20.42 
 feet beyond the two-chain point. When the chain to this 
 mark has been drawn straight and taut and pins are set, 
 two chains is the horizontal distance between them. This 
 the topographer may now plot on his map. The height of 
 the new point (twice 38, or 76 feet above the first one) may 
 also be used as the basis of sketching.
 
 132 A MANUAL FOR NORTHERN WOODSMEN 
 
 Two miles per day are readily covered by two men, 
 drawing topography carefully and estimating a good stand 
 of timber. Not only has cruising work been done by this 
 method, but control work as well, using more care and two 
 instruments. This last use of the method requires making 
 circuits several miles in length around either subdivisions of 
 
 tact*. 
 
 land or topographic areas. For cruising work the method 
 is carried at farthest two miles to a tie point. Errors in 
 direction and distance are seldom over \ chain per mile 
 and the average error in height work is 10 feet. In very 
 brushy country some tricks of the trade are introduced in 
 the interest of speed, as sighting to the flash of a mirror or 
 the metal note holder of the cruiser. In country of long
 
 METHODS OF MAP MAKING 133 
 
 open slopes an alternative method is to take longer shots to 
 noted objects, chain up, and compute the elevation. 
 
 Above is practice developed; in the United States For- 
 est Service. The cost is given as 12 cents per acfe as a 
 total for topography and cruise. Some commercial work 
 is done on the same general plan, a five-chain tape being 
 used and correction for distance made from tables in the 
 field. 
 
 The accompanying map of mountainous land in Idaho 
 shows at the left the topography along two miles of section 
 line as developed by a survey for control purposes which 
 surrounded four sections. This control work naturally is 
 performed and checked in advance of the detail work. 
 To the right the topography of the greater part of the area 
 has been filled in, but a strip left blank indicates how it is 
 built up, from parallel lines 10 chains' apart crossing the 
 territory. This map is completed in the field, a board and 
 outline section sheets facilitating the purpose. 
 
 This method, though developed in special conditions in 
 the West, promises, with some of its modifications, to win 
 a considerable field of employment. 
 
 SECTION VIII 
 ADVANTAGES OF A MAP SYSTEM 
 
 Following are the advantages which a good set of maps 
 renders to a large business concern. To secure these a 
 good man will be required in the field to keep up lines, 
 map the cutting of successive years, and watch the con- 
 dition of the timber. 
 
 1. Great saving in the aggregate can be effected through 
 the detection of small losses, such as windfalls and insect 
 depredations, also by finding bodies of unhealthy timber, 
 and as far as possible having such material cut and hauled. 
 
 2. The location of all sorts of roads, whether railroads, 
 logging roads, or supply roads, is greatly facilitated. 
 Exploring is saved, and distances are accurately known. 
 
 3. Operations can be planned and largely controlled 
 from a center with all sources of information at hand.
 
 134 A MANUAL FOR NORTHERN WOODSMEN 
 
 The timber resources are known; also their location, and 
 all related facts. The cut can be located for years ahead 
 to the best advantage, sotli to make driving and the haul- 
 ing of supplies, for instance, come cheapest and handiest. 
 
 4. A map system preserves information about the land.' 
 An old lumberman or cruiser has a lot of information in 
 his head that is lost to a business when he dies or steps out, 
 unless it is fixed in some permanent form. 
 
 5. A concern knows what it is possessed of, and has that 
 information in the form most easily taken in by all intelli- 
 gent men whom it may be desirable to inform ; for instance, 
 stockholders, and possible money lenders. 
 
 6. A good map system in a business may pay for itself at 
 the first change of management. A new manager coming 
 into a business is in the hands of his employees for years 
 until he can get first-hand knowledge of his country. With 
 the aid of a good map system working command of a big 
 property may be had in a year. 
 
 7. A reliable map system followed up for a term of 
 years through a series of pictures of the land furnishes a 
 record of its growth, and so enables a concern to grapple 
 with the question of future supplies.
 
 PART III 
 LOG AND WQOD MEASUREMENT
 
 PART HI. LOG AND WOOD MEASUREMENT 
 
 SECTION I. CUBIC CONTENTS 
 
 SECTION II. CORD WOOD RULE 
 
 SECTION III. NEW HAMPSHIRE RULE 
 
 SECTION IV. BOARD MEASURE 
 
 1. General 
 
 2. Scribner and Decimal Rules 
 
 3. Spaulding or Columbia River Rule 
 
 4. Doyle Rule 
 
 5. Maine Rule 
 
 6. New Brunswick Rule 
 
 7. Quebec Rule 
 
 8. Theory of Scale Rules and Clark's International 
 
 Log Rule 
 
 SECTION V. NEW YORK STANDARD RULE 
 
 SECTION VI. SCALING PRACTICE 
 
 SECTION VII. MILL TALLIES 
 
 SECTION VHI. CORD MEASURE
 
 PART III. LOG AND WOOD MEASUREMENT 
 
 SECTION I 
 CUBIC CONTENTS 
 
 THE simplest way to measure the contents of a log is to 
 take its length and mid-diameter and ascertain the cubic 
 contents of a cylinder having those dimensions. Bark may 
 be taken in or left out. By the use of a caliper and tape, 
 a very close result may be had on logs that are not too 
 long, provided care is taken either by inspection or by cross 
 measurement to get a true mid-diameter. Trees cut nearly 
 full length are given as a rule too large a value when 
 measured in this way, larger, that is to say, than their 
 actual cubic contents. The percentage of overrun for large 
 spruce cut off at 5 to 8 inches diameter in the top is about 
 
 6 per cent of their true volume. 
 
 When logs are placed in a pile the best that can be done 
 is to use a diameter which is an average between the diam- 
 eters of the ends, swell at the stump, if present, being 
 disregarded. 
 
 First among the tables for log measurement given in the 
 back of this work is a table of cylinders with contents 
 in cubic feet, standard measure. The lengths in feet are 
 given in the first vertical column, the diameters in inches 
 on the upper horizontal line, and the contents of any log is 
 read off opposite its length and beneath its diameter. If 
 the length is not given, add together such lengths as will 
 make it up. Thus a log 12 inches in diameter and 47 feet 
 long has the contents of a log 40 feet long + that of a log 
 
 7 feet long, or 31 + 5.5 cu. ft. = 36.5 cu. ft. 
 
 For practical purposes results near enough will be had 
 if fractions of inches more than \ inch are taken as of the 
 inch above, and fractions of \ inch and less are disregarded.
 
 138 A MANUAL FOR NORTHERN WOODSMEN 
 
 For convenient use in scaling, these figures should be 
 stamped on the bar of a log caliper. They may be so ar- 
 ranged on a bar as to throw out a fair proportion for bark. 
 This system of log measurement is in actual use in but 
 one business concern, so far as known to the writer, yet it 
 is the simplest and most natural measurement for logs that 
 are to be converted into pulp, shingles, excelsior, etc. It 
 is not a difficult matter to arrange a factor or factors for 
 converting cubic measure into board measure. 
 
 SECTION II 
 CORD WOOD RULE 
 
 The figures given in the table on page 239, those for cord 
 measure, are not cubic feet of solid wood, but what have 
 been called " stacked cubic feet " ; the space which wood 
 will occupy in a pile. 128 of these make a cord. Like the 
 preceding, these figures are ordinarily placed for conven- 
 ient use on the bar of a caliper rule. 
 
 These figures have been long and widely tested in prac- 
 tice, and when used as designed have given satisfaction. 
 Logs should not be measured in too long lengths, for whole 
 trees measured in this way may not hold out. Again, 
 small, crooked, and knotty timber will pile up rather more 
 cords than the rule gives. On a good quality of pulp wood 
 these figures yield just about the same return as the re- 
 sults of piling. For further details see Section VIII, on 
 cord measure. 
 
 SECTION III 
 THE NEW HAMPSHIRE RULE 
 
 The New Hampshire Log Rule is exactly the same as 
 the last in principle, only an artificial unit of measure has 
 been created. The " cubic foot " of New Hampshire log 
 measure is 1.4 times the cubic foot of standard measure, 
 and nearly twice the foot of the cord wood rule. The New 
 Hampshire law regarding the matter is as follows : 
 
 All round timber, the quantity of which is estimated by the 
 thousand, shall be measured according to the following rule: A
 
 BOARD MEASURE 139 
 
 stick of timber sixteen inches in diameter and twelve inches in 
 length shall constitute one cubic foot, and the same ratio shall 
 apply to any other size and quantity. Each cubic foot shall con- 
 stitute ten feet of a thousand board feet. 
 
 This rule is extensively used in scaling spruce in Maine, 
 New Hampshire, and Vermont. A broad caliper bar is 
 stamped with the figures, and the stiff iron jaws attached 
 throw out f inch from the diameter for bark. The diam- 
 eter is taken in the middle of the log, and in ordinary 
 practice logs of any length are measured as one piece. 
 The values given by the rule run parallel to actual cubic 
 contents and the rule is therefore a fair one as applied to 
 pulp wood. It is not a satisfactory measure of the yield 
 of logs at the saw, small logs being for that purpose over- 
 valued and very large logs undervalued. As with cubic 
 measure, however, its values could be readily converted 
 into board measure by the use of different factors for logs 
 of different sizes. 
 
 It is now the uniform practice wherever the New Hamp- 
 shire rule is in use to take 115 feet by the rule for 1000 
 feet of lumber. 
 
 SECTION IV 
 BOARD MEASURE 
 
 1. General. A board foot is a piece of sawed lumber 12 
 inches square and one inch thick, or any piece, as 3 X 4 
 or 2 X 6, which if reduced to 1 inch thickness has 144 
 square inches of area. It is properly the unit of sawed 
 lumber, and there must always be more or less difficulty in 
 adjusting it to the measurement of logs. 
 
 There are a large number of rules in the country to-day 
 purporting to give the contents of logs of given dimensions 
 in feet, board measure. Among these rules there is wide 
 variation in the value given to logs of the same dimensions. 
 In the manner of their use, too, there is a good deal of 
 divergence, resulting sometimes in dispute and loss. 
 
 The figures of eight rules in extensive use in the United 
 States and Canada the Scribner, the Doyle, the Deci- 
 mal, the Maine, the New Brunswick, the Quebec, the
 
 140 A MANUAL FOR NORTHERN WOODSMEN 
 
 Spaulding, and the British Columbia are printed in 
 this work (see pages 243-260). The International rule, 
 devised by Dr. Judson F. Clark, formerly forester of On- 
 tario, is also given (page 254). In regard to these rules 
 and their relation to log measurement and saw product 
 several general observations may be made. 
 
 (1.) On sound, smooth, soft-wood logs when manufac- 
 tured according to the best present practice, the figures of 
 all the commercial rules are conservative with the exception 
 of the Doyle rule on very large logs. This is especially 
 true with reference to small logs. 
 
 (2.) Board rules give to large logs a greater valuation in 
 proportion to cubic contents (actual amount of wood) than 
 to small ones. Thus the Scribner log rule to 8-inch logs 
 of small taper allows five feet per cubic foot of wood con- 
 tents; to 16-inch logs seven feet, to 30-inch logs eight feet. 
 This principle is a just one for logs that are in fact to be 
 sawn, because the waste in manufacturing in the case of 
 small logs is much greater, but on this account a board 
 rule is not a just measure for logs designed for pulp or 
 other such uses. 
 
 (3.) The rules are adapted to use on short logs with little 
 taper. When logs are long enough to be cut in two for 
 sawing, or to yield side boards for a part of their length, 
 to derive contents from length and top diameter is not a 
 fair thing. In such cases a second measure of diameter 
 should be taken, and this can be done accurately only with 
 a caliper. Allowance for " rise " or toper, whether for each 
 log by judgment or according to some rule agreed upon, 
 is more or less inaccurate and should be resorted to only 
 in case of necessity. It may be said as a general rule that 
 20-foot lengths are as long as it is safe to scale logs in. 1 
 
 On the other hand, since strongly tapering logs in almost 
 every case are rougher than those of gentle taper, varying 
 taper in logs of reasonable length is largely neutralized 
 by quality. 
 
 (4.) There is wide variation in the details of scaling prac- 
 tice, and a trustworthy rule in consequence may, in the 
 hands of an unskilled or careless man, give very unsatis- 
 1 Except in the case of PaciBc Coast timber.
 
 BOARD MEASURE 
 
 141 
 
 factory results. In some matters, especially culling for 
 defects, latitude must be allowed to the sealer. In general, 
 however, practice is weak in the direction of strict mechan- 
 ical accuracy. Reference is made to section VI following. 
 The method of construction, field of use, and relation to 
 saw product of the above named rules are as follows : 
 
 2. Scribner and Decimal Rules. The figures of the 
 original Scribner rule were obtained by drawing diagrams 
 of the end sections of logs 12 to 48 inches in diameter and 
 the boards which in the mill practice of the time could be 
 sawed out of them. It is a very old rule and in wide use. 
 As printed, extended down to 6 niches, it is the legal rule 
 in the state of Minnesota. 
 
 Omitting unit figures of the Scribner rule and taking the 
 nearest tens has given the Decimal rule, so called, legal in 
 Wisconsin and adopted by the United States Forest 
 Service. 
 
 3. Spaulding or Columbia River Rule. This rule was 
 derived by similar methods as the preceding, 1 inch being 
 allowed for saw kerf. It is in more extensive use on the 
 Pacific Coast than any other. 
 
 4. Doyle Rule. This rule was constructed by the fol- 
 lowing formula : Deduct 4 inches from the diameter of 
 
 Diameter 
 
 No. Logs 
 
 Doyle 
 Scale 
 
 Product 
 
 Overrun 
 
 6-8 in. 
 
 28 
 
 289 
 
 903 
 
 213% 
 
 7-9 in. 
 
 54 
 
 831 
 
 2159 
 
 159% 
 
 8-12 in. 
 
 101 
 
 2603 
 
 5471 
 
 110% 
 
 10-17 in. 
 
 104 
 
 6324 
 
 9976 
 
 58% 
 
 18-20 in. 
 
 90 
 
 15440 
 
 20215 
 
 31% 
 
 21-24 in. 
 
 126 
 
 30929 
 
 37744 
 
 22% 
 
 25-33 in. 
 
 31 
 
 11866 
 
 13368 
 
 12% 
 
 the log for slab, square J of the remainder, and multiply 
 by the length of the log in feet. This is a very illogical 
 rule and gives results widely varying from saw product in
 
 142 A MANUAL FOR NORTHERN WOODSMEN 
 
 logs jof different sizes, though in a run of logs the results 
 obtained may approximate a fair thing. Very small values 
 are given to small logs, too small by far for normal logs 
 economically manufactured, while beyond about 36 inches 
 in diameter values are given that are above the product of 
 the saw. It crosses the Scribner rule at 25 inches in 
 diameter, the Maine rule at 34. A test made by Dr. J. F. 
 Clark in 1905 in a Canadian band mill cutting sound, 
 straight pine into boards resulted as shown on page 141. 
 
 The Doyle rule is in more general use than any other in 
 the United States and Canada, and is the one printed in 
 recent editions of Scribner's " Lumber and Log Book." 
 
 This rule has been combined with the Scribner into the 
 Doyle-Scribner rule, the figures of the Doyle rule being 
 taken for small logs where the Doyle figures are lower, 
 and of the Scribner rule on the largest logs where these 
 figures are less. This Doyle-Scribner rule has been used 
 largely on hard woods. 
 
 5. Maine, also called Holland Rule. The figures of this 
 rule were derived from diagrams. That is to say, circles 
 6, 7, 8, etc. inches in diameter were plotted and within 
 these the boards that could be sawed, an inch thick with 
 J inch for saw kerf. Not only the boards derived from the 
 inscribed square were reckoned, but the side boards if 
 they were as much as 6 inches wide. No rounding off of 
 the figures was done, so they are a little irregular, but that 
 takes care of itself in a run of logs. 
 
 This rule is used largely in Maine and to some extent 
 elsewhere. It has been carefully tested at the saw, and 
 the conclusions are as follows : Sound spruce and pine 
 logs 12 to 18 feet long, of best merchantable quality, 
 manufactured at a circular saw cutting J-inch kerf will 
 yield in the shape of inch boards just about the number of 
 feet of edged lumber that the rule gives. A band saw will 
 get more, and there will be a larger product if the logs are 
 put into plank or timber. More will also be got the longer 
 the logs run, up to the poinl where they are scaled in two 
 pieces. 
 
 How sawing practice affects the product at the saw was 
 clearly shown by a test made by the United States Forest
 
 BOARD MEASURE 
 
 143 
 
 Service in Various spruce mills of Maine. Some results of 
 this test are given in tabular form. All logs were straight 
 and sound, and exact conditions were as follows: 
 
 Band Mill No. 1, |-inch saw kerf, lumber cut just 1 inch 
 thick. Mill run for economy and utmost product of long 
 lumber, giving product of about 40 M daily. 
 
 Band Mill No. 2, same saw kerf. Mill run for speed 
 rather than economy, product being 58 M a day. 
 
 Rotary Mill, ffr-inch saw kerf, lumber even inch thick. 
 
 Gang Saw, ^-inch kerf, lumber even inch thick, logs 
 sawed alive or through and through. 
 
 TABLE I. YIELD IN INCH BOARDS OF LOGS 16 FEET 
 LONG AS SAWED IN DIFFERENT MILLS 
 
 Top 
 Diam. 
 
 s a 
 
 11 
 
 1| 
 
 nd Mill No. 2 
 Sawed alive 
 
 !j 
 
 Gang 
 
 Scale by 
 Maine 
 
 Rute 
 
 
 r 
 
 I 1 " 
 
 c3~" 
 
 m 
 
 
 
 
 6 in. 
 
 30 
 
 26 
 
 20 
 
 18 
 
 24 
 
 20 
 
 7 in. 
 
 41 
 
 36 
 
 29 
 
 25 
 
 34 
 
 31 
 
 Sin. 
 
 53 
 
 47 
 
 39 
 
 35 
 
 43 
 
 44 
 
 9 in. 
 
 66 
 
 59 
 
 51 
 
 46 
 
 54 
 
 52 
 
 10 in. 
 
 81 
 
 73 
 
 64 
 
 59 
 
 67 
 
 68 
 
 11 in. 
 
 96 
 
 88 
 
 79 
 
 73 
 
 80 
 
 83 
 
 12 in. 
 
 112 
 
 106 
 
 95 
 
 89 
 
 94 
 
 105 
 
 13 in. 
 
 130 
 
 125 
 
 113 
 
 107 
 
 109 
 
 120 
 
 14 in. 
 
 149 
 
 . . . 
 
 133 
 
 127 
 
 126 
 
 140 
 
 15 in. 
 
 171 
 
 
 154 
 
 
 145 
 
 161 
 
 16 in. 
 
 196 
 
 
 178 
 
 
 165 
 
 179
 
 144 A MANUAL FOR NORTHERN WOODSMEN 
 
 TABLE II. PRODUCT IN INCH BOARDS OF LOGS OF DIF- 
 FERENT LENGTHS AS SAWED IN BAND MILL NO. 1 
 
 Shows how in careful practice yield increases relative to 
 scale as the logs are longer. 
 
 
 Lengths in Feet 
 
 Top 
 
 
 Diam. 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 6 in. 
 
 13 
 
 17 
 
 22 
 
 26 
 
 30 
 
 34 
 
 39 
 
 44 
 
 50 
 
 Sin. 
 
 25 
 
 32 
 
 39 
 
 46 
 
 53 
 
 60 
 
 68 
 
 76 
 
 84 
 
 10 in. 
 
 39 
 
 49 
 
 59 
 
 70 
 
 81 
 
 91 
 
 101 
 
 113 
 
 124 
 
 12 in. 
 
 54 
 
 68 
 
 83 
 
 97 
 
 112 
 
 126 
 
 141 
 
 156 
 
 172 
 
 14 in. 
 
 73 
 
 92 
 
 111 
 
 130 
 
 149 
 
 170 
 
 ISO 
 
 211 
 
 232 
 
 16 in. 
 
 95 
 
 120 
 
 145 
 
 170 
 
 196 
 
 223 
 
 250 
 
 278 
 
 306 
 
 TABLE III. PRODUCT OF MILLS WHEN SAWING DIMEN- 
 SION STOCK, MOSTLY 2 AND 3 INCH PLANK 
 
 Overrun is the percentage by which the product ex- 
 ceeds the scale of the logs as given by the Maine log rule. 
 
 Band Mill No. 1 
 
 Rotary 
 
 Lengths 
 
 Average 
 Top 
 Diam. 
 
 Over- 
 run 
 
 Lengths 
 
 Average 
 Top ' 
 Diam. 
 
 Over- 
 run 
 
 16 ft. and under 
 
 10 in. 
 
 24% 
 
 16 ft. and under 
 
 10 in. 
 
 o% 
 
 17-20 ft. 
 
 10 in. 
 
 23% 
 
 17-20 ft. 
 
 10i in. 
 
 6% 
 
 21-24 ft. 
 
 81 in. 
 
 37% 
 
 21-24 ft. 
 
 12 in. 
 
 H% 
 
 
 
 
 25-28 ft. 
 
 9j in. 
 
 15% 
 
 6. New Brunswick Rule. This is the legal rule for scal- 
 ing lumber cut on the crown lands of New Brunswick, and 
 is generally employed for log measurement in that province. 
 Its values are somewhat below those of the Maine rule. 
 
 When logs of a smaller top diameter than 11 inches are 
 to be scaled, it is done under the following rule : A 7-inch
 
 BOARD MEASURE 145 
 
 log contains 2 ft. B. M. per foot of length, an 8-inch log 
 2j ft., a 9-inch log 3 ft., a 10-inch log 4 ft. 
 
 One notable thing about the New Brunswick rule is that 
 taper is allowed for in lengths over 24 feet. 
 
 7. Quebec Rule. This is the legal rule for measuring 
 logs in the province of Quebec. Values are close to the 
 Scribner Rule; in many cases they are identical. The 
 figures were derived by plotting. 
 
 8. Theory of Scale Rules and Clark's International 
 Log Rule. The theory of the measurement of saw logs 
 in board measure has been more carefully studied by 
 Dr. Judson F. Clark L than by anyone else, and a rule 
 called the International Log Rule was devised by him, 
 on the basis of this reasoning, which he also tested at 
 the saw. The main points in this study are as follows : 
 
 Taper of Logs. While logs exhibit a great variety of 
 taper, it has been found (1) that rough logs taper more 
 than clear, smooth logs, so that quality tends to neutralize 
 taper ; (2) that average taper does not differ greatly in dif- 
 ferent localities or with different species. This average 
 taper as a result of much measurement is found to be 
 safely 1 inch in 8 feet. This in modern economical mill 
 practice increases the yield of lumber in the form of side 
 boards, and the above stated allowance for taper is there- 
 fore introduced into the rule for all lengths over 8 feet. 
 
 Crook and Sweep. In this study due allowance was 
 made for irregularity of surface, and crook averaging l 
 inches in 12 feet of length, found to be characteristic of 
 white pine logs on the Ottawa River, was counted normal. 
 Above the limit of 1^ inches in 12 feet, any given degree 
 of crook was found to affect the product of small logs more 
 than of large logs, and that in proportion to their diameters. 
 That is to say, a crook of 3 inches in 12 feet throws out 
 twice as great a percentage from a 10-inch log as from one 
 20 inches in diameter. 
 
 Shrinkage and Seasoning. Logs are commonly scaled 
 green, while sawed lumber must hold out on a survey made 
 when it is dry. In computing his rule Dr. Clark figured 
 that boards would be cut 1^ inch thick to allow for this. 
 
 1 See Forestry Quarterly, Vol. IV, No. 2.
 
 146 A MANUAL FOR NORTHERN WOODSMEN 
 
 Saw Kerf. This loss in logs of different sizes is pro- 
 portional to the area of their cross-section, or tp the square 
 of the diameter. It varies in proportion to the thickness 
 of saw kerf as well. As embodying an average of good 
 present practice, J inch was allowed. 
 
 Loss in Edging Lumber. This includes not only that 
 portion of a log which is thrown away in the form of edg- 
 ings, but also the fractions of inches in the width of boards, 
 which in Dr. Clark's studies were uniformly thrown off. 
 It is counted to be in all logs proportional to the surface, 
 or, what amounts to the same thing, to the diameter. 
 Counting boards to be merchantable down to the size of 
 2 ft. B. M., Dr. Clark found that an allowance of .8 foot 
 board measure for each square foot of surface under the 
 bark, or, what amounts to much the same, a layer .8 inch 
 in thickness around the surface, would justly allow for 
 this waste. 
 
 Formula for the Rule. The above elements being put 
 into mathemetical form with D representing top diameter 
 inside bark, there is obtained for 4-foot sections the formula 
 (D 2 X .22) - .71 D = contents B. M. 
 
 Adaptation to Other Conditions. The product for other 
 widths of saw kerf than J inch may be obtained by apply- 
 ing the following per cents: 
 
 For fa inch kerf add 1.3 per cent 
 
 For -fs inch kerf subtract .5 per cent. 
 
 For { inch kerf subtract 9.5 per cent. 
 
 For J 5 inch kerf subtract 13.6 per cent. 
 
 For | inch kerf subtract 17.4 per cent. 
 
 For Js inch kerf subtract 20.8 per cent. 
 
 Should the ^-inch allowance for shrinkage not be made 
 in the mill practice in question, this may be allowed for 
 in a similar way. According to Dr. Clark's assumptions, 
 each board with its saw kerf means l-fo inch in thickness 
 taken out of the log. 
 
 If mill practice in other ways is not so economical as 
 the rule presupposes, that is to say, if logs are sawed 
 with more waste in slab and edging than has been assumed, 
 or if logs vary in taper and straightness from the standard, 
 that is considered by Dr. Clark to be proportional to the
 
 THE NEW YORK STANDARD RULE 147 
 
 surface or diameter, and he recommends that it be allowed 
 for by making a comparison between the scale and mill 
 product, and then adjusting the zero mark on the scale 
 stick more than one inch from the inch mark on the stick 
 in accordance with the results of that comparison. Dr. 
 Clarke's rule will be found on page 254 in the same section 
 with the other board rules. 
 
 SECTION V 
 THE NEW YORK STANDARD RULE 
 
 In northern New York logs are cut as a rule 1 3 feet long, 
 and a log of that length and 19 inches in diameter at the 
 top, inside bark, is the common unit of log measure- 
 ment. It is called a " market "or " standard," and logs 
 of other dimensions are valued in proportion. 
 
 The " standard " is thus another artificial unit of log 
 measurement, more artificial, perhaps, than any other here 
 dealt with. Standard measure in logs of the same length 
 runs very close to cubic measure. Thus a log 19 inches in 
 diameter at the top and 13 feet long has 26 cubic feet in it; 
 four logs 9j inches in diameter and 13 feet long, also 
 making one standard, contain the same amount of wood 
 approximately, while a 38-inch log of the same length has 
 four standards and 104 cubic feet of contents. A log 26 
 feet long, however, has more than twice the wood contents 
 of a 13-foot log on account of taper. For that reason the 
 use of standard measure outside of a region where short 
 standard lengths are cut would be likely to make trouble. 
 
 Standard measure does not run parallel to board measure 
 or to the yield of logs of different sizes at the saw. The 
 standard log, a log, that is to say, 19 inches in top diameter 
 and 13 feet long, scales by the Scribner rule 195 feet, and, 
 in practice, five standards are often reckoned as the equiv- 
 alent of a thousand. Four 9^-inch logs, together making 
 one standard, scale but 144 feet by the rule, or seven stand- 
 ards to the thousand, and the actual ratio between stand- 
 ards and thousands is stated to run all the way from 4' 
 to 14.
 
 148 A MANUAL FOR NORTHERN WOODSMEN 
 
 The ratio between cords and standards is nearly con- 
 stant in logs of all sizes if cut of equjil length. In the 
 Adirondack woods 2.92 standards are commonly reckoned 
 as one cord. 
 
 SECTION VI 
 SCALING PRACTICE 
 
 Logs are best scaled when they are being handled over, 
 as on a landing or mill brow, for then all parts can be seen 
 and got at. Measurement in the pile, especially for long 
 logs, is both difficult and unsatisfactory. 
 
 1. Length. A tape worked by two men is an accurate 
 measure of length. Short logs may be accurately measured 
 with a marked pole, and for long logs a carefully adjusted 
 wheel with brads in the ends of its spokes is cheap to use 
 and reasonably accurate. Measurement with a four-foot 
 stick has a very wide range of accuracy, according to 
 the way it is done. 
 
 pLiii 
 
 k^iOiaiu" 
 
 8"7St*: 
 
 GERMAN NUMBERING HAMMER 
 
 Valuable timber cut into standard log lengths is com- 
 monly allowed two inches extra to permit trimming at 
 the saw, this amount being disregarded in the scale. If 
 logs are cut without measuring, in which case they are as 
 likely to be ten inches over foot lengths as two inches, the 
 extra inches are commonly thrown off just the same. That 
 practice, however, means in 16-foot logs a loss of 2 per 
 cent on the scale or the timber. On 30-foot logs, it means 
 l per cent. 
 
 2. Diameter. The diameter measure for any board rule 
 is obtained at the small end of the log and inside the bark. 
 It is important in large and valuable timber that an aver- 
 age diameter be taken. In dealing with fractional inches,
 
 SCALING PRACTICE 149 
 
 there is a variety of practice. Some sealers read uniformly 
 from the inch nearest the exact diameter ; some disregard 
 all fractional inches and take the next inch below; some 
 vary the practice according to length and taper of the 
 individual logs. 
 
 Probably, the most just practice to follow, as a general 
 rule, is to throw off all fractions of inches up to and in- 
 cluding one half inch, and to read fractions over one half 
 as of the inch above. This practice, in logs under 16 
 inches in diameter, gives results from 7 to 10 per cent 
 greater than if all fractions of inches are thrown out. 
 
 3. Culling for Defects. Defects in logs consist in irregu- 
 larity of form, in shakiness, and in decay. Knots are not 
 properly considered as defects, but as a factor in general 
 quality. All these matters vary with the species, with the 
 locality, and with the individual log. They are matters 
 which have to be dealt with locally and individually, and 
 little can be written that is likely to be of service and not 
 liable to do more harm than good. 
 
 The curved or sweeping form is a common defect in 
 logs. Sealers frequently have rules for allowing for it, 
 but these differ so widely that they cannot be transcribed 
 here. (See page 145 for the result of this defect in logs of 
 different sizes.) 
 
 Irregular crooks in logs cannot be classified. A man can 
 sight along a log and estimate what proportion of it can be 
 utilized by the straight cuts of a saw, and this guided by 
 mill experience is the only way of dealing with the matter. 
 
 Seams caused by frost and wind form another class of 
 defect, more frequent in northern woods and in trees grown 
 on exposed places. Sometimes these are shoal and have 
 little or no effect on saw product. Sometimes they reach 
 nearly or quite to the heart of a log. 
 
 A fairly general practice on northern spruce cut for saw- 
 mill use is to discount 10 per cent for straight, deep seams, 
 and for twisting seams up to 33 per cent, or even to throw 
 out the whole log. 
 
 It is to be remarked that these defects have, when reck- 
 oned in percentage, a far greater effect on small logs than 
 on large ones. Thus a three-inch sweep in a 15-inch, 12-
 
 150 A MANUAL FOR NORTHERN WOODSMEN 
 
 foot log takes but a small percentage out of its total yield 
 at the saw, while a 6-inch log with the same sweep is 
 practically useless for full length, edged lumber. Again, 
 strong taper may largely neutralize the effect of consider- 
 able irregularity in outside form. Lastly, in practical 
 scaling, a certain amount of irregularity in outside form 
 must be considered normal and be taken care of by the 
 conservatism of the log rule. 
 
 Shakiness in logs is far more frequent in some species 
 than in others. Thus hemlock is largely affected by it, 
 while there is very little of it in spruce. In large measure, 
 it should be considered as an element of quality, affecting 
 the grade of the product, not a defect affecting the scale of 
 the logs. When, however, a considerable section of a log 
 is rendered worthless, it should be thrown off in the scale. 
 How much to throw off is a matter of judgment and of mill 
 experience. 
 
 Decay may be complete, utterly destroying the value of 
 a whole log or a section, or it may be partial, allowing the 
 production of a low grade of lumber. Decay varies much 
 according to species and locality, and it occurs in various 
 forms. Of the northern soft-wood trees, fir is most liable 
 to unseen defects, a log perfectly sound to all outside 
 appearance may " open out " very poor at the saw. To 
 a less extent white pine in some localities is affected in the 
 same way. 
 
 Generally, however, the ends of a log or some mark on 
 its surface, such as rotten knots, " punks," and flows of 
 pitch give indication to the practiced eye of defect beneath. 
 How much to allow is then a matter of judgment based 
 on mill experience. 
 
 The following table 1 has been made up, giving the loss 
 due to round center defects extending through or affecting 
 the full length of a log. For four- or five-inch defects, it 
 amounts to the same thing as throwing out a scantling 
 having the same side as the hole has diameter. 
 
 As stated at the start, careful mill training is the only 
 safe basis for the correct culling or discounting of logs. 
 Some sealers have that; some do not, and have to rely either 
 1 Graves' " Forest Mensuration."
 
 MILL TALLIES 
 
 151 
 
 TABLE OF LOSS BY HOLES OR ROT NEAR THE CENTER 
 
 OF LOGS, GOOD FOR DEFECTS MORE THAN 4 
 
 INCHES FROM THE BARK 
 
 Diam. 
 of Hole 
 
 Length of Logs in Feet 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 Inches 
 
 Board Feet 
 
 2 
 3 
 4 
 5 
 6 
 
 8 
 9 
 10 
 
 5 
 9 
 14 
 20 
 27 
 36 
 45 
 56 
 67 
 
 6 
 11 
 17 
 24 
 33 
 43 
 54 
 67 
 81 
 
 7 
 13 
 
 1 
 38 
 50 
 63 
 
 78 
 93 
 
 8 
 15 
 23 
 32 
 44 
 57 
 72 
 89 
 107 
 
 9 
 16 
 25 
 36 
 49 
 65 
 81 
 100 
 120 
 
 10 
 18 
 28 
 40 
 55 
 72 
 90 
 112 
 133 
 
 on arbitrary rules or on guesswork. Proper discount may 
 vary greatly, too, with the mill practice and product. A 
 mill with a box factory attached, or sawing round-edged 
 stuff which is measured regardless of crooks, wastes little 
 or nothing on account of defective form. For a mill 
 which can market only three-inch deals at a profit, an 
 entirely different system of scaling is appropriate. 
 
 SECTION VII 
 MILL TALLIES 
 
 Thousands of unrecorded tests of scale rules have doubt- 
 less been made at the saw, using local and current scaling 
 and sawing methods. During the last few years a number 
 of such tests have been made under stated conditions so 
 carefully guarded that they may serve a general purpose. 
 Reference is made to the tests recorded on pages 143 and 
 144 of this work. The following also are reliable and of 
 interest to northern workers in timber. 
 
 The wide variation in the yield of logs as sawed under 
 different conditions is a matter of great importance in 
 several ways to the worker in timber, chiefly, perhaps, for 
 its bearing upon timber estimates. The relative compe-
 
 152 A MANUAL FOR NORTHERN WOODSMEN 
 
 tence of sawyers is one cause of this, and that, according to 
 careful mill men, may readily amount to 10 per cent. Then 
 market demand affects the matter, some mills being so 
 situated that they can market only the larger sizes of lumber. 
 The type of saw employed and the methods of handling 
 on the carriage also have their effect. 
 
 TABLE I 
 
 Yield in inch boards, squared, of second growth white pine 
 logs. Based on 740 logs; study by Harvard Forest School. 
 
 Growth extra tall and smooth; large and small trees in 
 the stand, which was cut clean; logs with 2 in. crook or 
 over thrown out. Sawed by circular saw cutting }-inch 
 kerf. In scaling, fractions of inches up to .5 were thrown 
 off, fractions of .6 and over taken as if of inch above. 
 Boards merchantable down to 2 feet, surface measure; 
 some wane allowed. 
 
 Top 
 
 Yield B.M. 
 
 Diameter 
 
 12-foot Logs 
 
 14-foot Logs 
 
 5 inches 
 
 14 
 
 15 
 
 6 inches 
 
 20 
 
 23 
 
 7 inches 
 
 26 
 
 30 
 
 8 inches 
 
 34 
 
 39 
 
 9 inches 
 
 43 
 
 50 
 
 10 inches 
 
 53 
 
 61 
 
 11 inches 
 
 67 
 
 76 
 
 12 inches 
 
 81 
 
 90 
 
 13 inches 
 
 95 
 
 105 
 
 14 inches 
 
 110 
 
 122 
 
 15 inches 
 
 128 
 
 139 
 
 16 inches 
 
 147 
 
 160 
 
 17 inches 
 
 170 
 
 
 18 inches 
 
 202 
 
 
 A practice that in some localities of recent years has 
 greatly increased tjje merchantable product of logs is that 
 of sawing waney or round-edged boards. Portable mills in 
 southern New England sawing lumber for boxes or finish 
 follow this practice largely, and stationary mills in many 
 localities have a box or other saw to which they can turn 
 over the small and crooked logs for this most economical
 
 MILL TALLIES 
 
 153 
 
 form of manufacture. When boards in this form are sur- 
 veyed they are measured at the average width, inside bark, 
 on the narrow side, without discount for crooks. - 
 
 This practice has brought about great economy in the 
 use of timber, and when done with thin saws, has secured 
 from logs a far greater product than current scale rules 
 give. Several of the tables given herewith are of special in- 
 terest in this connection. In all these tables top diameter 
 means diameter of the upper end of the log inside bark. 
 
 TABLE II 
 
 Yield in inch boards of second growth white pine logs, 
 saived with a circular saw cutting \-inch kerf. Greater part 
 of boards not edged, but measured for width at an average 
 width, inside bark, on narrow side, without discount for 
 crook. 
 
 Based on 1180 logs. From Massachusetts State Forester. 
 
 
 Length of Log Feet 
 
 Inches 
 
 10 
 
 12 
 
 14 
 
 16 
 
 
 Vol. 
 
 Vol. 
 
 Vol. 
 
 Vol. 
 
 
 Bd. ft. 
 
 Bd. ft. 
 
 Bd. ft. 
 
 Bd. ft. 
 
 4 
 
 9 
 
 13 
 
 17 
 
 21 
 
 5 
 
 13 
 
 17 
 
 21 
 
 26 
 
 6 
 
 17 
 
 22 
 
 27 
 
 32 
 
 7 
 
 23 
 
 29 
 
 35 
 
 40 
 
 8 
 
 30 
 
 37 
 
 44 
 
 51 
 
 9 
 
 
 47 
 
 55 
 
 64 
 
 10 
 
 48 
 
 58 
 
 68 
 
 79 
 
 11 
 
 58 
 
 70 
 
 82 
 
 98 
 
 12 
 
 69 
 
 83 
 
 97 
 
 115 
 
 13 
 
 80 
 
 96 
 
 113 
 
 136 
 
 14 
 
 92 
 
 111 
 
 131 
 
 158 
 
 15 
 
 104 
 
 129 
 
 150 
 
 180 
 
 16 
 
 117 
 
 146 
 
 170 
 
 205 
 
 17 
 
 131 
 
 165 
 
 192 
 
 230 
 
 18 
 
 
 184 
 
 220 
 
 256 
 
 As the edged lumber was taken from the larger and 
 straighter logs and after those logs had been sided on the 
 carriage and turned down, the yield was probably as large 
 as if all boards had been left round-edged.
 
 154 A MANUAL FOB NORTHERN WOODSMEN 
 
 TABLE III 
 
 Same logs but grouped according to mid diameter outside 
 bark. 
 
 
 Length of Log Feet 
 
 Mid 
 
 
 Diam. 
 
 10 
 
 12 
 
 14 
 
 Inches 
 
 Contents Board Feet 
 
 5 
 
 7 
 
 8 
 
 10 
 
 6 
 
 10 
 
 13 
 
 16 
 
 7 
 
 15 
 
 19 
 
 23 
 
 8 
 
 22 
 
 27 
 
 31 
 
 9 
 
 28 
 
 34 
 
 40 
 
 10 
 
 35 
 
 43 
 
 50 
 
 11 
 
 44 
 
 53 
 
 63 
 
 12 
 
 53 
 
 64 
 
 77 
 
 13 
 
 61 
 
 76 
 
 91 
 
 14 
 
 70 
 
 88 
 
 106 
 
 15 
 
 82 
 
 104 
 
 125 
 
 16 
 
 95 
 
 119 
 
 144 
 
 17 
 
 109 
 
 136 
 
 163 
 
 18 
 
 
 155 
 
 184 
 
 19 
 
 
 173 
 
 204 
 
 20 
 
 
 193 
 
 226 
 
 21 
 
 
 211 
 
 247 
 
 22 
 
 
 235 
 
 273 
 
 23 
 
 
 256 
 
 298 
 
 24 
 
 
 281 
 
 328 
 
 25 
 
 
 304 
 
 355 
 
 26 
 
 
 
 384 
 
 The figures of the above tables were closely confirmed, 
 except in the smallest sizes of logs, by similar figures ob- 
 tained by the U. S. Forest Service for the Forest Commis- 
 sion of New Hampshire. The saws in this latter test cut 
 J-inch kerf; 60 per cent of the product was round-edged 
 stuff, the balance being squared ; 70 per cent of the lumbei 
 was cut 1 inch thick, the balance 2^ and measured as 2 
 inches. In the sizes under 8 inches the Massachusetts 
 mills cut somewhat closer.
 
 MILL TALLIES 
 
 155 
 
 TABLE IV 
 
 Comparison of Maine Log Rule and results of sawing 
 as shown in Tables I and II. IZ-foot logs. 
 
 
 
 Results of Sawing 
 
 Top Diameter 
 Inches 
 
 Maine Log 
 Rule 
 
 Edged Lumber 
 Table I 
 
 Round-edged 
 Lumber 
 Table II 
 
 4 
 
 
 
 13 
 
 5 
 
 
 i4 
 
 17 
 
 6 
 
 'is 
 
 20 
 
 22 
 
 7 
 
 23 
 
 26 
 
 29 
 
 8 
 
 33 
 
 34 
 
 37 
 
 9 
 
 39 
 
 43 
 
 47 
 
 10 
 
 51 
 
 53 
 
 58 
 
 11 
 
 62 
 
 67 
 
 70 
 
 12 
 
 78 
 
 81 
 
 83 
 
 13 
 
 90 
 
 95 
 
 96 
 
 14 
 
 107 
 
 110 
 
 111 
 
 15 
 
 121 
 
 128 
 
 129 
 
 16 
 
 134 
 
 147 
 
 146 
 
 17 
 
 154 
 
 170 
 
 165 
 
 18 
 
 174 
 
 202 
 
 184 
 
 TABLE V 
 
 Yield in %-inch boards of pine logs 4 feet long (+ 2 inches 
 for trimming). 
 
 
 Yield 
 
 Basis 
 
 
 Surface Measure 
 
 
 4 inches 
 
 4 feet 
 
 3 logs 
 
 5 inches 
 
 6 feet 
 
 48 logs 
 
 6 inches 
 
 9 feet 
 
 121 logs 
 
 7 inches 
 
 13 feet 
 
 109 logs 
 
 8 inches 
 9 inches 
 
 17 feet 
 22 feet 
 
 75 logs 
 84 logs 
 
 10 inches 
 
 28 feet 
 
 40 logs 
 
 11 inches 
 
 34 feet 
 
 36 logs 
 
 12 inches 
 
 41 feet 
 
 21 logs 
 
 13 inches 
 
 49 feet 
 
 11 logs 
 
 14 inches 
 
 57 feet 
 
 6 logs 
 
 15 inches 
 
 66 feet 
 
 4 logs 
 
 16 inches 
 
 75 feet 
 
 6 logs
 
 156 A MANUAL TOR NORTHERN WOODSMEN 
 
 Log diameter taken at top end, inside bark. Saw kerf 
 inch. Boards not edged, but measured at an average 
 width on narrow side. From Massachusetts State Forester. 
 
 A cord of pine wood sawed and measured in {his fashion 
 yields about 1000 feet of box boards. Sawed one inch 
 thick, it is counted by Massachusetts box board men to 
 yield about 650 feet surface measure. 
 
 TABLE VI 
 
 Yield in round-edged boards of second growth hard 
 wood logs 12 feet long cut 1% inch thick with circular saw 
 cutting \-inch kerf. Based on 1831 logs. 
 
 Grouped according to top 
 diameter. 
 
 Grouped according to mid 
 diameter. 
 
 Top Diameter 
 Inside Bark 
 
 Yield, Surface . 
 Measure, of 12- 
 foot Logs 
 
 4 inches 
 
 8 feet 
 
 5 inches 
 
 11 feet 
 
 6 inches 
 
 16 feet 
 
 7 inches 
 
 22 feet 
 
 8 inches 
 
 30 feet 
 
 9 inches 
 
 39 feet 
 
 10 inches 
 
 51 feet 
 
 11 inches 
 
 65 feet 
 
 12 inches 
 
 82 feet 
 
 13 inches 
 
 100 feet 
 
 14 inches 
 
 120 feet 
 
 15 inches 
 
 141 feet 
 
 16 inches 
 
 165 feet 
 
 17 inches 
 
 192 feet 
 
 18 inches 
 
 222 feet 
 
 Mid Diameter 
 Outside Bark 
 
 Yield, Surface 
 Measure, of 12- 
 foot Logs 
 
 6 inches 
 
 11 feet 
 
 7 inches 
 
 15 feet 
 
 8 inches 
 
 21 feet 
 
 9 inches 
 
 29 feet 
 
 10 inches 
 
 37 feet 
 
 11 inches 
 
 49 feet 
 
 12 inches 
 
 61 feet 
 
 13 inches 
 
 75 feet 
 
 14 inches 
 
 91 feet 
 
 15 inches 
 
 107 feet 
 
 16 inches 
 
 126 feet 
 
 17 inches 
 
 143 feet 
 
 18 inches 
 
 165 feet 
 
 19 inches 
 
 187 feet 
 
 20 inches 
 
 210 feet 
 
 From New Hampshire Forestry Report for 1905-1906.
 
 CORD MEASURE 157 
 
 SECTION VIII 
 CORD MEASURE 
 
 The exact legal definition of the term " cord " varies in 
 different localities. For the present purpose it is a pile of 
 wood 8 feet long and 4 feet high, with the top sticks ris- 
 ing somewhat above the line, the sticks themselves sawed 
 4 feet long or chopped so as to give an equivalent. Such 
 a pile occupies 128 cubic feet of space. A cord foot is of 
 a cord, or a pile 4 feet high, 4 feet wide, and 1 foot long. 
 
 The actual solid contents of the wood which a piled cord 
 contains depends on a number of factors. First is the care 
 used in piling, a matter which need only be mentioned 
 here. Other factors are the straightness and smoothness 
 of the wood, its size, assortment, and whether split or not. 
 
 In regard to the first of these factors, while it is per- 
 fectly evident that straight, smooth, well-trimmed wood 
 must pile closer than its opposite, no hard and fast rules 
 can be given. Taking round wood of given quality, the 
 following rules can be laid down : 
 
 1. Large wood piles closer than small wood. 
 
 2. The same wood put up in one pile with sizes mixed 
 occupies a little less space than if the larger and smaller 
 sizes are piled separately. 
 
 3. The effect of splitting varies much with the quality. 
 Smooth, straight-grained wood when split may be packed 
 into the same space that it occupied before. On the other 
 hand, small or crooked wood when split piles much more 
 loosely. 
 
 In regard to the actual solid contents of a piled cord, 
 the following rules will approximately hold. 
 
 1. Smooth, round wood 8 inches and up in diameter, 
 such, for instance, as the best pulp wood, has .8 of its 
 contents in solid wood or yields 102 cubic feet solid to 
 the cord. White birch of best quality will yield nearly 
 or quite the same. 
 
 2. Small pulp wood from 3 to 8 inches in diameter con- 
 tains about .7 of its stacked volume in solid wood, or 9Q
 
 158 A MANUAL FOB NORTHERN WOODSMEN 
 
 cubic feet to the cord. Smooth hard wood yields about the 
 same. 
 
 3. Still smaller round wood, wood that is crooked and 
 knotty, and good split hard wood contains in solid wood 
 about .6 of the outside contents of the pile or 77 cubic feet 
 per cord. 
 
 4. Small, crooked wood cut from limbs may run down 
 as low as 27 solid cubic feet per cord. 
 
 5. 1 The longer a lot of wood is cut, the greater will be 
 the vacant space left in piling. Fair sized pulp wood, for 
 instance, which when cut 4 feet long will measure a cord, 
 if cut in 2-foot lengths will pile up in 2 to 3 per cent less 
 space. The same wood, on the other hand, if cut 8 feet 
 long and measured in the pile will measure nearly 6 per 
 cent more; if 12 feet long, about 12 per cent more. 
 
 Wood in thorough air-drying shrinks about 10 per cent 
 on the average, hard woods as a rule more than soft. If 
 wood checks and cracks freely, something like half the 
 total shrinkage is taken up in this form. Two inches extra 
 height in the pile are commonly allowed on green wood 
 in Massachusetts. 
 
 To Measure Wood in Cords. When the wood is 4 feet 
 long, measure the height and length of the pile in feet, 
 multiply together, and divide by 32. The result will be 
 contents in cords. If the wqod is more or less than 4 feet 
 long, multiply length, width, and height of the pile together, 
 and divide by 128. If wood is piled on sloping ground, 
 the length and height should be measured perpendicular 
 to one another. 
 
 For measurement of logs into cord measure, see page 138. 
 
 The French cord of the Province of Quebec is 8' 6" X 4' 
 X 4' 3", containing, therefore, 144 cubic feet, as against 
 128 for the cord current elsewhere. 
 
 1 See Zon on this subject in Forestry Quarterly, Vol. I, No. IV.
 
 PART IV 
 TIMBER ESTIMATING
 
 PART IV. TIMBER ESTIMATING 
 
 SECTION I. INTRODUCTION 
 
 SECTION II. INSTRUMENTAL HELPS 
 
 SECTION III. HEIGHT MEASUREMENT 
 
 SECTION IV. VOLUME TABLES AND TREE FORM 
 SECTION V. PRACTICE OF TIMBER ESTIMATING 
 
 A. Small and Valuable Tracts 
 
 B. Larger and Less Valuable Tracts .... 
 
 1. Type and Plot System 
 
 2. The Strip System 
 
 3. Line and Plot System 
 
 C. Summary 
 
 D. Pacific Coast Methods 
 
 161 
 162 
 165 
 167 
 173 
 174 
 186 
 187 
 188 
 192 
 195 
 196
 
 PART IV. TIMBER ESTIMATING 
 
 SECTION I 
 INTRODUCTION 
 
 METHODS of estimating timber vary greatly in different 
 regions and with different men. They vary also with the 
 value of the timber involved and with the purpose for 
 which the work is done. In this last connection cost is 
 a guiding principle; in general, that method of doing a 
 piece of work is best which secures a result sufficiently 
 accurate for the purpose with the smallest expenditure 
 of time and money. 
 
 Lump Estimate by the eye has not gone out of use, and 
 in fact never will cease to be employed. The immediate 
 judgment that a good lumberman forms, simply by walk- 
 ing through a piece of timber, that it contains a hundred 
 thousand, a million, or ten million feet, is for many pur- 
 poses close enough to the mark. 
 
 Similarly an experienced man, in timber of a kind 
 with which he is familiar, forms an idea by direct impres- 
 sion of how much a piece of land will yield per acre. The 
 men who can do that are more numerous than those who 
 are able to judge the whole piece. The faculty is easier 
 to acquire, and in general the results are safer and more 
 reliable. 
 
 Such estimates as these are indispensable in actual 
 business. Frequently they enable a man to pass correctly 
 upon a proposition for purchase or sale. But while 
 their necessity and their reliability within limits may be 
 admitted, no illusions should be indulged in with regard 
 to them. For one woodsman who can actually give a 
 close and reliable estimate after these methods, there are 
 many who only think they can ; nothing is better known 
 in the timber business than widely variant and totally 
 erroneous estimates of standing timber. Further, a man
 
 162 A MANUAL FOR NORTHERN WOODSMEN 
 
 who uses these methods is frequently very lame when he 
 gets into a country with which he is unfamiliar. Lastly, 
 when time consumed and training involved are considered, 
 estimates of this nature may not be the cheapest by any 
 means. 
 
 There is a general tendency among timber estimators, 
 commendable in the main on the ground of safety and 
 conservatism, to put their figures below the mark. As for 
 the general degree of accuracy obtained, there seems to 
 be no reason founded on experience this side of the At- 
 lantic to greatly change the verdict of experience in Europe ' 
 that good and experienced men in timber with which they 
 are familiar are liable to errors up to 25 per cent. 
 
 It is true, moreover, that the weakness of these tra- 
 ditional methods is generally recognized. More careful 
 and elaborate methods are in fact practiced in many 
 sections of the country, and the area is fast extending in 
 which the treatment demanded by the situation is not 
 really an estimate but a survey. 
 
 SECTION II 
 INSTRUMENTAL HELPS 
 
 The helps that may be used in the survey of standing 
 timber are as follows: 
 
 1. FOR DIAMETER MEASUREMENT 
 Calipers for measuring the diameter of trees may be 
 constructed by the woodsman himself, or they can be 
 purchased of dealers. The best are made of light-colored 
 hard wood and have the inches plainly marked on both 
 flat sides of the bar. The jaws are detachable for con- 
 venience in transportation, and the sliding arm is so fitted 
 with adjustable metal bearings that it is truly square and 
 gives a correct diameter when pressed firmly against a 
 tree or log. 
 
 Substitutes for the caliper, useful in some circumstances, 
 are the Circumference Tape, a steel tape so graduated 
 that when a circumference is measured a diameter is read, 
 1 Schlich's "Manual of Forestry."
 
 INSTRUMENTAL HELPS 
 
 163 
 
 and the Biltmore Stick. This last is in construction a 
 wooden bar of about the dimensions of an ordinary scale 
 rule; in use it is held horizontal, tangent to the tree being 
 measured, and at the natural (but a constant) distance 
 from the eye of the observer. Then, one end of the stick 
 being aligned with one side of the tree, where the line of 
 sight to the other side cuts the stick it is graduated for the 
 given diameter. 1 Both instruments have proved service- 
 able on the Pacific Coast, where the timber is so large that 
 a caliper is cumbersome, and because of their portability 
 they have a field of use elsewhere. They are not, however, 
 as quickly manipulated as the caliper hi steady work on 
 timber of ordinary dimensions. 
 
 ] 
 
 TREE CALIPER 
 
 2. COUNTER OR TALLYING MACHINE. TIMBER SCRIBE. 
 BARK BLAZER 
 
 These simple little instruments, the last of which can 
 be home-made if necessary, are very serviceable in forest 
 work, particularly in timber estimating. 
 
 3. THE DENDROMETER 
 
 The dendrometer is an instrument for measuring the 
 diameter of a tree at a considerable distance above the 
 ground. There are several forms of this instrument, 
 most of them costly and complicated, that are employed 
 in scientific investigation. With these the practical woods- 
 
 1 See Appendix on theory and accuracy of this instrument.
 
 164 A MANUAL FOR NORTHERN WOODSMEN 
 
 man has no concern. Such a man when he wishes to 
 know the diameter of a standing tree at a point out of 
 reach will ordinarily either estimate it or cut the tree 
 down. 
 
 ARK BLAZER 
 
 Occasionally, however, timber 
 may be met with which is of suf- 
 ficient value for special purposes 
 to require measurement in this 
 way. In such a case the engineer's 
 ( ,^ -^-^ ^^ transit may be employed, and by 
 3 1 its aid it is not a difficult matter 
 
 * to determine either the height at 
 which any given diameter is at- 
 tained or the diameter at any given 
 height. A very simple little in- 
 strument for diameter measure- 
 ment has been devised, which is described by its inventor 
 as follows : * 
 
 TIMBER SCRIBE 
 
 " The Biltmore pachymeter is used in connection with 
 a target or piece of board graduated in inches, marked 
 
 1 Forestry Quarterly, Vol. IV, p. 8.
 
 HEIGHT MEASUREMENT 165 
 
 black and white, which target is fixed horizontally at any 
 point desirable at the base of the tree. 
 
 " The instrument itself consists of a piece of metal about 
 18 inches long and l inches wide, containing a longi- 
 tudinal slot about J inch wide and 17 inches long. The 
 edges of this slot must be strictly parallel. Its actual 
 width is entirely irrelevant from the mathematical stand- 
 point. 
 
 " It might be stated that any stick or pole, even a walking- 
 cane, having parallel edges, will answer the purpose of 
 establishing and measuring upper diameters. The Bilt- 
 more pachymeter is merely a device convenient to handle. 
 
 " The observer holds the pachymeter pendulum fashion 
 by the hand of the outstretched arm in a position parallel 
 to the tree trunk, and moves the instrument backward 
 or forward until the edges of the slot cut off even with the 
 desired diameter shown on the target. Then, the eye 
 following upward along the trunk and sighting through 
 the slot, that point on the tree bole is readily obtained 
 where the bole cuts off with the edges of the slot. The 
 position of this point above ground can be ascertained 
 easily with the help of any hypsometer." 
 
 SECTION III 
 HEIGHT MEASUREMENT 
 
 There are many methods of measuring the height of 
 trees. As serviceable as any are the following: 
 
 1. Windfalls are often of great assistance in ascertain- 
 ing the height of timber. 
 
 2. A pole 15 or 20 feet in length may be set up along- 
 side the tree to be estimated and then, standing some dis- 
 tance away, the cruiser may run his eye up the tree and 
 judge how many times the length of the pole will be con- 
 tained in it. A pencil held erect at arm's length in range 
 of the pole and then run up the tree will help the eye in 
 making the judgment. 
 
 3. A cane or staff may be used on the principle of similar 
 triangles. Hold the staff firmly in the hand with the arm 
 straight and horizontal. Swing the end of the staff down
 
 166 A MANUAL FOR NORTHERN WOODSMEN 
 
 by the face and adjust the hold till the end of the staff 
 just comes by the eye. The distance from the e"ye to the 
 staff and from the hand up to the end of the staff are now 
 equal. Go off from the tree to be measured, holding the 
 staff erect, until you can sight by the fist to the base of the 
 tree and by the top of the staff to the top of the tree. Pace 
 or measure to the tree and this will give its height. 
 
 4. The Abney clinometer, shown on page 93 of this 
 work, may be used for height measurement in much the 
 same manner. Set the level tube at an angle of 45 with 
 the line of sight and go off from the tree on a level with 
 
 FAUSTMANN'S HEIGHT MEASURE 
 
 its base until, sighting at the top of the tree, you see by 
 the bubble that the tube is level. The distance from the 
 observer to the tree is then equal to the tree's height. 
 
 5. A second method employing the same instrument 
 is as follows : Stand at a point where both the top and the 
 base of the tree can be seen and at some convenient dis- 
 tance from it, as 100 feet. Sight to the top of the tree and 
 observe the angle of inclination, and again to the base of 
 the tree, observing that angle also. Go into the table of 
 tangents with the angles in turn, find the decimals corre- 
 sponding, and multiply by the length of base. The sum 
 of the two figures is the total height of the tree.
 
 VOLUME TABLES AND TREE FORM 167 
 
 Example : Standing 80 feet from a tree, the angle to the top is 
 found to be 31 and that to the base 8} , of depression. From the 
 tables the tangent of 31 is found to be .6009 ; multiplying this by 
 80 gives 48 feet for the height of the tree above the level of the eye. 
 Again the tangent of 8J is found from the tables to be .1495 and 
 this multiplied by 80 gives 12 feet. 48 + 12 = 60 feet, the total 
 height of the tree. 
 
 6. Faustmann's height measure works in much the 
 same manner, but gives the desired height directly without 
 the use of tables. This instrument may be had of dealers 
 at a cost of from $6.50 up. It is compact, not complicated, 
 and will be found of great service in estimating. 
 
 SECTION IV 
 VOLUME TABLES AND TREE FORM 
 
 A competent woodsman can tell from the looks of a 
 tree somewhere near what it will scale, saw out, or yield 
 in cord wood according to the practice with which he is 
 familiar, and this without any measurements. Or a 
 caliper may be used instead of the eye for diameter, and 
 some kind of determination made of the height of the 
 tree or the length and size of the logs into which it may 
 be cut. The point of such judgment and measurements 
 as a rule is their wider application. The single tree so 
 examined is taken as the type of many, and the stand of 
 an acre or of a considerable territory is thus estimated. 
 
 In this process the assumption is made that trees of the 
 same dimensions are approximately similar in shape, 
 while for the individual tree the fundamental factors de- 
 termining contents are recognized as height and diameter. 
 These two factors in any kind of timber work cannot 
 possibly be disregarded. Whatever the scaling or mill 
 practice of a locality may be, and into whatever form a 
 tree's trunk is dissected before manufacture, the height of 
 the tree and its diameter at some point near the base are 
 the chief factors determining contents. These factors, 
 consciously or unconsciously, are in the mind of every 
 estimator. 
 
 Scientific study of tree form began by making the same 
 assumption and selecting the same factors. While it
 
 168 A MANUAL FOR NORTHERN WOODSMEN 
 
 was known that single trees depart widely from the 
 type, it was assumed that for trees having the same di- 
 ameter and height an average volume could be ascer- 
 tained which would hold approximately throughout the 
 distribution of the species. Proceeding on this assump- 
 tion, tables were worked out for the different tree species 
 and these when applied in actual business proved close to 
 the fact and vastly improved the work of timber valuation 
 in Germany a hundred years ago. 
 
 European measurements of logs and standing timber do 
 not recognize anything corresponding to the board foot, 
 but everything is reckoned in solid contents. The same 
 rule holds in the scientific study of tree form in all coun- 
 tries where it has been pursued, the unit in the United 
 States being the cubic foot. For all such studies, too, the 
 total height of the tree as a well-defined factor capable 
 of ready measurement has usually been employed rather 
 than any size limit set part way up, and a diameter breast 
 high, or 4^ feet above the ground, has been settled upon 
 as the basis of all diameter comparisons. The area of a 
 cross-section of a tree at this point is called the basal area, 
 and the same term is applied to a number of trees or to a 
 stand of timber. In the study of tree form, the term form 
 factor has proved to be a useful one. The form factor of a 
 tree is the percentage which the volume of any tree (usu- 
 ally reckoned in cubic feet, outside the bark) makes of 
 the volume of a cylinder having the same height and the 
 tree's breast diameter. Illustration: A tree 15 inches in 
 breast diameter and 75 feet high may, after caliper meas- 
 urement every 4 feet along it, prove to have 38.6 cubic feet 
 in it. A cylinder of these dimensions contains 92 cubic 
 feet. The form factor, therefore, is .42. 
 
 For many years past the study of tree form has been 
 ardently pursued, and many interesting facts and laws 
 have been ascertained. In large measure these results 
 have been brought to bear on the actual business of Euro- 
 pean countries where timber is grown as a crop under 
 uniform conditions. In this country, where the forests 
 are natural and as a rule irregular, it will be many years 
 before the same can be true. The following, however,
 
 VOLUME TABLES AND TREE FORM 169 
 
 may for one reason or another be of interest to the worker 
 in timber: 
 
 (a) Near the ground a section taken lengthwise of a 
 tree is concave outward, due to the swell of the roots. 
 Above that, to a point somewhere near the lower limbs of 
 a forest-grown tree, the stem has almost a true taper. 
 From the lower limbs up, the form is roughly conical, with 
 a sharper taper than below, the taper usually increasing 
 toward the top. 
 
 (6) Of two trees having the same breast diameter, the 
 shorter will usually have the larger form factor. This 
 results from the relation just mentioned. Of two trees 
 having the same height, the stouter, more openly grown 
 tree will usually have a little larger form factor than the 
 other. 
 
 (c) Of two trees having the same dimensions, the older 
 one, as a rule, has the larger form factor. The effect of 
 other conditions of growth can seldom be clearly traced. 
 
 (d) Different soft wood species do not differ from one 
 another so greatly but that a volume table made for one 
 may for some purposes be used for others. 
 
 A large form factor in all these cases simply means 
 that the given tree more nearly approaches the form of a 
 cylinder, or, in other words, that it has a large amount of 
 wood for its height and diameter. That carries with it 
 more scale, more sawed lumber, or more cord wood. 
 
 A table giving the contents of trees of stated dimensions 
 is called a Volume Table. For scientific purposes solid 
 content is given, standard measure, but a table may be 
 worked out in cords, board feet, or any other unit required. 
 The tables employed by European foresters at the present 
 day are worked out commonly on the basis not only of 
 height and diameter but of age classes or of some other 
 determining factor, and they have proved to give the con- 
 tents of standing timber very accurately. 
 
 Tables of this kind have also been frequently devised 
 for estimating in this country. Usually these are local, 
 worked out in the timber of the region in question accord- 
 ing to local scaling methods; often also allowing the cull 
 which is found to characterize the region. Such volume
 
 170 A MANUAL FOR NORTHERN WOODSMEN 
 
 tables have frequently been based on diameter alone. In 
 other cases and this is essential unless a region is very 
 uniform in its timber growth height has been taken 
 into consideration as well. 
 
 Thus many western and southern cruisers have made up 
 tables giving the contents of trees of each inch in diameter 
 and yielding 2, 3, 4, etc., logs as these would be cut in 
 local practice. Again, an old Adirondack manager made 
 up a table showing the number of spruce required per 
 cord of pulp wood for trees 7, 8, 9, etc., inches in di- 
 ameter, and short, medium, or tall, as the case for his 
 region might be. Local volume tables, thoroughly based 
 and used correctly, are the most reliable kind. 
 
 General Volume Tables for business purposes are of 
 two varieties, the trees being classified either by total 
 height or by length of merchantable timber. The assump- 
 tion on which the first is based, that trees which have the 
 same diameter and total height do not, when taken in 
 numbers, vary in form throughout the region of their 
 distribution, may, with a caution on the matter of age, 1 
 be considered safe for most purposes. It is true, however, 
 that some Pacific Coast timbers, with a very variable 
 thickness of bark and the root swelling of large trees run- 
 ning above a man's height oftentimes, have to be handled 
 with special caution. 
 
 The other variety of tables classifies trees in height by 
 the number of standard log lengths they will yield or the 
 height at which their boles attain a specified diameter. 
 Under this plan the point to be observed is brought nearer 
 the estimator. It is not, however, as sharply defined a 
 point as in the other case, while, as explained on pages 
 277-278, special opportunities for error arise through vari- 
 ability in lumbering practice. 
 
 Another matter that has to be reckoned with in the 
 valuation of standing timber, and which becomes in some 
 species and regions a consideration of great importance, is 
 defectiveness in quality. This no general volume table can 
 allow for. It has to be worked out for each locality accord- 
 ing to the judgment or experience of the estimator. 
 1 See pages 169, 262, and 275.
 
 VOLUME TABLES AND TREE FORM 171 
 
 Thirdly, a general volume table given in units of mer- 
 chantable material assumes certain standards of lumber- 
 ing practice. In one region, or on a property carefully 
 handled, stumps may be sawed close to the ground, tops 
 taken up to a small diameter, and every economy em- 
 ployed in cutting to advantage the material between; 
 while in another region, or on another property, a large 
 percentage of the wood of every tree cut down may be 
 left to rot on the ground. Similarly in the mill there is 
 great variety of practice, location, equipment, market re- 
 quirement, and men's capacity all having their effect here, 
 as was explained and illustrated in earlier pages of this 
 work. Then the question may not be at all of saw practice, 
 but of the results of scaling, and here, as every lumberman 
 knows, there is the widest diversity. The scale rules in 
 actual use differ from one another in the values they give 
 to the same log, in some cases by a ridiculous amount, 
 while the practices that have grown up in their application 
 are in some cases entirely artificial. Details need not be 
 entered into here a word to the wise is sufficient but 
 an example will bring the fact home. The Maine log rule, 
 for instance, is believed by many to be the best commercial 
 rule on the market, agreeing closely with the results of 
 good saw practice; yet a Penobscot mill man once testi- 
 fied before a legislative committee that buying 26 million 
 feet of logs by market scale for a season's stock, he sawed 
 30 million feet of long lumber out of it and slabbed heavily 
 for a pulp mill besides. 
 
 Of the volume tables included in this work it may be 
 said that their basis is clearly stated, including the num- 
 ber of trees involved, the standards of cutting and mill or 
 scaling practice assumed, and the responsibility for the 
 observations. They can, therefore, to a large extent be 
 changed over to suit practice of another type. The tables 
 original with this work, those for spruce and white pine, 
 are based on figures taken from a large number of trees. 
 These came from a wide range of country, and the compu- 
 tations show that no clear difference of form was intro- 
 duced by the element of locality. Each tree was computed 
 separately for its volume in the units desired (cubic feet,
 
 172 A MANUAL FOR NORTHERN WOODSMEN 
 
 board feet, or cords); the results have been averaged, 
 evened by curves, and then the board-foot tables have 
 been discounted by a small percentage to allow for normal 
 defects of form and quality. Cutting practice that is 
 economical, but not extreme, has been supposed through- 
 out, the idea being to get, as nearly as possible, a conserva- 
 tive figure for good and economical practice. 
 
 In applying all these tables, considerable defects must be 
 allowed for in the form of a discount. It is further to be 
 clearly understood that they apply to timber as it runs 
 and may be considerably off as applied to single trees. 
 
 In volume tables for hard woods merchantable length 
 is in most cases preferable to total height as a factor 
 because these trees characteristically spread out at the 
 top, at once rendering total height hard to measure and 
 destroying utility for lumber. Such tables also, because 
 of greater irregularity of form and greater liability to 
 defect in hard woods, are in general less trustworthy than 
 soft wood tables. Several "graded volume tables," 
 classifying the yield of trees by lumber grades, are in 
 existence, but their utility apart from the local conditions 
 in which they were constructed does not seem clear. 
 
 The way in which these volume tables may be tested 
 and made to conform to the practices of any given locality 
 is illustrated as follows: 
 
 A spruce property is to be explored on which cutting and 
 scaling methods are as follows : Timber runs up to about 
 20 inches in diameter and 75 feet in height ; trees are cut 
 down to the size of 12 inches on the stump or 11 breast high. 
 Logs cut for saw lumber, one log from a tree, cut off where 
 it will scale best. Logs are therefore seldom over 40 feet 
 long and run from that down to 28 or 30. Scaling done 
 with Maine log rule. If a log is 26 feet long or under, it is 
 scaled as one log with the top diameter inside bark ; if 27 
 to 30 feet, as two logs of equal length giving the butt log 
 an inch larger diameter than the top ; from 31 to 35 feet in 
 the same way but allowing 2 inches "rise," and 3 inches on 
 log lengths of 36 to 40 feet. In addition a level discount 
 of 10 per cent is made on all logs to cover defects. 
 
 A half day's time spent following the logging crew and
 
 PRACTICE OF TIMBER ESTIMATING 
 
 173 
 
 examining trees as they are felled results as follows: 
 20 normal trees 17 to 20 inches in breast diameter when 
 scaled by the above methods give 4730 feet B. M., while 
 trees of the same dimensions are given in the volume table 
 on page 238 5720 feet. The actual scale, therefore, is 17 
 per cent less than the tabular values. 
 
 24 trees 14 to 16 inches in diameter which by the table 
 should yield 4080 feet scale up 3480, or 15 per cent less. 
 
 30 trees 11 to 13 inches in diameter that by the table 
 should yield 4380 feet, actually scale 3500, or 20 per cent 
 less. 
 
 The figures of the volume table may now be reduced by 
 these percentages in those heights and sizes where on the 
 given job the figures are required. The working table 
 will then be as follows: 
 
 Breast 
 
 Feet in Height 
 
 
 
 Inches 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 11 
 12 
 
 1 
 
 56 
 68 
 
 64 
 80 
 
 72 
 88 
 
 % 
 
 92 
 108 
 
 13 
 
 72 
 
 80 
 
 92 
 
 100 
 
 112 
 
 125 
 
 14 
 
 85 
 
 100 
 
 110 
 
 125 
 
 140 
 
 155 
 
 15 
 
 100 
 
 115 
 
 130 
 
 145 
 
 160 
 
 175 
 
 16 
 
 
 130 
 
 143 
 
 155 
 
 175 
 
 ISO 
 
 17 
 
 
 142 
 
 158 
 
 175 
 
 ISO 
 
 210 
 
 18 
 
 
 155 
 
 175 
 
 195 
 
 210 
 
 230 
 
 19 
 
 
 175 
 
 195 
 
 215 
 
 240 
 
 265 
 
 20 
 
 
 195 
 
 220 
 
 245 
 
 270 
 
 295 
 
 SECTION V 
 PRACTICE OF TIMBER ESTIMATING 
 
 The methods that should be employed in a survey of 
 standing timber depend on a great variety of facts of which 
 the main ones are these: the size of the tract to be ex- 
 amined, the method and fineness of its subdivision, the 
 variety in its stand of timber, the value of the timber, and 
 the experience and qualifications of the estimator. These 
 methods are best discussed in two divisions, first, 
 methods for small tracts with valuable timber as a rule; 
 and second, those for large tracts where more extensive 
 processes must be employed.
 
 174 A MANUAL FOR NORTHERN WOODSMEN 
 
 A. SMALL TRACTS 
 
 1. In the case of very valuable timber it may pay the 
 owner or purchaser to examine each tree individually, 
 ascertain its contents carefully, and study it for defects. 
 The net contents of each tree as so ascertained will then 
 be put down separately in the notes, and in case several 
 parties are interested, each tree may be stamped with a 
 number to correspond with one in the notes. At any rate, 
 blazing each tree examined is a good means to make sure 
 that all are taken and to prevent measuring any twice. 
 
 Such procedure as this is appropriate to very large and 
 valuable pine or to valuable but over-mature hard woods, 
 which are especially liable to be defective. Volume tables 
 might help in such cases, but they cannot be fully trusted ; 
 a scale rule at hand would be to many men of quite as 
 much assistance. For instruments, a caliper would come 
 in play along with an instrument to measure heights 
 accurately, while use might be found for some form of 
 the dendrometer. But the best part of the equipment of 
 the estimator in such cases is local experience in cutting 
 and sawing the same class of timber. 
 
 2. When timber in good stand and of considerable 
 value is involved, it may be advisable to caliper each of 
 the trees and measure a sufficient number to obtain the 
 range of heights. After the stand is measured, sample 
 trees of different sizes may be estimated after careful 
 examination, or such trees may be felled and measured. 
 Better than either of these methods, however, is a volume 
 table giving the yield of trees of the given kind and dimen- 
 sions. Volume tables, however, cannot be depended on 
 to allow justly for defects. That is a matter for the judg- 
 ment of the estimator. 
 
 The above method works well in woods of approximately 
 even type. When, however, the stand has a great variety 
 of form and quality, the difficulty in making a true valua- 
 tion is greater. In that case it may be practicable to cut 
 it up into nearly homogeneous parts. 
 
 The following example taken from practice will illus- 
 trate the methods of working in a simple case.
 
 PRACTICE OF TIMBER ESTIMATING 
 
 175 
 
 Estimate of about 7 acres of land, covered nearly throughout 
 with white pine standing fairly evenly, but not as a rule very dense. 
 Concluded after inspection that no such differences of type or 
 
 Field Observations 
 
 Computed Volumes 
 
 Breast 
 Diam. 
 
 No. 
 Trees 
 
 Observed Heights 
 
 Deduced 
 Height 
 
 Scale 
 Each 
 
 Total 
 Scale 
 
 8" 
 
 85 
 
 51-47-50-54-59 
 
 50' 
 
 50' 
 
 4250' 
 
 9 
 
 70 
 
 50-47-52-48-56-57 
 
 55 
 
 70 
 
 4900 
 
 10 
 
 70 
 
 69-55 
 
 60 
 
 95 
 
 6650 
 
 11 
 
 75 
 
 56-56-66-67-68 
 
 65 
 
 130 
 
 9750 
 
 12 
 
 78 
 
 72-75-69-80-69-63 
 
 69 
 
 162 
 
 12636 
 
 13 
 
 69 
 
 57-65-71-75-73 
 
 73 
 
 203 
 
 14007 
 
 14 
 
 66 
 
 77-75 
 
 76 
 
 245 
 
 16170 
 
 15 
 
 81 
 
 74-78-80-79-83 
 
 78 
 
 290 
 
 23490 
 
 16 
 
 71 
 
 74-80-85 
 
 80 
 
 335 
 
 23785 
 
 17 
 
 63 
 
 77-77-86-81 
 
 80 
 
 370 
 
 23310 
 
 18 
 
 63 
 
 77-83-86 
 
 80 
 
 405 
 
 25515 
 
 19 
 
 52 
 
 80-77 
 
 80 
 
 445 
 
 23140 
 
 20 
 
 47 
 
 75-82 
 
 80 
 
 485 
 
 21855 
 
 21 
 
 32 
 
 79-83-81 
 
 80 
 
 525 
 
 17800 
 
 22 
 
 12 
 
 76 
 
 80 
 
 570 
 
 6840 
 
 23 
 
 11 
 
 79-82-83 
 
 80 
 
 620 
 
 6820 
 
 24 
 
 6 
 
 77-86-77-82 
 
 80 
 
 665 
 
 3990 
 
 25 
 
 8 
 
 87 
 
 80 
 
 715 
 
 5720 
 
 26 
 
 3 
 
 
 80 
 
 770 
 
 2310 
 
 Total 252938 
 
 Plot of Observed Heights and 
 Deduced Height Curve 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 . 
 
 
 
 
 
 
 
 
 
 
 did 
 
 ?- 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 ss? 
 
 : 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A fin 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7> rr 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 B M 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 40 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 9 10 11 12 ia 14 15 16 17 18 19 20 21 22 23 24 25 26 27 
 
 Diameter Breast High Inches 
 
 form existed as to call for differentiation of treatment. Instru- 
 ments employed, caliper and Faustmann's hypsometer. Steps of 
 the survey as follows: 
 
 a. Merchantable trees (those 8 inches and over in diameter 
 breast high) calipered and scored in inch diameter classes.
 
 176 A MANUAL FOR NORTHERN WOODSMEN 
 
 b. Some 60 heights measured with the hypsometer. These 
 might have been averaged for each diameter class, but a better 
 plan is to plot all the heights on cross-section paper and draw a 
 curve through them as in the accompanying sketch. From this curve 
 the average height of the 8-inch trees is read off as 50 feet, of the 
 9-inch trees as 55 feet, and so on. The larger trees of the grove, 
 those 16 inches and over in diameter, averaged 80 feet in height. 
 
 c. From the proper volume table the contents of a single tree of 
 each size class is now taken and multiplied by the number of trees 
 in the class. For the tract in question Table No. 4 gives the 
 figures wanted, the product of the trees in boards, both round-edged 
 and square-edged lumber. In this table the contents of a tree 8 
 inches m breast diameter and 50 feet high is given as 50 feet B. M. ; 
 that of a tree 9 inches x 55 feet, 70 feet, and so on. No discount 
 appearing necessary for defects, by addition of the contents of the 
 size classes the total stand of the lot is obtained. This comes to 
 253 M feet, of which in the practice of the locality 20 per cent may 
 be sawed into good plank, 30 per cent into edged boards, and the 
 balance of 50 per cent, the smaller trees and rougher logs, put into 
 round-edged box-board lumber. The recorded figures, the plot 
 and height curve, and a table showing the way the figures are put 
 together, are given on the preceding page. 
 
 The estimate after this fashion of 250 M feet of timber 
 of this size is a light day's work for two men. Three men 
 form an economical crew for big jobs. 
 
 3. In the valuable timber lands of the Lake States and 
 South it is customary to estimate each forty acres by 
 itself, and the methods of estimation frequently cover 
 the whole stand. Pacing is largely used as a measure of 
 distance, and the cruiser is generally equipped with some 
 kind of volume table giving as often as not the board 
 contents of trees of different diameters yielding 2, 3, 4, or 
 5 16- ft. logs. Usually two men work together. In that case 
 the helper may run a compass line across one end of the 
 " forty," ten rods or so from its boundary, leaving marks 
 enough so that on the return trip it can be followed. 
 Through the strip so cut off the cruiser circulates, keep- 
 ing watch of his other bound and scoring down, as he 
 passes, the merchantable trees according to species and 
 in appropriate classes. As a rule very little measurement 
 of height or diameter has been done in the past. The two 
 men keep abreast of one another. When one strip has 
 been covered another is taken in the same way. After 
 the whole " forty " has been covered addition of the
 
 PRACTICE OF TIMBER ESTIMATING 
 
 177 
 
 figures obtained gives its timber stand. In well-timbered 
 land two to four " forties " a day can usually be covered 
 by these methods. 
 
 In recording the results of such an estimate the size 
 and quality of the timber are of course noted as well as 
 its amount, and general notes on the growth, topography, 
 and lumbering conditions of the land are also recorded. 
 Following are sample notes of such an exploration: 
 
 Twp. 29 N. R. 7 W. S. E. i of S. E. i of Sec. 8. 
 White Pine, 7 logs average to M. ; 30% uppers 835,000 
 Norway Pine, 8 logs to M. 110,000 
 
 Hemlock, 11 logs to M. 175,000 
 
 Basswood, 7 logs to M. 15,000 
 
 Maple, 14 logs to M. 65,000 
 
 Total 1,200,000 
 
 Land slopes to North. Clay soil; very stony. Two ravines 
 running N. W. and S. E. through the " forty." Tamarack swamp 
 of about five acres in N. W. corner. 
 
 Another method of timber cruising carried out by one 
 man alone is described as follows in the "Woodsman's 
 Handbook " : 
 
 A "forty" is 80 rods square. The cruiser who uses the method 
 now to be described has found by trial that 500 of his natural 
 paces are required to go 80 
 rods. He begins at the cor- 
 ner of a " forty," say at the 
 southeast corner, and steps 
 off 125 paces on the south 
 line, and so covers one- 
 quarter of the side. He then 
 stops and, facing north, 
 counts the trees of the 
 "forty," first to an estimated 
 distance of 125 paces on the 
 right hand, and then to an 
 estimated distance of 125 
 paces on the left hand, and 
 m each case to a distance 
 of 100 paces in front of him, thus including the area represented 
 in the diagram as Plot I. He then steps north 100 paces, and 
 in the same way counts the trees in Plot II, and repeats the opera- 
 tion successively for Plots III, IV, and V. He has then a complete 
 count of the trees on the eastern half of the " forty." He then 
 walks west 250 paces along the north line of the " forty." Facing 
 south, he now counts all the trees on Plots VI, VH, Mil, TK, 
 and X in the same way as before, and thus completes counting 
 the trees on the entire " forty. " 
 
 
 Plot 
 
 VI 
 
 Plot 
 
 V 
 
 
 Plot 
 
 VII 
 
 Plot 
 
 TV 
 
 
 Plot 
 
 VIII 
 
 Plot 
 
 III 
 
 
 Plot 
 
 IX 
 
 Plot 
 
 II 
 
 
 Plot 
 
 X 
 
 Plot 
 
 I
 
 178 A MANUAL FOR NORTHERN WOODSMEN 
 
 There is, of course, great variety in the details of the 
 work as practiced by different men, and a plan that is 
 really inadequate may be effective nevertheless because 
 of the ability of the cruiser. Such a method as the fore- 
 going cannot be called a survey. It is an estimate purely, 
 depending on the training of the cruiser and subject to the 
 errors which change in his condition and his surroundings 
 introduce. Nor does the fact that all the area is supposed 
 to be covered give assurance on the matter of accuracy. 
 It may indeed set up a standard too difficult to be actually 
 carried out, so becoming a source of additional error. 
 
 4. The following, from an old Michigan cruiser whose 
 work has been largely in hard woods, serves to introduce 
 the principle of covering a percentage of the tract to be 
 estimated, a principle more fully illustrated in connection 
 with large tracts on later pages. 
 
 I have been a surveyor, engineer, "land-looker" since boyhood, 
 and the system that I use is based upon the information that I 
 have been able to pick up along that line during that period. 
 The work has carried me to the forests of nearly every state that 
 counts forest products among its most important assets. 
 
 The usual object of an estimate is to fix a value that can be 
 used as a medium of exchange, although I have recently been 
 called upon to estimate many tracts just before the commence- 
 ment of logging operations in order to ascertain what the probable 
 product would be. 
 
 The report of the cruiser is required to show the log scale of a 
 given tract, also the amount of tan bark, cord wood, telephone 
 poles, railroad ties, etc., in fact the entire forest product that is 
 of value. This must be not only of standing timber, but of down 
 timber that has a value as well. 
 
 His report must also show the topography of the tract, and the 
 channels through which the product must be passed in the course 
 of its transportation from the land, whether by railroad, water, or 
 logging road. 
 
 This work must be based upon some system that will eliminate 
 so far as is possible all guesswork. There are many systems of 
 cruising now in use, each of which has its advocates. I do not 
 know of any other cruiser who is using the same system that I use, 
 perhaps for the reason that I have made it up from my own work. 
 
 In my work I use a tree caliper. I have a book printed especially 
 for the tally of the trees as I call them off to my assistant. I have 
 also a form of report blank made to fit the rest of the scheme. 
 
 You will note that I number each forty-acre parcel in an undi- 
 vided section on the same plan that sections are numbered in a
 
 PRACTICE OF TIMBER ESTIMATING 
 
 179 
 
 township, except of course that there are only 16 lots in this case. 
 Hereafter the term " lot " applies to a forty-acre tract. 
 
 Arriving at the tract to be examined, I usually first go entirely 
 around the area so as to discover if there are any high ridges, and 
 if so to determine their course ; also to see whether or not the tract 
 is all timbered, and to locate any vacant areas on its outer edges. 
 While making this circuit we mark points at each 125 paces on the 
 boundary. If the land is uniformly level, it is immaterial at which 
 point on the boundary line the work is commenced. If the tract 
 is very rolling, the strips taken must be 
 at as nearly right angles as is possible. 
 
 'R3.W.. 
 
 ____________ Go..Cheboygan. ___ Sta.te.Mich 
 
 Suppose we are at the southeast corner of the section and that we 
 have an entire section of fairly level land to examine. My pacer 
 and compassman (I have but one assistant) steps off 125 paces, 
 say in a westerly direction, along the south line of lot 16, starting 
 from the southeast corner of the section. This brings us to a 
 point 20 rods west of this corner and a line drawn directly north 
 from this point should be parallel with the east line of the lot, also 
 parallel with the center line, if one were in existence, and 20 rods 
 distant from each of them. We proceed north from this point. At 
 50 paces the assistant halts, gets his tally-book and hard pencil into 
 action, and jots down each tree as I call them off to him. He 
 heads the vertical columns with the varieties of timber common to 
 the tract and tallies each kind under the proper heading.
 
 180 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 Examination Lot.../. 
 
 Made by. 
 
 Sec,__29 
 
 May, 1908- 
 
 C. L. 
 
 12- 
 
 12- 
 
 13- 
 
 13- 
 
 13 
 
 14 
 
 14 
 
 14 
 
 15 
 
 15 
 
 15 
 
 16 
 
 10 
 
 It! 
 
 10 
 
 Maple 
 
 Bass 
 
 Beech 
 
 ffemloct 
 
 11 
 
 | 
 
 
 4S 
 
 i>;a 
 
 
 
 
 
 
 
 
 
 
 
 
 II 
 
 
 19 
 
 fii 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 nil m 
 
 
 ISO 
 4W 
 
 
 
 
 Vi 
 
 ft 
 
 I'HI 
 
 
 J,V) 
 
 1 
 
 
 50 
 
 iltl 
 
 
 Uf) 
 
 
 
 
 
 1 
 
 
 
 110 
 
 1 
 
 
 r 
 
 11 
 ta mil 
 
 
 UB 
 
 V,-r> 
 
 
 
 
 
 II 
 
 
 
 3M 
 
 II 
 
 
 72 
 140 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ml 
 
 H,ltHj. 
 
 // 
 
 Kr,4, 
 
 KM 
 
 
 
 
 <tf) 
 
 II 
 
 II 
 
 1 
 
 
 57f> 
 510 
 
 III 
 
 
 <32 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 As soon as the assistant reports that he is ready I take the 
 nearest tree and put the calipers upon it at a point where it would 
 be cut in ordinary logging operations. I then walk around the tree 
 and " size it up " generally to find any defect that may exist, also 
 to judge how many 16-ft. logs would be cut from this particular 
 tree. Suppose it is a maple and that it calipers 22 inches, and that 
 it will yield a 48-ft. stem or three 16-ft. logs. I call to my pacer 
 " Maple, 22 3," and he tallies in the maple column opposite the 
 22 3 of the figures in the left-hand margin of the page. In this 
 way we get a record of every tree in a strip 4 rods wide, 2 rods each 
 side of our compass line. My caliper blade is graduated to 57 
 inches from the stationary arm, just $th of two rods, and if there is 
 any question as to a tree's being in the strip it is very quickly set- 
 tled by taking seven lengths of the caliper blade as I walk toward 
 the tree from the compass line. 
 
 Having taken the trees to a point a little in advance of my as- 
 sistant, he proceeds on for 50 paces more and the calipering process 
 is repeated. If the undergrowth is of sufficient density to prevent 
 our seeing any large pine, bit of cedar swamp, or anything else 
 that we should see, we make frequent explorations from the end 
 of each 100 steps, my assistant going in one direction at the same 
 time that I go in the opposite. No trees are measured in these 
 side explorations unless we find something that is not common to 
 the entire tract. Having returned to our line we proceed north, 
 halting at each 50 steps -to take the timber, also to note any ridges, 
 logging roads, streams, springs, or other points that should appear 
 in the report. When we have arrived at 500 paces my assistant 
 changes his tally to lot 9 and we proceed north in the same way, 
 changing at 1000 paces to lot 8 and at 1500 to lot 1. At 2000 
 paces, if the section is "full" we should be at the north line of the 
 section, at a point 20 rods west of the northeast corner. As it 
 rarely occurs that our compass line has been so accurate as to 
 bring MS out at exactly this point, we find the mark made during
 
 PRACTICE OF TIMBER ESTIMATING 181 
 
 our circuit of the section and pace from it westerly along the north 
 line of the section for 250 paces, 40 rods. This brings us to a point 
 from which a line drawn south will be parallel with the center line 
 of lots 1, 8, 9, and 16, and with the west line of these lots and 20 
 rods distant from them. We proceed south on this line, taking the 
 timber in the same manner as we took it in going north in the east 
 half of the same lots. Arriving at the south side of the section we 
 again go west 250 steps and then north through the easterly half of 
 lots 15, 10, 7, and 2, and so on until the section is completed. A 
 single "forty" or "eighty" or any sized tract is handled in the 
 same way. This gives a caliper measure of every tree on 4 acres 
 of each lot or on ^th of its area. Should a closer estimate be nec- 
 essary the strips are taken every 10 rods instead of 20 rods, which 
 gives Jth of each lot. If there are places in the tract from which 
 owing to any cause the timber has been removed, the area must 
 be shown on the report and proper deductions made from the esti- 
 mate. If these vacant areas are crossed by the strips, care must be 
 taken that they are not crossed lengthwise, as that would lessen 
 the estimate too much; on the other hand, if they are crossed 
 properly no deduction need be made from the tally. 
 
 When the calipering of the trees on the tract is completed 
 the contents of the trees tallied are taken from the volume table, the 
 scales footed, and the several footings multiplied by 10 or 5 accord- 
 ing to the number of the strips taken. 
 
 My volume table is of my own making. During the last twenty 
 years I have been called upon very frequently to measure trespass 
 until measures have been taken of thousands of trees of each 
 diameter. This work has been done in every section of the State 
 in which hard wood has been cut during that period, and has been 
 added to at every opportunity that has offered. The stumps were 
 calipered by taking the measure both outside and inside the bark ; 
 the length of the stem was taken, together with the diameter of 
 the top, inside the bark. On this basis the log scale was made ac- 
 cording to the Doyle rule. The scale of trees of the same diameter 
 and even of the same stump diameter and length vary considerably 
 on account of the different tapers toward the tops, making it nec- 
 essary to get a large number of trees from which to work up a table. 
 The average of the total scale of all the trees of a certain diameter 
 has been taken as the amount of scale to be allowed for all trees of 
 a certain stump diameter and height. 
 
 The results of the work as I have stated have been very satis- 
 factory. Many of the tracts have been cut the same season that 
 we made the estimate, and the log scale is usually from 10 per cent 
 to 20 per cent above my estimate. I should not care to get much 
 nearer than this. It would not be safe, as some firms cut the 
 timber much more closely than others, depending upon the article 
 to be made from the timber, the disposal of the waste product for 
 fuel, and so on. 
 
 No accurate estimate can be made without the use of the cali- 
 per. It entirely eliminates all favoritism on account of ownership
 
 182 A MANUAL FOR NORTHERN WOODSMEN 
 
 or employer, and it makes possible a close acquaintance with the 
 trees which shows up the defects. No cruiser sees the timber alike 
 every day. His judgment varies as the man himself varies each 
 day. The caliper eliminates this trouble, as it always measures the 
 trees just as they are. 
 
 Care should be taken to get the smallest diameter at the base ; 
 many trees, especially on slopes, are flat and measure several inches 
 more one way than another. Trees that show much defect are an 
 unknown quantity and should be thrown out entirely. 
 
 Two active men will get over a half-section in a day, and do it 
 well if the timber is not too small and the undergrowth is not too 
 dense. 
 
 Sometimes I am called upon to give a rough estimate of a tract 
 in a hurry. I handle this in the same way that I have shown above, 
 except that I do not use the calipers, but guess at the diameters as 
 well as at the length. In this manner one can get over the ground 
 as fast as the assistant can tally the trees, and we usually estimate 
 about 12 lots per day under this system. Of course the results are 
 not so accurate as when the caliper is used. 
 
 The above is illuminating in many directions, suggestive 
 of varying conditions and requirements, and varying 
 methods of treatment in response. Further under this 
 subdivision there will be included only a reference to the 
 "horseshoe" plan of cruising employed by many Lake 
 States and Southern cruisers. Diagrams of a northeast 
 
 quarter- section and of a forty illustrate the plan of travel, 
 so designed as to reach into all parts of the subdivision 
 concerned. Along this route the cruiser commonly covers 
 by detail estimate a strip 50 paces wide, which gives a 
 large percentage of the whole area. 
 
 5. The field of ocular estimate is to be found especially
 
 PRACTICE OF TIMBER ESTIMATING 183 
 
 in small bodies of timber and in tracts of small dimensions. 
 This is because a man can really see and grasp them. 
 Such estimates are particularly useful for timber of small 
 value or in very bunchy and irregular woods, which it is 
 hard to survey. In such circumstances the judgment of a 
 good woodsman is sometimes the best valuation that is 
 practicable. 
 
 The ability to estimate timber after this fashion is gained 
 by practice, and is based on personal experience and ca- 
 pacity ; consequently each man goes about it in a way of his 
 own. To know the area of the tract in question is generally 
 of great assistance, and most men will be continually study- 
 ing the matter of average stand per acre. As a prelimi- 
 nary step in arriving at this it is generally desirable to settle 
 maximum and minimum stand as well. 
 
 For the contents of single trees a woodsman may rely 
 on a mere glance, or he may figure carefully. A northern 
 Maine lumberman, for instance, looking at a fair-sized 
 spruce might estimate that it will cut a log 10 inches in 
 diameter at the top and 30 feet long, and such a log he 
 might know will measure 180 feet in local scaling prac- 
 tice. Again, in regions where logs are cut short, and 
 several are taken from a good-sized tree, men frequently 
 jot down the estimated contents of the several logs and 
 add up the figures to get the tree's total contents. Using 
 such methods to get at the size of the trees, lumbermen 
 then go on, in one way or another, to get the contents of 
 bodies of timber or stand per acre. 
 
 Frequently, however, the impression gained is a direct 
 one, of quantity on a whole tract or of constituent bunches. 
 A man cannot tell just how such figures come into his 
 mind, but they do arise there, dependent somehow on his 
 experience, perhaps in laying out roads or chopping timber. 
 Such training is effective, and when the judgment arising 
 as a result of it has been actually tested and found suffi- 
 ciently close and reliable for any given purpose, it would be 
 folly not to use it. But every one knows that such judg- 
 ments are fallible, as in the nature of the case they could 
 not fail to be. Differences in size and height may escape 
 a man if the stands traversed look generally alike; the 
 atmosphere and the lav of the land both have an effect on
 
 184 A MANUAL FOR NORTHERN WOODSMfiN 
 
 the appearance of timber; a man's condition also varies 
 from day to day, affecting his judgment in this matter, as 
 in every other. 
 
 The above is the faculty of the old lumberman. On 
 the other hand, the forester who has studied the rate of 
 growth and the yield of timber has, in area, soil quality, 
 and density of stocking, factors which he can profitably 
 use to help him in his estimate of quantity. A fully stocked 
 acre of white pine on good soil in Massachusetts, for in- 
 stance, will yield at forty to sixty years of age a thousand 
 feet of lumber for each year it has been growing, a 
 standard which a man may use to check the judgment 
 through a considerable range of conditions. 
 
 Ocular estimate has been spoken of as especially ap- 
 propriate to small tracts of land, but as a matter of fact 
 the methods and principles here stated are still employed 
 to a large extent in the valuation of the largest tracts as 
 well, and even for the purposes of sale and purchase. 
 This is perhaps not as it should be, but it has at least 
 partial justification in the fact that as business goes the 
 amount of timber on a tract is not the only element in 
 value; often it is not the largest, even, for in addition 
 availability, safety, the suitability of a tract to given pur- 
 poses, and the financial situation of the parties concerned 
 must all be considered. Sometimes a tract by reason of 
 its relation to a given investment or manufacturing enter- 
 prise really must be had, almost regardless of its timber 
 resources ; while, on the other hand, though rich in timber, 
 another tract may be dear at a small price. Accurate es- 
 timates of the quantity of timber, therefore, may be a 
 secondary matter. 
 
 When large tracts are estimated by the eye, it is com- 
 monly done on the basis of so much to the acre, either 
 from the looks of the stand or by comparison with some 
 similar tract already cut. Subdivisions, if they exist, might 
 be estimated separately, and the estimated area of waste 
 lands would then be thrown out of account. Some old 
 lumbermen might also estimate by valleys, judging quan- 
 tity from the density of the timber and the length of the 
 roads necessary to operate it. 
 
 6. Recount of the work done on a tract of 89 acres
 
 PRACTICE OF TIMBER ESTIMATING 185 
 
 in Massachusetts, having considerable value and a varied 
 stand of timber, will illustrate the different methods of 
 timber estimation and the way of going to work in a par- 
 ticular case. This tract was mapped topographically. The 
 methods employed for that purpose are described in Part 
 II and a complete map of the tract is given on page 114. 
 The steps contributing to the timber estimate are as follows : 
 
 a. Boundaries run out to get area; chainage marks left 
 at frequent intervals. 
 
 b. Some 65 M feet of heavy and valuable pine timber cal- 
 ipered tree by tree; numerous heights measured; con- 
 tents ascertained from volume table. 
 
 c. Three bodies of thick young pine circled by staff 
 compass and pacing to get area. Average stand of each 
 bunch ascertained by laying out quarter-acre sample plots 
 representing 10 to 20 per cent of the area. Trees on these 
 plots calipered; heights measured or estimated; contents 
 taken from volume tables. 
 
 d. Ten acres of hard-wood swamp in north end esti- 
 mated for cord wood by similar but quicker methods. 
 
 e. Balance of 60 acres of ground is covered with scatter- 
 ing pine and hemlock, chestnut fit either for box boards 
 or railway ties, poplar, red oak, and other hard woods. 
 Northerly 37 acres considerably better than the other 23. 
 Ran strip surveys across the two parts representing 10 per 
 cent of the area, running the strips across the ridges 
 and the belts of timber. Calipered the trees into classes 
 of pine, hemlock, chestnut, poplar, hard woods fit to saw, 
 and cord wood; estimated saw contents from tables, such 
 as were at hand, adjusted to the locality and practice, 
 with due reference to heights; estimated cord wood from 
 tables, experience, and judgment. 
 
 The field work involved in steps b, c, d, and e represented 
 one day's work for four men. Result was the following : 
 
 ESTIMATE OF CLARK BROS'. PARKER LOT, WOODSTOCK, 
 
 MASS. 
 
 White Pine (including 50 M good plank) 660 M 
 
 Hemlock 35 " 
 
 Chestnut 156 " 
 
 Poplar 63 " 
 
 Red oak, etc. 67 " 
 
 Total saw timber 981 " 
 Also hard-wood fire wood, 600 cords.
 
 186 A MANUAL FOR NORTHERN WOODSMEN 
 
 These methods are those of an estimator not in frequent 
 dealings with timber of this class. The owner of the lot, 
 a man of long experience and in constant practice, would 
 have chained or paced out the pine areas, and estimated 
 their stand per acre from experience. The scattering soft 
 wood and the heavy bunch of pine he would have esti- 
 mated in a lump sum. The main elements of value being 
 then dealt with, he would probably rely on his judgment 
 for the rest after looking carefully through it. With a 
 helper, he would take as much time as was actually con- 
 sumed, or more. This man, one of the most successful 
 operators in Massachusetts, says that using these methods 
 he can estimate pine lots within 5 to 10 per cent as a rule, 
 but occasionally makes a blunder of 30 to 50 per cent. 
 
 Other successful men in the same region, a region where 
 stumpage values are high and competition for merchant- 
 able lots very sharp, show great variety in their methods. 
 One man calipers all the timber on a lot he expects to pur- 
 chase, assuring himself about stand and value in that way, 
 and in addition securing data which tell him what he can 
 best put the trees into. Others use no instruments but, 
 relying on experience and taking plenty of time to look 
 around, make a lump estimate. That there is great dif- 
 ference in cost among all these methods is not certain. It 
 is sure, however, that for most men that method is best 
 which has in it less guess work than measuring. But the 
 facts recounted illustrate the principle that there may be 
 several good methods of doing a given piece of work, and 
 that the choice may turn on the training and habits of the 
 estimator. 
 
 B. ESTIMATION OF LARGER TRACTS 
 
 When land areas, as is frequently the case in the United 
 States, are of large size, and particularly if the stand upon 
 them is small and the value low, only a percentage of the 
 area can be covered by a timber survey, and the problem 
 is to make that percentage as representative of the whole 
 as possible. Amidst the great variety of methods em- 
 ployed, three main types of work may be distinguished.
 
 PRACTICE OF TIMBER ESTIMATING 187 
 
 1. TYPE AND PLOT SYSTEM 
 
 According to this method the land to be passed on is 
 divided up into types of known area and approximately 
 like stand, without, however, necessarily leaving marks on 
 the ground. Through these subdivisions of his area the 
 cruiser travels, studying the size, height, density, and con- 
 dition of his timber, and forming as he goes an estimation 
 of the average stand. This estimate he checks by a number 
 of sample plots, run out with the tape, and examined with 
 care. The plots are usually laid out either in square 
 or circular form, though the strip system is perfectly 
 applicable. 
 
 Very satisfactory results have been arrived at by this 
 method where a considerable area in sample plots has 
 been surveyed or where the estimator is a man of judg- 
 ment and experience. But choosing a few sample plots to 
 represent a tract is recognized as a very delicate matter. 
 Beginners generally select too good a piece, and the man 
 who is really competent to do it can usually make a close 
 guess at the whole thing. As with all other methods of 
 estimating, area should be known from surveys, and. that 
 in not too large units. 
 
 A good example of the application of this 
 system comes from a national forest super- 
 visor who had to estimate for a timber sale 
 a tract of some 1200 acres. It lay in the 
 form shown, with a ridge running down 
 the middle of it, which naturally formed 
 the first line of subdivision. The tract was 
 therefore surveyed with compass and chain and a dividing 
 line run along the ridge top. 
 
 Then on each side of the ridge three distinct types of 
 timber stand were recognized. The heaviest timber, red 
 fir of good size, was in the middle; the north end was 
 lighter, with a mixture of lodgepole pine; the south end 
 had been damaged and rendered very thin by fire. These 
 blocks were therefore blazed out and roughly surveyed? 
 Thus the land was divided into six compartments of ap- 
 proximately even stand and of known area.
 
 188 A MANUAL FOR NORTHERN WOODSMEN 
 
 Then with a party of three men the supervisor ran 4-rod 
 strip surveys l through each compartment, covering in each 
 from 10 to 15 per cent of the area. Having no volume 
 tables, he scored down instead the logs judged to be in the 
 trees passed, in 16-ft lengths and by inch-diameter classes. 
 In the office the contents of these logs were ascertained 
 from the scale rule, multiplied by the number of each size, 
 and added together. If then 10 per cent of a compartment 
 had been covered, multiplying by 10 gave the stand of 
 the compartment, which was the result desired. 
 
 With trustworthy volume tables and calipers better re- 
 sults could probably be had. but those here obtained were 
 satisfactory. General good judgment is essential in carry- 
 ing out such a survey, but, that given, a man can do it 
 who has not had long woods and mill training. In fact, 
 in the same forest one or two green but intelligent men are 
 said 'to have been quickly trained so that their figures 
 could be relied on within 10 or 15 per cent. 
 
 2. THE STRIP SYSTEM 
 
 The strip system of estimating has been used rather 
 widely in woods work, not infrequently in connection with 
 .land subdivision. . As a survey party is running through 
 the woods, it is sometimes made the duty of the chainmen 
 to count the merchantable trees for a stated distance on 
 each side of the line run, the contents of the trees being 
 determined oftenest by an estimate of the number neces- 
 sary to make up a thousand feet. The same system in 
 effect is sometimes used by the cruiser who counts the 
 trees passed within a certain distance as he travels across 
 a lot, or the work may be done more elaborately, and the 
 caliper and hypsometer introduced to any extent thought 
 advisable. 
 
 The methods of a Michigan cruiser who employs this 
 system were described on page 178. Following are 
 methods pursued on tracts of considerable size by a 
 number of progressive concerns at the South dealing with 
 pine and a variety of hard wood timbers. 
 
 The strip lines are usually % mile apart; they may be 
 1 See next article.
 
 PRACTICE OF TIMBER ESTIMATING 
 
 189 
 
 carefully run and marked in advance by a survey party, 
 or a compassman going along with the timber estimator 
 may run and pace them. Topography may be mapped; 
 notes are taken of swamp boundaries and other changes 
 in the character of ground or timber. 
 
 The strip estimated is either one or two chains wide, 
 split by the line of travel; thus either 5 or 10 per cent of 
 the gross area is covered. The estimating party proper 
 consists of three men, two to caliper the timber breast 
 high, and one of good training who is responsible for the 
 work as a whole and who does the recording and estimat- 
 ing. His note book has separate space for each species 
 and under each a line for diameters by inch classes. Each 
 tree on the strip is scored down as calipered, or it may be 
 the number of 16-foot log lengths. 
 
 In such a vast region there is bound to be much varia- 
 tion in utilization, scaling, and mill practice so that when 
 volume tables are employed they are usually of local 
 origin to correspond. Since, however, the country is of 
 very gentle topography, height and taper within the same 
 species are unusually even. Two inches taper for each 
 -16-foot log above the butt log has been found to be widely 
 characteristic of pine timber, and three inches of hard 
 wood timber. Some tables then have been made up on 
 the basis of these regular tapers. 
 
 Small Diameter 
 of Butt Log 
 Inside Bark 
 
 Number of 16-foot logs 
 
 1 
 
 2 
 
 3 
 
 * 
 
 5 
 
 6 
 
 Contents in Feet Board Measure 
 
 15 
 16 
 
 17 
 18 
 
 160 
 180 
 200 
 230 
 
 280 
 320 
 360 
 410 
 
 360 
 420 
 480 
 550 
 
 410 
 480 
 560 
 650 
 
 440 
 520 
 610 
 710 
 
 540 
 640 
 750 
 
 Accompanying is an extract from a volume table J con- 
 structed on this plan, giving figures that, when manufac- 
 
 1 From "Southern Timber Tables" by Howard R. Krinbill, 
 Newbern, N. C. Copyrighted.
 
 190 A MANUAL FOR NORTHERN WOODSMEN 
 
 ture of highest present economy is practiced, approximate 
 mill output. A peculiar feature will be noted in this 
 table that the base diameter employed is not diameter 
 breast high, but diameter inside bark at the top of the 
 first log length. A reduction from calipered diameters is 
 required therefore, for bark thickness and for taper. 
 This reduction is made either tree by tree in the field by 
 estimate or in the office by classes on the basis of meas- 
 ures taken in logging operations. Timber quality is a 
 matter of importance. It is seldom or never dealt with 
 in the field other than by way of general comparison and 
 experience. 
 
 The strip system was also largely employed in the 
 early years of the United States Forest Service, with the 
 object of ascertaining not merely the merchantable tim- 
 ber on the tracts examined but also the number and 
 kind of young trees growing there as a basis for re- 
 commendations as to treatment. The method and cost of 
 strip survey work as carried out by the Service men are 
 indicated in the following extract from the " Woodsman's 
 Handbook": 
 
 Sample acres are laid off in the form of strips, 10 surveyor's 
 chains long and 1 chain wide, and the diameters of all trees to be 
 included in the estimate are measured at breast height with 
 calipers. At least three men are required to do effective work 
 under this method. One man carries a note book, or tally sheet, 
 and notes the species and their diameters as they are called out 
 by the men who take the measurements. The tallyman carries 
 the forward end of the chain, the other end of which is carried 
 by one of the men taking the measurements. The chain is first 
 stretched on the ground and the trees are calipered within an 
 estimated distance of 33 feet (one half chain) on each side of the 
 chain. When all trees adjacent to the chain have been calipered 
 the whole crew moves on the length of another chain in the direc- 
 tion chosen (by the tallyman). The chain is again stretched on 
 the ground and the trees are calipered on each side of it as before. 
 This same operation is repeated until the trees have been measured 
 on a strip 10 chains long. Notes are then made of the general 
 character of the forest and the land, according to the requirements 
 of the investigation. If heights are desired they may be taken 
 by a separate crew, or as the calipering crew encounter from time 
 to time trees whose heights are desired, they may stop long enough 
 to take such measurements. 
 
 In an average virgin forest a crew of three men will caliper the 
 trees on from 20 to 40 acres in one day if only trees of merchant-
 
 PRACTICE OF TIMBER ESTIMATING 
 
 191 
 
 able size are included, or from 15 to 25 acres if the small trees also 
 are calipered. Small trees are measured principally in studying 
 the question of future growth. 
 
 FORM OF NOTES 
 
 Local ity.. T. 5. R 18,.. W..E..L.S. f Maine. 
 
 Tjpe-Hardu-ood. Slope..... I)ate-Sept..l7^.1901 
 Sheet No. A. 41 
 
 D.B.H 
 
 Spruce 
 
 Dead 
 
 Fir 
 
 White 
 Birch 
 
 Beech 
 
 Hard 
 
 Maple 
 
 Pine 
 
 Popl. 
 
 2 in. 
 
 Hn 
 
 
 H 
 
 
 
 
 
 
 3 
 
 la :. 
 
 
 
 
 
 
 
 
 4 
 
 0. 
 
 
 
 
 
 
 
 
 
 6 " 
 
 M. 
 
 
 
 
 
 
 
 
 6 " 
 
 
 
 
 K. . 
 
 
 
 
 
 7 " 
 
 11 
 
 
 
 M' 
 
 
 
 
 
 8 " 
 
 
 
 
 K. 
 
 
 
 
 
 9 " 
 
 
 
 . 
 
 R:. 
 
 
 
 
 RT. 
 
 10 
 
 
 
 
 
 
 
 
 
 11 " 
 
 
 
 
 
 
 
 
 
 On large tracts satisfactory estimates can be made by the 
 measurement of about 1 out of every 30 acres. In very extensive 
 forest tracts the Bureau of Forestry usually measures not more 
 than one or two out of every hundred acres. 
 
 This method is clearly adapted to securing knowledge 
 of the make-up of a forest, and of its stand of merchant- 
 able timber if good volume tables are at hand to go with 
 it. In the latter connection perhaps the greatest difficulty 
 that arises is in applying the proper heights to the different 
 diameters. This is slight if the tract is of small size and 
 uniform character, but considerable on large tracts with 
 uneven topography and varying stand. In addition con- 
 stant care is required to make sure that the strip is kept 
 of right width, in other words that all trees less than 2 
 rods from the line run are included and none at a greater 
 distance. Careful men do indeed quickly get trained to
 
 192 A MANUAL FOR NORTHERN WOODSMEN 
 
 this so that their eyes are true, but with the best of men 
 an occasional swing-off of the chain is necessary. Defects 
 in timber also remain to be allowed for. 
 
 As applied to large tracts the strip system may either 
 be employed within types the boundaries of which have 
 been ascertained, as was explained in the last article, or 
 it may be laid out in long lines across country and itself 
 be used to define those boundaries and to get the topog- 
 raphy. A number of townships in Maine have been 
 surveyed in the following manner: 
 
 a. Township lines re-run and re-blazed ; chainage marks 
 left every half mile. 
 
 b. A center line run through the township, this also 
 being chained and marks left each half mile. ' 
 
 c. From a main camp on the center line, 4-man parties 
 ran strip surveys from a mark on the center line out to 
 the boundary, checked on the mark there, set over a half- 
 mile, and ran back. This was 2 days' work, and the 
 party consequently carried outfit required to stay out one 
 night, the main camp meanwhile being moved along the 
 center line. Note was kept of the ridges and streams 
 crossed, also of the lay of the land, of the bounds of cut- 
 tings, and of marked types of timber. Elevations on such 
 a survey may be got by barometer, and a topographic 
 map made up as a result. 
 
 3. LINE AND PLOT SYSTEM 
 
 A third system employed with some variations in different 
 parts of the country, most largely perhaps among spruce 
 men in the East, combines features from both the fore- 
 going. Under this system the cruiser while at work 
 travels in straight lines through the country to be ex- 
 plored, using his eyes as well as may be while actually 
 traveling, but stopping at regular intervals to count and 
 estimate the trees on an area about him. The area usually 
 chosen is a quarter acre, which has a radius of 59 feet, 
 or, for most men, of 23 paces. For a check on this dis- 
 tance a tape line should always be carried in the pocket, 
 and every morning, as well as occasionally through the 
 day, the eye should be checked by actual measurements.
 
 PRACTICE OF TIMBER ESTIMATING 193 
 
 Carefully training in this way, a man will find himself 
 able to guess within 2 feet of the 59. 
 
 The timber may be estimated according to any method 
 deemed most satisfactory. It may be calipered by an 
 assistant and the factor of height gone into to any extent 
 thought best, but most men in the spruce region do that 
 only as a check, while in common practice, after count- 
 ing the trees of any species or class, they estimate their 
 contents on the basis of so many to the cord or to the 
 thousand. Occasional calipering and height measurement 
 as a check on the eye* are highly desirable, and volume 
 tables also are a help in most cases. But some species of 
 trees (as cedar and beech in many localities) are so im- 
 perfect and defective that volume tables, if they were in 
 existence, could not be depended upon. Such timber 
 has to be estimated out of hand, and lumbering expe- 
 rience, together with the figures of the scale rule carried 
 either in a man's head or in his pocket, will prove the best 
 equipment for it. 
 
 One advantage of this method is its cheapness one 
 man may do the work alone. Further, all doubtful points 
 are settled on the ground, face to face with the timber - 
 there is no discounting or computing afterwards more 
 than to add up the results. Then the small size of the 
 area and the nearness of the observer to the trees under 
 consideration enable him, if he has proper experience and 
 judgment, to set contents very close. Lastly it will be 
 seen that the systematic travel followed gives, in a simple 
 country, material for mapping its timber types, also its 
 topography, as was explained in Part 2 of this volume. 
 
 Following are specimen notes of a line of estimate run 
 directly across a section with quarter-acre counts taken 
 150 paces apart. The timber is scored in the following 
 classes : (a) spruce above cutting limit of 14 inchej 
 stump diameter in board feet; (6) smaller spruce down 
 to 6 inches breast diameter in cords; (c) fir in cords; 
 (d) cedar in feet B. M. ; (e) pine; (/) good hard- wood 
 logs. Number and contents of trees both given. 
 
 This method of timber cruising may be employed on 
 land areas of any size, and has been largely employed on 
 areas of a mile square, or " sections."
 
 194 A MANUAL FOR NORTHERN WOODSMEN 
 
 To travel the boundaries of a square mile and twice 
 across it, taking quarter acres each 20 rods as determined 
 by pacing, gives about 2^ per cent of the area actually 
 covered by the estimate, and that percentage can be 
 relied upon to give, in land which has any regularity of 
 type, a close approximation to the truth. To do that 
 and what goes with it, section after section through a 
 township, is just about a fair day's work. 
 
 ^~ 
 
 SflLqgs 
 
 Sp.Pa/p 
 
 Fjr 
 
 Cedar 
 
 PJne 
 
 HardtYoort 
 
 
 4-400 
 
 3 -.3 
 
 16- Is 
 
 & -300 
 
 
 
 
 9-1200 
 
 28-4 
 
 
 
 
 
 
 8-/80O 
 
 2. 
 
 8-1 
 
 
 
 Soft no 
 
 QC/S on f/af 
 
 3-400 
 
 7-1 
 
 
 
 f-100 
 
 /and, S/o 
 
 r?y buf~ 
 
 3-SOO 
 
 7-1 
 
 34-4 
 
 
 
 Smooth 
 
 /ogg/ng. 
 
 fO-2000 
 
 7-JB 
 
 24-3 
 
 4-100 
 
 
 dbunctan 
 
 f rejorocfucf"- 
 
 9 -/3OO 
 
 a 
 
 9-J.3 
 
 
 
 /on of fi 
 
 7 wMyruce 
 
 8-/OOO 
 
 7-1 
 
 IZ-li 
 
 
 2-300 
 
 & occasio, 
 
 Kr/p/fK 'tf 
 
 //- ISOO 
 
 23-2^ 
 
 8-1 
 
 
 
 O/Xf?mg~ 
 
 
 s-iooo 
 
 37-3 
 
 
 
 
 
 
 S-80O 
 
 /3-2 
 
 Uf 
 
 as1-6l 
 
 roofs //? 
 
 2-300 
 
 
 3 -700 
 
 6- 
 
 4-.3 
 
 mixed 
 
 fifVIYft? 
 
 J--900 
 
 
 "SSfjod 
 
 S.4C. 
 
 4.7C 
 
 /J3' 
 
 J33' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The last two methods described as usually employed 
 are alike in this, that in the endeavor to get at a fair sample 
 of the country they depend mainly, on mechanical arrange- 
 ments rather than choice. This as a general rule is a 
 safe thing to do. There will always be enough things left 
 to exercise the best judgment of the estimator. On the 
 other hand, neither this nor any other system should be 
 followed blindly. If part of the tract is especially valua- 
 ble, especial pains should be taken with it. As a rule it 
 will be found safe to ascertain the area of such tracts and
 
 PRACTICE OF TIMBER ESTIMATING 195 
 
 estimate them separately, while on the other hand the 
 area of bogs, burnt lands, barren mountain tops, etc., 
 should be ascertained and thrown out of account. 
 
 C. SUMMARY 
 
 The above described ate well tried methods of timber 
 estimating and survey, but what has been written affords 
 hardly more than suggestions as to how any particular 
 job may best be done. Each method has its merits which 
 may strongly recommend it for some particular circum- 
 stances. Very much too depends on the training and 
 qualifications of the man doing the work. Every man 
 long in the business commonly has a line of work in which 
 he becomes proficient, developing methods best suited 
 to himself to which in ordinary cases he will adhere. In 
 conclusion, the following guiding principles may be laid 
 down: 
 
 1. Estimates by lump sum are not usually reliable or 
 at the present day sufficient. 
 
 2. Estimates of so much to the acre are much easier 
 to make and more likely to be close to the fact. 
 
 3. In any kind of timber estimate or survey, the area 
 of the land ought to be known, and that in units not too 
 large. Within limits the smaller they are the better, all 
 the more so if each unit contains but one timber type. 
 
 4. Every time a measurement is substituted for a guess 
 or judgment, the more reliable will be the result. On the 
 other hand, experience and good judgment never cease 
 to be required in the business. 
 
 5. No estimate is worth much, practically speaking, 
 which fails to take height into account as well as diameter. 
 
 6. Quality in some circumstances is quite as material to 
 an adequate timber survey as quantity. Its determination 
 is fully as difficult. 
 
 7. "The more defective the trees are, the more pref- 
 erable is the cruiser's judgment and long local experience 
 in the mill and in the woods to mere measuring." 1 The 
 same is true where great differences in value are dependent 
 upon quality or grade. 
 
 1 Schenck's "Forest Mensuration."
 
 196 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 8. Very bunchy timber can be estimated only in bunches 
 or tree by tree. No general system of lines or plots can 
 be trusted to give safe results. 
 
 ft. In the emergencies which arise in actual business, 
 a little rough and ready land surveying is often the most 
 vital part of a reliable timber estimate. One or two lines 
 run with compass and chain will frequently check areas 
 of waste land or of different stand in effective fashion. 
 Transit and stadia work on streams or roads often 
 affords very material help. There is continual call for 
 the sort of results that can best be obtained by means of 
 compass and pacing. 
 
 D. PACIFIC COAST METHODS 
 
 Much Pacific Coast timber is 200 feet and over in height 
 and of diameter to correspond, while the stand sometimes 
 passes 20 million feet per quarter section. It is evident, 
 therefore, that because of the values involved intensive 
 methods of cruising are appropriate, .while peculiarities 
 of method are suggested by the very size and height of 
 the timber. Of the region as a whole the portion west of 
 the Cascade Mountains in Washington and Oregon, pro- 
 ducing Douglas fir, "Oregon pine" as it was called form- 
 erly, is most active and characteristic, and the following 
 refers to that region unless specified otherwise. 
 
 SUCCESSIVE LOGS IN A FIR ' 
 
 
 Top 
 Diam. 
 
 Scale 
 
 Total 
 
 1st 32-foot log 
 
 31 
 
 1420 
 
 33 
 
 2nd 32-foot log 
 3rd 32-foot log 
 4th 32-foot log 
 
 28 
 25 
 20 
 
 1160 
 920 
 560 
 
 27 
 21 
 14 
 
 5th 32-foot log 
 
 14 
 
 230 
 
 5 
 
 Total 
 
 
 4290 
 
 100 
 
 Adjustment of methods to the conditions is illustrated 
 particularly by the volume tables employed, for those 
 at present in most extensive and responsible use are.;
 
 PRACTICE OF TIMBER ESTIMATING 197 
 
 constructed on principles that have very seldom been 
 employed elsewhere. After basal diameter, taper per 
 32-foot 1 log is the next factor allowed for, total height of 
 the tree is disregarded, and number of logs is the third 
 factor in the tabulation. This has reason behind it as 
 well as experience. In timber of such dimensions total 
 height is not readily estimated; the lower logs of the tree 
 are very much the largest and far the best in quality; 
 a log more or less in the top, comparatively small in size, 
 full of large knots and liable to be broken up in felling, is 
 of small account in the estimate anyway. 
 
 In connection with these tables, basal diameter also is 
 handled in a peculiar manner. In some tree species thick- 
 ness of bark is very variable, while the root swelling of 
 large trees frequently reaches to the height of a man and 
 higher. Diameter therefore is taken as nearly as may be 
 where the tree takes on its regular form, considerably 
 above breast height as a rule; deduction is made for any 
 swelling not thus allowed for, and double the thickness 
 of bark as actually found is then subtracted. By this 
 means, the wood alone is dealt with, and basal diameter 
 is aligned with the general shape of the tree. 
 
 In view of the facts above mentioned it is clear further 
 how windfalls furnish the best obtainable assistance to 
 the cruiser's judgment in respect to height and taper, 
 also that the diameter tape and Biltmore stick possess 
 advantages over the caliper. Then two additional prob- 
 lems arising out of the size of the trees confront the cruiser : 
 first, breakage in felling is a much more important factor 
 than elsewhere, and its amount varies widely with the 
 ground conditions; second, the defect arising from decay 
 and other sources, very hard to judge, to detect even, in 
 timber of this height, has to be handled with extreme 
 care careful looking, the examination of windfalls, 
 experience, perhaps the outturn of adjacent timber serv- 
 ing as a guide to it. 
 
 The "forty" is the ordinary unit of area for cruising 
 and a timber report, and it is gridironed with straight 
 line travel. Pacing serves ordinary purposes as a dis- 
 
 1 Tables based on 16-foot logs are also in existence.
 
 198 A MANUAL FOR NORTHERN WOODSMEN 
 
 tance measure; a vernier compass is usually employed 
 for the sake of more accurate line running. Twenty to 
 fifty per cent of the gross area is commonly covered by 
 actual estimate, one hundred per cent in some cases. 
 The unit party for the work consists of two men, compass- 
 man and cruiser, of whom one handles distance, area, 
 and topography, while the other is responsible for the 
 timber. Details of practice vary much, as elsewhere, in 
 accordance with the purpose of a cruise, conditions 
 found, and the training of different estimators. Follow- 
 ing is a description of a method as near standard as any, 
 widely employed in work of high responsibility. 
 
 a. Section lines are usually freshened up and re- 
 chained, and a center line may be run through each sec- 
 tion. The main purpose of this work is to set stakes for 
 the guidance of the cruising party. It is so laid out that 
 the actual cruise or estimating lines will run as nearly 
 as may be across the features of the topography. 
 
 b. The cruising party, starting at one corner of the 
 section to be examined, proceeds to the nearest stake, 
 2J^ chains from it, whence the compassman, with the 
 declination set off in his staff compass, travels parallel 
 to the side line of the section, keeping account of his 
 pacing, taking aneroid readings at changes of the ground, 
 and sketching topography. Behind him follows the cruiser, 
 who for a width of 5 rods on each side, estimates the timber. 
 500 steps, 4 tallies, make a quarter mile, the width of a 
 40. At that point the scoring of timber begins anew, for 
 the new forty being entered. So the work proceeds until 
 the opposite section line is met (or at half that distance 
 if the section is subdivided), when the pacing is checked 
 up, the compass work tested on the stake and declination 
 reset if necessary. Offset is then made to the second 
 stake, lYi chains from the corner, from which point a 
 parallel line is run in the opposite direction. Four such 
 lines are run across each tier of forties. With 1C such 
 lines the cruise of the section is completed. 
 
 c. The detail of the estimating work is as follows: 
 First, in nearby timber being cut, or in ordinary circum- 
 stances by examination of windfalls, the cruiser trues up
 
 PRACTICE OF TIMBER ESTIMATING 
 
 199 
 
 his judgment on the contents of the trees. In this con- 
 nection his volume table is of assistance since study of 
 the height and taper of the down timber shows to what 
 portion of his tables its form relates it. Two and three 
 inches per 32 foot log are light tapers, not infrequent in 
 hemlock and young fir, but four and five are usual in 
 mature fir timber. This examination also tells something 
 as to log quality and the amount of defect. Along with 
 it the cruiser makes sure by numerous tests that his eye 
 is true on basal diameter. With these points settled his 
 preliminary work is done and, with an eye out for factors 
 that influence breakage and particularly for "conks" 
 and other signs of unsoundness, he will proceed confi- 
 dently. The figures he sets down on his tablet represent 
 his judgment of the merchantable contents of trees as he 
 passes them, species, individual form, defect, and breakage 
 all being allowed for. The conscientious man, however, 
 applies frequent check by further examination of wind- 
 falls and occasional measurement of strip width and of 
 basal diameters. 
 
 SAMPLE OF CRUISER'S FIELD NOTES 
 (Usually made on celluloid sheets) 
 
 
 Dead 
 
 
 
 
 
 Poles 
 
 Fir 
 
 
 Cedar 
 
 D & D 
 
 
 
 
 
 Down 
 
 
 
 
 
 Fir 
 
 Hem. 
 
 Cedar 
 
 2-6 M 
 
 2 
 
 1-.7 
 
 .8 
 
 1-1.5 
 
 1-5 M 
 
 1 
 
 1 
 
 111 
 
 1-2.5 
 
 1.5 
 
 1-.4 
 
 
 2-2.5 
 
 
 
 
 
 6-30 
 2-7.5 
 
 
 1-3. 
 
 
 1-.3 
 1-1. 
 
 
 Average 45' long 
 9' diam. at middle 
 
 d. Checks from outside are a feature of the work as 
 carried out on a large scale commercially. The different 
 cruisers in a large party may be set to check one another 
 as a corrective and for uniformity; a head cruiser period- 
 ically checks each man to catch up any slackness, correct 
 any wrong tendencies, and give advice or directions. 
 
 Two miles of line per day are the standard product 
 for this method of cruising, giving eight working days to
 
 00 A MANUAL FOR NORTHERN WOODSMEN 
 
 the section, which involves a cost of about 25 cents per 
 acre outside of the checking, overhead and office work. 
 Ordinary variations are : 
 
 a. Double running each forty instead of running four 
 times through it as above, a method widely practiced as 
 costing less and considered sufficiently accurate in many 
 circumstances. The cruise lines in this case are started 
 5, 15, 25, etc. chains from the section corner to divide 
 the area equally. Sometimes, also, the strip is widened. 
 
 6. For preliminary work, one strip only may be run 
 per quarter mile, and after a certain amount of that with 
 its results in training, even this may be discontinued and 
 a man rely on general observation. 
 
 c. A 100 per cent cruise is carried out in some cases. 
 In this case a second compassman may advantageously 
 be employed and the cruiser work between lines run and 
 marked by the two men, the "exact width of the strip 
 being then of no consequence. Sometimes, also, a second 
 estimator is employed to take care of certain classes of the 
 timber. 
 
 d. Some men, instead of estimating the timber on 
 strips, estimate circular areas so spaced along the compass 
 line that they touch one another. For this practice it is 
 claimed that a man can do better estimating work stand- 
 ing quietly at a center than while travelling, with his 
 mind more or less distracted about footing, etc. In 
 earlier times indeed a circular plot system was general, 
 
 - while another usual procedure was to count the trees on 
 these circles or on strips to the length of one tally, and 
 derive their contents from that of the average tree as 
 estimated. Few follow this last practice at present, 
 however. 
 
 In conclusion on this branch of the subject, the follow- 
 ing, by a man of long experience and acknowledged com- 
 petence in this line of work, is introduced for the light it 
 throws on the broad aspects of the matter. 
 
 We work in general by the strip system but under a less hard- 
 and-fast rule than formerly. More is left to the judgment of our 
 cruisers as to the number of runs through a subdivision neces- 
 sary to secure correct results. Thus, if we find one forty that
 
 PRACTICE OF TIMBER ESTIMATING 201 
 
 is densely timbered with a small uniform growth, we find that 
 we secure better results by taking narrower strips, the equivalent 
 of one sixteenth of a forty instead of one eighth. Where trees 
 stand so thickly on the ground it is almost an impossibility for 
 men to keep an accurate count on a wide strip as they can on 
 one of hah* the width, and we find that the basis of much of the 
 error that occurs in our work is due to inaccurate tree counting. 
 
 If the timber is large and particularly accurate results are de- 
 sired, we now run 12 times through each forty and frequently work 
 between blazed lines. That is, instead of running through the 
 middle of the strip, the compassman sets over one-half its width 
 and spots the trees on the opposite side from the cruiser to give 
 the cruiser a line to work to on the return strip. This works very 
 satisfactorily where the brush is not too dense. 
 
 Again, under certain conditions where we have a uniform 
 stand of large timber, we run 4 times, taking strips equivalent 
 to one-twelfth of a forty. This plan, we believe, gives better results 
 than two strips each covering }/g of the whole. 
 
 These notes give some idea of how we attempt to carry on our 
 work, but in the last analysis this cruising business resolves itself 
 into one of personal capacity and attention upon the part of the 
 cruiser rather than the method employed. A careful, conscien- 
 tious and hard-working woodsman whom we can depend upon 
 to go over the ground is more valuable than a more expert cruiser 
 who takes much for granted. There was a. time when I hoped 
 to develop timber cruising to a point from which we could look 
 upon our estimates as being absolutely reliable, but so long as 
 there are influences that will work upon the minds of men, there 
 will be variation and error. A man may do excellent work to- 
 day and be totally unfit to be in the woods to-morrow, all for 
 reasons which none of us can explain. A man must have confi- 
 dence or he will be of little value. On the other hand I think I 
 may safely say that the greatest element of uncertainty and error 
 in men's work is their proneness to feel that familiarity has de- 
 veloped infallibility. The man who never develops absolute 
 confidence in his eye and judgment and who checks himself up 
 frequently, seldom goes far wrong. 
 
 There is, too, another side to this whole matter, one often 
 neglected, but of great importance, and that we consider in our 
 work as best we can. That is the standard of utilization of the 
 timber. As a matter of fact there is surprising difference in the 
 way timber is cut, though I could not define this as a percentage. 
 A concern milling its own timber cuts closer than one selling its 
 logs; and there is variation with the market itself. Then occa-
 
 202 A MANUAL FOR NORTHERN WOODSMEN 
 
 sionally a tract is cut with such carelessness that the yield is 
 very materially cut down. We have to meet the wishes of our 
 customers if clearly expressed, but we protect ourselves by an 
 explicit statement of the kind of utilization which our estimates 
 imply, and by an exact showing of the basis on which the work 
 was done. 
 
 Timber Quality. While the above applies specifically 
 to the Douglas fir country, much the same methods are 
 employed in the Interior and California, with resort to 
 others of less intensiveness, similar to those in use else- 
 where, when stands are lighter or less valuable. The pre- 
 ceding, however, is inadequate in one field of importance, 
 in that quality of timber has been given scant emphasis. 
 This throughout the region is no less important a factor 
 in value than quantity. In fact, in very much territory 
 timber has no commercial value unless its products are 
 suitable for other than ordinary building purposes. 
 
 In the case of Douglas fir and timbers associated with 
 it west of the Cascades this matter is simplified by the 
 fact that log grades instead of lumber grades are made 
 the usual basis of quality rating, the log grading rules in 
 force in the market thus furnishing the standard to which 
 the field man works. Since, however, both dimension 
 and lumber quality enter into these, their application is 
 not simple. 
 
 The grading rules for Douglas fir logs in force on Puget 
 Sound follow; those of the other log markets are very 
 similar. Spruce is commonly graded like fir. With cedar, 
 because of the variety of products into which the wood 
 may be manufactured, grading varies from time to time 
 and locally. Hemlock logs and those of the species 
 rarely met are sometimes classed in two log grades, those 
 above 16* in diameter and surface clear, and all others. 
 
 No. 1 (also called Flooring) 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, which in the 
 judgment of the sealer contain at least 50 per cent of the 
 scaled contents in lumber in the grades of No. 2 Clear 
 and better.
 
 PRACTICE OF TIMBER ESTIMATING 203 
 
 No. 2 (or Merchantable) logs shall be not less than 16 
 feet long and which, having defects which prevent their 
 grading No. 1, in the judgment of the sealer, will be 
 suitable for the manufacture of lumber principally in 
 the grades of Merchantable and better. (Merchantable 
 lumber must be free from knots or other defects in size 
 or numbers such as to weaken the piece.) 
 
 No. 3 (also called No. 2} logs shall be not less than 16 
 feet long which, having defects that prevent their being 
 graded higher, are, in the judgment of the sealer, suitable 
 for the manufacture of Common lumber. 
 
 Cull logs shall be any logs which in the judgment of 
 the sealer will not cut 33^ per cent of sound timber. 
 
 An essential to reliable timber grading is experience, a 
 background of knowledge of the out-turn of similar tim- 
 ber. In the next place, close examination of the stand 
 is required as to the number and size of limbs and knots 
 and for indications of these, or of other defects, that 
 may lie beneath the surface. Age is a help here (these 
 stands are commonly even-aged over considerable areas). 
 Many cruisers go no farther than this and set percentage 
 figures for log grades as the result of a broad judgment. 
 
 When further detail is thought desirable, the volume 
 tables before mentioned are of assistance, giving as some 
 of them do for a tree of given diameter, taper, and mer- 
 chantable length the percentage each successive 32-foot 
 log bears to total contents. One standard volume table 
 contains the following directions : 
 
 "Determine the percentages of the different grades as 
 contained in a given percentage of the trees on each 40 
 acres by selecting, for instance, an average tree on each 
 tally and carefully determining the percentage of the 
 different grades of logs contained in these sample trees 
 and apply ing the average to all trees on the forty." 
 
 To illustrate, in the notes on page 199, 11 trees, 46 M 
 feet, are scored down in the column of living fir, giving an 
 average volume of 4200. 4 inches taper and 4 logs may fit 
 this timber; if so, a tree yielding 4330 feet (see extract from 
 taper table) gives a close approximation. Of such a tree 
 a 32' butt log constitutes 37 per cent, the second log 28
 
 204 A MANUAL FOR NORTHERN WOODSMEN 
 
 per cent, and the third 21 per cent, while top diameters 
 are approximately 33, 29 and 25 inches respectively. 
 One of these logs is large enough for No. 1 ; it may or may 
 not be clear enough. Second and third logs are of suffi- 
 cient size, and likely to be of a quality, to put them in 
 the second grade. 
 
 Methods in this branch of the work, however, vary 
 greatly. A few, in the endeavor to reduce the field of 
 judgment, have gone into much detail and devised forms 
 of notes which record trees by sizes and log grades in each 
 tree as its contents is estimated. Of the percentage of 
 successive logs, it may be said that the above relations 
 are fairly typical that is to say in normal fir timber 
 large enough so that log grades are of importance, about 
 35 per cent of the total contents of trees is contained in 
 the butt log if cut 32 feet long, the second log will add 
 25 to 30 per cent more, and about 20 per cent will be 
 in the third log. Breakage and defect may throw out 
 these relations, and they are different in extremely tall 
 or short timber. 
 
 
 ti 
 
 3 Logs or 96 Feet 
 
 4 Logs or 128 Feet 
 
 Butt 
 Diam. 
 
 .a 
 
 .S 
 a 
 
 
 Logs 
 
 8 
 
 
 Logs 
 
 Inches 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , S ' 
 
 
 Contents 
 
 n 
 
 
 
 . 
 
 Contents 
 
 
 
 n 
 
 
 
 H 
 
 1 
 
 B. M 
 
 6 
 
 - 
 
 3 
 
 S 
 
 B. M 
 
 
 ~~ 
 
 t- 
 
 
 
 
 
 Q 
 
 
 SN 
 
 ^ 
 
 
 S 
 
 
 S 
 
 l~ 
 
 l- 
 
 l< 
 
 
 3 
 4 
 
 28 
 25 
 
 4230 
 3714 
 
 10 
 13 
 
 33 
 
 33 
 
 27 
 
 24 
 
 25 
 21 
 
 5128 
 4330 
 
 33 
 
 37 
 
 27 
 
 2s 
 
 22 
 
 '?! 
 
 18 
 14 
 
 
 5 
 
 22 
 
 3234 
 
 10 
 
 33 
 
 21 
 
 17 
 
 3610 
 
 4?, 
 
 2D 
 
 I'l 
 
 10 
 
 37 
 
 fi 
 
 19 
 
 2790 
 
 10 
 
 3;> 
 
 is 
 
 13 
 
 2979 
 
 17 
 
 30 
 
 17 
 
 00 
 
 
 7 
 
 16 
 
 2386 
 
 1.1 
 
 3" 
 
 11 
 
 
 
 
 
 
 
 
 S 
 
 13 
 
 2029 
 
 60 
 
 31 
 
 lid 
 
 
 
 
 
 
 
 
 9 
 
 10 
 
 1729 
 
 00 
 
 2s 
 
 00 
 
 
 
 
 
 
 
 NOTE. Half logs are given in the original tables. 
 
 Since a large share of the timber of the fir region is 
 realized on by its owners in the form not of lumber but 
 of logs, the inducement is small to go further than the log 
 in quality work in that region. It is otherwise, however, 
 in the regions characterized by pine, where there are no
 
 PRACTICE OF TIMBER ESTIMATING 205 
 
 log markets and timber enters the commercial field in 
 the shape of lumber with its great range in quality and 
 value. Here the Forest Service, endeavoring in its own 
 business to get away from the judgment of the individual 
 applied in too broad a way, has started a line of inquiry 
 that should in time prove serviceable to business. Log 
 grades in this case again are made the basis to which the 
 field man works, but mill and yard studies, carrying the 
 product of those logs through the process of manufacture 
 to point of sale, afford a means of going further, to an 
 estimate of lumber quality and value. Definitions of the 
 log grades that have been formed for yellow pine follow, 
 and brief notes on the yield of those grades may be serv- 
 iceable to some, although, with a small field covered, it 
 has beeti found already that logs graded by the same man 
 under the same rules vary considerably by locality in 
 their yield of high grade lumber. 
 
 Yellow Pine Log Grades of the U. S. Forest Service. 
 
 Clear logs shall be 22 inches or over in diameter inside 
 the bark at the small end and not less than 10 feet long. 
 They shall be reasonably straight-grained, practically 
 surface clear, and of a character which in the judgment 
 of the sealer are capable of cutting not less than 25 per 
 cent of their scaled contents into lumber of the grades of 
 C Select and better. 
 
 Shop logs shall be 18 inches or over in diameter inside 
 the bark at the small end, not less than 8 feet long, and 
 which in the judgment of the sealer are capable of cut- 
 ting not less than 30 per cent of their scaled contents 
 into lumber of the grades of No. 2 Shop and better. 
 
 Rough logs shall be 6 inches or over in diameter inside 
 the bark at the small end and not less than 8 feet long, 
 having defects which in the judgment of the sealer pre- 
 vent their classification into either of the two above 
 grades. 
 
 Logs cut from rather large and high class timber at 
 different points of interior Oregon, graded according to 
 the above rules, have yielded as follows: 
 
 Clear logs 60-65 per cent No. 2 Shop and better, about 
 half of it of grades B and C Select.
 
 206 A MANUAL FOR NORTHERN WOODSMEN 
 
 Shop logs 40-45 per cent No. 2 Shop and better, a fifth 
 to a fourth B and C. 
 
 Rough logs have yielded about 15 per cent No. 2 Shop 
 and better. 
 
 For the Novice. From the foregoing it will be inferred 
 that the best timber cruising in the Pacific region is a 
 highly expert business, requiring in addition to accuracy 
 and alertness, thorough personal training and judgment 
 in high degree. There are always learners in the field, 
 however, and occasionally inexpert men are so situated 
 that with whatever equipment they can command they 
 must do their best to size up the quantity and value of 
 timber. To such, a caution in respect to the loss of ap- 
 parent volume that breakage, shake and decay may 
 cause and the very large part that location, and especially 
 quality, play in the value of timber is an essential service. 
 Then it is true and worthy of regard that in these cir- 
 cumstances simple methods may actually give the best 
 results. 
 
 A man may learn much in a logging operation where 
 timber similar to that he is concerned with can be ex- 
 amined after it is felled and bucked into logs. He can 
 see how much is broken up, whether the timber is rotten 
 or sound, and from the cross cuts and surface indications 
 of the logs examined at close range get an idea of the prev- 
 alence of knots, shakes and other blemishes. Then he 
 can scale up the logs from a number of trees, ascertain- 
 ing the total length utilized and the quantity of mer- 
 chantable timber derived from each tree. This ' he will 
 attach to its length and base diameter and endeavor to 
 link up with trees of similar dimensions standing. 
 
 Such work as this will enable a man to understand a 
 volume table, and he may even get enough measures to 
 make one for himself iir some size groups, with which he 
 may check published volume tables. Or old devices and 
 short cuts 1 may be tried out with the idea of sharpening 
 
 1 Such as the following: 
 
 Average the base diameter of the tree and the top diameter of 
 its merchantable timber; get the scale of a log of that diameter
 
 PRACTICE OF TIMBER ESTIMATING 207 
 
 the observation and training the judgment. The best 
 result that can come from such work (it can be gained 
 only with time and experience, and some men never will 
 acquire it) is the capacity to make a close estimate of the 
 contents of a tree standing. 
 
 Contents of the average tree in a piece of timber, ob- 
 tained by methods of this kind, may be made a starting 
 point for the next step in the process. A man may count 
 all the trees standing on a small piece of ground, using 
 safeguards that he will readily think up to get all the 
 trees in and not to count any a second time. If the terri- 
 tory is too large for that, sample acres in any number 
 can be run out in fair average ground and the trees counted 
 up on them. 1 A square acre is 209 feet on a side, about 
 80 paces. A circular acre is 236 feet in diameter. Or, 
 some form of the strip method may be used as described 
 on the preceding pages. The area of ground without tim- 
 ber should be thrown out; single trees or bunches that are 
 of exceptional size and quality should be treated separately. 
 Material loss from breakage enters when about 100 feet 
 in merchantable length is passed, and runs up to nearly or 
 quite 50 per cent on very broken land with heavy timber. 
 
 The above, compared with really adequate, profes- 
 sional cruising, is only an expedient; still, carried out by 
 a clear-headed man, it might really be worth more than 
 what passes oftentimes as something more ambitious. 
 Such a man, too, can sometimes find out what he wants 
 to know, or manage to protect his own interests in matters 
 of this kind, without resort to timber cruising. Some 
 men also have judgment on the contents of a body of 
 timber as a whole who are unfamiliar with a systematic 
 timber estimate, and would be slow and uncertain in the 
 execution of it. 
 
 32 feet long; multiply by the number of 32-foot logs less one- 
 half log. 
 
 Or, to base diameter add one-half of base diameter and divide 
 by 2; multiply by .8, square and divide by 12. The result is the 
 number of feet in the stick per foot of its length. 3 to 5 per 
 cent may sometimes be added for contents above the point 
 stated. 
 
 1 For a caution on this head, see page 187.
 
 PART V 
 TABLES 
 
 SECTION I. TABLES RELATING TO PARTS I AND II . . 210 
 SECTION II. TABLES RELATING TO PARTS III AND IV . 235 
 SECTION III. MISCELLANEOUS TABLES AND INFORMATION 293
 
 SECTION I 
 TABLES RELATING TO PARTS I AND H 
 
 1. STADIA REDUCTIONS 211 
 
 2. SOLUTION OF TRIANGLES 212 
 
 3. TRAVERSE TABLES 214 
 
 4. LOGARITHMS OF NUMBERS 220 
 
 5. LOGARITHMIC SINES, COSINES, TANGENTS, AND CO- 
 
 TANGENTS . . 222 
 
 6. SUPPLEMENTARY TABLES OF SMALL ANGLES .... 228 
 
 7. NATURAL SINES AND COSINES 230 
 
 8. NATURAL TANGENTS AND COTANGENTS 232 
 
 9. SPECIMEN LETTERING . . 234
 
 TABLES RELATING TO PARTS I AND II 211. 
 
 STADIA REDUCTIONS 
 
 Horizontal Distance 
 
 
 1 ' i 
 
 
 
 
 I 
 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 40' 
 
 50' 
 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 40' 
 
 50' 
 
 100.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 1000 
 
 M* 
 
 92.4 
 
 92.3 
 
 92.1 91.9 
 
 91.8 
 
 91.6 
 
 1 100.0 
 2 99.9 
 
 100.0 
 99.8 
 
 99.9 
 99.8 
 
 99.9) 99.9 
 99.8 99.8 
 
 99.9 
 99.8 
 
 17 
 
 18 
 
 91.5 
 90.4 
 
 91.391.1191.0 
 90.390.189.9 
 
 90.890.6 
 89.8 89.6 
 
 3 
 
 4 
 
 99.7 
 99.5 
 
 99.7 
 99.5 
 
 99.7 
 99.4 
 
 99.6 
 99.4 
 
 99.6 
 99.3 
 
 99.6 
 99.3 
 
 19 
 20 J 
 
 89.4 
 88.3 
 
 89.2!89.0 88.9 88.7 
 88.1,87.987.7187.5 
 
 88.5 
 87.3 
 
 5 
 
 99.2 
 
 99.2 
 
 99.1 
 
 99.1 
 
 99.0 
 
 99.0 
 
 21 
 
 87.2 
 
 87.0186.8 
 
 86.686.4 
 
 86.2 
 
 6- 
 
 98.9 
 
 98.9 
 
 98.8 
 
 98.7 
 
 98.6 
 
 98.6 
 
 22 ; 
 
 86.0 
 
 85.8:85.6 
 
 85.4J85.2 
 
 84.9 
 
 7 ; 
 
 98.5 
 
 98.4 
 
 98.4 
 
 98.3 
 
 98.2 
 
 98.1 
 
 23 
 
 84.7 
 
 84.5i84.3 
 
 84.1 83.9 
 
 83.7 
 
 8 
 
 98.1 
 
 98.0 
 
 97.9 
 
 97.8 
 
 97.7 
 
 97.6 
 
 24 
 
 83.5 
 
 83.2 
 
 83.0 
 
 82.8 
 
 82.6 
 
 82.4 
 
 V 
 
 97.5 
 
 97.5 
 
 97.4 
 
 97.3 
 
 97.2 
 
 97.1 
 
 25;' 
 
 82.1 
 
 81.9181.7 
 
 81.5 
 
 81.2 
 
 81.0 
 
 10- 
 
 97.0 
 
 96.9 
 
 96.8 
 
 96.7 
 
 96.6 
 
 96.5 
 
 2(i'- 
 
 80.8 
 
 80.6180.3 
 
 MM 
 
 79.9 
 
 79.6 
 
 11 
 
 96.4 
 
 96.3 
 
 96.1 
 
 96.0 
 
 95.9 
 
 95.8 
 
 27 
 
 79.-1 
 
 79.2 
 
 78.'.) 
 
 78.7 
 
 78.4 
 
 78.2 
 
 12 
 
 95.7 
 
 95.6 
 
 95.4 
 
 95.3 
 
 95.2 
 
 95.1 
 
 28' 
 
 7.x. o 
 
 77.7 
 
 77.5 
 
 77.2 
 
 77.0 
 
 76.7 
 
 13- 
 
 94.9 
 
 94.8 
 
 94.7 
 
 94.5 
 
 94.4 
 
 94.3 
 
 29" 
 
 7 (',..-, 
 
 7(1.2 
 
 76.0 
 
 75.7 
 
 75.5 
 
 75.2 
 
 
 94.2 
 
 94.0 
 
 93.9 
 
 93.7 
 
 93.6 
 
 93.4 
 
 :50 C 
 
 75.0 
 
 74.7 
 
 74.5 
 
 74.2 
 
 74.0 
 
 73.7 
 
 15 
 
 93.3 
 
 93.2 
 
 93.0 
 
 92.9 
 
 92.7 
 
 92.6 
 
 
 
 
 
 
 
 
 Difference of Elevation 
 
 
 Proportional Parts 
 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 4W 
 
 50' 
 
 1' 
 
 2' 
 
 V 
 
 4' 
 
 5' 
 
 6' 
 
 7' 
 
 8' 
 
 9' 
 
 
 
 0.00 
 
 0.29 
 
 0.58 
 
 0.87 
 
 1.16 
 
 1.45 
 
 03 
 
 .06 
 
 .09 
 
 .12 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .26 
 
 1 
 
 1.74 
 
 2.04 
 
 2.33 
 
 2.62 
 
 2.91 
 
 3.20 
 
 .03 
 
 .06 
 
 .()!> 
 
 .12 
 
 .14 
 
 .18 
 
 .20 
 
 .2:; 
 
 .26 
 
 2 
 
 3.49 
 
 3.78 
 
 4.07 
 
 4.36 
 
 4.65 
 
 4.94 
 
 .03 .06 
 
 .09 
 
 .12 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .26 
 
 3 
 
 5.23 
 
 5.52 
 
 5.80 
 
 6.09 
 
 6.38 
 
 6.67 
 
 ;.03 .06 
 
 .09 
 
 .12 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .26 
 
 4 
 
 6.96 
 
 7.25 
 
 7.5:', 
 
 7.82 
 
 8.11 
 
 8.40 
 
 1.03 i. 06 1.09 
 
 .12 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .26 
 
 5 
 
 8.68 
 
 8.971 9.25 
 
 9.54 
 
 9.83 10.11 
 
 '.03 : .06 .08 
 
 .11 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .25 
 
 6 
 
 10.40 
 
 10.68 10.96ill.25 
 
 11.53 11.81 
 
 .03 .06 
 
 .08 
 
 .11 
 
 .14 
 
 .17 
 
 .20 
 
 .23 
 
 .25 
 
 7 
 
 12.10 
 
 12.38 
 
 12.66 12.94 
 
 13.22 13.50 
 
 .03 .06 
 
 .08 
 
 .11 
 
 .14 
 
 .17 
 
 .20 
 
 .22 
 
 :ir> 
 
 8 
 9 
 
 13.78 
 15.45 
 
 14.06 
 15.73 
 
 14.34 14.62 
 16.0016.28 
 
 14.90 15.17 
 16.55 16.83 
 
 .03 .06 
 .03 .06 
 
 .08 
 .08 
 
 .11 
 .11 
 
 .14 
 .14 
 
 .17 
 .17 
 
 .1!) 
 .1!) 
 
 .22 
 .22 
 
 .25 
 .25 
 
 10 
 
 17.10 
 
 17.37 
 
 17.65 17.92 
 
 18.19.18.46 
 
 .03 1. 05 : . 08 
 
 .11 
 
 .14 
 
 .16 
 
 .19 
 
 .22 
 
 .24 
 
 11 
 
 18.73 
 
 19.00 
 
 19.27 19.54 
 
 19.80 20.07 
 
 .031.05 .08 
 
 .11 
 
 .13 
 
 .16 
 
 .19 
 
 .21 
 
 .24 
 
 12 
 13 
 
 20.:M 
 
 21.'.)2 
 
 20.80 20.87 21.13 
 22.18 22.44 22.70 
 
 21.39 
 
 22.96 
 
 21.66 
 23.22 
 
 .03 
 
 03 
 
 .05 
 .05 
 
 .08 
 
 .08 
 
 .11 
 .10 
 
 .13 
 
 . 1 3 
 
 .16 
 .16 
 
 .18 
 .18 
 
 .21 
 .21 
 
 .24 
 .23 
 
 14 
 
 2:;. 17 
 
 23.73 23.99 24.24 
 
 24.49 
 
 24.75 
 
 03 
 
 05 
 
 .08 
 
 .10 
 
 .13 
 
 .15 
 
 .18 
 
 .20 
 
 .23 
 
 15 
 16 
 
 25.00 
 26.50 
 
 25.25 25.50 25.75 
 26.7426.9927.23 
 
 26.00 
 
 26.25 
 27.72 
 
 i03 
 .02 
 
 .05 
 .05 
 
 .07 
 .07 
 
 .10 
 .10 
 
 .13 
 
 .12 
 
 .15 
 .15 
 
 .17 
 .17 
 
 .20 
 .20 
 
 .23 
 .22 
 
 17 
 
 18 
 
 27.96 
 
 2'.).:;<i 
 
 28.20 28.44 28.68 28.92 
 29.62 29.86 30.09 30.32 
 
 29.15 
 30.55 
 
 .02 
 
 .02 
 
 .05 
 .05 
 
 .07 
 .07 
 
 .10J.12 
 .09 .12 
 
 .14 
 
 .14 
 
 .17 
 .16 
 
 .19 
 .19 
 
 .21 
 .21 
 
 19 
 20 
 
 30.78 
 32.14 
 
 31.01 31.24 
 32.3632.58 
 
 31.4731.69 
 32.80133.02 
 
 31.92 
 33.24 
 
 .02 
 .02 
 
 .05 
 .04 
 
 .07 
 .07 
 
 .09 
 
 .0!) 
 
 .11 
 
 .11 
 
 .14 
 .13 
 
 .16 
 .15 
 
 .18 
 .18 
 
 .21 
 .20 
 
 21 
 
 22 
 
 33.46 
 
 U.73 
 
 33:67 
 
 :;',.<)! 
 
 :;:i.X'.i 
 :;r,.ir, 
 
 34.1034.31 
 35.36135.56 
 
 34.52 
 35.76 
 
 .02 
 .02 
 
 .04 
 .04 
 
 .06 .08 .11 
 .06 .081.10 
 
 .13 
 .12 
 
 .15 
 
 .14 
 
 .17 
 .16 
 
 .19 
 .19 
 
 23 
 24 
 
 15.07 
 37.16 
 
 30.17 
 37.35 
 
 :;i',.:>,7 
 37.54 
 
 36.57 36.77 
 37.7437.93 
 
 36.96 
 38.11 
 
 .02.04 
 .02 .04 
 
 .06 .08 L 10 
 .06 .08 .09 
 
 .12 
 .11 
 
 .14 
 .13 
 
 .16 
 .15 
 
 .18 
 .17 
 
 25 
 
 38.30 38.49 
 
 38.6738.86 
 
 39.04 
 
 39.22 
 
 .02 .04 
 
 .06 .07 
 
 .09 
 
 .11 
 
 .13 
 
 .15 
 
 .17 
 
 26 
 
 39.40 139.58 
 
 39.7639.93 
 
 10.11 
 
 40.28 
 
 .02 .04 
 
 .05 .07 
 
 .09 
 
 .11 
 
 .12 
 
 .14 
 
 .16 
 
 27 
 28 
 29 
 30 
 
 40.45 
 
 41.45 
 42.40 
 43.30 
 
 40.62 
 41.61 
 42.56 
 43.45 
 
 40.79 
 
 41.77 
 42.71 
 43.59 
 
 40.96 41.12 
 41.93 42.09 
 42.8643.01 
 43.73 43.87 
 
 41.29 
 42.25 
 43.16 
 44.01 
 
 .02 
 
 02 
 .02 
 .01 
 
 .03 
 .0:; 
 .03 
 .03 
 
 .05 
 
 .05 
 
 .05 
 .04 
 
 .07 
 .06 
 01 i 
 .06 
 
 .08 
 .08 
 .08 
 .07 
 
 .10 
 .10 
 
 .09 
 .09 
 
 .12 
 .11 
 .11 
 .10 
 
 .13 
 .13 
 .12 
 .11 
 
 .15 
 .14 
 .14 
 .13
 
 212 A MANUAL FOR NORTHERN WOODSMEN 
 
 SOLUTION OF TRIANGLES 
 
 The figure may refresh to good pur- 
 pose the memory of the field worker. 
 In it are graphically represented the 
 functions (sine, cosine, secant, and 
 tangent) of the angle BAC. The 
 cosine, cosecant, 
 /\ and cotangent of 
 
 triangle A B C are as follows : 
 
 BAC are respect- 
 ively the sine, 
 secant, and tangent of CAD, the 
 complement of BAC. 
 
 Represented as ratios, the functions 
 of the angle A in the right-angled 
 
 
 Tangent^ - 
 
 By these formulas, and the use of the tables of sines and 
 tangents, all the parts of any right-angled triangle may be 
 obtained if two sides, or an acute angle and a side, are 
 given. 
 
 All the parts and the area of an 
 oblique triangle may be obtained if 
 any three parts including one side 
 are given. Let A, B, C represent 
 the angles, and a, b, c the opposite 
 sides, of any oblique triangle ; then A , 
 the solutions are as given on the 
 next page.
 
 TABLES RELATING TO PARTS I AND II 213 
 
 Given 
 
 Sought 
 
 
 A, B, a 
 
 A, a, b 
 
 A,B,C,a 
 C,a, b 
 
 a, b, c 
 
 C, 6, c 
 
 B, C, c 
 
 Area 
 i(A+B) 
 *(A-B) 
 
 A 
 B 
 
 c 
 
 Area 
 A 
 
 B, C 
 Area 
 
 C = 180 - (A + B) 
 b a -in B 
 
 sin A 
 a -in C 
 
 sin A 
 b sin A 
 
 a 
 C = 180 - (A + B) 
 a sin C 
 
 sin A 
 a 2 sin B sin C 
 
 2 sin A 
 i (X + B) = 90 - i C 
 
 ta n 4 f 4 R^ - t*n 4- />4 4- J^ 
 
 4 = -J (4 + B) + i (4 - B) 
 
 - i (4 + ; B)>- i (4 - ) 
 
 C -fa 1 M COS ^(^+ B ) 
 
 6) cos i (X - B) 
 fa M sin * ( ^ 45) 
 
 fc) S ini(^-B) 
 Area = % ab sin C 
 Let s = \ (a + b + c) 
 
 Then S in \ i \ /(8 ~ b}(s ~ C) 
 
 be 
 
 K i i \/ s (s - a) 
 
 oc 
 
 ln 1 i A/(> -V(*~ C) 
 
 . ( - a) 
 Similar formulas 
 
 V* ( a) '(* b) (s c)
 
 214 
 
 TRAVERSE TABLE 
 
 j Dist. 5 
 [ Lat. DepT 
 !5.0000 0.0218 
 
 1 9(53 
 2181 
 
 1)931 
 9920 
 
 9726 5226 84 
 
 9703 5443 
 
 9679 5660 
 
 9653 5877 
 
 9627 j 0013 83 
 
 MOO 
 9672 
 
 6526 
 
 4.9543 0.6743 
 
 9278 8467 
 9240 8682 
 4.9202lo.8897 
 91631 9112 
 9123 9326 
 9081 9540 
 
 ;nioj 
 
 9089 
 
 9039 9755 
 8996: 9968 
 89521.0182 
 89071 0396 
 8862 0609 
 8815| 0822 
 4.87C7 1.1035 
 
 8719 1248 77 
 
 8669 1460 
 
 8618 1672 
 
 8567, 1884 
 
 8515i 2096 
 
 8462! 23<'8 
 
 84' 7 2519 
 
 8*52 2730 
 
 8296J 2941 
 
 Dep7|~Lat. 
 ~~Dtat5~~ 
 
 45 
 30 
 15 
 
 87 
 45 
 
 45 
 
 45 
 
 30 
 
 15 
 
 
 
 45 
 
 30 
 
 15 
 
 75 
 
 Course
 
 TRAVERSE TABLE 
 
 215 
 
 Pep. Lat. j Pep. Lat. Dep.| Lat. Pep. Lat. 
 Dist. 6 I Dist. 7 Diet. 8 Dist. 9
 
 216 
 
 TRAVERSE TABLE 
 
 2.8944 0.7S91 3.8591 
 8909J 8017J 854; 
 8874 8143 
 
 0.9140 3.809C 1.2195 4.7621 
 
 45 0.9222 0.3S67 
 
 23 9205 3907 
 15 > 9188 3947 
 30 | 9171! 3987 
 45 9153 ! 4027 
 
 24 9135 4007 
 15' 9118 4107 
 30 9100 4147 
 45 90811 4187 
 
 25 0| 90631 422C 
 15 0.9045 0.426C 
 
 4305 
 45' 9007 
 
 Pep. Lat. j _Dep. Lat. i Pep. Lat. J)ep. ILat. ! Pep. Lat. I 
 I Dist. 1 I ~Dist2 II IMst. 3 ~~Digt'4~l' Dist. 5 '
 
 TRAVERSE TABLE 
 
 217 
 
 Course 
 
 i Dist. 6 
 
 Dist. 7 
 
 Dist. 8 
 
 Dist. 9 
 
 Dist. 10 
 
 
 
 | Lat. i Dep. 
 
 Lat. i Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Pep- 
 
 Lat. Dep. 
 
 
 15 15 5.7887 1.5782 
 
 6.7335 1 8412 
 
 7.7183 
 
 2.1042 
 
 8.C831 
 
 2.3673 
 
 9.64792.C303 
 
 74 45 
 
 30 
 
 7818 
 
 6034 
 
 7454 
 
 8707 
 
 7090 
 
 1379 
 
 6727 
 
 4051 
 
 G363 
 
 (,724 
 
 30 
 
 45 
 
 7747 
 
 6286 
 
 7372 
 
 9001 
 
 6996 
 
 1715 
 
 6621 
 
 4430 
 
 6246 
 
 7144 
 
 15 
 
 16 
 
 7676 
 
 6538 
 
 7288 
 
 9295 
 
 6901 
 
 2051 
 
 6514 
 
 4807 
 
 6126 
 
 7564 
 
 74 
 
 15 
 
 7603 
 
 6790 
 
 7203 
 
 9588 
 
 6804 
 
 2386 
 
 6404 
 
 5185 
 
 6005 
 
 7983 
 
 45 
 
 30 
 
 7529 
 
 7041 
 
 7117 
 
 9881 
 
 6706 
 
 2721 
 
 6294 
 
 5561 
 
 5882 
 
 8402 
 
 30 
 
 45 
 
 7454 
 
 7292 
 
 7030 
 
 2.0174 
 
 6606 
 
 3056 
 
 6181 
 
 5938 
 
 5757 
 
 882C 
 
 15 
 
 17 
 
 7378 
 
 7542 
 
 6941 
 
 0466 
 
 6504 
 
 3390 
 
 6067 
 
 6313 
 
 5630 
 
 9237 
 
 73 
 
 15 
 
 ! 7301 
 
 7792 
 
 6851 
 
 0758! 
 
 6402 
 
 3723 
 
 5952 
 
 6689 
 
 5502 
 
 9654 
 
 45 
 
 30 
 
 7223 
 
 8040 
 
 6760 
 
 1049 
 
 6297 
 
 4056 
 
 5835 
 
 7064 
 
 5372 
 
 3.0071 
 
 30 
 
 45 
 
 5.7144 
 
 1.8292 
 
 6.6668 
 
 2.1341 
 
 7.6192 
 
 2.4389 
 
 8.5716 
 
 2.7438 
 
 9.5240 
 
 3.0486 
 
 15 
 
 18 
 
 7063 
 
 8541 
 
 6574 
 
 1631 
 
 6085 
 
 4721 
 
 5595 
 
 7812 
 
 5106 
 
 0902 
 
 72 
 
 15 
 
 6982 
 
 8790 
 
 6479 
 
 1921 
 
 5976 
 
 5053 
 
 5473 
 
 8185 
 
 4970 
 
 1316 
 
 45 
 
 30 
 
 6899 
 
 9038 
 
 6383 
 
 2211 
 
 5866 
 
 5384 
 
 5349 
 
 8557 
 
 4832 
 
 1730 
 
 30 
 
 45 
 
 6816 
 
 93SG 
 
 6285 
 
 2501 
 
 5754 
 
 5715 
 
 5224 
 
 8930 
 
 4693 
 
 2144 
 
 15 
 
 19 
 
 6731 
 
 9534 
 
 6186 
 
 2790 
 
 5641 
 
 6045 
 
 5097 
 
 93C1 
 
 4552 
 
 2557 
 
 71 
 
 15 
 
 6645 
 
 9781 
 
 6086 
 
 3078 
 
 5527 
 
 6375 
 
 4968 
 
 1672 
 
 4409 
 
 2969 
 
 45 
 
 30 
 
 6658 1 2.0028 
 
 5986 
 
 3366 
 
 5411 
 
 6705 
 
 4838 
 
 3.0043 
 
 42C4 
 
 3381 
 
 30 
 
 45 
 
 6471 0275 
 
 5882 
 
 3654 
 
 5294 
 
 7033 
 
 4706 
 
 C413 
 
 4118 
 
 3792 
 
 15 
 
 20 
 
 6382 0521 
 
 5778 
 
 3941 
 
 5176 
 
 7362 
 
 4562 
 
 0782 
 
 3969 
 
 4202 
 
 70 
 
 15 
 
 5.6291 20767 
 
 65673 
 
 2.4228 
 
 7.5055 
 
 2.7689 
 
 8.4437 
 
 3.1151 
 
 9.3819 
 
 3.4612 
 
 45 
 
 30 
 
 6200 
 
 1012 
 
 5565 
 
 4515 
 
 4934 
 
 8017 
 
 4300 
 
 1519 
 
 37 C7 
 
 5021 
 
 30 
 
 45 
 
 6108 
 
 1257 
 
 5459 
 
 4800 
 
 4811 
 
 8343 
 
 4162 
 
 1886 
 
 3514 
 
 5429 
 
 15 
 
 21 
 
 6dl5 
 
 1502 
 
 5351 
 
 5086 
 
 4686 
 
 8669 
 
 4022 
 
 2253 
 
 3358 
 
 5837 
 
 69 
 
 15 
 
 5920 
 
 1746 
 
 5241 
 
 6371 
 
 4561 
 
 8995 
 
 3881 
 
 2619 
 
 3201 
 
 6244 
 
 45 
 
 30 
 
 
 1990 
 
 5129 
 
 5655 
 
 4433 
 
 089 
 
 3738 
 
 2985 
 
 3042 
 
 6650 
 
 30 
 
 45 
 
 5720 
 
 2233 
 
 5017 
 
 6939 
 
 4305 
 
 9645 
 
 3593 
 
 3350 
 
 2881 
 
 7056 
 
 15 
 
 22 
 
 5631 
 
 2476 
 
 4903 
 
 6222 
 
 4176 
 
 9909 
 
 3447 
 
 3715 
 
 271 i- 
 
 7461 
 
 68 
 
 15 
 
 5532 
 
 2719 
 
 4788 1 6505 
 
 4043 
 
 3.0292 
 
 3299 
 
 4078 
 
 2554 
 
 7865 
 
 45 
 
 30 
 
 5433 
 
 2961 
 
 4672 i 6788 
 
 3910 
 
 0615 
 
 3149 
 
 4442 
 
 2388 
 
 8268 
 
 30 
 
 45 
 
 5.5332 
 
 2.3203 
 
 6.45542.7070 
 
 7.3776 
 
 3.0937 
 
 8.2998 
 
 3.4804 
 
 9.2220 
 
 3.8671 
 
 15 
 
 23 
 
 5230 
 
 3414 
 
 4435 7351 
 
 3640 
 
 1258 
 
 2845 
 
 6166 
 
 2050 
 
 S073 
 
 67 
 
 15 
 
 5127 
 
 3685 
 
 4315J 7632 
 
 3503 
 
 1580 
 
 2691 
 
 5527 
 
 1879| 9474 
 
 45 
 
 30 
 
 5(124 
 
 3925 
 
 ltf 7912 
 
 3365 
 
 1900 
 
 2535 
 
 5887 
 
 1706 9875 
 
 30 
 
 45 
 
 4919 
 
 4165 
 
 4072 8192 
 
 3225 
 
 2220 
 
 2375 
 
 6247 
 
 1531 4.0275 
 
 15 
 
 24 
 
 4813 
 
 4404 
 
 3948 8472 
 
 3084 
 
 2539 
 
 2219 
 
 6006 
 
 1355 
 
 0674 
 
 66 
 
 15 
 
 4706 
 
 4643 
 
 3823; 8750 
 
 2941 
 
 2858 
 
 2059 
 
 0965 
 
 1176 
 
 1072 
 
 45 
 
 30 
 
 4598 
 
 4882 
 
 3697 i 9029 
 
 2797 
 
 3175 
 
 1897 
 
 7322 
 
 0996 
 
 1469 
 
 30 
 
 45 
 
 4489 
 
 5120 
 
 3570 1 9306 
 
 2651 
 
 3493 
 
 1733 
 
 7U79 
 
 0814 
 
 1866 
 
 15 
 
 25 
 
 4378 
 
 5357 
 
 3442! 9583 
 
 2505 
 
 3809 
 
 1568 8036 
 
 0631 
 
 226265 
 
 15 
 
 5.4267 
 
 2.5594 
 
 6.3312 2 9800 
 
 7.2356 
 
 3.4125 
 
 8.1401 3.8391 
 
 9.0446 
 
 4.2657 
 
 45 
 
 30 
 
 4155 
 
 5831 
 
 3181 3.0136 
 
 2207 
 
 4441 
 
 1233 8746 
 
 H259 
 
 3051 
 
 30 
 
 45 
 26 
 
 4042 
 3928 
 
 6067 
 6302 
 
 3049 0411 
 2916| 0686 
 
 2056 
 1904 
 
 4756 
 5070 
 
 1063 
 0891 
 
 9100 0070 
 9453 8.9879 
 
 3445 15 
 383764 
 
 15 
 
 3812 
 
 6537 
 
 2781 0960 
 
 1750 
 
 5383 
 
 0719 
 
 9806 
 
 9687 
 
 4229 
 
 45 
 
 30 
 
 3696 
 
 6772 
 
 2645 1234 
 
 1595 
 
 5696 
 
 0644 
 
 4.0158' 
 
 9493 
 
 4620 
 
 30 
 
 45 
 
 3579 
 
 7006 
 
 2509 1507 
 
 1438 
 
 6008 
 
 0368 
 
 0509 
 
 9298 
 
 5010 
 
 15 
 
 27 
 
 3460 
 
 7239 
 
 2370 1779 
 
 1281 
 
 6319 
 
 0191 
 
 0859 ' 
 
 9101 
 
 5399 
 
 63 
 
 15 
 
 3341 
 
 7472 
 
 2231! 2051 
 
 1121 
 
 6630 
 
 0012 
 
 1209: 
 
 8902 
 
 5787 
 
 45 
 
 30 
 
 3221 
 
 7705 
 
 2091 1 2322 ! 
 
 0961 
 
 6940 
 
 7.9831 
 
 15571 
 
 8701 
 
 6175 
 
 30 
 
 45 
 
 5.3099 
 
 2.7937 
 
 6.1949 3.2593 1 7.0799 
 
 3.7249 
 
 7.9649 
 
 4.1905 
 
 88499 
 
 4.6561 
 
 15 
 
 28 
 
 2977 
 
 8168 
 
 18(6 2863 
 
 0636 
 
 7558 
 
 9465 
 
 2252 
 
 8295 
 
 6947 
 
 62 
 
 15 
 
 2853 
 
 8399 
 
 1662 3132 
 
 6471 
 
 7866 
 
 9280 
 
 2599 
 
 8089 
 
 7^32 
 
 45 
 
 30 
 
 2729 
 
 8630 
 
 15171 3401 
 
 0305 
 
 8173 
 
 9094 
 
 2944 
 
 7882 
 
 7716 
 
 30 
 
 45 
 
 2604 
 
 8859 
 
 1371 1 3669 
 
 0138 
 
 8479 
 
 8905 
 
 3289 
 
 7673 
 
 8(99 
 
 15 
 
 29 
 
 2477 
 
 9089 
 
 1223 3937 6.9970 
 
 8785 
 
 8716 
 
 3683 
 
 7462 
 
 8481 
 
 61 
 
 15 
 
 2350 
 
 9317 
 
 1075 4203 
 
 9800 
 
 9090 
 
 8525 
 
 3976! 
 
 7250 
 
 8862 
 
 45 
 
 30 
 
 2221 
 
 9545 
 
 0925 4470 
 
 9628 
 
 9394 
 
 8332 
 
 4318! 
 
 7036 
 
 9242 
 
 30 
 
 45 
 
 2092 
 
 9773 
 
 0774 4735 
 
 945i ; 
 
 9697 
 
 8148 
 
 4659 1 
 
 6820 ! 9622 
 
 15 
 
 30 
 
 1962 3.0000 
 
 0622 1 50CO 9282 
 
 4.0000 
 
 7942 
 
 5000 
 
 66035.0000 
 
 50 
 
 
 Dep. 1 Lat. 
 
 Dep. Lat. j Dep. 
 
 TatT 
 
 ^pTTatT 
 
 Dep. Lat. 
 
 
 
 Dist. 6 
 
 Dist. 7 i| Dist. 8 
 
 Dist. 9 
 
 Dist. 10 
 
 Course
 
 218 
 
 TRAVERSE TABLE
 
 TRAVERSE TABLE 
 
 Course 
 
 30 15 5.1830 3.0226 
 0462 
 
 0(178 
 0902 
 1120 
 1350 
 1573 
 1795 
 2017 
 
 45 
 
 31 
 15 
 
 30 
 45 
 
 32 
 15 
 
 '30 
 
 0744 
 0603 
 
 45 5.0462 3.2458 
 
 3? 0320 
 15 0177 
 30| 0033 
 45^4.9888 
 34 9742 
 15| 9595 
 9448 
 45 
 9149 
 
 3G 
 15 
 30 
 45 
 
 37 
 15 
 
 
 
 15 
 30 
 45 
 
 39 
 15 
 30 
 46 
 
 40 
 
 30 
 45 
 
 41 
 15 
 
 30 
 45 
 
 42 
 15 
 
 30 
 
 43 
 15 
 30 
 45 
 
 44 
 15 
 30 
 45 
 
 45 
 
 7018 
 77m 
 
 1.7441 3.C733 
 
 7281 
 
 79i e 
 
 6131 
 
 85G7 
 15 4.5794 3.8767 
 
 5624 
 
 r,4r,4 
 
 45 4.4059 4.0728 
 
 6110 
 
 4037 
 4763 
 4589 4 0148 
 
 9628 
 9363 
 
 !t'n! 
 9037 
 5.88733.7868 
 
 8707 
 
 6024 
 
 5312 
 
 5532 
 6.5331 4.6172 
 6456 
 
 21109 
 2391 
 
 2172 
 
 I'.o.i 
 
 1730 
 1.-.07 
 
 5.M03 4.7516 
 1195 7740 
 0986 7963 
 0776! 8185 
 0565^ 8406 
 0354 i 8626 
 0141 8845 
 
 4.9928; fc 9064 
 9713 ' 9281 
 9477| 9497 
 
 7547 
 7.".04 
 
 70. ;o 
 
 Pep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. : Pep. Lat. 
 
 Lat. Dep 
 
 .-.4 SO 
 
 5266 
 
 5050 
 
 Dist. 10 
 Lat. I DeB 
 
 9340 
 9674 
 4832 5.0001 
 4613 0327 
 
 c,it;3 
 
 5941 
 5717 
 5491 
 5264 
 
 .-oar, 
 
 4so5 
 4.773 
 
 901811 3867 1 
 
 439! 
 41 
 
 3! US 
 3724 
 7.3498 5.1943 
 2263 
 3042 
 
 258( 
 2347 
 2113 
 
 1877 
 I04C 
 
 1401 
 
 0436 
 
 0190 
 6.9943 
 9695 
 944lj 
 9191 
 8944 
 
 0662 
 
 0077 
 
 1300 
 1022 
 
 321 * 
 353,4 
 
 3147 
 
 2!K.I4 
 
 21 1 u 
 1015 
 
 8.1664 5.7715 
 
 1412 
 
 1157 8425 
 
 0902 8779 
 
 0644 913: 
 
 0386 9482 
 0125 
 
 1129 15 
 150459 
 
 15 
 
 45 
 30 
 15 
 
 446457 
 45 
 30 
 15 
 
 56 
 45 
 30 
 15 
 
 '35855 
 45 
 
 .98646.018253 
 45 
 30 
 15 
 
 156652 
 
 1909 
 
 2251 
 
 15 
 
 821 ;i 
 7988 
 
 77 ir 
 743; 
 
 7102 
 
 5751' 
 5471 
 
 2537 
 
 _'_: it; 
 1934 
 
 2'J3L 
 
 1946 
 
 5276 
 
 560649 
 45 
 30 
 15 
 
 691348
 
 220 A MANUAL FOR NORTHERN WOODSMEN 
 
 LOGARITHMS OF NUMBERS 
 
 No. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 0000 
 
 0043 
 
 0086 
 
 0128 
 
 0170 
 
 0212 
 
 0253 
 
 0294 
 
 0334 
 
 0374 
 
 11 
 
 0414 
 
 0453 
 
 0492 
 
 0531 
 
 05(39 
 
 0607 
 
 0645 
 
 0682 
 
 0719 
 
 0755 
 
 12 
 
 0792 
 
 0828 
 
 0864 
 
 0899 
 
 0934 
 
 OJ69 
 
 1004 
 
 1038 
 
 1072 
 
 1106 
 
 13 
 
 1139 
 
 1173 
 
 1206 
 
 1239 
 
 1271 
 
 1303 
 
 1335 
 
 1367 
 
 1399 
 
 1430 
 
 14 
 
 1461 
 
 1492 
 
 1523 
 
 1553 
 
 1584 
 
 1614 
 
 1644 
 
 1673 
 
 1703 
 
 1732 
 
 15 
 
 1761 
 
 1790 
 
 1818 
 
 1847 
 
 1875 
 
 1903 
 
 1931 
 
 1959 
 
 1987 
 
 2014 
 
 16 
 
 2041 
 
 2068 
 
 2095 
 
 2122 
 
 2148 
 
 2175 
 
 2201 
 
 2227 
 
 2253 
 
 2279 
 
 17 
 
 2304 
 
 2330 
 
 2355 
 
 2380 
 
 2405 
 
 2430 
 
 2455 
 
 2 ISO 
 
 2504 
 
 2529 
 
 18 
 
 2553 
 
 2577 
 
 2601 
 
 2625 
 
 2648 
 
 2672 
 
 2695 
 
 2718 
 
 2742 
 
 2765 
 
 19 
 
 2788 
 
 2810 
 
 2833 
 
 2856 
 
 2878 
 
 2900 
 
 2923 
 
 2945 
 
 2967 
 
 2989 
 
 20 
 
 3010 
 
 3032 
 
 3054 
 
 3075 
 
 3096 
 
 3118 
 
 3139 
 
 3160 
 
 3181 
 
 3201 
 
 21 
 
 3222 
 
 3243 
 
 3263 
 
 3284 
 
 3304 
 
 3324 
 
 3345 
 
 3365 
 
 3385 
 
 3404 
 
 22 
 
 3424 
 
 3444 
 
 3464 
 
 3483 
 
 3502 
 
 3522 
 
 3541 
 
 3560 
 
 3579 
 
 3598 
 
 23 
 
 3617 
 
 3636 
 
 3655 
 
 3674 
 
 3692 
 
 3711 
 
 3729 
 
 3747 
 
 3766 
 
 3784 
 
 24 
 
 3802 
 
 3820 
 
 3838 
 
 3856 
 
 3874 
 
 3892 
 
 3909 
 
 3927 
 
 3945 
 
 3962 
 
 25 
 
 3979 
 
 3997 
 
 4014 
 
 4031 
 
 4048 
 
 4065 
 
 4082 
 
 4099 
 
 4116 
 
 4133 
 
 26 
 
 4150 
 
 4166 
 
 4183 
 
 4200 
 
 4216 
 
 4232 
 
 4249 
 
 4265 
 
 4281 
 
 4298 
 
 27 
 
 4314 
 
 4330 
 
 4346 
 
 4362 
 
 4378 
 
 4393 
 
 4409 
 
 4425 
 
 4440 
 
 4456 
 
 28 
 
 4472 
 
 4487 
 
 4502 
 
 4518 
 
 4533 
 
 4548 
 
 4564 
 
 4579 
 
 4594 
 
 4609 
 
 29 
 
 4624 
 
 4639 
 
 4654 
 
 4669 
 
 4683 
 
 4698 
 
 4713 
 
 4728 
 
 4742 
 
 4757 
 
 30 
 
 4771 
 
 4786 
 
 4800 
 
 4814 
 
 4829 
 
 4843 
 
 4857 
 
 4871 
 
 4886 
 
 4900 
 
 31 
 
 4914 
 
 4928 
 
 4942 
 
 4955 
 
 4969 
 
 4983 
 
 4997 
 
 5011 
 
 5024 
 
 5038 
 
 32 
 
 5051 
 
 5065 
 
 5079 
 
 5092 
 
 5105 
 
 5119 
 
 5132 
 
 5145 
 
 5159 
 
 5172 
 
 33 
 
 5185 
 
 5198 
 
 5211 
 
 5224 
 
 5237 
 
 5250 
 
 5263 
 
 5276 
 
 5289 
 
 5302 
 
 34 
 
 5315 
 
 5328 
 
 5340 
 
 5353 
 
 5366 
 
 5378 
 
 5391 
 
 5403 
 
 5416 
 
 5428 
 
 35 
 
 5441 
 
 5453 
 
 5465 
 
 5478 
 
 5490 
 
 5502 
 
 5514 
 
 5527 
 
 5539 
 
 5551 
 
 36 
 
 5563 
 
 5575 
 
 5587 
 
 5599 
 
 5611 
 
 5623 
 
 5635. 
 
 5647 
 
 5058 
 
 5670 
 
 37 
 
 5382 
 
 5694 
 
 5705 
 
 5717 
 
 5729 
 
 5740 
 
 5752 
 
 5763 
 
 5775 
 
 5786 
 
 38 
 
 5798 
 
 5809 
 
 5821 
 
 5832 
 
 5843 
 
 5855 
 
 5866 
 
 5877 
 
 5S8S 
 
 5899 
 
 39 
 
 5911 
 
 5922 
 
 5933 
 
 5944 
 
 5955 
 
 5966 
 
 5977 
 
 5988 
 
 5999 
 
 6010 
 
 40 
 
 6021 
 
 6031 
 
 6042 
 
 6053 
 
 6064 
 
 6075 
 
 6085 
 
 6096 
 
 6107 
 
 6117 
 
 41 
 
 6128 
 
 6138 
 
 6149 
 
 6160 
 
 6170 
 
 6180 
 
 6191 
 
 6201 
 
 6212 
 
 6222 
 
 42 
 
 6232 
 
 6243 
 
 6253 
 
 6263 
 
 6274 
 
 6284 
 
 6294 
 
 6304 
 
 6314 
 
 6325 
 
 43 
 
 6335 
 
 6345 
 
 6355 
 
 6365 
 
 6375 
 
 0385 
 
 6395 
 
 6405 
 
 6415 
 
 6425 
 
 44 
 
 6435 
 
 6444 
 
 6454 
 
 6464 
 
 6474 
 
 6484 
 
 6493 
 
 6503 
 
 6513 
 
 6522 
 
 45 
 
 6532 
 
 6542 
 
 6551 
 
 6561 
 
 6571 
 
 6580 
 
 6590 
 
 6599 
 
 6609 
 
 6618 
 
 46 
 
 6628 
 
 6637 
 
 6646 
 
 6656 
 
 6065 
 
 0075 
 
 6684 6693 
 
 6702 
 
 6712 
 
 47 
 
 6721 
 
 6730 
 
 6739 
 
 6749 
 
 6758 
 
 0767 
 
 6776 ; 6785 
 
 6794 
 
 6803 
 
 48 
 
 6812 
 
 6821 
 
 6830 
 
 6839 
 
 6848 
 
 6857 
 
 6866 
 
 6875 
 
 6884 
 
 6893 
 
 49 
 
 6902 
 
 6911 
 
 6920 
 
 6928 
 
 6937 
 
 6946 
 
 6955 
 
 6964 
 
 6972 
 
 6981 
 
 50 
 
 6990 
 
 6998 
 
 7007 
 
 7016 
 
 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 51 
 
 7076 
 
 7084 
 
 7093 
 
 7101 
 
 7110 
 
 7118 
 
 7126 
 
 7135 
 
 7143 
 
 7152 
 
 62 
 
 7160 
 
 7168 
 
 7177 
 
 7185 
 
 7193 
 
 7202 
 
 7210 
 
 7218 
 
 7226 
 
 7235 
 
 53 
 
 7243 
 
 7251 
 
 7259 
 
 7267 
 
 7275 
 
 7284 
 
 7292 
 
 7300 
 
 7308 
 
 7316 
 
 54 
 
 7324 
 
 7332 
 
 7340 
 
 7348 
 
 7356 
 
 7364 
 
 7372 
 
 7380 
 
 7388 
 
 7396 
 
 No. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9
 
 TABLES RELATING TO PARTS I AND II 
 
 221 
 
 LOGARITHMS OF NUMBERS 
 
 7404 
 7482 
 7669 
 
 7634 
 
 7993 
 8062 
 
 8129 
 8196 
 
 8261 
 8325 
 8388 
 
 8451 
 
 8692 
 
 76 8751 
 
 76 8808 
 
 77 8865 
 
 78 8921 
 
 79 
 
 81 
 
 897 
 
 9085 
 9138 
 9191 
 9243 
 
 9294 
 9345 
 9395 
 9445 
 9494 
 
 9542 
 9590 
 9638 
 9685 
 9731 
 
 9777 
 9823 
 9868 
 9912 
 9956 
 
 8704 
 
 8762 
 8820 
 
 8S76 
 8932 
 8987 
 
 9042 
 9096 
 9149 
 9201 
 9253 
 
 9304 
 9355 
 9405 
 9455 
 9504 
 
 9552 
 9600 
 9647 
 9694 
 9741 
 
 9877 
 9921 
 
 7803 
 7875 
 7945 
 
 8280 
 834 1 
 8407 
 
 8531 
 
 8591 
 st',51 
 
 8768 
 ss-_>5 
 
 9047 
 9101 
 
 9309 
 
 9460 
 
 9557 
 
 8156 
 
 8222 
 M'S 7 
 8351 
 8414 
 
 8637 
 
 8597 
 8657 
 
 8774 
 
 9063 
 
 9106 
 
 9315 
 
 9465 
 
 9562 
 
 9750 
 
 8663 
 
 9004 
 
 9165 
 
 9320 
 
 9754 
 
 7752 
 
 8299 
 
 9325 
 
 9523 
 
 9619 
 
 9759 
 
 7459 
 
 7973 
 8041 
 8109 
 
 8848 
 
 9015 
 
 9175 
 
 9528 
 
 7619 
 7094 
 7767 
 
 8182 
 8248 
 
 8500 
 
 8739 
 
 8854 
 
 9074 
 9128 
 
 9533 
 
 9675 
 
 9814 
 
 7474 
 7551 
 7627 
 7701 
 
 7774 
 
 7846 
 7917 
 7987 
 8055 
 8122 
 
 8254 
 8319 
 
 8445 
 
 8567 
 8627 
 8686 
 
 8745 
 
 8802 
 8859 
 8915 
 8971 
 9025 
 
 9079 
 9133 
 9186 
 9238 
 9289 
 
 7340 
 9390 
 9440 
 
 9586 
 9633 
 
 9727 
 9773 
 
 9952 
 9996
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 LOGARITHMIC SINES, COSINES, 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos. 
 
 D.I' 
 
 Tan. 
 
 D.I' 
 
 Cot. 
 
 
 0' 
 
 00 
 
 
 10.0000 
 
 
 00 
 
 
 00 
 
 90 0' 
 
 10' 
 20' 
 30' 
 40' 
 50' 
 
 7.4637 
 .7648 
 .9408 
 8.0656 
 .1627 
 
 301.1 
 176.0 
 125.0 
 96.9 
 79 2 
 
 .0000 
 .0000 
 .0000 
 .0000 
 .0000 
 
 .0 
 .0 
 .0 
 .0 
 
 7.4637 
 .7648 
 .9409 
 8.0658 
 .1627 
 
 301.1 
 176.1 
 124.9 
 96.9 
 792 
 
 2.5363 
 .2352 
 .0591 
 1.9342 
 .8373 
 
 89 50' 
 89 40' 
 89 30' 
 89 20' 
 89 10' 
 
 1 0' 
 
 8.2419 
 
 66 9 
 
 9.9999 
 
 o 
 
 8.2419 
 
 67 
 
 1.7581 
 
 89 0' 
 
 1 10' 
 
 1 20' 
 1 30' 
 1 40' 
 1 50' 
 
 .3088 
 .3668 
 .4179 
 .4637 
 .5050 
 
 58.0 
 51.1 
 45.8 
 41.3 
 37 8 
 
 .9999 
 .9999 
 .9999 
 .9998 
 .9998 
 
 .0 
 .0 
 .1 
 .0 
 1 
 
 .3089 
 .3669 
 .4181 
 .4638 
 .5053 
 
 58.0 
 51.2 
 45.7 
 41.5 
 
 .6911 
 .6331 
 .5819 
 .5362 
 .4947 
 
 88 50' 
 88 40' 
 88 30' 
 88 20' 
 88 10' 
 
 2 0' 
 
 8.5428 
 
 
 9.9997 
 
 o 
 
 8.5431 
 
 
 1.4569 
 
 88 0' 
 
 2 10' 
 2 20' 
 2 30' 
 2 40' 
 2 50' 
 
 .5776 
 .6097 
 .6397 
 .6677 
 .6940 
 
 32.1 
 30.0 
 28.0 
 26.3 
 
 .9997 
 .9996 
 .9996 
 .9995 
 .9995 
 
 .1 
 
 .0 
 
 .1 
 
 .0 
 
 .5779 
 .6101 
 .6401 
 .6682 
 .6945 
 
 32.2 
 30.0 
 28.1 
 26.3 
 
 .4221 
 .3899 
 .3599 
 .3318 
 .3055 
 
 87 50' 
 87 40' 
 87 30' 
 87 20' 
 87 10' 
 
 3 0' 
 
 8.7188 
 
 23 5 
 
 9.9994 
 
 1 
 
 8.7194 
 
 23 5 
 
 1.2806 
 
 87 0' 
 
 3 10' 
 3 20' 
 3 30' 
 3 40' 
 3 50' 
 
 .7423 
 .7645 
 .7857 
 .8059 
 .8251 
 
 22.2 
 21.2 
 20.2 
 19.2 
 
 .9993 
 .9993 
 .9992 
 .9991 
 .9990 
 
 .0 
 
 .7429 
 .7652 
 .7865 
 .8067 
 .8261 
 
 22.3 
 21.3 
 20.2 
 19.4 
 
 .2571 
 .2348 
 .2135 
 .1933 
 .1739 
 
 86 50' 
 86 40' 
 86 30' 
 86 20' 
 86 10' 
 
 4 0' 
 
 8.8436 
 
 17 7 
 
 9.9989 
 
 
 8.8446 
 
 17 8 
 
 1.1554 
 
 86 0' 
 
 4 10' 
 4 20' 
 4 30' 
 4 40' 
 4 50' 
 
 .8613 
 .8783 
 .8946 
 .9104 
 .9256 
 
 17.0 
 16.3 
 15.8 
 15.2 
 
 .9989 
 .9988 
 .9987 
 .9986 
 .9985 
 
 
 .8624 
 .8795 
 ;8960 
 .9118 
 .9272 
 
 17.1 
 16.5 
 15.8 
 15.4 
 14 8 
 
 .1376 
 .1205 
 .1040 
 .0882 
 .0728 
 
 85 50' 
 85 40' 
 85 30' 
 85 20' 
 85 10' 
 
 5 0' 
 
 8.9403 
 
 14 2 
 
 9.9983 
 
 
 8.9420 
 
 
 1.0580 
 
 85 0' 
 
 5 10' 
 5 20' 
 5 30' 
 5 40' 
 5 50' 
 
 .9545 
 .9682 
 .9816 
 .9945 
 9.0070 
 
 13.7 
 13.4 
 12.9 
 12.5 
 
 .9982 
 .9981 
 .9980 
 .9979 
 .9977 
 
 
 .9563 
 .9701 
 .9836 
 .9966 
 9.0093 
 
 13.8 
 13.5 
 13.0 
 12.7 
 
 .0437 
 .0299 
 .0164 
 .0034 
 0.9907 
 
 84 50' 
 84 40' 
 84 30' 
 84 20' 
 84 10' 
 
 0' 
 
 9.0192 
 
 11 9 
 
 9.9976 
 
 
 9.02 10 
 
 12 
 
 0.9784 
 
 84 0' 
 
 6 10' 
 6 20' 
 6 30' 
 6 40' 
 6 50' 
 
 .0311 
 .0426 
 .0539 
 .0648 
 .0755 
 
 11.5 
 11.3 
 10.9 
 10.7 
 10 4 
 
 .9975 
 .9973 
 .9972 
 .9971 
 .9969 
 
 
 .0336 
 .0453 
 .0567 
 .0678 
 .0786 
 
 11.7 
 11.4 
 11.1 
 10.8 
 
 .9664 
 .9547 
 .9433 
 .9322 
 .9214 
 
 83 50' 
 83 40' 
 83 30' 
 83 20' 
 83 10' 
 
 7 0' 
 
 9.0859 
 
 10 2 
 
 9.9968 
 
 
 9.0891 
 
 
 0.9109 
 
 83 0' 
 
 7 10' 
 7 20' 
 7 30' 
 
 .0961 
 .1060 
 .1157 
 
 9.9 
 9.7 
 
 .9966 
 .9964 
 .9963 
 
 .2 
 
 .1 
 
 .0<)'.!5 
 .1096 
 .1194 
 
 10.1 
 9.8 
 
 .9005 
 .8904 
 .8806 
 
 82 50' 
 82 40' 
 82 30' 
 
 
 Cos. 
 
 D.I' 
 
 Sin. 
 
 D.I' 
 
 Cot. 
 
 D.r 
 
 Tan. 
 
 Angle
 
 TABLES RELATING TO PARTS I AND II 
 
 223 
 
 TANGENTS, AND COTANGENTS 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos. 
 
 D. r 
 
 Tan. 
 
 D.I' 
 
 Cot. 
 
 
 7 30' 
 7 40' 
 7 50' 
 8 0' 
 8 10' 
 8 20' 
 8 30' 
 8 40' 
 8 50' 
 9 0' 
 9 10' 
 9 20' 
 9 30' 
 9 40' 
 9 50' 
 10 0' 
 10 10' 
 10 20' 
 10 30' 
 10 40' 
 10 50' 
 11 0' 
 11 10' 
 11 20' 
 11 30' 
 11 40' 
 11 50' 
 12 0' 
 12 10' 
 12 20' 
 12 30' 
 12 40' 
 12 50' 
 13 0' 
 13 10' 
 13 20' 
 13 30' 
 13 40' 
 13 50' 
 14 0' 
 14 10' 
 14 20' 
 14 30' 
 14 40' 
 14 50' 
 16 0' 
 
 9.1157 
 .1252 
 .1345 
 
 9.5 
 9.3 
 9.1 
 8.9 
 8.7 
 8.5 
 8.4 
 8.2 
 8.0 
 7.9 
 7.8 
 7.6 
 7.5 
 7.3 
 7.3 
 7.1 
 7.0 
 6.8 
 6.8 
 6.6 
 6.6 
 6.4 
 6.4 
 6.3 
 6.1 
 6.1 
 6.0 
 5.9 
 5.8 
 5.7 
 5.7 
 5.6 
 5.5 
 5.4 
 5.4 
 5.3 
 5.2 
 5.2 
 5.1 
 5.0 
 5.0 
 4.9 
 4.9 
 ' 4.8 
 4.7 
 
 9.9963 
 .9961 
 .9959 
 
 .2 
 .2 
 .1 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .2 
 .3 
 .2 
 .2 
 .3 
 .2 
 .3 
 .2 
 .3 
 .2 
 .3 
 .2 
 .3 
 .3 
 .2 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .3 
 .4 
 .3 
 .3 
 .4 
 
 9.1194 
 .1291 
 .1385 
 
 9.7 
 9.4 
 9.3 
 9.1 
 8.9 
 8.7 
 8.6 
 8.4 
 8.2 
 8.1 
 8.0 
 7.8 
 7.7 
 7.6 
 7.4 
 7.3 
 7.3 
 7.1 
 7.0 
 6.9 
 6.8 
 6.6 
 6.7 
 6.5 
 6.4 
 6.3 
 6.3 
 6.1 
 6.1 
 6.1 
 5.9 
 5.9 
 5.8 
 5.7 
 5.7 
 5.6 
 5.5 
 5.5 
 5.4 
 5.3 
 5.3 
 5.3 
 5.1 
 5.2 
 5.1 
 
 0.8806 
 .8709 
 .8615 
 
 82 30' 
 82 20' 
 82 10' 
 82 0' 
 81 50' 
 81 40' 
 81 30' 
 81 20' 
 81 10' 
 81 0' 
 80 50' 
 80 40' 
 80 30' 
 80 20' 
 80 10' 
 80 0' 
 79 50' 
 79 40' 
 79 30' 
 79 20' 
 79 10' 
 79 0' 
 78 50' 
 78 40' 
 78 30' 
 78 20' 
 78 10' 
 78 0' 
 77 50' 
 77 40' 
 77 30' 
 77 20' 
 77 10' 
 77 0' 
 76 50' 
 76 40' 
 76 30' 
 76 20' 
 76 10' 
 76 0' 
 75 50' 
 75 40' 
 75 30' 
 75 20' 
 75 10' 
 75 0' 
 
 9.1436 
 
 9.9958 
 
 9.1478 
 
 0.8522 
 
 .1525 
 .1612 
 .1697 
 .1781 
 .1863 
 
 .9956 
 .9954 
 .9952 
 .9950 
 .9948 
 
 ,1569 
 .1658 
 .1745 
 .1831 
 .1915 
 
 .8431 
 .8342 
 .8255 
 .8169 
 .8085 
 
 9.1943 
 
 9.9946 
 
 9.1997 
 
 0.8003 
 
 .2022 
 .2100 
 .2176 
 .2251 
 .2324 
 
 .9944 
 .9942 
 .9940 
 .9938 
 .9936 
 
 .2078 
 .2158 
 .2236 
 .2313 
 .2389 
 
 .7922 
 .7842 
 .7764 
 .7687 
 .7611 
 
 9.2397 
 
 9.9934 
 
 9.2463 
 
 0.7537 
 
 .2468 
 .2538 
 .2606 
 .2674 
 .2740 
 
 .9931 
 .9929 
 .9927 
 .9924 
 .9922 
 
 .2536 
 .2609 
 .2680 
 .2750 
 .2819 
 
 .7464 
 .7391 
 .7320 
 .7250 
 .7181 
 
 9.2806 
 
 9.9919 
 
 9.2887 
 
 0.7113 
 
 .287Q 
 .2934 
 .2997 
 .3058 
 .3119 
 
 .9917 
 .9914 
 .9912 
 .9909 
 .9907 
 9.9604 
 
 .2953 
 .3020 
 .3085 
 .3149 
 .3212 
 
 .7047 
 .6980 
 .6915 
 .6851 
 .6788 
 
 9.3179 
 
 9.3275 
 
 0.6725 
 
 .3238 
 .3296 
 .3353 
 .3410 
 .3466 
 
 .9901 
 .9899 
 .9896 
 .9893 
 .9890 
 
 .3336 
 .3397 
 .3458 
 .3517 
 .3576 
 
 .6664 
 .6603 
 .6542 
 .6483 
 .6424 
 
 9.3521 
 
 9.9887 
 
 9.3634 
 
 0.6366 
 
 .3575 
 .3629 
 .3682 
 .3734 
 .3786 
 
 .9884 
 .9881 
 
 !9875 
 .9872 
 
 .3691 
 .3748 
 .3804 
 .3859 
 .3914 
 
 .6309 
 .6252 
 .6196 
 .6141 
 .6086 
 
 9.3837 
 
 9.9869 
 
 9.3968 
 
 0.6032 
 
 .3887 
 .3937 
 .3986 
 .4035 
 .4083 
 
 .9866 
 .9863 
 .9859 
 .9856 
 .9853 
 
 .4021 
 .4074 
 .4127 
 .4178 
 .4230 
 
 .5979 
 .5926 
 .5873 
 .5822 
 .5770 
 
 9.4130 
 
 9.9849 
 
 9.4281 
 
 0.5719 
 
 
 Cos. 
 
 D.I' 
 
 Sin. 
 
 D.I' 
 
 Cot. 
 
 D.I' 
 
 Tan. 
 
 Angle
 
 224 A MANUAL FOR NORTHERN WOODSMEN 
 
 LOGARITHMIC SINES, COSINES, 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos. 
 
 D.I' 
 
 Tan. 
 
 D.I' 
 
 5.0 
 5.0 
 4.9 
 4.9 
 4.8 
 4.8 
 4.7 
 4.7 
 4.7 
 4.6 
 4.6 
 4.5 
 4.5 
 4.5 
 4.4 
 4.4 
 4.4 
 4.3 
 4.3 
 4.2 
 4.2 
 4.2 
 4.2 
 4.1 
 4.1 
 4.0 
 4.0 
 4.0 
 4.0 
 4.0 
 3.9 
 3.9 
 3.8 
 3.9 
 3.8 
 3.8 
 3.7 
 3.8 
 3.7 
 3.7 
 3.7 
 3.6 
 3.6 
 3^ 
 3.6 
 
 Cot. 
 
 
 15 0' 
 
 15 10' 
 15 20' 
 15 30' 
 15 40' 
 15 50' 
 16 0' 
 16 10' 
 16 20' 
 16 30' 
 16 40' 
 16 50' 
 17 0' 
 17 10' 
 17 20' 
 17 30' 
 17 40' 
 17 50' 
 18 0' 
 18 10' 
 18 20' 
 18 30' 
 18 40' 
 18 50' 
 19 0' 
 19 10' 
 19 20' 
 19 30' 
 19 40' 
 19 50' 
 20 0' 
 20 10' 
 20 20' 
 20 30' 
 20 40' 
 20 50' 
 21 0' 
 21 10' 
 21 20' 
 21 30' 
 21 40' 
 21 50' 
 22 0' 
 22 10' 
 22 20' 
 22 30' 
 
 9.4130 
 
 4.7 
 4.6 
 4.6 
 4.5 
 4.5 
 4.4 
 4.4 
 4.4 
 4.2 
 4.3 
 4.2 
 4.1 
 4.1 
 4.1 
 4.0 
 4.0 
 4.0 
 3.9 
 3.9 
 3.8 
 3.8 
 3.7 
 3.8 
 3.6 
 3.7 
 3.6 
 3.6 
 3.5 
 3.6 
 3.5 
 3.4 
 3.4 
 3.4 
 3.4 
 3.3 
 3.3 
 3.3 
 3.3 
 3.2 
 3.2 
 3.1 
 3.2 
 3.1 
 3.1 
 3.0 
 
 9.9849 
 
 .3 
 .3 
 .4 
 .3 
 .4 
 .4 
 .3 
 .4 
 .4 
 .3 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .4 
 .5 
 .4 
 .4 
 .5 
 .4 
 .5 
 .4 
 .5 
 .4 
 .5 
 .4 
 .5 
 .5 
 .5 
 .4 
 .5 
 .5 
 .5 
 .5 
 5 
 .5 
 .5 
 .6 
 .5 
 
 9.4281 
 
 0.5719 
 
 75 O 7 
 
 74 50' 
 74 40' 
 74 30' 
 74 20' 
 74 10' 
 74 0' 
 73 50' 
 73 40' 
 73 30' 
 73 20' 
 73 10' 
 73 0' 
 72 50' 
 72 40' 
 72 30' 
 72 20' 
 72 10' 
 72 0' 
 7 50' 
 7 40' 
 7 30' 
 7 20' 
 7 10' 
 71 0' 
 70 50' 
 70 40' 
 70 30' 
 70 20' 
 70 10' 
 70 0' 
 69 50' 
 69 40' 
 69 30' 
 69 20' 
 69 10' 
 69 0' 
 68 50' 
 68 40' 
 68 30' 
 68 20' 
 68 10' 
 68 0' 
 67 50' 
 67 40' 
 67 30' 
 
 .4177 
 .4223 
 .4269 
 .4314 
 .4359 
 
 .9846 
 .9843 
 .9839 
 .9836 
 .9832 
 
 .4331 
 .4381 
 .4430 
 .4479 
 .4527 
 
 .5669 
 .5619 
 .5570 
 .5521 
 
 .5473 
 
 9.4403 
 
 9.9828 
 
 9.4575 
 
 0.5425 ' 
 
 .4447 
 .4491 
 .4533 
 .4576 
 .4618 
 
 .9825 
 .9821 
 .9817 
 .9814 
 .9810 
 
 .4622 
 .4669 
 .4716 
 .4762 
 .4808 
 
 .5378 
 .5331 
 .5284 
 .5238 
 .5192 
 
 9.4659 
 
 9.9806 
 
 9.4853 
 
 0.5147 
 
 .4700 
 .4741 
 .4781 
 .4821 
 .4861 
 
 .9802 
 .9798 
 .9794 
 .9790 
 .9786 
 
 .4898 
 .4943 
 .4987 
 .5031 
 .5075 
 
 .5102 
 .5057 
 .5013 
 .4969 
 .4925 
 
 9.4900 
 
 9.9782 
 
 9.5118 
 
 0.4882 
 
 .4939 
 .4977 
 .5015 
 .5052 
 .5090 
 
 .9778 
 .9774 
 .9770 
 .9765 
 .9761 
 
 .5161 
 .5203 
 .5245 
 .5287 
 .5329 
 
 .4839 
 .4797 
 .4755 
 .4713 
 .4671 
 
 9.5126 
 
 9.9757 
 
 9.5370 
 
 0.4630 
 
 .5163 
 .5199 
 .5235 
 .5270 
 .5303 
 
 .9752 
 .9748 
 .9743 
 .9739 
 .9734 
 
 .5411 
 .5451 
 .5491 
 .5531 
 .5571 
 
 .4589 
 .4549 
 .4509 
 .4469 
 .4429 
 
 9.5341 
 
 9.9730 
 
 9.5611 
 
 0.4389 
 .4350 
 .4311 
 .4273 
 .4234 
 .4196 
 
 .5375 
 .540.) 
 .5143 
 .5477 
 .5510 
 
 .9725 
 .9721 
 .9716 
 .9711 
 .9706 
 
 .5650 
 .5689 
 .5727 
 .5766 
 .5804 
 
 9.5543 
 
 9.9702 
 
 9.5842 
 
 0.4158 
 
 .5576 
 .5509 
 .5541 
 .5673 
 .5704 
 
 .9697 
 .9692 
 .9687 
 .9682 
 .9677 
 
 .5879 
 .5917 
 .5954 
 .5991 
 .6028 
 
 .4121 
 .4083 
 .4046 
 .4009 
 .3972 
 
 9.5736 
 
 9.9672 
 
 9.6064 
 
 0.3936 
 
 .5767 
 .5798 
 .5828 
 
 .9667 
 .9661 
 .9656 
 
 .6100 
 .6136 
 .6172 
 
 .3900 
 .3864 
 .3828 
 
 
 Cos. 
 
 D.I' 
 
 Sin. 
 
 D.I' 
 
 Got. 
 
 D.I' 
 
 Tan. 
 
 Angle
 
 TABLES RELATING TO PARTS i AND n 
 
 TANGENTS, AND COTANGENTS 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos. 
 
 D.r 
 
 Tan. 
 
 D.r 
 
 Cot. 
 
 
 22 30' 
 
 22 40' 
 22 50' 
 
 9.5828 
 .5859 
 .5889 
 
 3.1 
 3.0 
 
 9.9656 
 .9651 
 .9646 
 
 .5 
 .5 
 
 9.6172 
 .6208 
 .6243 
 
 3.6 
 3.5 
 
 0.3828 
 .3792 
 .3757 
 
 67 30' 
 67 20' 
 67 10' 
 
 23 0' 
 
 9.5919 
 
 
 9.9640 
 
 
 9.6279 
 
 
 0.3721 
 
 67 0' 
 
 23 10' 
 23 20' 
 23 30' 
 23 40' 
 23 50' 
 
 .5948 
 .5978 
 .6007 
 .6036 
 .6065 
 
 3.0 
 
 2.9 
 2.9 
 2.9 
 2 8 
 
 .9635 
 .9629 
 .9624 
 .9618 
 .9613 
 
 .6 
 .5 
 .6 
 .5 
 6 
 
 .6314 
 .6348 
 .6383 
 .6417 
 .6452 
 
 3.4 
 3.5 
 3.4 
 3.5 
 3 4 
 
 .3686 
 .3652 
 .3617 
 .3583 
 .3548 
 
 66 50' 
 66 40' 
 66 30' 
 66 20' 
 66 10' 
 
 24 0' 
 
 9.6093 
 
 2 8 
 
 9.9607 
 
 5 
 
 9.6486 
 
 3 4 
 
 0.3514 
 
 66 0' 
 
 24 10' 
 24 20' 
 24 30' 
 24 40' 
 24 50' 
 
 .6121 
 .6149 
 .6177 
 .6205 
 .6232 
 
 2.8 
 2.8 
 2.8 
 2.7 
 2 7 
 
 .9602 
 .9596 
 .9590 
 .9584 
 .9579 
 
 .6 
 .6 
 .6 
 .5 
 g 
 
 .6520 
 .6553 
 .6587 
 .6620 
 .6654 
 
 3.3 
 3.4 
 3.3 
 3.4 
 3 3 
 
 .3480 
 .3447 
 .3413 
 .3380 
 .3346 
 
 65 50' 
 65 40' 
 65 30' 
 65 20' 
 65 10' 
 
 25 0' 
 
 9.6259 
 
 2 7 
 
 9.9573 
 
 g 
 
 9.6687 
 
 3 3 
 
 0.3313 
 
 65 0' 
 
 25 10' 
 25 20' 
 25 30' 
 25 40' 
 25 50' 
 
 .62SG 
 .6313 
 .6340 
 .6366 
 .6392 
 
 2.7 
 2.7 
 2.6 
 2.6 
 2 6 
 
 .9567 
 .9561 
 .9555 
 .9549 
 .9543 
 
 .6 
 .6 
 .6 
 .6 
 3 
 
 .6720 
 .6752 
 .6785 
 .6817 
 .6850 
 
 3.2 
 3.3 
 3.2 
 3.3 
 3 2 
 
 .3280 
 .3248 
 .3215 
 .3183 
 .3150 
 
 64 50' 
 64 40' 
 64 30' 
 64 20' 
 64 10' 
 
 26 0' 
 
 9.6418 
 
 2 6 
 
 9.9537 
 
 
 9.6882 
 
 3 2 
 
 0.3118 
 
 64 0' 
 
 26 10' 
 26 20' 
 26 30' 
 20 40' 
 26 50' 
 
 .6444 
 .6470 
 .6495 
 .6521 
 .6546 
 
 2.6 
 2.5 
 2.6 
 2.5 
 2 4 
 
 .9530 
 .9524 
 .9518 
 .9512 
 .9505 
 
 .6 
 .6 
 .6 
 
 .7 
 g 
 
 .6914 
 .6946 
 .6977 
 .7009 
 .7040 
 
 3.2 
 3 1 
 3.2 
 3.1 
 3 2 
 
 .3086 
 .3054 
 .3023 
 .2991 
 .2960 
 
 63 50' 
 63 40' 
 63 30' 
 63 20' 
 63 10' 
 
 27 0' 
 
 9.6570 
 
 25 
 
 9.9499 
 
 7 
 
 9.7072 
 
 3 1 
 
 0.2928 
 
 63 0' 
 
 27 10' 
 27 20' 
 27 30' 
 27 40' 
 27 50' 
 
 .6595 
 .6620 
 .6644 
 .6668 
 .6692 
 
 2.5 
 2.4 
 2.4 
 2.4 
 2 4 
 
 .9492 
 .9486 
 .9479 
 .9473 
 .9466 
 
 .6 
 
 .7 
 .6 
 .7 
 
 7 
 
 .7103 
 
 .7134 
 .7165 
 .7196 
 .7226 
 
 3.1 
 3.1 
 3.1 
 3.0 
 3 1 
 
 .2897 
 .2866 
 .2835 
 .2804 
 .2774 
 
 62 50' 
 62 40' 
 62 30' 
 62 20' 
 62 10' 
 
 28 0' 
 
 9.6716 
 
 2 4 
 
 9.9459 
 
 5 
 
 9.7257 
 
 3 
 
 0.2743 
 
 62 0' 
 
 28 10' 
 28 20' 
 28 30' 
 28 40' 
 28 50' 
 
 .6740 
 .6763 
 .6787 
 .6810 
 .6833 
 
 2!4 
 2.3 
 2.3 
 2 3 
 
 .9453 
 .9446 
 .9439 
 .9432 
 .9425 
 
 '.7 
 .7 
 .7 
 7 
 
 .7287 
 .7317 
 .7348 
 .7378 
 .7408 
 
 3.0 
 3.1 
 3.0 
 3.0 
 3 
 
 .2713 
 .2683 
 .2652 
 .2622 
 .2592 
 
 61 50' 
 61 40' 
 61 30' 
 61 20' 
 61 10' 
 
 29 0' 
 
 9.6856 
 
 2 2 
 
 9 .9418 
 
 
 9.7438 
 
 2 9 
 
 0.2562 
 
 61 0' 
 
 29 10' 
 29 20' 
 29 30' 
 29 40' 
 29 50' 
 
 .6878 
 .6901 
 .6923 
 .6946 
 .6968 
 
 2.3 
 2.2 
 2.3 
 2.2 
 2 2 
 
 .9411 
 .9404 
 .9397 
 .9390 
 .9383 
 
 .7 
 '.7 
 
 .7467 
 .7497 
 .7526 
 .7556 
 .7585 
 
 3.0 
 2.9 
 3.0 
 2.9 
 
 .2533 
 .2503 
 .2474 
 .2444 
 .2415 
 
 60 50' 
 60 40' 
 60 30' 
 60 20' 
 60 10' 
 
 30 0' 
 
 9.6990 
 
 
 9.9375 
 
 
 9.7614 
 
 
 0.2386 
 
 60 0' 
 
 
 Cos. 
 
 D.r 
 
 Sin. 
 
 D.I' 
 
 Cot. 
 
 D.r 
 
 Tan. 
 
 Angle
 
 226 A MANUAL FOR NORTHERN WOODSMEN 
 
 LOGARITHMIC SINES, COSINES, 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos. 
 
 D.I' 
 
 Tan. 
 
 D.I' 
 
 Cot. 
 
 
 30 0' 
 
 9.6990 
 
 
 9.9375 
 
 
 9.7614 
 
 3 
 
 0.2386 
 
 60 0' 
 
 30 10' 
 30 20' 
 30 30' 
 30 40' 
 30 50' 
 
 .7012 
 .7033 
 .7055 
 .7076 
 .7097 
 
 2.1 
 2.2 
 2.1 
 2.1 
 2 1 
 
 .9368 
 .9361 
 .9353 
 .9346 
 .9338 
 
 .7 
 .8 
 
 .7 
 .8 
 
 7 
 
 .7644 
 .7673 
 .7701 
 .7730 
 .7759 
 
 2.9 
 23 
 
 2.9 
 2.9 
 2 9 
 
 .2356 
 .2327 
 .2299 
 .2270 
 .2241 
 
 59 50' 
 59 40' 
 59 30' 
 59 20' 
 59 10' 
 
 31 0' 
 
 9.7118 
 
 
 9.9331 
 
 
 9.7788 
 
 2 8 
 
 0.2212 
 
 59 0' 
 
 31 10' 
 31 20' 
 31 30' 
 31 40' 
 31 50' 
 
 .7139 
 .7160 
 .7181 
 .7201 
 .7222 
 
 2.1 
 2.1 
 2.0 
 2.1 
 20 
 
 .9323 
 .9315 
 .9308 
 .9300 
 .9292 
 
 .8 
 .7 
 .8 
 .8 
 g 
 
 .7816 
 .7845 
 .7873 
 .7902 
 .7930 
 
 2.9 
 2.8 
 2.9 
 2.8 
 2 8 
 
 .2184 
 .2155 
 .2127 
 .2098 
 .2070 
 
 58 50' 
 58 40' 
 58 30' 
 58 20' 
 58 10' 
 
 32 0' 
 
 9.7242 
 
 2 
 
 9.9284 
 
 g 
 
 9.7958 
 
 2 8 
 
 0.2042 
 
 58 0' 
 
 32 10' 
 32 20' 
 32 30' 
 32 40' 
 32 50' 
 
 .7262 
 .7282 
 .7302 
 .7322 
 .7342 
 
 2.0 
 2.0 
 2.0 
 2.0 
 1.9 
 
 .9276 
 .9268 
 .9260 
 .9252 
 .9244 
 
 .8 
 .8 
 .8 
 .8 
 8 
 
 .7986 
 .8014 
 .8042 
 .8070 
 .8097 
 
 2.8 
 2.8 
 2.8 
 2.7 
 28 
 
 .2014 
 .1986 
 .1958 
 .1930 
 .103 
 
 57 50' 
 57 40' 
 57 30' 
 57 20' 
 57 10' 
 
 33 0' 
 
 9.7361 
 
 1 9 
 
 9.9236 
 
 g 
 
 9.8125 
 
 28 
 
 0.1875 
 
 57 0' 
 
 33 10' 
 33 20' 
 33 30' 
 33 40' 
 33 50' 
 
 .7380 
 .7400 
 
 .7419 
 .7438 
 
 .7457 
 
 2.0 
 1.9 
 1.9 
 1.9 
 1 9 
 
 .9228 
 .9219 
 .9211 
 .9203 
 .9194 
 
 .9 
 
 .8 
 .8 
 .9 
 g 
 
 .8153 
 .8180 
 .8208 
 .8235 
 .8263 
 
 2.7 
 
 2.8 
 2.7 
 2.8 
 2 7 
 
 .1847 
 .1820 
 .1792 
 .1765 
 .1737 
 
 56 50' 
 56 40' 
 56 30' 
 56 20' 
 56 10' 
 
 34 0' 
 
 9.7476 
 
 1 8 
 
 9.9186 
 
 9 
 
 9.8290 
 
 2 7 
 
 0.1710 
 
 56 0' 
 
 34 10' 
 34 20' 
 34 30' 
 34 40' 
 34 50' 
 
 .7494 
 .7513 
 .7531 
 .7550 
 
 .7568 
 
 1.9 
 1.8 
 1.9 
 1.8 
 1 8 
 
 .9177 
 .9169 
 .9160 
 .9151 
 .9142 
 
 .8 
 .9 
 .9 
 .9 
 g 
 
 .8317 
 .8344 
 .8371 
 .8398 
 .8425 
 
 2.7 
 2.7 
 2.7 
 2 7 
 
 .1683 
 .1656 
 .1629 
 .1602 
 .1575 
 
 55 50' 
 55 40' 
 55 30' 
 55 20' 
 55 10' 
 
 35 0' 
 
 9.7586 
 
 1 8 
 
 9.9134 
 
 g 
 
 9.8452 
 
 2 7 
 
 0.1548 
 
 55 0' 
 
 35 10' 
 35 20' 
 35 30' 
 35 40' 
 35 50' 
 
 .7604 
 .7622 
 .7640 
 .7657 
 .7675 
 
 1.8 
 1.8 
 1.7 
 1.8 
 1 7 
 
 .9125 
 .9116 
 .9107 
 .9098 
 .9089 
 
 .9 
 .9 
 .9 
 .9 
 g 
 
 .8479 
 .8506 
 .8533 
 .8559 
 .8586 
 
 2.7 
 2.7 
 2.6 
 2.7 
 2 7 
 
 .1521 
 .1494 
 .1467 
 .1441 
 .1414 
 
 54 50' 
 54 40' 
 54 30' 
 54 20' 
 54 10' 
 
 36 0' 
 
 9.7692 
 
 1 8 
 
 9.9080 
 
 1 
 
 9.8613 
 
 2 Q 
 
 0.1387 
 
 54' 0' 
 
 36 10' 
 36 20' 
 36 30' 
 36 40' 
 36 50' 
 
 .7710 
 .7727 
 .7744 
 .7761 
 
 .7778 
 
 1.7 
 1.7 
 1.7 
 1.7 
 1 7 
 
 .9070 
 .9061 
 .9052 
 .9042 
 .9033 
 
 .9 
 .9 
 1.0 
 .9 
 1 
 
 .8639 
 .8666 
 .8692 
 .8718 
 .8745 
 
 2.7 
 2.6 
 2.6 
 2.7 
 2 6 
 
 .1361 
 .1334 
 .1308 
 .1282 
 .1255 
 
 53 50' 
 53 40' 
 53 30' 
 53 20' 
 53 10' 
 
 37 0' 
 
 9.7795 
 
 1 6 
 
 it.'. ()->:{ 
 
 9 
 
 9.8771 
 
 26 
 
 0.1229 
 
 53 0' 
 
 37 10' 
 37 20' 
 37 30' 
 
 .7811 
 .7828 
 .7844 
 
 1.7 
 1.6 
 
 .8014 
 .9004 
 .8995 
 
 1.0 
 .9 
 
 .8797 
 .8824 
 .8850 
 
 2.7 
 2.6 
 
 .1203 
 .1176 
 .1150 
 
 52 50' 
 52 40' 
 52 30' 
 
 
 Cos. 
 
 D.I' 
 
 Sin. 
 
 D.I' 
 
 Cot. 
 
 D.I' 
 
 Tan. 
 
 Angle
 
 TABLES RELATING TO PARTS I AND II 
 
 227 
 
 TANGENTS, AND COTANGENTS 
 
 Angle 
 
 Sin. 
 
 D.I' 
 
 Cos 
 
 D.I' 
 
 Tan. 
 
 D.I' 
 
 Cot. 
 
 
 37 30' 
 37 40' 
 37 50' 
 
 9.7844 
 .7861 
 .7877 
 
 1.7 
 1.6 
 1 6 
 
 9.8995 
 .8985 
 .8975 
 
 1.0 
 1.0 
 1 
 
 9.8850 
 .8876 
 .8902 
 
 2.6 
 2.6 
 2 6 
 
 0.1150- 
 .1124 
 .1098 
 
 52 30' 
 52 20' 
 52 10' 
 
 38 0' 
 
 9.7893 
 
 1 7 
 
 9.8965 
 
 1 
 
 9.8928 
 
 2 6 
 
 0.1072 
 
 52 0' 
 
 38 10' 
 38 20' 
 38 30' 
 38 40' 
 38 50' 
 
 .7910 
 .7926 
 .7941 
 .7957 
 .7973 
 
 1.6 
 1.5 
 1.6 
 
 1.6 
 1 6 
 
 .8955 
 
 .8945 
 .8935 
 .8925 
 .8915 
 
 1.0 
 1.0 
 1.0 
 1.0 
 1 
 
 .8954 
 .8980 
 ..9006 
 .8032 
 .S058 
 
 2.6 
 
 2.6 
 2.6 
 2.6 
 2 6 
 
 .1046 
 .1020 
 .0994 
 .0968 
 .0942 
 
 51 50 
 51 40' 
 51 30' 
 51 20' 
 51 10' 
 
 39 0' 
 
 9.7989 
 
 1 5 
 
 9.8905 
 
 
 9.9084 
 
 2 6 
 
 0.0916 
 
 51 0' 
 
 39 10' 
 39 20' 
 39 30' 
 39 40' 
 39 50' 
 
 .8004 
 .8020 
 .8035 
 .8050 
 .8066 
 
 1.6 
 1.5 
 1.5 
 1.6 
 1 5 
 
 .8895 
 .8884 
 .8874 
 .8864 
 .8853 
 
 1.1 
 
 1.0 
 1.0 
 1.1 
 
 .9110 
 .9135 
 .9161 
 .9187 
 .9212 
 
 2.5 
 2.6 
 2.6 
 2.5 
 2 6 
 
 .0860 
 .0865 
 .0839 
 .0813 
 0788 
 
 50 50' 
 50 40' 
 50 30' 
 50 20' 
 50 10' 
 
 40 0' 
 
 9.8081 
 
 1 5 
 
 9.8843 
 
 
 9.9238 
 
 2 6 
 
 0.0762 
 
 50 0' 
 
 40 10' 
 40 20' 
 40 30' 
 40 40' 
 40 50' 
 
 .8096 
 .8111 
 .8125 
 .8140 
 .8155 
 
 1.5 
 1.4 
 1.5 
 1.5 
 
 .8832 
 .8821 
 .8810 
 .8800 
 .8789 
 
 1.1 
 1.1 
 
 1.0 
 
 1.1 
 
 .9264 
 .9289 
 .9315 
 .9341 
 .9366 
 
 2.5 
 2.6 
 2.6 
 2.5 
 2 6 
 
 .0736 
 .0711 
 .0685 
 .0659 
 .0634 
 
 49 50' 
 49 40' 
 49 30' 
 49 20' 
 49 10' 
 
 41 0' 
 
 9.8169 
 
 
 9.8778 
 
 
 P.9392 
 
 2 5 
 
 0.0608 
 
 49 0' 
 
 41 10' 
 41 20' 
 41 30' 
 41 40' 
 41 50' 
 
 .8184 
 .8198 
 .8213 
 .8227 
 .8241 
 
 1.4 
 1.5 
 1.4 
 1.4 
 1 4 
 
 .8767 
 ,8756 
 .8745 
 .8733 
 .8722 
 
 1.1 
 1.1 
 
 1.2 
 
 1.1 
 
 .9417 
 .9443 
 .9468 
 .9494 
 .9519 
 
 2.6 
 2.5 
 2.6 
 2.5 
 2 5 
 
 .0583 
 .0557 
 .0532 
 .0506 
 .0481 
 
 48 50' 
 48 40' 
 48 30' 
 48 20' 
 48 10' 
 
 42 0' 
 
 9.8255 
 
 1 4 
 
 9.8711 
 
 
 9.9544 
 
 2 6 
 
 0.0456' 
 
 48 0' 
 
 42 10' 
 42 20' 
 42 30' 
 42 40' 
 42 50' 
 
 .8269 
 .8283 
 .8297 
 .8311 
 .8324 
 
 1.4 
 1.4 
 1.4 
 1.3 
 1 4 
 
 .8699 
 .8688 
 .8676 
 .8665 
 .8653 
 
 1.1 
 
 1.2 
 1.1 
 
 1.2 
 
 .9570 
 .9585 
 .9621 
 .9646 
 .9671 
 
 2.5 
 2.6 
 2.5 
 2.5 
 2 6 
 
 .0430 
 .0405 
 .0379 
 .0354 
 .0329 
 
 47 50' 
 47 40' 
 47 30' 
 47 20' 
 47 10' 
 
 43 0' 
 
 9.8338 
 
 1 3 
 
 9.8641 
 
 
 9.9697 
 
 2 5 
 
 0.0303 
 
 47 0' 
 
 43 10' 
 43 20' 
 43 30' 
 43 40' 
 43 50' 
 
 .8351 
 .8365 
 .8378 
 .8391 
 .8405 
 
 1.4 
 1.3 
 1.3 
 1.4 
 1 3 
 
 .8629 
 .8618 
 .8606 
 .8594 
 
 .8582 
 
 1.1 
 1.2 
 1.2 
 1.2 
 
 .9722 
 .9747 
 .9772 
 .9798 
 .9823 
 
 2.5 
 
 2.5 
 2.6 
 2.5 
 25 
 
 .0278 
 .0253 
 .0228 
 .0202 
 .0177 
 
 46 50' 
 46 40' 
 46 30' 
 46 20' 
 46 10' 
 
 44 0' 
 
 9.8418 
 
 
 9.8569 
 
 
 9.9848 
 
 2 6 
 
 0.0152 
 
 46 0' 
 
 44 10' 
 44 20' 
 44 30' 
 44 40' 
 44 50' 
 
 .8431 
 .8444 
 .8457 
 .8469 
 .8482 
 
 1.3 
 1.3 
 1.2 
 1.3 
 
 .8557 
 .8545 
 .8532 
 .8520 
 .8507 
 
 1.2 
 1.3 
 1.2 
 1.3 
 
 .9874 
 .9899 
 .9924 
 .9949 
 .9975 
 
 2.5 
 2.5 
 2.5 
 2.6 
 
 .0126 
 .0101 
 .0076 
 .0051 
 .0025 
 
 45 50' 
 45 40' 
 45 30' 
 45 20' 
 45 10' 
 
 45 0' 
 
 9.8495 
 
 
 9.8495 
 
 
 0.0000 
 
 
 0.0000 
 
 45 0' 
 
 
 Cos. 
 
 D.I' 
 
 Sin. 
 
 D.1- 
 
 Cot. 
 
 D.I' 
 
 Tan. 
 
 Angle
 
 228 A MANUAL FOR NORTHERN WOODSMEN 
 
 
 Ifc 
 
 a ^ 
 
 ;?s 
 
 SSSSSSSSS8S 
 
 X XXXXXXXXX 
 
 XXXXXXXXX X 
 
 
 -C--OC CC 
 
 -.OSCSOS|. 
 
 XXXXXX XXX 
 
 . 
 
 iOCC-iXtO-*'N 
 COOOOi-HCOOt- 
 
 
 cd x'x'x'x'x'xx'xx' 
 
 x' x' x x' x* x' x' x' x* 
 
 5:153 
 
 XXX X X X X X X 
 X X X X X X X X X 
 
 5^ 
 
 X XXXXXXXXX 
 
 XXXXXXX| 
 
 x x' x x" x x x x c 
 
 -HCOiOt^O-HC 
 H CO O (^ O I 
 
 t^ x o cq co 
 
 
 x'x'x'x'x'xx'x'oc GO 
 
 >!--< ic cs 
 
 x x' x' x' 06 x x GO x' 
 
 riox ccoot^xo 
 
 iiiiiiiii i 
 
 0900.00 co co ao o c 
 
 ** 
 
 Bi 
 
 GO WOO 00 00 00 00 00 00 ICO 
 
 XOSOSOOCSOSXX 
 C^ 1O X C^J U5 t^ O M CO 
 
 X X X X X X X X X 
 
 c^ScSSSSSSS: 
 8ft&cS?5Sw 
 
 x' x' x' x' x 06 x' x' x' 
 
 _ 
 GO X X X X X X X X' 
 
 -* 
 S 
 
 S?S?5*MCO g 
 
 X X X X x" X X x' X 
 
 o o a> x 10 N x co 
 
 ^Ht^C^X^fOO-l 
 
 ^SS??? 
 
 X GO X' X X 
 
 x x x x x x aoflOoo 
 
 Sco^x^SS.o 
 
 t--- CO X X X X X; OS C> ;O> 
 
 OtftOt^t^Kt^t^t^lb- 
 
 31H-f3S^t>- iOS ^ ! 
 OtoOCO X OCCS 
 
 o -222:2SC:22 8 SS
 
 TABLES RELATING TO PARTS i AND n 
 
 
 X' X O> O> O3 OS O> O5 OS 
 
 SXOCOiOt^OC^-^f 
 -COTflOCOXOSO 
 
 q q q q q q q q q 
 os' os os as os os' os os os 
 
 Cs CS CS. CS. Cs. CS. . 
 
 in x ococox i-tcocox 
 * ot-xosOMcoi'in 
 
 . .ssssss 
 
 
 
 qqqqqqqqq 
 Os' Cs cs cs' cs os cs c: cs 
 
 O'MX'fOcD t^CO X 
 
 CSCSOOOOOO-H -i 
 X X 05 OS C3CS050505 |05 
 
 ao oo oo oo oo oo x x x x' 
 
 Ci C5 OS OS OS. OS. OS OS 
 
 OS OS 05 03 OS OS OS 05 OS 
 
 x' x" x x" x' oo' x oo' x j oo' 
 
 -H ^ i M 71 M 
 
 OS OS CS. OS. CS OS CS CS OS 
 
 -H co ~4 in o m os * x 
 t^-xot-icc^in^x 
 
 COWWWWWM 
 
 OS OS OS. OS O OS OS CS OS 
 
 x' x x x x x x x 
 
 
 
 xxxxxxxxx 
 
 X X X. X X X. X. X 00 
 
 xxxxxxxx 
 
 X X t^ t^ CD in 
 
 xo- 
 
 co-^*^ 
 x is 
 
 X XXXXXXXXX 
 
 O X f~ 10 W I CS b- * 
 
 ^H ^ to ^ CD ^H in o 
 
 sssssssss 
 
 xx'x'x'x'x'x'x'x x 
 
 xxxxxxxx 
 
 xxxxxxxxx 
 
 S^r~-tot 
 MinX^HC 
 
 5SSg32ig i 
 
 D'X'X'X'X'X'X'X'X' X 
 
 xx'x'x'x'x'xx'x 
 
 rtCO 
 
 * *'****** 
 
 x IN to o in os co t^ ^ 
 
 CO t- t- X X X CS CS O 
 
 x'x'xx'x'x'x'x'x 
 
 cs co t> o * x <N >o 
 
 ssssssss 
 
 x'x'xx'x'x'x'x'x 
 
 NMWCO-^^OL-:..': 
 
 CO t^ t~ X X X OS OS 
 
 00 00 00 00 00 00 0000 " 
 
 5582^2222 
 
 t^ t~ X OS O -H i-l CN CO 
 rH --< IM (N (M (M CN 
 
 CO 1^ O -H ^H OS C 
 
 
 incOt^XO5 O ^^C^CO^iOOt>-XOi i-HC^CO^iOCOt^XCl O 
 MWCCMCO * Tf * TP ^ ^ ^ Tf * 10 US 10 U5 m U5 10 10 S 10 5
 
 A MANUAL FOB NORTHERN WOODSMEN 
 
 NATURAL SINES AND COSINES 
 
 A. 
 
 Sin. 
 
 Cos. 
 
 
 A. 
 
 Sin. 
 
 Cos. 
 
 
 A. 
 
 Sin. 
 
 Cos. 
 
 
 
 
 .000000 
 
 1.0000 90 
 
 30' 
 
 .1305 
 
 .9914 
 
 30' 
 
 15 
 
 .2588 
 
 .9659 
 
 75 
 
 10' 
 20' 
 
 .002909 
 .005818 
 
 1.0000 50' 
 
 1.0000 40' 
 
 40' 
 50' 
 
 .1334 
 .1363 
 
 .9911 
 
 .9907 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .2616 
 
 .2114 I 
 
 .9652 
 .9644 
 
 50' 
 40' 
 
 30' 
 
 .008727 
 
 1.0000 30' 
 
 8" 
 
 .139? 
 
 .9903 
 
 82" 
 
 30' 
 
 
 
 30' 
 
 40' 
 
 .011635 
 
 .9999 j 20' 
 
 10' 
 
 
 
 
 40' .2700 
 
 ( tt)"S 
 
 20' 
 
 50' 
 
 .014544 
 
 .9999 ' 10' 
 
 20' 
 
 .1449 
 
 9894 
 
 40' 
 
 50' 
 
 .2728 
 
 .9621 
 
 10' 
 
 1 
 
 .017452 
 
 .9998 i 89 
 
 30' 
 
 .1478 
 
 .9890 
 
 30' 
 
 16 
 
 .2756 
 
 .9613 
 
 74 
 
 10' 
 
 20' 
 
 .02036 
 .02327 
 
 .9998 50' 
 .9997 , 40' 
 
 40' 
 50' 
 
 .1507 
 .1536 
 
 .9886 
 .9881 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .2784 
 
 .2X12 
 
 .9605 
 
 /.i.V.iii 
 
 50' 
 
 40' 
 
 30' 
 
 .02618 
 
 .9997 30' 
 
 9" 
 
 .1564 
 
 .9877 
 
 81" 
 
 30' 
 
 .2840 
 
 
 30' 
 
 40' 
 50' 
 
 .02908 
 .03199 
 
 .9996 20' 
 .9995 10' 
 
 10' 
 20' 
 
 .1593 
 .1622 
 
 .9872 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .2868 
 .2896 
 
 .'.'.T-ii 
 .9572 
 
 20' 
 10' 
 
 2 
 
 .03490 
 
 .9994 88 
 
 30' 
 
 .1650 
 
 .9863 
 
 30' 
 
 17" 
 
 .2924 
 
 .9563 
 
 73 
 
 10' 
 
 .03781 
 
 .9993 50' 
 
 40' 
 
 .1679 
 
 .!iX5X 
 
 20' 
 
 10' 
 
 .2952 
 
 .9555 
 
 50' 
 
 20' 
 
 .04071 
 
 .9992 40' 
 
 
 
 ,9x t >. > 
 
 
 20' 
 
 ."979 
 
 .9546 
 
 40' 
 
 30' 
 
 .04362 
 
 .9990 I 30' 
 
 10 
 
 .1736 
 
 .9848 
 
 80" 
 
 30' 
 
 .3007 
 
 .9537 
 
 30' 
 
 40' 
 50' 
 
 .04653 
 .04943 
 
 .9989 | 20' 
 .9988 10' 
 
 10 7 
 20' 
 
 .1765 
 .1794 
 
 .9843 
 9838 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .3035 .9528 
 .3062 .9520 
 
 20' 
 10' 
 
 3 
 
 .05234 
 
 .9986 ; 87 
 
 30' 
 
 .1822 
 
 
 30' 
 
 18 
 
 .3090 
 
 .9511 
 
 72 
 
 10' 
 
 .05524 
 
 .9985 50' 
 
 40' 
 
 .1851 
 
 .9X2, 
 
 20' 
 
 10' 
 
 .3118 
 
 .9502 
 
 50' 
 
 20' 
 
 .05814 
 
 .9983 i 40' 
 
 50' 
 
 
 .9822 
 
 10' 
 
 20' 
 
 .3145 
 
 9-192 
 
 40' 
 
 30' 
 
 .06105 
 
 .9981 j 30' 
 
 11" 
 
 .1908 
 
 .9816 
 
 79" 
 
 30' 
 
 .3173 
 
 .9483 
 
 30' 
 
 40' 
 50' 
 
 .06395 
 .06685 
 
 .9980 
 .9978 
 
 20' 
 10' 
 
 10' 
 
 20' 
 
 .1937 
 1965 
 
 .9811 
 
 9SU5 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .3201 
 .3228 
 
 .9474 
 .9465 
 
 20' 
 10' 
 
 4 
 
 .06976 
 
 .9976 
 
 86 
 
 30' 
 
 .1994 
 
 .9799 
 
 30' 
 
 19 
 
 .3256 
 
 .9455 
 
 71 
 
 10' 
 20' 
 
 .07266 
 .07556 
 
 .9974 
 .9971 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .2051 
 
 .9787 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .3283 
 
 .3311 
 
 .9446 
 .9436 
 
 50' 
 40' 
 
 30' 
 
 .07846 
 
 .9969 
 
 30' 
 
 12" 
 
 .2079 
 
 .97X1 
 
 78" 
 
 30' 
 
 .3338 
 
 .9426 
 
 30' 
 
 40' 
 50' 
 
 .08136 
 .08423 
 
 .9967 
 .9964 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .2108 
 .2136 
 
 .9775 
 .9769 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .3365 
 .3393 
 
 .9417 
 .9407 
 
 20' 
 10' 
 
 5 
 
 .08716 
 
 .9962 
 
 85 
 
 30' 
 
 2164 
 
 .9763 
 
 30' 
 
 20 
 
 .3420 
 
 .9397 
 
 70" 
 
 10' 
 20' 
 
 .09005 
 .092J5 
 
 .9959 
 .9957 
 
 50' 
 40' 
 
 40' 
 50' 
 
 2193 
 2221 
 
 .9757 
 .9750 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .3448 
 .3475 
 
 .9387 
 !i>377 
 
 50' 
 40' 
 
 30' 
 
 .09585 
 
 .9954 
 
 30' 
 
 13 
 
 2250 
 
 .9744 
 
 77 
 
 30' 
 
 .3502 
 
 
 30' 
 
 40' 
 50' 
 
 .09874 
 .10164 
 
 .9951 
 .9948 
 
 20' 
 10' 
 
 10' 
 
 2278 
 2306 
 
 .9737 
 .9730 
 
 50' 
 40' 
 
 40' 
 
 50' 
 
 3529 
 3557 
 
 .9356 
 .9346 
 
 20' 
 10' 
 
 6 
 
 .10153 
 
 .9945 
 
 84 
 
 30' 
 
 2334 
 
 .9724 
 
 30' 
 
 21" 
 
 8584 
 
 9336 
 
 69" 
 
 10' 
 20' 
 
 .10742 
 .11031 
 
 .9942 
 .9939 
 
 50' 
 40' 
 
 40' 
 50' 
 
 2363 
 2391 
 
 .9717 
 9710 
 
 20' 
 10' 
 
 10' 
 20' 
 
 3611 
 3638 
 
 9325 
 9315 
 
 50' 
 40' 
 
 30' 
 
 .11320 
 
 .9936 
 
 30' 
 
 14 
 
 2419 
 
 9703 
 
 76" 
 
 30' 
 
 36f>5 
 
 9304 ! 30' 
 
 40' 
 
 .11609 
 
 .9932 
 
 20' 
 
 
 
 
 50' 
 
 40' 
 
 3692 
 
 9293 
 
 20' 
 
 50' 
 
 .11898 
 
 .9929 
 
 10' 
 
 20' 
 
 2476 
 
 
 40' 
 
 50' 
 
 3719 
 
 9283 
 
 10' 
 
 r 
 
 .12187 
 
 .9925 
 
 83 
 
 30' 
 
 2504 
 
 imVi 
 
 30' 
 
 22" 
 
 3746 
 
 9272 
 
 68 U 
 
 10' 
 20' 
 
 .12476 
 .12764 
 
 .9922 
 .9918 
 
 50' 
 40' 
 
 40' 
 50' 
 
 2532 
 2560 
 
 9674 
 
 9667 
 
 20' 
 10' 
 
 10' 
 20' 
 
 3773 
 3KOO 
 
 9261 
 
 9250 
 
 50' 
 40' 
 
 30' 
 
 .13053 
 
 .9914 
 
 30' 
 
 15 
 
 2588 
 
 9659 
 
 75" 
 
 30' 
 
 3827 
 
 9239 
 
 30' 
 
 
 Cos. 
 
 Sin. 
 
 A. 
 
 
 Cos. 
 
 Sin. 
 
 A. 
 
 
 Cos. 
 
 Sin. 
 
 A. 
 
 
 
 
 
 
 
 
 1 
 
 

 
 TABLES RELATING TO PARTS I AND II 231 
 
 NATURAL SINES AND COSINES continued 
 
 A. 
 
 30' 
 40' 
 50' 
 23 
 10' 
 20' 
 30' 
 40' 
 50' 
 24 
 10' 
 20' 
 30' 
 40' 
 50' 
 25 
 10' 
 20' 
 30' 
 40' 
 50' 
 26 
 10' 
 20' 
 30' 
 40' 
 50' 
 27 
 10' 
 20' 
 30' 
 40' 
 50' 
 28 
 10' 
 20' 
 30' 
 40' 
 50' 
 29 
 10' 
 20' 
 30' 
 40' 
 50' 
 30 
 
 Sin. 
 
 Cos. 
 
 
 A. 
 
 Sin. 
 
 .5000 
 
 Cos. 
 
 
 A. 
 
 30' 
 40' 
 50' 
 38 
 10' 
 20' 
 30' 
 40' 
 50' 
 39 
 10' 
 20' 
 30' 
 40' 
 50' 
 40 
 10' 
 20' 
 30' 
 40' 
 50' 
 41 
 10' 
 20' 
 30' 
 40' 
 50' 
 42 
 10' 
 20' 
 30' 
 40' 
 50' 
 43 
 10' 
 20' 
 30' 
 40' 
 50' 
 44 
 10' 
 20' 
 30' 
 40' 
 50' 
 45 
 
 Sin. 
 
 .6088 
 .6111 
 .6134 
 
 Cos. 
 
 .7934 
 .7916 
 
 .7898 
 
 
 .3827 
 .3854 
 .3881 
 
 .9239 
 
 .9228 
 .9216 
 
 30' 
 20' 
 10' 
 67 
 50' 
 40' 
 30' 
 20' 
 10' 
 66 
 50' 
 40' 
 30' 
 20' 
 10' 
 65 
 50' 
 40' 
 30' 
 20' 
 10' 
 64 
 50' 
 40' 
 30' 
 20' 
 10' 
 63 
 50' 
 40' 
 30' 
 20' 
 10' 
 62 
 50' 
 40' 
 30' 
 20' 
 10' 
 61 
 50' 
 40' 
 30' 
 20' 
 10' 
 60 
 
 30 
 
 10' 
 20' 
 30' 
 40' 
 50' 
 31 
 10' 
 20' 
 30' 
 40' 
 50' 
 32 
 10' 
 20' 
 30' 
 40' 
 50' 
 33 
 10' 
 20' 
 30' 
 40' 
 50' 
 34 
 10' 
 20' 
 30' 
 40' 
 50' 
 35 
 10' 
 20' 
 30' 
 40' 
 50' 
 38 
 10' 
 20' 
 30' 
 40' 
 50' 
 37 
 10' 
 20' 
 30' 
 
 .8660 
 
 60 
 
 50' 
 40' 
 30' 
 20' 
 10' 
 59 
 50' 
 40' 
 30' 
 20' 
 10' 
 58 
 50' 
 40' 
 30' 
 20' 
 10' 
 57 
 50' 
 40' 
 30' 
 20' 
 10' 
 56 
 50' 
 40' 
 30' 
 20' 
 10' 
 55 
 50' 
 40' 
 30' 
 20' 
 10' 
 54 
 50' 
 40' 
 30' 
 20' 
 10' 
 53 
 50' 
 40' 
 30' 
 
 30' 
 20' 
 10' 
 62 
 50' 
 40' 
 30' 
 20' 
 10' 
 51 
 50' 
 40' 
 30' 
 20' 
 10' 
 5tt 
 50' 
 40' 
 30' 
 20' 
 10' 
 49 
 50' 
 40' 
 30' 
 20' 
 10' 
 48 
 50' 
 40' 
 30' 
 20' 
 10' 
 47 
 50' 
 40' 
 30' 
 20' 
 10' 
 46 
 50' 
 40' 
 30' 
 20' 
 10' 
 46 
 
 .5025 
 .5050 
 .5075 
 .5100 
 .5125 
 
 .8646 
 .8631 
 .8616 
 .8601 
 
 .8587 
 
 .3607 
 
 .9205 
 
 .6157 
 
 .7880 
 .7862 
 .7844 
 .7826 
 .7808 
 .7790 
 
 .3934 
 .3961 
 .3987 
 .4014 
 .4041 
 
 .9194 
 .9182 
 .9171 
 .9159 
 .9147 
 
 .6180 
 .6202 
 .6225 
 .6248 
 .6271 
 
 .5150 
 
 .8572 
 
 .5175 
 .5200 
 .5225 
 .5250 
 .5275 
 
 .8557 
 .8542 
 .8526 
 .8511 
 .8496 
 
 .4067 
 .4094 
 .4120 
 .4147 
 .4173 
 .4200 
 
 .9135 
 .9124 
 .9112 
 .9100 
 .9088 
 .9075 
 
 .6293 
 
 .7771 
 .7753 
 .7735 
 .7716 
 .7698 
 .7679 
 
 .6316 
 .6338 
 .6361 
 .6383 
 .6406 
 
 .5299 
 .5324 
 .5348 
 .5373 
 .5398 
 .5422 
 
 .8480 
 .8465 
 .8450 
 .8434 
 .8418 
 .8403 
 
 .4226 
 
 .9063 
 
 .6428 
 
 .7660 
 
 .4253 
 .4279 
 .4305 
 .4331 
 .4358 
 
 .9051 
 .9038 
 .9026 
 .9013 
 .9001 
 
 .6450 
 .6472 
 .6494 
 .6517 
 .6539 
 .6561 
 .6583 
 .6604 
 .6626 
 .6648 
 .6670 
 
 .7642 
 .7623 
 .7604 
 
 .5446 
 
 .8387 
 
 .5471 
 .5495 
 .5519 
 .5544 
 
 .5568 
 
 .8371 
 .8355 
 .8339 
 .8323 
 .8307 
 
 .7585 
 .7566 
 
 .4384 
 .4410 
 .4436 
 .4462 
 .4488 
 .4514 
 .4540 
 .4566 
 .4592 
 .4617 
 .4643 
 .4669 
 .4695 
 
 .8988 
 .8975 
 .8962 
 .8949 
 .8936 
 .8923 
 .8910 
 .8897 
 .8884 
 .8870 
 .8857 
 .8843 
 .8829 
 
 .7547 
 
 .7528 
 .7509 
 .7490 
 .7470 
 .7451 
 
 .5592 
 
 .8290 
 
 .5616 
 .5640 
 .5664 
 .5688 
 .5712 
 
 .8274 
 .8258 
 .8241 
 .8225 
 .8208 
 
 .6691 
 
 .7431 
 
 .6713 
 .6734 
 .6756 
 .6777 
 .6799 
 
 .7412 
 .7392 
 .7373 
 .7353 
 .7333 
 
 .5736 
 
 .8192 
 .8175 
 .8158 
 .8141 
 .8124 
 .8107 
 
 .5760 
 
 .5783 
 .5807 
 .5831 
 .5854 
 
 .6820 
 
 .7314 
 
 .4720 
 .4746 
 .4772 
 .4797 
 .4823 
 
 .8816 
 .8802 
 .8788 
 .8774 
 .8760 
 
 .6841 
 .6862 
 .6884 
 .6905 
 .6926 
 
 .7294 
 .7274 
 .7254 
 .7234 
 .7214 
 
 .5878 
 .5901 
 .5925 
 .5948 
 .5972 
 .5995 
 
 .8060 
 
 .8073 
 .8056 
 .8039 
 .8021 
 .8004 
 
 .4848 1 .8746 
 
 .6947 
 .6967 
 .6988 
 .7009 
 .7030 
 .7050 
 .7071 
 
 .7193 
 
 .4874 
 .4899 
 .4924 
 .4950 
 .4975 
 
 , .8732 
 .8718 
 .8704 
 .8689 
 .8675 
 
 .7173 
 .7153 
 .7133 
 
 .6018 
 
 .7986 
 
 .6041 
 .6065 
 .6088 
 
 Cos. 
 
 .7969 
 .7951 
 .7934 
 
 .7112 
 .7092 
 
 .5000 
 
 .8660 
 
 Sin. 
 
 .7071 
 
 
 Cos. 
 
 A. 
 
 
 Sin. A. 
 
 
 Cos. 
 
 Sin. 
 
 A.
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 A. 
 
 Tan. 
 
 Cot. 
 
 90 
 
 50' 
 40' 
 30' 
 20' 
 10' 
 89 
 50' 
 40' 
 30' 
 20' 
 10' 
 88 
 50' 
 40' 
 30' 
 20' 
 10' 
 87 
 50' 
 40' 
 30' 
 20' 
 10' 
 86 
 50' 
 40' 
 30' 
 20' 
 10' 
 86 
 50' 
 40' 
 30' 
 20' 
 10' 
 84 
 50' 
 40' 
 30' 
 20' 
 10' 
 83 
 50' 
 40' 
 30' 
 
 A. 
 
 Tan. 
 
 .1317 
 
 .1346 
 
 .IMTti 
 
 Cot. 
 
 
 A. 
 
 Tan. 
 
 Cot. 
 
 75 
 
 50' 
 40' 
 30' 
 20' 
 10' 
 74 
 50' 
 40' 
 30' 
 20' 
 10' 
 73 
 50' 
 40' 
 30' 
 20' 
 10' 
 72 
 50' 
 40' 
 30' 
 20' 
 10' 
 71 
 50' 
 40' 
 30' 
 20' 
 10' 
 70 
 50' 
 40' 
 30' 
 20' 
 10' 
 69 
 50' 
 40' 
 30' 
 20' 
 10' 
 68 
 50' 
 40' 
 30' 
 
 
 
 10' 
 20' 
 30' 
 40' 
 50' 
 1 
 10' 
 20' 
 30' 
 40' 
 50' 
 2 
 10' 
 20' 
 30' 
 40' 
 50' 
 3 
 10' 
 20' 
 30' 
 40' 
 50' 
 4 
 10' 
 20' 
 30' 
 40' 
 50' 
 5 
 10' 
 20' 
 30' 
 40' 
 50' 
 6 
 10' 
 20' 
 30' 
 40' 
 50' 
 7 
 10' 
 20' 
 30' 
 
 .000000 
 
 00 
 
 30' 
 
 40' 
 50' 
 8 
 
 10' 
 21)' 
 
 30' 
 
 40' 
 00' 
 9 D 
 10' 
 20' 
 
 30' 
 
 10' 
 50' 
 10 
 
 10' 
 20' 
 :;o' 
 10' 
 50' 
 
 II 3 
 
 10' 
 20' 
 30' 
 40' 
 50' 
 12 3 
 10' 
 20' 
 30' 
 10' 
 50' 
 13' 
 10' 
 20' 
 
 :;<)' 
 
 40' 
 50' 
 14 
 10' 
 20' 
 :;o' 
 10' 
 50' 
 15 
 
 7.5958 
 
 7.I2S7 
 7.2687 
 
 30' 
 20' 
 10' 
 82 
 50' 
 40' 
 30' 
 20' 
 10' 
 81 
 50' 
 40' 
 30' 
 20' 
 10' 
 80 
 50' 
 40' 
 30' 
 20' 
 10' 
 79 
 50' 
 40' 
 30' 
 20' 
 10' 
 78 
 50' 
 40' 
 30' 
 20' 
 10' 
 77 
 50' 
 40' 
 30' 
 20' 
 10' 
 76 
 50' 
 .40' 
 30' 
 20' 
 10' 
 75 
 
 15 
 
 10' 
 20' 
 30' 
 40' 
 50' 
 16 
 10' 
 20' 
 30' 
 40' 
 50' 
 17 
 10' 
 20' 
 30' 
 40' 
 50' 
 18 
 10' 
 20' 
 30' 
 40' 
 50' 
 19 
 10' 
 20' 
 30' 
 40' 
 50' 
 20 
 10' 
 20' 
 30' 
 40' 
 50' 
 21 
 10' 
 20' 
 30' 
 40' 
 50' 
 22 
 10' 
 20' 
 30' 
 
 .2679 
 
 3.7321 
 
 .002909 
 .005818 
 .008727 
 .011636 
 .014515 
 
 343.7737 
 171.8854 
 114.5887 
 85.9398 
 68.7501 
 
 .2711 
 
 .2742 
 
 .277:-! 
 
 .2M)5 
 
 .283J 
 
 .2867 
 .2899 
 .2931 
 .2962 
 .2994 
 .:;o2i 
 
 3.6891 
 3.6470 
 3.6059 
 
 5.5650 
 5.5261 
 
 5.4874 
 3.4495 
 3.4124 
 
 ;.:;75'.i 
 
 !.:i102 
 
 ;.::0o2 
 
 .1405 
 
 7.1154 
 
 .1435 
 .1465 
 .1495 
 .1524 
 .1554 
 
 6.9682 
 1) S2'i! 
 6.6912 
 6.5606 
 6.4348 
 
 .017455 
 
 57.2900 
 
 .02036 
 .02328 
 .02619 
 .02910 
 .03201 
 
 49.1039 
 42.9641 
 38.1885 
 34.3678 
 31.2416 
 
 .1584 
 .1614 
 .1644 
 
 6.3138 
 
 6.1970 
 6.0S44 
 
 .03492 
 
 28.6363 
 
 .1673 
 .1703 
 .1733 
 
 5.'.)7f)S 
 5.8708 
 5.7694 
 
 .3057 
 
 ,5.2709 
 
 .03783 
 .04075 
 .04366 
 .04658 
 .04949 
 
 26.4316 
 24.5418 
 22.9038 
 21.4701 
 20.205") 
 
 .3089 
 .3121 
 .3153 
 .3185 
 .3217 
 .3249 
 
 3.2371 
 
 i.20ii 
 
 5.171(1 
 
 ;.i:;<>7 
 
 3.1084 
 
 .1763 
 
 5.6713 
 
 .1793 
 .1823 
 .1853 
 .1883 
 .1914 
 
 5.5704 
 5. is 15 
 5.396 
 
 5.:iO'.i: 
 5.2257 
 
 05241 
 
 19.0811 
 
 3.0777 
 
 05533 
 05824 
 06116 
 06408 
 06700 
 
 18.0750 
 17.1693 
 16.3499 
 15.6048 
 14.9244 
 
 .3281 
 .3314 
 .3346 
 
 .:r,7s 
 .3411 
 
 3.0475 
 3.0178 
 
 2>.)SS7 
 2.'. K100 
 2.9319 
 
 .1944 
 .1974 
 
 .2004 
 
 .20:; 5 
 .20(15 
 .2095 
 
 5.1446 
 
 5.0658 
 4.9894 
 4.9152 
 
 -l..vi:;< 
 4.7729 
 
 06993 
 
 14.3007 
 
 .3443 
 
 2.-J012 
 
 07285 
 07578 
 07870 
 08163 
 08456 
 
 13.7267 
 13.1969 
 12.7052 
 12.2505 
 11.8262 
 
 .3476 
 .3508 
 .3541 
 
 2.S770 
 2.8502 
 
 2.s2:;'.i 
 
 o 7<)X() 
 
 2:7725 
 
 .2126 
 
 4.7046 
 
 .2156 
 .2186 
 .2217 
 .2247 
 
 .227* 
 
 4.6382 
 !. 57:ic 
 4.5107 
 I.11H1 
 4.3897 
 
 .36,4 
 .3607 
 .3640 
 
 08749 
 
 11.4301 
 
 2.7475 
 
 09042 
 09335 
 09629 
 09923 
 10216 
 
 11.0594 
 10.7119 
 10.3854 
 10.0780 
 9.7882 
 
 .3673 
 .3706 
 
 :!7:',!i 
 .3772 
 .3805 
 
 2.722S 
 2.6985 
 
 2. (17 1(1 
 2.(1511 
 2.(>27!l 
 
 .2309 
 
 4.3315 
 
 .2339 
 .2370 
 .2401 
 21M2 
 .2462 
 .2493 
 2524 
 2555 
 
 25SI1 
 
 2(117 
 2(1 IS 
 
 2679 
 
 Cot. 
 
 4.2747 
 4.2193 
 4.1653 
 4.1126 
 4.0611 
 
 10510 
 
 9.5144 
 
 3839 
 
 2.6051 
 
 10805 
 11099 
 11394 
 11688 
 11983 
 
 9.2553 
 9.0038 
 8.7769 
 8.5555 
 8.3450 
 
 3872 
 
 3<lOf> 
 3!3<l 
 3!)73 
 4006 
 
 2.582(1 
 !'5(">05 
 
 4.0108 
 3.9617 
 
 5.<>i:;ii 
 ;.si;r,7 
 ;.s2()s 
 
 1.77(10 
 
 2 5:;st; 
 2.5172 
 2 I'.ind 
 
 12278 
 
 8.1443 
 
 4040 
 
 -1071 
 41 OS 
 4142 
 
 2.4751 
 
 12574 
 12869 
 13165 
 
 7.9530 
 7.7704 
 7.5958 
 
 2.4545 
 
 2.4:; 12 
 2.4142 
 
 3.7321 
 
 Cot. 
 
 Tan. 
 
 A. 
 
 Tan. 
 
 A. 
 
 
 Cot. 
 
 Tan. 
 
 A.
 
 TABLES RELATING TO PARTS I AND II 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 A. 
 
 Tan. 
 
 Cot. 
 
 
 A. 
 
 Tan. 
 
 Cot. 
 
 
 A. 
 
 Tan. 
 
 Cot. 
 
 
 30' 
 
 4142 
 
 2.4142 
 
 30' 
 
 30 
 
 5774 
 
 1.7321 
 
 60 
 
 30' 
 
 7673 
 
 1.3032 
 
 30' 
 
 40' 
 50' 
 
 4176 
 4210 
 
 2.3945 
 2.3750 
 
 20' 
 10' 
 
 10' 
 20' 
 
 5812 
 5851 
 
 1.7205 
 1.7090 
 
 50' 
 40' 
 
 40' 
 50' 
 
 7720 
 7766 
 
 1.2E54 
 1.2876 
 
 20' 
 10' 
 
 23 
 
 4245 
 
 2.3559 
 
 67 
 
 30' 
 
 5890 
 
 1.6977 
 
 30' 
 
 38 
 
 7813 
 
 1.271S9 
 
 62 
 
 10' 
 20' 
 30' 
 
 4279 
 4314 
 4348 
 
 2.3369 
 2.3183 
 2.2998 
 
 50' 
 40' 
 30' 
 
 40' 
 50' 
 31 
 
 5930 
 5969 
 6009 
 
 1 .6864 
 1.6753 
 1.6643 
 
 20' 
 10' 
 59 
 
 10' 
 20' 
 30' 
 
 .7860 
 .7907 
 .7954 
 
 1.2723 
 1.2647 
 1.2572 
 
 50' 
 40' 
 SO' 
 
 40' 
 50' 
 
 4383 
 4417 
 
 2.2817 
 2.2637 
 
 20' 
 10' 
 
 10' 
 20' 
 
 6048 
 6088 
 
 1.6534 
 1 6426 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .8002 
 .8050 
 
 1.2497 
 1.2423 
 
 20' 
 10' 
 
 24 
 
 4452 
 
 2.2460 
 
 66 
 
 30' 
 
 6129 
 
 1.6319 
 
 30' 
 
 39 
 
 .8098 
 
 1.2349 
 
 51 
 
 10' 
 20' 
 
 4487 
 4522 
 
 2.2286 
 22113 
 
 50' 
 40' 
 
 50' 
 
 6168 
 6208 
 
 1.6212 
 1.6107 
 
 10' 
 
 10' 
 20' 
 
 .8146 
 .8195 
 
 1.2276 
 1.2203 
 
 50' 
 40' 
 
 30' 
 
 4557 
 
 2.1943 
 
 30' 
 
 32 
 
 6249 
 
 1.6003 
 
 58" 
 
 30' 
 
 .8243 
 
 1.2131 
 
 30' 
 
 40' 
 50' 
 
 4592 
 4628 
 
 2.1775 
 2.160J 
 
 20' 
 10' 
 
 10' 
 
 90' 
 
 6289 
 6330 
 
 1.5SOO 
 1.5798 
 
 50' 
 
 40' 
 
 40' 
 50' 
 
 .8292 
 .8342 
 
 1.2059 
 1.1988 
 
 20' 
 10' 
 
 25 
 
 4663 
 
 2.1445 
 
 65 
 
 30' 
 
 6371 
 
 1.5697 
 
 30' 
 
 40 
 
 .8391 
 
 1.1918 
 
 50 
 
 10' 
 20' 
 
 4699 
 4734 
 
 2.1283 
 2.1123 
 
 50' 
 40' 
 
 40' 
 50' 
 
 6412 
 6453 
 
 1.5597 
 1.5497 
 
 10' 
 
 10' 
 
 ?0' 
 
 .8441 
 .8491 
 
 1.1847 
 1.1778 
 
 50' 
 40' 
 
 30' 
 
 4770 
 
 2.0965 
 
 30' 
 
 33 U 
 
 6494 
 
 1.5399 
 
 57 U 
 
 30' 
 
 .8541 
 
 1.1708 
 
 30' 
 
 40' 
 50' 
 
 4808 
 4841 
 
 2.0809 
 2.0655 
 
 20' 
 10' 
 
 10' 
 20' 
 
 6536 
 
 6577 
 
 1 .5301 
 1 5204 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .8591 
 .8642 
 
 1.1640 
 1.1571 
 
 20' 
 10' 
 
 26 
 
 4877 
 
 2.0503 
 
 64 
 
 30' 
 
 6619 
 
 1.5108 
 
 30' 
 
 41 
 
 .8683 
 
 1.1504 
 
 49 
 
 10' 
 20' 
 
 4913 
 4950 
 
 2.0353 
 20204 
 
 50' 
 40' 
 
 40' 
 50' 
 
 6661 
 6703 
 
 1.5013 
 1.4919 
 
 20' 
 10' 
 
 10' 
 
 90' 
 
 .8744 
 .8796 
 
 1.1436 
 1.1369 
 
 50' 
 40' 
 
 30' 
 40' 
 50' 
 
 4986 
 .5022 
 5059 
 
 2.0057 
 1.9912 
 1.9768 
 
 30' 
 20' 
 10' 
 
 34 
 10' 
 ?,0' 
 
 6745 
 ^787 
 .6830 
 
 1.4826 
 Y.4733 
 1.4641 
 
 56 
 
 50' 
 40' 
 
 30' 
 40' 
 50' 
 
 .8847 
 .8899 
 .8952 
 
 1.1303 
 1.1237 
 1.1171 
 
 30' 
 20' 
 10' 
 
 27 
 
 .50J5 
 
 1.9626 
 
 63 
 
 30' 
 
 .6873 
 
 1.4550 
 
 30' 
 
 42 
 
 .6004 
 
 1.1106 
 
 48 
 
 10' 
 W 
 
 .5132 
 .5169 
 
 1.9486 
 1.9347 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .6916 
 .6959 
 
 1.4460 
 1.4370 
 
 20' 
 10' 
 
 10' 
 
 20' 
 
 .6057 
 .9110 
 
 1.1041 
 1.0977 
 
 50' 
 40' 
 
 30' 
 
 .5206 
 
 1.9210 
 
 30' 
 
 35 U 
 
 .7002 
 
 1.4281 
 
 55 
 
 30' 
 
 .9163 
 
 1.0913 
 
 30' 
 
 40' 
 50' 
 
 .5243 
 .5280 
 
 1.9074 
 1.8940 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .7046 
 7089 
 
 1.4193 
 1 4106 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .9217 
 .9271 
 
 1.0786 
 
 10' 
 
 28 
 
 .5317 
 
 1.8807 
 
 62 
 
 30' 
 
 .7133 
 
 1.4019 
 
 30' 
 
 43 
 
 .9325 
 
 1.0724 
 
 47 
 
 10' 
 20' 
 
 .5354 
 .5392 
 
 1.8676 
 1.8546 
 
 50' 
 40f 
 
 40' 
 50' 
 
 .7177 
 
 1.3934 
 1.3848 
 
 20' 
 10' 
 
 10' 
 
 20' 
 
 .9380 
 .9435 
 
 1.0661 
 1.0599 
 
 50' 
 40' 
 
 30' 
 
 .5430 
 
 1.8418 
 
 30' 
 
 36 a 
 
 .7265 
 
 1.3764 
 
 54 
 
 30' 
 
 .9460 
 
 1.0538 
 
 30' 
 
 40' 
 50' 
 
 .5467 
 .5505 
 
 1.8291 
 1.8165 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .7310 
 7355 
 
 1.3680 
 1 3597 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .9545 
 .9601 
 
 1.0416 
 
 10' 
 
 29 
 
 .5543 
 
 1.8040 
 
 61 
 
 30' 
 
 .7400 
 
 1.3514 
 
 30' 
 
 44 
 
 .9657 
 
 1.0355 
 
 46 
 
 10' 
 20' 
 
 .5581 
 .5519 
 
 1.7917 
 1.7796 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .7445 
 .7490 
 
 1.3432 
 1.3351 
 
 20' 
 10' 
 
 10' 
 20' 
 
 .9713 
 .9770 
 
 1 .0295 
 1.0235 
 
 50' 
 40' 
 
 30' 
 
 .5858 
 
 1.7675 
 
 30' 
 
 37 
 
 .7536 
 
 1.3270 
 
 53 
 
 30' 
 
 .9827 
 
 1.0176 
 
 30' 
 
 40' 
 50' 
 
 .5896 
 .5735 
 
 1.7553 
 1.7437 
 
 20' 
 10' 
 
 10' 
 
 20' 
 
 .7581 
 7627 
 
 1.31CO 
 1 3111 
 
 50' 
 40' 
 
 40' 
 50' 
 
 .9884 
 .9942 
 
 1.0117 
 1.0058 
 
 10' 
 
 30 
 
 .5774 
 
 1.7321 
 
 60 
 
 30' 
 
 .7673 
 
 1.3032 
 
 30' 
 
 45 
 
 1.0000 
 
 1.0000 
 
 45 
 
 
 Cot. 
 
 Tan. 
 
 A. 
 
 
 Cot. 
 
 Tan. 
 
 A. 
 
 
 Cot. 
 
 Tan. 
 
 A.
 
 234 A MANUAL FOR NORTHERN WOODSMEN
 
 SECTION II 
 TABLES RELATING TO PARTS III AND IV 
 
 1. VOLUMES OF CYLINDERS (Locs) IN CUBIC FEET . . 236 
 
 2. AREAS OF CIRCLES OR BASAL AREAS 238 
 
 3. CORD WOOD RULE . 239 
 
 4. NEW HAMPSHIRE RULE 240 
 
 5. NEW YORK STANDARD RULE 242 
 
 6. SCRIBNER LOG RULE, LEGAL IN MINNESOTA . . . 243 
 
 7. DECIMAL RULE OF THE U. S. FOREST SERVICE . . . 244 
 
 8. DOYLE RULE 246 
 
 9. MAINE LOG RULE 248 
 
 10. QUEBEC RULE 250 
 
 11. NEW BRUNSWICK RULE " 253 
 
 12. CLARK'S INTERNATIONAL RULE 254 
 
 13. SPAULDING RULE OF COLUMBIA RIVER 255 
 
 14. BRITISH COLUMBIA RULE 258 
 
 15. VOLUME TABLES 
 
 A. Eastern 
 
 1. White Pine by the Scribner Rule 261 
 
 2, 3. Red (Norway) Pine by the Scribner Rule . . 262 
 
 4. White Pine as sawed in Massachusetts ... 263 
 
 5. White Pine in Cords 264 
 
 6. Spruce in Cubic Feet 264 
 
 7. Spruce in Feet, Board Measure 265 
 
 8. Spruce in Cords 266 
 
 9. Hemlock by the Scribner Rule 267 
 
 10. Hemlock as sawed in New Hampshire . . . 268 
 
 11. White (paper) Birch in Cords 268 
 
 12. Red Oak as sawed in New Hampshire .... 269 
 . 13. Peeled Poplar in Cords 270 
 
 14. Second Growth Hard Woods in Cords .... 270 
 
 - 15 . Form Height Factors for Southern Hard Woods 27 1 
 
 16,17. Northern Hard Woods in Board Measure . 272,273 
 
 18. Longleaf Pine in Board Measure 274 
 
 19. Loblolly Pine by the Scribner Rule .... 275 
 
 B. Western; Notes on Western Volume Tables .... 276 
 
 20. Western White Pine in Board Feet 281 
 
 21. Western Yellow Pine in Board Feet 282 
 
 22. Western Yellow Pine (16-foot log lengths) . . 283 
 
 23. Lodgepole Pine in Feet, Board Measure, and 
 
 in Railroad Ties 284 
 
 24. Western Larch in Board Measure 285 
 
 25. Engelmann Spruce in Board Measure .... 286 
 
 26. Douglas Fir of the Coast 287 
 
 27. Douglas Fir of the Interior 288 
 
 28. Washington Hemlock in Board Measure . . . 289 
 
 29. Washington Red Cedar in Board Measure . . 290 
 
 30. California Sugar Pine in Board Measure ... 292
 
 -. C-|iOX?J>C 
 
 I - ' - -.". M -H 
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 05 odiHiHC*c^:oeccc^ac:oa6c*o^Q< 
 
 I i 1 1 i tN ?i rc cc - 
 
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 CO <N CS 00 rt t>- CC O CO IN 
 
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 rH ^H ^H IN IN CO M 
 
 t-tWCC^^Ot^C
 
 238 A MANUAL FOR NORTHERN WOODSMEN 
 
 AREA OF CIRCLES OR BASAL AREAS 
 (Gives also Contents of Cylinders one foot long) 
 
 fl 
 
 lj 
 
 * 
 "*? 
 
 iameter 
 inches 
 
 11 
 
 iameter 
 inches 
 
 11 
 
 Oi 
 
 111 
 11 
 
 ! 
 
 iameter 
 inches 
 
 gd 
 
 a 1 " 1 
 
 
 Q 
 
 02 
 
 O 
 
 
 Q 
 
 x 
 
 Q" 
 
 OJ 
 
 1.0 
 
 .005 
 
 13.0 
 
 0.92 
 
 25.0 
 
 3.41 
 
 37.0 
 
 7.47 
 
 49.0 
 
 13.10 
 
 1.5 
 
 .012 
 
 13.5 
 
 0.99 
 
 25.5 
 
 3.55 
 
 37.5 
 
 7.67 
 
 49.5 
 
 13.37 
 
 2.0 
 
 .022 
 
 14.0 
 
 1.07 
 
 26.0 
 
 3.69 
 
 38.0 
 
 7.88 
 
 50.0 
 
 13.64 
 
 2.5 
 
 .034 
 
 14.5 
 
 1.15 
 
 26.5 
 
 3.83 
 
 38.5 
 
 8.08 
 
 50.5 
 
 13.91 
 
 3.0 
 
 .049 
 
 15.0 
 
 1.23 
 
 27.0 
 
 3.98 
 
 39.0 
 
 8.30 
 
 51.0 
 
 14.19 
 
 3.5 
 
 .067 
 
 15.5 
 
 1.31 
 
 27.5 
 
 4.12 
 
 , 39.5 
 
 8.51 
 
 51.5 
 
 14.47 
 
 4.0 
 
 .087 
 
 16.0 
 
 1.40 
 
 28.0 
 
 4.28 
 
 ! 40.0 1 8.73 
 
 52.0 
 
 14.75 
 
 4.5 
 
 .111 
 
 16.5 
 
 1.48 
 
 28.5 
 
 4.43 
 
 40.5 8.95 
 
 52.5 
 
 15.03 
 
 5.0 
 
 .136 
 
 17.0 
 
 1.58 
 
 29.0 
 
 4.59 
 
 i 41.0 1 9.17 
 
 53.0 
 
 15.32 
 
 5.5 
 
 .165 
 
 17.5 
 
 1.67 
 
 29.5 
 
 4.75 
 
 41.5 ' 9.39 
 
 53.5 
 
 15.59 
 
 6.0 
 
 .196 
 
 18.0 
 
 1.77 
 
 30.0 
 
 4.91 
 
 42.0 9.62 
 
 54.0 
 
 15.90 
 
 6.5 
 
 .230 
 
 18.5 
 
 1.87 
 
 30.5 
 
 5.07 
 
 ; 42.5 . 9.85 
 
 54.5 
 
 16.20 
 
 7.0 
 
 .267 
 
 19.0 
 
 1.97 
 
 31.0 
 
 5.24 
 
 43.0 10.08 
 
 55.0 
 
 16.50 
 
 7.5 
 
 .307 
 
 19.5 
 
 2.07 
 
 31.5 
 
 5.41 
 
 43.5 1 10 32 
 
 55.5 
 
 16.80 
 
 8.0 
 
 .349 
 
 20.0 
 
 2.18 
 
 32.0 
 
 5.59 
 
 i 44.0 10.56 
 
 56.0 
 
 17.10 
 
 8.5 
 
 .394 
 
 20.5 
 
 2.29 
 
 32.5 
 
 5.76 
 
 i 44.5 i 10.80 
 
 56.5 
 
 17.41 
 
 9.0 
 
 .442 
 
 21.0 
 
 2.41 
 
 33.0 
 
 5.94 
 
 I 45.0 11.04 
 
 57.0 
 
 17.72 
 
 9.5 
 
 .492 
 
 21.5 
 
 2.52 
 
 33.5 
 
 6.12 
 
 I 45.5 
 
 11.29 
 
 57.5 
 
 18.03 
 
 10.0 
 
 .545 
 
 22.0 
 
 2.64 
 
 34.0 
 
 6.30 
 
 1 46.0 
 
 11.54 
 
 58.0 
 
 18.35 
 
 10.5 
 
 .601 
 
 22.5. 
 
 2.76 
 
 34.5 
 
 6.49 
 
 I 46.5 11.79 
 
 58.5 
 
 18.67 
 
 11.0 
 
 .660 
 
 23.0 
 
 2.89 
 
 35.0 
 
 6.68 
 
 ! 47.0 12.05 
 
 39.5 
 
 18.99 
 
 11.5 
 
 .721 
 
 23.5 
 
 3.01 
 
 35.5 
 
 6.87 
 
 , 47.5 12.26 
 
 59.5 
 
 19.31 
 
 12.0 
 
 .785 
 
 24.0 
 
 3.14 
 
 36.0 
 
 7.07 
 
 1 48.0 j 12.57 
 
 60.0 
 
 19.63 
 
 12.5 
 
 .852 
 
 24.5 
 
 3.27 
 
 36.5 
 
 7.27 
 
 1 48.5 12.83 
 
 60.5 
 
 19.96
 
 TABLES RELATING TO PARTS III AND IV 239 
 
 COO^H 
 ?- 1- OCT 
 
 t~Tt<ao.-<coaocot~05.-ic 
 
 
 G> ^' i-H (N N (N CO CO CO ***'***' 10 l 
 
 1-< i-H rt r-i (N <N <N IN <N N C<i CO
 
 240 A MANUAL FOR NORTHERN WOODSMEN 
 
 8 :8 : :! 
 
 : :S : :S : : :S 
 
 2 2 
 
 5 -H^C 
 
 CO 00 -OSO --<(N * 
 
 -"5 -t- -00 -O^ 
 
 -O^ -IN 
 -H -SlN -IN 
 
 tO -t^ -00 -O '^H -IN -CO * -U3 -b- -00 -OS 
 
 o -s 
 
 O --H -IN -CO * -10 -CO 
 
 OJ -O
 
 TABLES RELATING TO PARTS III AND IV 241 
 
 OO -O ^H t^ CO OS 1C ^H t^. ( 
 
 qoqqqqqqqqqqqqqqqqqqqqqqioqqop
 
 242 A MANUAL FOR NORTHERN WOODSMEN 
 
 NEW YORK STANDARD, DIMICK, OR 
 GLENN'S FALLS RULE 
 
 
 DIAMETER IN INCHES 
 
 H 
 
 
 
 
 w 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 j 
 ft. 
 
 
 
 
 
 
 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 .009 
 
 .01 
 
 ,02 
 
 .03 
 
 .04 
 
 .06 
 
 .07 
 
 .09 
 
 .10 
 
 .12 
 
 .14 
 
 .17 
 
 .19 
 
 5 
 
 .01 
 
 .02 
 
 .03 
 
 .04 
 
 .05 
 
 .07 
 
 .08 
 
 .11 
 
 .13 
 
 .15 
 
 .18 
 
 .21 
 
 .24 
 
 6 
 
 .01 
 
 .02 
 
 .03 
 
 .05 
 
 .06 
 
 .08 
 
 .10 
 
 .13 
 
 .16 
 
 .18 
 
 .22 
 
 .25 
 
 .29 
 
 7 
 
 .02 
 
 .02 
 
 .04 
 
 .05 
 
 .08 
 
 .10 
 
 .12 
 
 .15 
 
 .18 
 
 .22 
 
 .25 
 
 .29 
 
 .33 
 
 8 
 
 .02 
 
 .02 
 
 .04 
 
 .06 
 
 .09 
 
 .11 
 
 .14 
 
 .17 
 
 .21 
 
 .25 
 
 .29 
 
 .33 
 
 .38 
 
 9 
 
 .02 
 
 .03 
 
 .05 
 
 .07 
 
 .10 
 
 .12 
 
 .15 
 
 .19 
 
 .24 
 
 .28 
 
 .33 
 
 .37 
 
 .43 
 
 10 
 
 .02 
 
 .03 
 
 .05 
 
 .08 
 
 .11 
 
 .14 
 
 .17 
 
 .22 
 
 .26 
 
 .31 
 
 .36 
 
 .42 
 
 .48 
 
 11 
 
 .03 
 
 03 
 
 or, 
 
 08 
 
 1? 
 
 15 
 
 19 
 
 ?4 
 
 ?9 
 
 34 
 
 40 
 
 46 
 
 .52 
 
 12 
 
 .03 
 
 .04 
 
 .06 
 
 .09 
 
 .13 
 
 .17 
 
 .20 
 
 .26 
 
 .31 
 
 .37 
 
 .43 
 
 .50 
 
 .57 
 
 13 
 
 .03 
 
 .04 
 
 .07 
 
 .10 
 
 .14 
 
 .18 
 
 .22 
 
 .28 
 
 .34 
 
 .40 
 
 .47 
 
 .54 
 
 .62 
 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 4 
 
 .22 
 
 .25 
 
 .28 
 
 .31 
 
 .34 
 
 .38 
 
 .41 
 
 .45 
 
 .49 
 
 .53 
 
 .58 
 
 .62 
 
 .67 
 
 5 
 
 .27 
 
 .31 
 
 .35 
 
 .38 
 
 .43 
 
 .47 
 
 .52 
 
 .57 
 
 .62 
 
 .67 
 
 .72 
 
 .78 
 
 .83 
 
 6 
 
 .33 
 
 .37 
 
 .42 
 
 .46 
 
 .51 
 
 .56 
 
 .62 
 
 .68 
 
 .74 
 
 .80 
 
 .86 
 
 .93 
 
 1.00 
 
 7 
 
 .38 
 
 .43 
 
 .48 
 
 .54 
 
 .60 
 
 .66 
 
 .72 
 
 .79 
 
 .86 
 
 .93 
 
 1.01 
 
 1.09 
 
 1.17 
 
 8 
 
 .44 
 
 .49 
 
 .55 
 
 .62 
 
 .68 
 
 .75 
 
 .82 
 
 .90 
 
 .98 
 
 1.06 
 
 1.15 
 
 1.24 
 
 1.34 
 
 9 
 
 .49 
 
 .55 
 
 .62 
 
 .69 
 
 .77 
 
 .84 
 
 .93 
 
 1.02 
 
 1.11 
 
 1.20 
 
 1.29 
 
 1.40 
 
 1.50 
 
 10 
 
 .55 
 
 .62 
 
 .69 
 
 .77 
 
 .85 
 
 .94 
 
 1.03 
 
 1.13 
 
 1.23 
 
 1.33 
 
 1.44 
 
 1.55 
 
 1.67 
 
 11 
 
 .60 
 
 .08 
 
 .76 
 
 .85 
 
 .94 
 
 1 .03 
 
 1.13 
 
 1.24 
 
 1.35 
 
 1.46 
 
 1.58 
 
 1.71 
 
 1.84 
 
 12 
 
 .66 
 
 .74 
 
 .83 
 
 .92 
 
 1.02 
 
 1.13 
 
 1.24 
 
 1 .36 
 
 1.48 
 
 1.60 
 
 1.73 
 
 1.86 
 
 2.00 
 
 13 
 
 .71 
 
 .80 
 
 .90 
 
 1.00 
 
 1.11 
 
 1.22 
 
 1.34 
 
 1.47 
 
 1.60 
 
 1.73 
 
 1.87 
 
 2.02 
 
 2.17 
 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 40 
 
 
 i 
 
 .72 
 
 .77 
 
 .82 
 
 .87 
 
 .93 
 
 .98 
 
 1.04 
 
 1.10 
 
 1.17 
 
 1.23 
 
 1.30 
 
 1.33 
 
 
 5 
 
 .90 
 
 .or, 
 
 1.02 
 
 1.09 
 
 Lie 
 
 1.23 
 
 1.30 
 
 1.38 
 
 1.46 
 
 1.54 
 
 1.62 
 
 1.70 
 
 
 6 
 
 1.08 
 
 1.15 
 
 1.23 
 
 1.31 
 
 1.39 
 
 1 .48 
 
 1.56 
 
 1 .GO 
 
 1.75 
 
 1.85 
 
 1.94 
 
 2.04 
 
 
 7 
 
 1.25 
 
 1.34 
 
 1 .43 
 
 1.53 
 
 1.63 
 
 1.72 
 
 1.83 
 
 1.93 
 
 2.04 
 
 2.15 
 
 2.27 
 
 2.39 
 
 
 8 
 
 1.43 
 
 1.53 
 
 1.64 
 
 1 .75 
 
 1 .SO 
 
 1 .97 
 
 2.09 
 
 2.21 
 
 2.33 
 
 2.46 
 
 2.59 
 
 2.73 
 
 
 9 
 
 1.61 
 
 1.72 
 
 1.84 
 
 1.97 
 
 2.09 
 
 2.22 
 
 2.35 
 
 2.49 
 
 2.62 
 
 2.77 
 
 2.91 
 
 3.07 
 
 
 10 
 
 1.79 
 
 1.92 
 
 2.05 
 
 2. IS 
 
 2.32 
 
 2.46 
 
 2.61 
 
 2.70 
 
 2.92 
 
 3.08 
 
 3.24 
 
 3.41 
 
 
 11 
 
 1.97 
 
 2.11 
 
 2.25 
 
 2.40 
 
 2.56 
 
 2.71 
 
 2.87 
 
 3.04 
 
 3.21 
 
 3.38 
 
 3.56 
 
 3.75 
 
 
 12 
 
 2.15 
 
 2.30 
 
 2.46 
 
 2.62 
 
 2.79 
 
 2.95 
 
 3.13 
 
 3.31 
 
 3.50 
 
 3.69 
 
 3.89 
 
 4.09 
 
 
 13 
 
 2.33 
 
 2.49 
 
 2.66 
 
 2.84 
 
 3.02 
 
 3.20 
 
 3.39 
 
 3.59 
 
 3.79 
 
 4.00 
 
 4.21 
 
 4.43 
 
 
 
 
 
 
 | 
 
 
 
 
 
 
 

 
 TABLES RELATING TO PARTS III AND IV 243 
 
 II 
 
 Q 
 
 I s - CC O> lO i-i X <* 
 
 iO ~3 O 00 CO CO i-t 
 
 5^SSS 
 
 ioScoP^oo 
 
 CM CS CO CO * * lO 
 
 oooooooooc 
 -H co "O i^ 03 ^ c 
 
 22S2S8! 
 
 oo t^ oo oo oo 
 
 omo 
 
 i-H Ol 00 C 
 
 S3SS3e 
 O> * CM <* "3 t~ C 
 
 ii 
 
 S?^SSS2S 
 
 >OC01>000>0-< 
 
 _j CM cN O O5 00 CO J 
 
 j co CM I-H os oo r~ 5
 
 244 A MANUAL FOR NORTHERN WOODSMEN 
 
 Is 
 
 |! 
 
 DOST^OCOC^h-COOltOC 
 JOJCO^^iOtfJCOCOr^C 
 
 W t^. N t^. I-H O ^-< i 
 
 ^TfiOiOOOI^I 
 
 CO t~ 00 O -H <N C 
 
 ; T _, COT J, CD0 OQrHCS|Tt'!0 
 
 ;s3$5a 
 
 i33!52S|2Sig
 
 TABLES RELATING TO PARTS III AND IV 245 
 
 , . o *M ~ ' ~ ~ ] ~ ' t r j /: t : v: -f 
 
 ^ oocor^wt^-'-HcO'-'OC'^r:"?* 
 
 
 
 s SiilllllliSIl 
 
 
 10 CO r*. O 
 
 
 Oi I s * Tt< i-< oo O co O : 
 
 3 2222SS;^S 
 
 ^Ht^.Mt^tNxcox-fcri^oio 
 
 O W IO l~* C C^J ' ^ [ - ~ T ] r~ f - 
 
 
 MOCOOO 
 
 )t^ Tf ^H 
 
 
 rj<or^roc:O' 'G 
 
 J5 c3f^cooo5SSoo2t2c 
 
 (N(NCOCO-^TffOOCOt>-t^-C 
 
 w lllll^llsl^is 
 
 00 O IN * to 00 C
 
 246 A MANUAL FOR NORTHERN WOODSMEN 
 
 ^Suaq | 
 
 3 *5 
 
 as 
 
 ;ciO'- ( Wro^>ocDr--cccio
 
 TABLES RELATING TO PARTS in AND iv 247 
 
 
 1 IN <N <N <N IN CO CO C 
 
 . 
 
 t" c I - i - 
 4 CM M (M ?\ ( 
 
 8 5 
 
 5 SE 
 
 MCCC 
 lOO' 'M 
 
 '" C "'" i ~ :" /. C '- "C "1 
 
 T 10 o o o r~ t^ oo CTJ o o ^- ~ 
 
 ^O ^ <: 

 
 248 A MANUAL FOR NORTHERN WOODSMEN 
 
 O-*"5t^OOO-HI 
 
 -- =; -- - i - - ~i 
 
 IN co ra A CQ ra 4 ^ 
 
 cc x o <N cc 
 
 c 10 r^ cc o c<j ?: c i - H c ?J -r c i ^ c; 
 
 OroDO-HT 
 
 - O 1^ 
 
 < rt -H -H -H ,-JT- NNMNNOliNNCOC 
 
 2 35 
 
 cD I w 5
 
 TABLES RELATING TO PARTS III AND IV 249 
 
 
 co t^t^oowoo22Sroro^*Stot2t 
 
 > CO t^ r*- CO C5 Oi O 
 
 < <oo ooco 
 
 O O i < I-H (M < 
 
 Oi^Ol^ 
 
 1 C^O t^-^ i 'OOiOrOO t^^ T-iO5CDCOOI>*OlNOiO 
 i-H I t i-H CO ( CD O *Q O O 0i ^J* O5 CO 00 CO 00 C<l t^ C^ <> I-H 
 CO I * *O iO CD CD t^ l> GO X X Oi CS O O -< i ' W (N CO CO ^ 
 
 S-^OCSt-lO^OOOOt 
 5NDwr^rtlOCB<N
 
 250 
 
 MANUAL FOR NORTHERN WOODSMEN 
 
 PROVINCE OF QUEBEC 
 
 Table of Contents of Saw Logs, Boom and Dimension Timber in 
 Feet Board Measure 
 
 DIAMETER IN INCHES 
 
 J * 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 ft. 
 10 6 
 
 9 
 
 10 
 
 15 
 
 20 
 
 28 
 
 37 
 
 42 
 
 50 
 
 62 
 
 75 
 
 83 
 
 100 
 
 117 
 
 133 
 
 154 
 
 175 
 
 11 7 
 12 8 
 13 9 
 1410 
 15 11 
 
 10 
 11 
 12 
 13 
 14 
 
 11 
 12 
 13 
 14 
 15 
 
 16 
 
 18 
 19 
 21 
 22 
 
 22 
 
 24 
 26 
 28 
 30 
 
 31 
 34 
 37 
 
 40 
 42 
 
 40 
 44 
 48 
 51 
 55 
 
 46 
 50 
 54 
 58 
 62 
 
 55 
 80 
 
 65 
 70 
 75 
 
 69 
 75 
 81 
 87 
 
 94 
 
 82 
 
 90 
 97 
 105 
 112 
 
 92 
 100 
 108 
 117 
 125 
 
 110 
 120 
 130 
 140 
 150 
 
 128 
 140 
 
 152 
 163 
 175 
 
 147 
 160 
 173 
 187 
 200 
 
 170 
 185 
 200 
 216 
 231 
 
 192 
 210 
 227 
 245 
 262 
 
 1612 
 17 .. 
 18 .. 
 19 .. 
 20 .. 
 
 15 
 
 16 
 
 17 
 IS 
 19 
 20 
 
 24 
 25 
 27 
 28 
 
 30 
 
 32 
 34 
 
 36 
 38 
 
 40 
 
 45 
 48 
 51 
 54 
 57 
 
 59 
 62 
 66 
 70 
 73 
 
 67 
 71 
 75 
 79 
 83 
 
 80 
 85 
 90 
 95 
 
 100 
 
 100 
 106 
 
 112 
 
 119 
 125 
 
 120 
 127 
 135 
 142 
 150 
 
 133 
 142 
 150 
 158 
 167 
 
 160 
 
 170 
 180 
 190 
 200 
 
 187 
 
 198 
 210 
 222 
 233 
 
 213 
 
 227 
 240 
 253 
 267 
 
 247 
 
 262 
 277 
 293 
 308 
 
 280 
 297 
 315 
 332 
 350 
 
 21 . . 
 22 . . 
 23 .. 
 24 .. 
 25 .. 
 
 
 21 
 22 
 23 
 24 
 25 
 
 31 
 33 
 34 
 36 
 37 
 
 42 
 
 44 
 
 46 
 48 
 50 
 
 59 
 
 62 
 65 
 
 68 
 
 71 
 
 77 
 81 
 84 
 88 
 
 92 
 
 87 
 92 
 96 
 100 
 104 
 
 105 
 110 
 115 
 1 20 
 125 
 
 131 
 137 
 144 
 150 
 
 156 
 
 157 
 165 
 172 
 180 
 
 187 
 
 175 
 183 
 192 
 200 
 208 
 
 210 
 220 
 230 
 240 
 
 250 
 
 245 
 257 
 268 
 280 
 292 
 
 280 
 293 
 307 
 320 
 333 
 
 324 
 339 
 355 
 370 
 385 
 
 367 
 385 
 402 
 420 
 437 
 
 26 . . 
 27 .. 
 28 . . 
 29 . . 
 30 .. 
 
 
 20 
 27 
 
 28 
 29 
 30 
 
 39 
 40 
 42 
 43 
 45 
 
 52 
 54 
 
 56 
 58 
 
 60 
 
 74 
 76 
 79 
 82 
 85 
 
 95 
 
 99 
 
 103 
 106 
 110 
 
 108 
 112 
 117 
 121 
 
 125 
 
 130 
 1 35 
 140 
 145 
 150 
 
 162 
 1 69 
 
 
 
 187 
 
 195 
 202 
 210 
 217 
 225 
 
 217 
 225 
 233 
 242 
 250 
 
 260 
 270 
 280 
 290 
 300 
 
 303 
 315 
 
 327 
 338 
 350 
 
 347 
 360 
 373 
 387 
 
 400 
 
 401 
 416 
 432 
 447 
 462 
 
 455 
 472 
 490 
 507 j 
 
 525 
 
 31 .. 
 32 .. 
 33 .. 
 34 .. 
 35 .. 
 
 
 31 
 32 
 33 
 
 34 
 35 
 
 46 
 
 48 
 49 
 51 
 52 
 
 02 
 
 64 
 66 
 
 6S 
 70 
 
 88 
 91 
 93 
 96 
 99 
 
 114 
 117 
 121 
 125 
 128 
 
 129 
 133 
 
 137 
 142 
 146 
 
 155 
 
 160 
 165 
 170 
 175 
 
 194 
 
 200 
 206 
 212 
 219 
 
 232 
 210 
 247 
 225 
 262 
 
 258 
 267 
 275 
 2S3 
 292 
 
 310 
 320 
 330 
 340 
 350 
 
 362 
 
 373 
 385 
 397 
 
 108 
 
 413 
 427 
 440 
 453 
 
 467 
 
 478 
 493 
 509 
 324 
 340 
 
 542 
 560 
 577 
 595 
 612 
 
 36 .. 
 37 .. 
 38 .. 
 39 .. 
 40 .. 
 
 
 36 
 
 37 
 38 
 39 
 40 
 
 r >4 
 55 
 -,6 
 37 
 60 
 
 72 
 74 
 76 
 
 78 
 SO 
 
 102 
 105 
 10S 
 111 
 114 
 
 132 
 
 136 
 139 
 143 
 147 
 
 150 
 154 
 
 158 
 162 
 
 ,., 
 
 ISO 
 185 
 190 
 
 195 
 
 200 
 
 225 
 231 
 237 
 244 
 250 
 
 270 
 277 
 285 
 292 
 300 
 
 ;oo 
 
 308 
 317 
 325 
 333 
 
 360 
 370 
 580 
 390 
 400 
 
 420 
 432 
 443 
 455 
 467 
 
 480 
 493 
 507 
 520 
 533 
 
 555 
 
 1 
 
 601 
 617 
 
 630 
 647 
 665 
 682 
 700
 
 TABLES RELATING To PARTS in AND iv 
 
 PROVINCE OF QUEBEC 
 
 Table of Contents of Saw Logs, Boom and Dimension Timber in 
 Feet Board Measure 
 
 DIAMETER IN INCHES 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 32 | 
 
 192 
 
 217 
 
 240 
 
 262 
 
 283 
 
 317 
 
 333 
 
 362 
 
 392 
 
 421 
 
 450 
 
 ft. 
 47510 
 
 211 
 
 238 
 
 264 
 
 289 
 
 312 
 
 348 
 
 367 
 
 399 
 
 431 
 
 463 
 
 495 
 
 52211 
 
 230 
 
 260 
 
 2S8 
 
 315 
 
 340 
 
 380 
 
 400 
 
 435 
 
 470 
 
 505 
 
 540 
 
 57012 
 
 249 
 
 282 
 
 312 
 
 341 
 
 368 
 
 412 
 
 433 
 
 471 
 
 509 
 
 547 
 
 585 
 
 617 13 
 
 268 
 
 303 
 
 336 
 
 367 
 
 397 
 
 443 
 
 467 
 
 507 
 
 548 
 
 589 
 
 630 
 
 665 14 
 
 287 
 
 325 
 
 360 
 
 394 
 
 425 
 
 475 
 
 500 
 
 544 
 
 587 
 
 631 
 
 675 
 
 71215 
 
 307 
 
 347 
 
 384 
 
 420 
 
 453 
 
 507 
 
 533 
 
 580 
 
 627 
 
 673 
 
 720 
 
 76016 
 
 326 
 
 368 
 
 408 
 
 446 
 
 482 
 
 538 
 
 567 
 
 616 
 
 666 
 
 715 
 
 765 
 
 80717 
 
 345 
 
 390 
 
 432 
 
 472 
 
 510 
 
 570 
 
 600 
 
 652 
 
 705 
 
 757 
 
 810 
 
 855 18 
 
 364 
 
 412 
 
 456 
 
 499 
 
 538 
 
 602 
 
 633 
 
 689 
 
 744 
 
 800 
 
 855 
 
 90219 
 
 383 
 
 433 
 
 480 
 
 525 
 
 567 
 
 633 
 
 667 
 
 725 
 
 783 
 
 842 
 
 900 
 
 95020 
 
 402 
 
 455 
 
 504 
 
 551 
 
 595 
 
 665 
 
 700 
 
 761 
 
 822 
 
 884 
 
 945 
 
 99721 
 
 422 
 
 477 
 
 528 
 
 577 
 
 623 
 
 697 
 
 733 
 
 797 
 
 862 
 
 926 
 
 990 
 
 1045 22 
 
 441 
 
 498 
 
 552 
 
 604 
 
 652 
 
 728 
 
 767 
 
 834 
 
 901 
 
 968 
 
 1035 
 
 1092 23 
 
 460 
 
 520 
 
 576 
 
 630 
 
 680 
 
 760 
 
 800 
 
 870 
 
 940 
 
 1010 
 
 1080 
 
 114024 
 
 479 
 
 542 
 
 600 
 
 656 
 
 708 
 
 792 
 
 833 
 
 906 
 
 979 
 
 1052 
 
 1125 
 
 118725 
 
 498 
 
 563 
 
 624 
 
 682 
 
 737 
 
 823 
 
 867 
 
 942 
 
 1018 
 
 1094 
 
 1170 
 
 1235 26 
 
 517 
 
 585 
 
 648 
 
 709 
 
 765 
 
 855 
 
 900 
 
 979 
 
 1057 
 
 1136 
 
 1215 
 
 1282 27 
 
 537 
 
 607 
 
 672 
 
 735 
 
 793 
 
 887 
 
 933 
 
 1015 
 
 1097 
 
 1178 
 
 1260 
 
 1330 28 
 
 556 
 
 628 
 
 696 
 
 761 
 
 822 
 
 918 
 
 967 
 
 1051 
 
 1136 
 
 1220 
 
 1305 
 
 1377 29 
 
 575 
 
 650 
 
 720 
 
 787 
 
 850 
 
 950 
 
 1000 
 
 1087 
 
 1175 
 
 1262 
 
 1350 
 
 1425 30 
 
 j594 
 
 672 
 
 744 
 
 814 
 
 878 
 
 982 
 
 1033 
 
 1124 
 
 1214 
 
 1305 
 
 1395 
 
 1472 31 
 
 613 
 
 693 
 
 768 
 
 840 
 
 907 
 
 1013 
 
 1067 
 
 1160 
 
 1253 
 
 1347 
 
 1440 
 
 1520 32 
 
 632 
 
 715 
 
 792 
 
 866 
 
 935 
 
 1045 
 
 1100 
 
 1196 
 
 1292 
 
 1389 
 
 1485 
 
 1567 33 
 
 652 
 
 737 
 
 816 
 
 892 
 
 963 
 
 1077 
 
 1133 
 
 1232 
 
 1332 
 
 1431 
 
 1530 
 
 161534 
 
 671 
 
 758 
 
 840 
 
 919 
 
 992 
 
 1108 
 
 1167 
 
 1269 
 
 1371 
 
 1473 
 
 1575 
 
 166235 
 
 690 
 
 780 
 
 864 
 
 945 
 
 1020 
 
 1140 
 
 1200 
 
 1305 
 
 1410 
 
 1515 
 
 1620 
 
 171036 
 
 709 
 
 802 
 
 888 
 
 971 
 
 1048 
 
 1172 
 
 1233 
 
 1341 
 
 1449 
 
 1557 
 
 1665 
 
 1757 37 
 
 728 
 
 823 
 
 912 
 
 997 
 
 1077 
 
 1203 
 
 1267 
 
 1377 
 
 1488 
 
 1599 
 
 1710 
 
 1805 38 
 
 747 
 
 845 
 
 936 
 
 1024 
 
 1105 
 
 1235 
 
 1300 
 
 1414 
 
 1527 
 
 1641 
 
 1755 
 
 1852 39 
 
 767 
 
 867 
 
 960 
 
 1050 
 
 1133 
 
 1267 
 
 1333 
 
 1450 
 
 1567 
 
 1683 
 
 1800 
 
 1900 40
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 PROVINCE OF QUEBEC 
 
 Table of Contents of Saw Logs, Boom and Dimension Timber in 
 Feet Board Measure 
 
 DIAMETER iv INCHES 
 
 1 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 40 
 
 41 
 
 42 
 
 43 
 
 ft. 
 10 525 
 
 542 
 
 567 
 
 592 
 
 617 
 
 655 
 
 692 
 
 733 
 
 758 
 
 792 
 
 833 
 
 11 577 
 
 596 
 
 623 
 
 651 
 
 678 
 
 715 
 
 761 
 
 807 
 
 834 
 
 871 
 
 917 
 
 12 630 
 
 650 
 
 680 
 
 710 
 
 740 
 
 780 
 
 830 
 
 880 
 
 910 
 
 950 
 
 1000 
 
 13 682 
 
 704 
 
 737 
 
 769 
 
 802 
 
 845 
 
 899 
 
 953 
 
 986 
 
 1029 
 
 1083 
 
 14 735 
 
 758 
 
 793 
 
 828 
 
 863 
 
 910 
 
 968 
 
 1027 
 
 1062 1108 
 
 1177 
 
 15 787 
 
 812 
 
 850 
 
 887 
 
 925 
 
 975 
 
 1037 
 
 1100 1137 
 
 1187 
 
 1250 
 
 16 840 
 
 867 
 
 907 
 
 947 
 
 987 
 
 1040 
 
 1107 
 
 1173 
 
 1213 
 
 1267 
 
 1333 
 
 17 892 
 
 921 
 
 963 
 
 1006 
 
 1048 
 
 1105 
 
 1176 
 
 1247 
 
 1289 
 
 1346 
 
 1417 
 
 18 945 
 
 975 
 
 1020 
 
 1065 
 
 1110 
 
 1170 
 
 1245 
 
 1320 
 
 1365 
 
 1 425 i 1500 
 
 19 997 
 
 1029 
 
 1077 
 
 1124 
 
 1172 
 
 1235 
 
 1314 
 
 1393 
 
 1441 1504J1583 
 
 20 1050 
 
 1083 
 
 1133 
 
 1183 
 
 1233 
 
 1300 
 
 1383 
 
 1467 
 
 1517 
 
 1583 1667 
 
 21 1102 
 
 1137 
 
 1190 
 
 1242 
 
 1295 
 
 1365 
 
 1452 
 
 1540 
 
 1592 
 
 1662 1750 
 
 22 1155 
 
 1192 
 
 1247 
 
 1302 
 
 1357 
 
 1430 
 
 1522 
 
 1613 
 
 1668 
 
 1742 1833 
 
 23 1207 
 
 1246 
 
 1303 
 
 1361 
 
 1418 
 
 1495 
 
 1591 
 
 1687 
 
 1744 
 
 1821 1917 
 
 24 1260 
 
 1300 
 
 1360 
 
 1420 
 
 1480 
 
 1550 
 
 1660 
 
 1760 
 
 1820 
 
 1900 2000 
 
 25 1312 
 
 1354 
 
 1417 
 
 1479 
 
 1542 
 
 1625 
 
 1728 
 
 1833 
 
 1896 
 
 1979 
 
 2083 
 
 26 1365 
 
 1408 
 
 1473 
 
 1538 
 
 1603 
 
 1690 
 
 1796 
 
 1907 
 
 1972 
 
 2058 
 
 2167 
 
 27 1417 
 
 1462 
 
 1530 
 
 1597 
 
 1665 
 
 1755 
 
 1867 
 
 1980 
 
 2047 
 
 2137 
 
 2250 
 
 28 1470 
 
 1517 
 
 1587 
 
 1657 
 
 1727 
 
 1820 
 
 1937 
 
 2053 
 
 2123 
 
 2217 
 
 2333 
 
 29 1522 
 
 1571 
 
 1643 
 
 1716 
 
 1788. 
 
 1885 
 
 2006 
 
 2127 
 
 2199 
 
 2296 
 
 2417 
 
 30 1575 
 
 1625 
 
 1700 
 
 1775 
 
 1850 
 
 1950 
 
 2075 
 
 2200 
 
 2275 
 
 2375 
 
 2500 
 
 31 1627 
 
 1679 
 
 1757 
 
 1834 
 
 1912 
 
 2015 
 
 2144 
 
 2273 
 
 2351 
 
 2454 
 
 2583 
 
 32 1680 
 
 1733 
 
 1813 
 
 1893 
 
 1973 
 
 2080 
 
 2213 
 
 2347 
 
 2427 
 
 2533 
 
 2667 
 
 33 1732 
 
 1787 
 
 1870 
 
 1952 
 
 2035 
 
 2145 
 
 2282 
 
 2420 
 
 2502 
 
 2612 
 
 2750 
 
 34 1785 
 
 1842 
 
 1927 
 
 2012 
 
 2097 
 
 2210 
 
 2352 
 
 2493 
 
 2578 
 
 2692 
 
 2X33 
 
 35 1837 
 
 1896 
 
 1983 
 
 2071 
 
 2158 
 
 2275 
 
 2421 
 
 2567 
 
 2654 
 
 2771 
 
 2917 
 
 36 1890 
 
 1950 
 
 2040 
 
 2130 
 
 2220 
 
 2340 
 
 2490 
 
 2640 
 
 2730 
 
 2850 
 
 3000 
 
 37 1942 
 
 2004 
 
 2097 
 
 2189 
 
 2282 
 
 2405 
 
 2559 
 
 2713 
 
 2806 2929 
 
 3083 
 
 38 1995 
 
 2058 
 
 2153 
 
 2248 
 
 2343 
 
 2470 
 
 2628 
 
 2787 
 
 2882 i 3008 
 
 3167 
 
 39 2047 
 
 2112 
 
 2210 
 
 2307 
 
 2405 
 
 2535 
 
 2697 
 
 2860 
 
 2957 3087 
 
 3250 
 
 40 2100 
 
 2167 
 
 2267 
 
 2367 
 
 2467 
 
 2600 
 
 2767 
 
 2933:3033 3167 
 
 3333
 
 TABLES RELATING TO PARTS III AND IV 253 
 
 NEW BRUNSWICK LOG RULE 
 
 p 
 
 Diameter at Top in Inches 
 
 11 
 
 12 
 
 13 
 
 14 15. 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 12 
 
 60 
 
 72 
 
 84 
 
 98 
 
 112 
 
 28 
 
 149 
 
 172 
 
 196 
 
 225 
 
 247 
 
 272 
 
 297 
 
 324 
 
 14 
 
 70 
 
 84 
 
 98 
 
 114 
 
 131 
 
 49 
 
 174 
 
 200 
 
 228 
 
 262 
 
 288 
 
 317 
 
 336 
 
 380 
 
 16 
 
 80 
 
 96 
 
 112 
 
 130 
 
 150 
 
 170 
 
 198 
 
 229 
 
 261 
 
 300 
 
 327 
 
 362 
 
 376 
 
 432 
 
 18 
 
 90 
 
 10S 
 
 126 
 
 147 
 
 168 
 
 192 
 
 223 
 
 258 
 
 294 
 
 337 
 
 370 
 
 408 
 
 445 
 
 486 
 
 20 
 
 100 
 
 120 
 
 140 
 
 163 
 
 187 
 
 213 
 
 248 
 
 286 
 
 326 
 
 375 
 
 411 
 
 453 
 
 495 
 
 540 
 
 21 
 
 105 
 
 126 
 
 147 
 
 171 
 
 196 
 
 223 
 
 261 
 
 301 
 
 343 
 
 393 
 
 432 
 
 476 
 
 519 
 
 569 
 
 22 
 
 110 
 
 132 
 
 154 
 
 179 
 
 205 
 
 234 
 
 275 
 
 315 
 
 359 
 
 412 
 
 453 
 
 498 
 
 544 
 
 594 
 
 24 
 
 120 
 
 144 
 
 168 
 
 196'224 
 
 256 
 
 298 
 
 344 
 
 392 
 
 450 
 
 494 
 
 544 
 
 594 
 
 648 
 
 26 
 
 142 
 
 168 
 
 196226 
 
 259 
 
 298 
 
 346 
 
 396 
 
 453 
 
 509 
 
 560 
 
 614 
 
 660 
 
 730 
 
 28 
 30 
 
 154 
 
 164 
 
 182 
 
 194 
 
 212 245 
 226 ' 261 
 
 280 
 299 
 
 523 
 344 
 
 374 
 398 
 
 428 
 457 
 
 490 
 523 
 
 550 
 
 588 
 
 605 
 644 
 
 653 
 698 
 
 716 
 
 756 
 
 788 
 840 
 
 32 
 
 176 
 
 208 
 
 242280320 
 
 568 
 
 427 
 
 490 
 
 561 
 
 627 
 
 689 
 
 738 
 
 808 
 
 898 
 
 34 
 
 36 
 
 186 
 198 
 
 220 
 
 234 
 
 256 
 
 273 
 
 297336 
 315360 
 
 590 
 415 
 
 452 
 481 
 
 519 
 552 
 
 594 
 631 
 
 664 
 707 
 
 732 
 778 
 
 784 
 853 
 
 877 
 931 
 
 952 
 1011 
 
 38 
 
 208 
 
 246 
 
 287 
 
 331 
 
 379 
 
 436 
 
 506 
 
 580 
 
 663 
 
 745 
 
 829 
 
 898 
 
 981 
 
 1065 
 
 40 
 
 220 
 
 260 
 
 303 
 
 350 
 
 400 
 
 461 
 
 534 
 
 612 
 
 701 
 
 786 
 
 864 
 
 948 
 
 1035 
 
 1123 
 
 42 
 
 231 
 
 273 
 
 318 
 
 367 
 
 419 
 
 484 
 
 562 
 
 644 
 
 736 
 
 825 
 
 908 
 
 995 
 
 1088 
 
 1181 
 
 44 
 
 242 
 
 286 
 
 333 
 
 384 
 
 43< 
 
 509 
 
 590 
 
 674 
 
 771 
 
 865 
 
 951 
 
 1042 
 
 1138 
 
 1235 
 
 46 
 
 252 
 
 298 
 
 347 
 
 401 
 
 458 
 
 531 
 
 613 
 
 703 
 
 804 
 
 903 
 
 992 
 
 1088 
 
 1188 
 
 1289 
 
 48 
 50 
 
 264 
 
 280 
 
 312 364 
 336392 
 
 420 480 
 450515 
 
 554 
 596 
 
 642 
 690 
 
 736 
 
 788 
 
 842 
 903 
 
 944 
 1003 
 
 1038 
 1104 
 
 1138 
 1208 
 
 1242 
 1308 
 
 1348 
 1430 
 
 UNDERSIZED LOGS 
 
 A log measuring 7 inches at the top contains twice as many superficial 
 feet as its own length. 
 
 A log measuring 8 inches, 2 times its length. 
 A log measuring 9 inches, 3 times its length. 
 A log measuring 10 inches, 4 times its length.
 
 254 A MANUAL FOR NORTHERN WOODSMEN 
 
 CLARK'S INTERNATIONAL LOG RULE 
 
 1 
 
 Length Feet 
 
 Q 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 Ins. 
 
 Volume 
 
 Board Feet 
 
 6 
 
 10 
 
 10 
 
 10 
 
 15 
 
 15 
 
 15 
 
 20 
 
 20 
 
 20 
 
 25 
 
 25 
 
 30 
 
 30 
 
 7 
 
 15 
 
 15 
 
 15 
 
 20 
 
 20 
 
 25 
 
 25 
 
 30 
 
 30 
 
 35 
 
 35 
 
 40 
 
 45 
 
 8 
 
 20 
 
 20 
 
 25 
 
 25 
 
 30 
 
 35 
 
 35 
 
 40 
 
 45 
 
 45 
 
 50 
 
 55 
 
 60 
 
 9 
 
 25 
 
 30 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 10 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 85 
 
 90 
 
 95 
 
 11 
 
 40 
 
 45 
 
 50 
 
 55 
 
 65 
 
 70 
 
 75 
 
 80 
 
 90 
 
 95 
 
 105 
 
 110 
 
 115 
 
 12 
 
 50 
 
 55 
 
 65 
 
 70 
 
 75 
 
 85 
 
 90 
 
 100 
 
 105 
 
 115 
 
 125 
 
 130 
 
 140 
 
 13 
 
 60 
 
 65 
 
 75 
 
 85 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 145 
 
 155 
 
 165 
 
 14 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 175 186 
 
 196 
 
 15 
 
 80 
 
 90 
 
 105 
 
 115 
 
 125 
 
 140 
 
 150 
 
 160 
 
 175 
 
 185 
 
 200 215 
 
 225 
 
 16 
 
 95 
 
 105 
 
 120 
 
 130 
 
 145 
 
 160 
 
 170 
 
 185 
 
 200 
 
 215 
 
 230, 245 260 
 
 17 
 
 105 
 
 120 
 
 135 
 
 150 
 
 165 
 
 180 
 
 195 
 
 210 
 
 225 
 
 245 
 
 260 275 296 
 
 18 
 
 120 
 
 135 
 
 155 
 
 170 
 
 185 
 
 205 
 
 220 
 
 240 
 
 255 
 
 275 
 
 295 310 330 
 
 19 
 
 135 
 
 155 
 
 175 
 
 190 
 
 210 
 
 230 
 
 250 
 
 270 
 
 290 
 
 310 
 
 330 350 370 
 
 20 
 
 150 
 
 170 
 
 195 
 
 215 
 
 235 
 
 255 
 
 
 300 
 
 320 
 
 345 
 
 365 
 
 390 
 
 410 
 
 21 
 
 170 
 
 190 
 
 215 
 
 235 
 
 260 
 
 285 
 
 305 
 
 330 
 
 355 
 
 380 
 
 405 
 
 430 
 
 455 
 
 22 
 
 185 
 
 210 
 
 235 
 
 260 
 
 285 
 
 315 
 
 340 
 
 365 
 
 390 
 
 420 
 
 445 
 
 475 
 
 500 
 
 23 
 
 205 
 
 230 
 
 260 
 
 285 
 
 315 
 
 345 
 
 370 
 
 400 
 
 430 
 
 460 
 
 490 
 
 520 
 
 550 
 
 24 
 
 225 
 
 255 
 
 285 
 
 315 
 
 345 
 
 375 
 
 405 
 
 440 
 
 470 
 
 500 
 
 535 
 
 565 
 
 600 
 
 25 
 
 245 
 
 275 
 
 310 
 
 345 
 
 375 
 
 410 
 
 445 
 
 475 
 
 510 
 
 545 
 
 580 
 
 615 
 
 650 
 
 26 
 
 265 
 
 300 
 
 335 
 
 370 
 
 405 
 
 445 
 
 480 
 
 520 
 
 555 
 
 595 
 
 630 
 
 670 
 
 705 
 
 27 
 
 290 
 
 325 
 
 365 
 
 405 
 
 440 
 
 480 
 
 520 
 
 560 
 
 600 
 
 640 
 
 680 
 
 725 
 
 765 
 
 28 
 
 310 
 
 350 
 
 395 
 
 435 
 
 475 
 
 520 
 
 560 
 
 605 
 
 645 
 
 690 
 
 735 
 
 780 
 
 825 
 
 29 
 
 335 
 
 380 
 
 425 
 
 470 
 
 510 
 
 560 
 
 605 
 
 650 
 
 695 
 
 740 
 
 790 
 
 835 885 
 
 30 
 
 360 
 
 405 
 
 455 
 
 500 
 
 550 
 
 600 
 
 645 
 
 695 
 
 745 
 
 795 
 
 845 
 
 895 950 
 
 31 
 
 385 
 
 435 
 
 485 
 
 540 
 
 590 
 
 640 
 
 695 
 
 745 
 
 800 
 
 850 
 
 905 960 1015 
 
 32 
 33 
 
 410 
 440 
 
 465 
 495 
 
 520 
 555 
 
 575 
 610 
 
 630 
 670 
 
 685 
 730 
 
 740 
 790 
 
 795 
 850 
 
 850 910 965 1025 1080 
 9051 970103010901150 
 
 34 
 
 470 
 
 530 
 
 590 
 
 650 
 
 715 
 
 775 
 
 840 
 
 900 
 
 965 
 
 1030 1095 1160 1225 
 
 1 
 
 495 
 525 
 
 560 
 595 
 
 625 1 690 
 665 735 
 
 755 
 800 
 
 825 
 875 
 
 890 
 945 
 
 965 1025 1095 
 1015 1085 1160 
 
 1160 1230 1300 
 1230 1305 1375 
 
 37 
 
 560 
 
 630 
 
 705 
 
 775 
 
 850 
 
 925 
 
 1000 
 
 1075 
 
 1150 
 
 1225 
 
 1300 1380 1455 
 
 38 
 39 
 
 590 
 020 
 
 665 
 705 
 
 745 
 785 
 
 820 
 865 
 
 895 975 1055'! 135 1210 
 945 1030 1110 1195 1280 
 
 1295 
 1365 
 
 1375 1455 1535 
 1450 1535 1620 
 
 40 
 
 655 
 
 740 
 
 825 
 
 910 
 
 995 
 
 1085 
 
 1170 
 
 1260 
 
 1345 
 
 1 435 ! 1525 1615 1705 
 
 41 
 42 
 
 690 
 725 
 
 780 
 820 
 
 870 960 1050 1140 1230 
 915 1010 1100 1200 1295 
 
 1325 1415 1510 1605 1700 1795 
 1390 1490-1585 1685 1785 1885 
 
 43 
 
 760 
 
 860 
 
 960 
 
 1060 
 
 1155 
 
 1260 
 
 1360 
 
 1460 
 
 1500 
 
 1665 1770 1870 1975 
 
 44 
 45 
 
 800 
 
 835 
 
 900 1005 1110 1215 1320 1425 
 945 1055 1160 1270 1380 1490 
 
 1530 1 635 i 1745 1855 1960 2070 
 1600 1715 1825 1940 2050 2165 
 
 46 
 
 875 
 
 990 
 
 1100 
 
 1215 
 
 1330 
 
 1445 
 
 1560 
 
 1675 
 
 1790 
 
 1910 2030 2145 2265 
 
 47 
 
 915 
 
 1035 
 
 1150 
 
 1270 
 
 1 390 
 
 1510 
 
 1630 
 
 1750 
 
 1870 
 
 1995;2120 2240 2365 
 
 48 
 
 955 
 
 1080 
 
 12051325 1450 1575 
 
 1700 
 
 1830 
 
 1955 
 
 2085 
 
 2210 
 
 2340 
 
 2470
 
 TABLES RELATING TO PARTS III AND IV 255 
 
 SPAULDING LOG RULE OF COLUMBIA RIVER 
 
 BI DIAMETER IN INCHES 
 
 " 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 16 
 
 17 
 
 18 
 
 19 1 SO 
 
 21 
 
 22 
 
 ft. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 12 38 
 
 47 
 
 58 
 
 71 
 
 86 
 
 103 
 
 121 
 
 141 
 
 162 
 
 184 
 
 207 
 
 231 
 
 256 
 
 14 44 
 
 55 
 
 67 
 
 82 
 
 100 
 
 120 
 
 141 
 
 164 
 
 IS'.) 
 
 214 
 
 241 
 
 269 
 
 298 
 
 16 50 
 
 63 
 
 77 
 
 94 
 
 114 
 
 137 
 
 161 
 
 188 
 
 210 
 
 245 
 
 276 
 
 308 
 
 341 
 
 18 57 
 
 70 
 
 87 
 
 106 
 
 129 
 
 154 
 
 181 
 
 211 
 
 243 
 
 276 
 
 310 
 
 346 
 
 384 
 
 20 63 
 
 78 
 
 96 
 
 118 
 
 143 
 
 171 
 
 201 
 
 235 
 
 270 
 
 306 
 
 345 
 
 385 
 
 426 
 
 22 69 
 
 86 
 
 106 
 
 130 
 
 157 
 
 188 
 
 221 
 
 258 
 
 297 
 
 337 
 
 379 
 
 423 
 
 469 
 
 24 76 
 
 94 
 
 116 
 
 142 
 
 172 
 
 208 
 
 242 
 
 282 
 
 324 
 
 368 
 
 414 
 
 462 
 
 512 
 
 26 82 
 
 101 
 
 125 
 
 153 
 
 186 
 
 22:i 
 
 262 
 
 305 
 
 351 
 
 398 
 
 448 
 
 500 
 
 554 
 
 28 88 
 
 109 
 
 134 
 
 164 
 
 200 
 
 240 
 
 282 
 
 328 
 
 378 
 
 428 
 
 482 
 
 538 
 
 596 
 
 30 94 
 
 117 
 
 144 
 
 176 
 
 214 
 
 257 
 
 302 
 
 352 
 
 405 
 
 459 
 
 517 
 
 577 
 
 639 
 
 32 101 
 
 125 
 
 154 
 
 188 
 
 228 
 
 274 
 
 322 
 
 376 
 
 432 
 
 490 
 
 552 
 
 616 
 
 682 
 
 34 107 
 
 132 
 
 164 
 
 200 
 
 243 
 
 2ni 
 
 342 
 
 399 
 
 459 
 
 521 
 
 586 
 
 654 
 
 725 
 
 36 113 
 
 140 
 
 174 
 
 212 
 
 258 
 
 308 
 
 362 
 
 422 
 
 486 
 
 552 
 
 620 
 
 692 
 
 768 
 
 38 120 
 
 148 
 
 183 
 
 224 
 
 272 
 
 325 
 
 382 
 
 446 
 
 513 
 
 582 
 
 655 
 
 731 
 
 810 
 
 40 126 
 
 156 
 
 192 
 
 236 
 
 286 
 
 342 
 
 402 
 
 470 
 
 540 
 
 612 
 
 690 
 
 770 
 
 852 
 
 42 132 
 
 164 
 
 202 
 
 248 
 
 300 
 
 359 
 
 422 
 
 493 
 
 567 
 
 643 
 
 724 
 
 808 
 
 895 
 
 44 138 
 
 172 
 
 212 
 
 260 
 
 314 
 
 376 
 
 442 
 
 516 
 
 5!H 
 
 674 
 
 758 
 
 846 
 
 938 
 
 46 145 
 
 179 
 
 222 
 
 272 
 
 329 
 
 KM 
 
 463 
 
 540 
 
 621 
 
 705 
 
 793 
 
 885 
 
 981 
 
 48 151 
 
 187 
 
 232 
 
 284 
 
 344 
 
 412 
 
 484 
 
 564 
 
 648 
 
 736 
 
 828 
 
 924 
 
 1024 
 
 50 157 
 
 195 
 
 241 
 
 295 
 
 358 
 
 429 
 
 504 
 
 587 
 
 675 
 
 766 
 
 862 
 
 962 
 
 1066 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 28 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 L2 282 
 
 309 
 
 337 
 
 36 
 
 39( 
 
 > 427 
 
 459 
 
 492 
 
 526 
 
 561 
 
 597 
 
 634 
 
 14 329 
 
 360 
 
 393 
 
 427 
 
 462 
 
 ! 498 
 
 535 
 
 574 
 
 613 
 
 654 
 
 696 
 
 739 
 
 16 376 
 
 412 
 
 449 
 
 48S 
 
 52J 
 
 569 
 
 612 
 
 656 
 
 701 
 
 748 
 
 796 
 
 845 
 
 18 423 
 
 463 
 
 505 
 
 54S 
 
 59-i 
 
 640 
 
 688 
 
 738 
 
 789 
 
 841 
 
 895 
 
 951 
 
 20 470 
 
 515 
 
 561 
 
 610 
 
 66C 
 
 711 
 
 765 
 
 820 
 
 876 
 
 935 
 
 995 
 
 1056 
 
 22 517 
 
 566 
 
 617 
 
 671 
 
 72 
 
 782 
 
 841 
 
 902 
 
 964 
 
 1028 
 
 1094 
 
 1162 
 
 24 564 
 
 618 
 
 674 
 
 732 
 
 792 
 
 854 
 
 918 
 
 984 
 
 1052 
 
 1122 
 
 1194 
 
 1268 
 
 26 611 
 
 669 
 
 730 
 
 793 
 
 85S 
 
 925 
 
 994 
 
 1066 
 
 1139 
 
 1215 
 
 1293 
 
 1373 
 
 28 658 
 
 720 
 
 786 
 
 854 
 
 924 
 
 996 
 
 1070 
 
 1148 
 
 1226 
 
 1308 
 
 1392 
 
 1478 
 
 30 705 
 
 772 
 
 842 
 
 915 
 
 99C 
 
 1067 
 
 1147 
 
 1230 
 
 1314 
 
 1402 
 
 1492 
 
 1584 
 
 32 752 
 
 824 
 
 898 
 
 976 
 
 105f 
 
 1138 
 
 1224 
 
 1312 
 
 1402 
 
 1496 
 
 1592 
 
 1690 
 
 34 799 
 
 875 
 
 954 
 
 1037 
 
 1122 
 
 1209 
 
 1300 
 
 1394 
 
 1490 
 
 1589 
 
 1691 
 
 1796 
 
 36 846 
 
 926 
 
 1010 
 
 1098 
 
 118 
 
 1280 
 
 1376 
 
 1476 
 
 1578 
 
 1682 
 
 1790 
 
 1902 
 
 38 893 
 
 978 
 
 1066 
 
 115S 
 
 125- 
 
 1351 
 
 1453 
 
 1558 
 
 1665 
 
 1776 
 
 1890 
 
 2007 
 
 40 940 
 
 1030 
 
 1122 
 
 122C 
 
 132( 
 
 ) 1422 
 
 1530 
 
 1640 
 
 1752 
 
 1870 
 
 1990 
 
 2112 
 
 42 987 
 
 1081 
 
 1178 
 
 1281 
 
 138f 
 
 > 1493 
 
 1606 
 
 1722 
 
 1840 
 
 1963 
 
 2089 
 
 2218 
 
 44 1034 
 
 1132 
 
 1234 
 
 1342 
 
 1452 
 
 ! 1564 
 
 1682 
 
 1804 
 
 1928 
 
 2056 
 
 2188 
 
 2324 
 
 46 1081 
 
 1184 
 
 1291 
 
 140S 
 
 1515 
 
 i 1636 
 
 1759 
 
 1886 
 
 2016 
 
 2150 
 
 2288 
 
 2430 
 
 48 1128 
 
 1236 
 
 1348 
 
 1464 
 
 158- 
 
 1708 
 
 1836 
 
 1968 
 
 2104 
 
 2244 
 
 2388 
 
 2536 
 
 60 1175 
 
 1287 
 
 1404 
 
 152 
 
 165( 
 
 ) 1779 
 
 1912 
 
 2050 
 
 2191 
 
 2337 
 
 2487 
 
 2641
 
 256 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 SPAULDING LOG RULE continued 
 
 x DIAMETER IN INCHES 
 
 o 
 
 " 35 
 
 36 
 
 07 
 
 38 
 
 39 
 
 
 
 
 
 
 
 46 
 
 
 
 Ol 
 
 
 
 
 
 
 
 
 
 
 ft. 
 
 
 
 
 
 
 
 
 
 
 
 
 12 673 
 
 713 
 
 755 
 
 798 
 
 843 
 
 889 
 
 936 
 
 984 
 
 1033 
 
 1086 
 
 1134 
 
 1186 
 
 14 785 
 
 831 
 
 880 
 
 931 
 
 983 
 
 1037 
 
 1092 
 
 1148 
 
 1205 
 
 1267 
 
 1323 
 
 1383 
 
 16 897 
 
 950 
 
 1006 
 
 1064 
 
 1124 
 
 1185 
 
 1248 
 
 1312 
 
 1377 
 
 1448 
 
 1512 
 
 1581 
 
 18 1009 
 
 1069 
 
 1132 
 
 1197 
 
 1264 
 
 1333 
 
 1404 
 
 1476 
 
 1549 
 
 1629 
 
 1701 
 
 1779 
 
 20 1121 
 
 1188 
 
 1258 
 
 1330 
 
 1405 
 
 1481 
 
 1560 
 
 1640 
 
 1721 
 
 1810 
 
 1890 
 
 1976 
 
 22 1233 
 
 1307 
 
 1384 
 
 1463 
 
 1545 
 
 1629 
 
 1716 
 
 1804 
 
 1893 
 
 1991 
 
 2079 
 
 2174 
 
 24 1346 
 
 1426 
 
 1510 
 
 1596 
 
 1686 
 
 1778 
 
 1872 
 
 1968 
 
 2066 
 
 2172 
 
 2268 
 
 2372 
 
 26 1458 
 
 1544 
 
 1635 
 
 1729 
 
 1826 
 
 1926 
 
 2028 
 
 2132 
 
 2238 
 
 2353 
 
 2457 
 
 2569 
 
 28 1570 
 
 1662 
 
 1760 
 
 1862 
 
 1966 
 
 2074 
 
 2184 
 
 2296 
 
 2410 
 
 2534 
 
 2646 
 
 2766 
 
 30 1682 
 
 1781 
 
 1886 
 
 1995 
 
 2107 
 
 2222 
 
 2340 
 
 2460 
 
 2582 
 
 2715 
 
 2835 
 
 2964 
 
 32 1794 
 
 1900 
 
 2012 
 
 2128 
 
 2248 
 
 2370 
 
 2496 
 
 2624 
 
 2754 
 
 2896 
 
 3024 
 
 3162 
 
 34 1906 
 
 2019 
 
 2138 
 
 2261 
 
 2osx 
 
 2518 
 
 2652 
 
 2788 
 
 2926 
 
 3077 
 
 3213 
 
 3360 
 
 36 2018 
 
 2138 
 
 2264 
 
 2394 
 
 2..2s 
 
 2666 
 
 2808 
 
 2952 
 
 3098 
 
 3258 
 
 3402 
 
 3558 
 
 38 2130 
 
 2257 
 
 2390 
 
 2527 
 
 L'. ;.;.! 
 
 2814 
 
 2964 
 
 3116 
 
 3270 
 
 3439 
 
 3591 
 
 3755 
 
 40 2242 
 
 2376 
 
 2516 
 
 2660 
 
 2810 
 
 2962 
 
 3120 
 
 3280 
 
 3442 
 
 3620 
 
 3780 
 
 3952 
 
 42 2354 
 
 2495 
 
 2642 
 
 2793 
 
 2950 
 
 3110 
 
 3276 
 
 3444 
 
 3614 
 
 3801 
 
 3969 
 
 4150 
 
 44 2466 
 
 2614 
 
 2768 
 
 2926 
 
 3090 
 
 3258 
 
 3432 
 
 3608 
 
 3786 
 
 3982 
 
 4158 
 
 4348 
 
 46 2579 
 
 2733 
 
 2894 
 
 3059 
 
 3231 
 
 3407 
 
 3588 
 
 3772 
 
 3959 
 
 4163 
 
 4347 
 
 4546 
 
 48 2692 
 
 2852 
 
 3020 
 
 3192 
 
 3372 
 
 3556 
 
 3744 
 
 3936 
 
 4132 
 
 4344 
 
 4536 
 
 4744 
 
 50 2804 
 
 2970 
 
 3145 
 
 3325 
 
 3512 
 
 3704 
 
 3900 
 
 4100 
 
 4304 
 
 4525 
 
 4725 
 
 4941 
 
 47 
 
 48 
 
 49 
 
 50 
 
 51 
 
 52 
 
 63 
 
 " 
 
 66 
 
 56 
 
 57 
 
 58 
 
 L2 1239 
 
 1293 
 
 1348 
 
 1404 
 
 1461 
 
 15.19 
 
 1578 
 
 1638 
 
 1700 
 
 1763 
 
 1827 
 
 1893 
 
 14 1445 
 
 1508 
 
 1572 
 
 1638 
 
 1704 
 
 1772 
 
 1841 
 
 1911 
 
 1983 
 
 2056 
 
 2131 
 
 2208 
 
 16 1652 
 
 1724 
 
 1797 
 
 1872 
 
 1948 
 
 2025 
 
 2104 
 
 2184 
 
 2266 
 
 2350 
 
 2436 
 
 2524 
 
 18 1858 
 
 1939 
 
 2022 
 
 2106 
 
 2191 
 
 2278 
 
 2367 
 
 2457 
 
 2 .-,,-)(] 
 
 2644 
 
 2740 
 
 2839 
 
 20 2065 
 
 2155 
 
 2246 
 
 2340 
 
 2435 
 
 2531 
 
 2630 
 
 2730 
 
 2833 
 
 2938 
 
 3045 
 
 3155 
 
 22 2271 
 
 2370 
 
 2470 
 
 2574 
 
 2678 
 
 2784 
 
 2893 
 
 3003 
 
 3116 
 
 3232 
 
 3349 
 
 3470 
 
 24 2478 
 
 2586 
 
 2696 
 
 2808 
 
 2922 
 
 3038 
 
 3156 
 
 3276 
 
 3400 
 
 3526 
 
 3654 
 
 3786 
 
 26 26S4 
 
 2801 
 
 2920 
 
 3042 
 
 3165 
 
 3291 
 
 3419 
 
 3549 
 
 3683 
 
 3819 
 
 3958 
 
 4101 
 
 28 2890 
 
 3016 
 
 3144 
 
 3276 
 
 3408 
 
 3544 
 
 3682 
 
 3>22 
 
 3966 
 
 4112 
 
 4262 
 
 4416 
 
 30 3097 
 
 3232 
 
 3369 
 
 3510 
 
 3652 
 
 3797 
 
 3945 
 
 4095 
 
 4249 
 
 4406 
 
 4567 
 
 4732 
 
 32 3304 
 
 3448 
 
 3594 
 
 3744 
 
 3896 
 
 4050 
 
 4208 
 
 4368 
 
 4532 
 
 4700 
 
 4872 
 
 5048 
 
 34 3510 
 
 3663 
 
 3819 
 
 3978 
 
 4139 
 
 4303 
 
 4471 
 
 4641 
 
 4816 
 
 4994 
 
 5176 
 
 5363 
 
 36 3716 
 
 3878 
 
 4044 
 
 4212 
 
 4:is2 
 
 4556 
 
 4734 
 
 4914 
 
 5100 
 
 .-,2s-, 
 
 5480 
 
 5678 
 
 38 3923 
 
 4094 
 
 4268 
 
 4446 
 
 4626 
 
 ISO!) 
 
 4997 
 
 5187 
 
 5383 
 
 r,.-,s2 
 
 5785 
 
 5994 
 
 40 4130 
 
 4310 
 
 4492 
 
 4680 
 
 4870 
 
 5062 
 
 5260 
 
 5460 
 
 5666 
 
 5876 
 
 6090 
 
 6310 
 
 42 4336 
 
 4525 
 
 4716 
 
 4914 
 
 5113 
 
 5315 
 
 5523 
 
 5733 
 
 5949 
 
 6170 
 
 6394 
 
 6625 
 
 44 4542 
 
 4740 
 
 4940 
 
 5148 
 
 5356 
 
 5568 
 
 5786 
 
 6006 
 
 6232 
 
 6464 
 
 r,r,os 
 
 6940 
 
 46 4749 
 
 4956 
 
 5166 
 
 5382 
 
 5600 
 
 5822 
 
 6049 
 
 6279 
 
 6516 
 
 ti7f).x 
 
 7003 
 
 7256 
 
 48 4956 
 
 5172 
 
 5392 
 
 5U16 
 
 5844 
 
 6076 
 
 6312 
 
 6552 
 
 tisoo 
 
 7052 
 
 7304 
 
 7572 
 
 60 5162 
 
 5387 
 
 5616 
 
 5850 
 
 6087 
 
 6329 
 
 6575 
 
 (1S25 
 
 7083 
 
 7345 
 
 7612 
 
 7887
 
 TABLES RELATING TO PARTS III AND IV 257 
 
 SPAULDING LOG RULE continued 
 
 K DIAMETER IN INCHES 
 
 J 
 
 60 
 
 61 
 
 62 
 
 63 
 
 64 
 
 65 
 
 66 
 
 67 
 
 68 
 
 69 
 
 70 
 
 ft. 
 12 1960 
 
 2028 
 
 2098 
 
 2169 
 
 2241 
 
 2315 
 
 2390 
 
 2467 
 
 2545 
 
 2625 
 
 2706 
 
 2789 
 
 14 2286 
 
 2366 
 
 2447 
 
 2530 
 
 2614 
 
 2700 
 
 2789 
 
 2878 
 
 2969 
 
 3062 
 
 3157 
 
 3253 
 
 16 2613 
 
 2704 
 
 2797 
 
 2V;,1> 
 
 2!NS 
 
 3086 
 
 3186 
 
 3289 
 
 3393 
 
 3500 
 
 3608 
 
 3718 
 
 18 2940 
 
 3042 
 
 3147 
 
 3253 
 
 3361 
 
 3472 
 
 3585 
 
 3700 
 
 3817 
 
 3937 
 
 4059 
 
 4183 
 
 20 3266 
 
 3380 
 
 3496 
 
 3615 
 
 3735 
 
 3858 
 
 3983 
 
 4111 
 
 4241 
 
 4375 
 
 4510 
 
 4648 
 
 22 3592 
 
 3718 
 
 3846 
 
 3976 
 
 4108 
 
 4244 
 
 4381 
 
 4522 
 
 4665 
 
 4812 
 
 4961 
 
 5113 
 
 24 3920 
 
 4056 
 
 4196 
 
 4338 
 
 4482 
 
 4630 
 
 4780 
 
 4934 
 
 5090 
 
 5250 
 
 5412 
 
 5578 
 
 26 4246 
 
 4394 
 
 4545 
 
 4699 
 
 4855 
 
 5015 
 
 5179 
 
 5345 
 
 5514 
 
 5687 
 
 5863 
 
 6042 
 
 28 4572 
 
 4732 
 
 4894 
 
 5060 
 
 5228 
 
 5400 
 
 5578 
 
 5756 
 
 5938 
 
 6124 
 
 6314 
 
 6506 
 
 30 4899 
 
 5070 
 
 5244 
 
 5422 
 
 5602 
 
 5786 
 
 5975 
 
 6167 
 
 6362 
 
 6562 
 
 6765 
 
 6971 
 
 32 5226 
 
 5408 
 
 5594 
 
 5784 
 
 5976 
 
 6172 
 
 6372 
 
 6578 
 
 6786 
 
 7000 
 
 7216 
 
 7436 
 
 34 5553 
 
 5746 
 
 5944 
 
 6145 
 
 6349 
 
 6558 
 
 6771 
 
 6989 
 
 7210 
 
 7437 
 
 7667 
 
 7901 
 
 36 5880 
 
 6084 
 
 6294 
 
 6506 
 
 6722 
 
 6944 
 
 7170 
 
 7400 
 
 7634 
 
 7874 
 
 8118 
 
 8366 
 
 38 6206 
 
 6422 
 
 6643 
 
 6868 
 
 7096 
 
 7330 
 
 7568 
 
 7811 
 
 8058 
 
 8312 
 
 8569 
 
 8831 
 
 40 6532 
 
 6760 
 
 6992 
 
 7230 
 
 7470 
 
 7716 
 
 7966 
 
 8222 
 
 8482 
 
 8750 
 
 9020 
 
 9296 
 
 42 6858 
 
 7098 
 
 7342 
 
 7591 
 
 7843 
 
 8102 
 
 8364 
 
 8633 
 
 8906 
 
 9187 
 
 9471 
 
 9761 
 
 44 7184 
 
 7436 
 
 7692 
 
 7952 
 
 8216 
 
 8488 
 
 8762 
 
 9044 
 
 9330 
 
 9624 
 
 9922 
 
 
 46 7512 
 
 7774 
 
 8042 
 
 8314 
 
 8590 
 
 8874 
 
 9161 
 
 9456 
 
 9755 
 
 
 
 
 48 7840 
 
 8112 
 
 8392 
 
 8676 
 
 8964 
 
 9260 
 
 9560 
 
 
 
 
 
 
 50 8166 
 
 8450 
 
 8741 
 
 9057 
 
 9337 
 
 9645 
 
 9959 
 
 
 
 

 
 258 A MANUAL FOR NORTHERN WOODSMEN 
 
 BRITISH COLUMBIA LOG SCALE 
 
 Established by the government, and derived from the 
 following rule: Deduct \y% inches from the mean diam- 
 eter of the log at the small end ; square the result and mul- 
 tiply by .7854; deduct %; divide by 12; multiply by the 
 length of the log in feet. 
 
 Logs more than 40 and not over 50 feet long to be scaled 
 as two logs of equal length, the butt log taken as 1 inch 
 larger than the top. Logs over 50 and not over 60 feet 
 long to be treated similarly, but with 2 inches rise allowed 
 to the butt log; and so on, 1 inch of rise being added for 
 each 10 feet or part thereof over 40 feet. 
 
 n DIAMETER IN INCHES 
 
 5 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 ft. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 9 
 
 10 
 
 11 
 
 ft 
 
 15 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 10 34 
 
 43 
 
 53 
 
 63 
 
 74 
 
 87 
 
 100 
 
 114 
 
 130 
 
 146 
 
 163 
 
 181 
 
 200 
 
 220 
 
 241 
 
 263 
 
 12 41 
 
 52 
 
 63 
 
 76 
 
 89 
 
 104 
 
 120 
 
 137 
 
 155 
 
 175 
 
 195 
 
 217 
 
 210 
 
 264 
 
 289 
 
 315 
 
 14 48 
 
 60 
 
 73 
 
 88 
 
 104 
 
 121 
 
 140 
 
 100 
 
 isl 
 
 204 
 
 22S 
 
 253 
 
 2x0 
 
 30S 
 
 337 
 
 368 
 
 16 55 
 
 69 
 
 84 
 
 101 
 
 119 
 
 139 
 
 160 
 
 1x3 
 
 207 
 
 23:-; 
 
 201 
 
 200 
 
 320 
 
 352 
 
 386 
 
 421 
 
 18 62 
 
 77 
 
 94 
 
 113 
 
 134 
 
 150 
 
 ISO 
 
 2.10 
 
 233 
 
 202 
 
 203 
 
 320 
 
 360 
 
 300 
 
 134 
 
 473 
 
 20 69 
 
 80 
 
 105 
 
 126 
 
 149 
 
 173 
 
 20!) 
 
 229 
 
 259 
 
 292 
 
 326 
 
 302 
 
 400 
 
 440 
 
 4s2 
 
 526 
 
 22 76 
 
 94 
 
 115 
 
 138 
 
 104 
 
 191 
 
 220 
 
 252 
 
 2S5 
 
 321 
 
 358 
 
 398 
 
 440 
 
 484 
 
 530 
 
 578 
 
 24 83 
 
 103 
 
 
 151 
 
 17s 
 
 2ox 
 
 240 
 
 274 
 
 311 
 
 {50 
 
 301 
 
 131 
 
 ISO 
 
 52 S 
 
 57S 
 
 631 
 
 26 89 
 
 112 
 
 130 
 
 161 
 
 193 
 
 220 
 
 21') 
 
 207 
 
 337 
 
 ',79 
 
 124 
 
 471 
 
 
 572 
 
 020 
 
 683 
 
 28 96 
 
 120 
 
 147 
 
 176 
 
 20x 
 
 213 
 
 280 
 
 320 
 
 303 
 
 108 
 
 150 
 
 507 
 
 500 
 
 010 
 
 075 
 
 736 
 
 30 103 
 
 129 
 
 157 
 
 189 
 
 223 
 
 200 
 
 300 
 
 343 
 
 889 
 
 137 
 
 189 
 
 513 
 
 000 
 
 600 
 
 723 
 
 789 
 
 32 110 
 
 137 
 
 168 
 
 201 
 
 238 
 
 278 
 
 320 
 
 360 
 
 415 
 
 466 
 
 521 
 
 579 
 
 640 
 
 704 
 
 771 
 
 841 
 
 34 117 
 
 140 
 
 17S 
 
 214 
 
 253 
 
 295 
 
 340 
 
 3X0 
 
 441 
 
 190 
 
 55 i 
 
 015 
 
 Ox() 
 
 748 
 
 xl9 
 
 894 
 
 36 124 
 
 155 
 
 189 
 
 227 
 
 20x 
 
 3 1 2 
 
 300 
 
 412 
 
 100 
 
 -,25 
 
 5SO 
 
 ,52 
 
 720 
 
 702 
 
 S07 
 
 946 
 
 38 131 
 
 103 
 
 199 
 
 239 
 
 2 S3 
 
 330 
 
 3X0 
 
 435 
 
 492 
 
 554 
 
 019 
 
 Oxx 
 
 700 
 
 S36 
 
 no 
 
 999 
 
 40 138 
 
 172 
 
 210 
 
 252 
 
 297 
 
 317 
 
 400 
 
 4.57 
 
 518 
 
 5S3 
 
 052 
 
 724 
 
 800 
 
 SSO 
 
 904 
 
 1051
 
 TABLES RELATING TO PARTS III AND IV 259 
 
 BRITISH COLUMBIA LOG SCALE continued 
 
 W DIAMETER IN INCHES 
 
 6 
 
 f, 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 ft. 
 
 1 29 
 
 31 
 
 33 
 
 36 
 
 39 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 57 
 
 60 
 
 10 286 
 
 309 
 
 334 
 
 360 
 
 387 
 
 414 
 
 443 
 
 472 
 
 503 
 
 534 
 
 567 
 
 600 
 
 12 343 
 
 371 
 
 401 
 
 432 
 
 464 
 
 497 
 
 531 
 
 567 
 
 603 
 
 641 
 
 680 
 
 720 
 
 14 400 
 
 433 
 
 468 
 
 504 
 
 541 
 
 580 
 
 620 
 
 661 
 
 704 
 
 748 
 
 793 
 
 840 
 
 16 457 
 
 495 
 
 535 
 
 576 
 
 619 
 
 663 
 
 708 
 
 756 
 
 804 
 
 855 
 
 906 
 
 960 
 
 18 514 
 
 557 
 
 602 
 
 648 
 
 G96 
 
 746 
 
 797 
 
 850 
 
 905 
 
 961 
 
 1020 
 
 1080 
 
 20 571 
 
 619 
 
 668 
 
 720 
 
 773 
 
 828 
 
 886 
 
 945 
 
 1005 
 
 1068 
 
 1133 
 
 1200 
 
 22 629 
 
 681 
 
 .735 
 
 791 
 
 850 
 
 911 
 
 974 
 
 1039 
 
 1106 
 
 1175 
 
 1246 
 
 1320 
 
 24 686 
 
 743 
 
 802 
 
 864 
 
 928 
 
 994 
 
 1063 
 
 1133 
 
 1207 
 
 1282 
 
 1360 
 
 1440 
 
 26 743 
 
 805 
 
 869 
 
 936 
 
 1005 
 
 1077 
 
 1151 
 
 1228 
 
 1307 
 
 1389 
 
 1473 
 
 1560 
 
 28 800 
 
 867 
 
 936 
 
 1008 
 
 1082 
 
 1160 
 
 1240 
 
 1322 
 
 1408 
 
 1496 
 
 1586 
 
 1679 
 
 30 857 
 
 928 
 
 1003 
 
 1080 
 
 1160 
 
 1243 
 
 1328 
 
 1417 
 
 1508 
 
 1602 
 
 1700 
 
 1799 
 
 32 914 
 
 990 
 
 1070 
 
 1152 
 
 1237 
 
 1325 
 
 1417 
 
 1511 
 
 1609 
 
 1709 
 
 1813 
 
 1919 
 
 34 971 
 
 1052 
 
 1136 
 
 1224 
 
 1314 
 
 1408 
 
 1505 
 
 1606 
 
 1709 
 
 1816 
 
 1926 
 
 2039 
 
 36 1028 
 
 1114 
 
 1203 
 
 1296 
 
 1392 
 
 1491 
 
 1594 
 
 1700 
 
 1810 
 
 1923 
 
 2039 
 
 2159 
 
 38 1086 
 
 1176 
 
 1270 
 
 1368 
 
 1469 
 
 1574 
 
 1682 
 
 1795 
 
 1910 
 
 2030 
 
 2153 
 
 2279 
 
 40 1143 
 
 1238 
 
 1337 
 
 1440 
 
 1546 
 
 1657 
 
 1771 
 
 1889 
 
 2011 
 
 2137 
 
 2266 
 
 2399 
 
 38 
 
 39 
 
 40 
 
 41 
 
 42 
 
 43 
 
 44 
 
 45 
 
 46 
 
 47 
 
 48 
 
 49 
 
 ft. 
 1 63 
 
 67 
 
 71 
 
 74 
 
 78 
 
 82 
 
 86 
 
 90 
 
 94 
 
 99 
 
 103 
 
 107 
 
 10 634 
 
 669 
 
 705 
 
 743 
 
 781 
 
 820 
 
 860 
 
 901 
 
 943 
 
 985 
 
 1029 
 
 1074 
 
 12 761 
 
 803 
 
 847 
 
 891 
 
 937 
 
 984 
 
 1032 
 
 1081 
 
 1131 
 
 1182 
 
 1235 
 
 1289 
 
 14 888 
 
 937 
 
 988 
 
 1040 
 
 1093 
 
 1148 
 
 1204 
 
 1261 
 
 1320 
 
 1379 
 
 1441 
 
 1503 
 
 16 1015 
 
 1071 
 
 1129 
 
 1188 
 
 1249 
 
 1312 
 
 1376 
 
 1441 
 
 1508 
 
 1577 
 
 1647 
 
 1718 
 
 18 1141 
 
 1205 
 
 1270 
 
 1337 
 
 1405 
 
 1475 
 
 1547 
 
 1621 
 
 1697 
 
 1774 
 
 1852 
 
 1933 
 
 20 1268 
 
 1339 
 
 1411 
 
 1485 
 
 1561 
 
 1639 
 
 1719 
 
 1801 
 
 1885 
 
 1971 
 
 2058 
 
 2148 
 
 22 1395 
 
 1472 
 
 1552 
 
 1634 
 
 1717 
 
 1803 
 
 1891 
 
 1981 
 
 2074 
 
 2168 
 
 2264 
 
 2362 
 
 24 1522 
 
 1606 
 
 1693 
 
 1782 
 
 1874 
 
 1967 
 
 2063 
 
 2161 
 
 2262 
 
 2365 
 
 2470 
 
 2577 
 
 26 1649 
 
 1740 
 
 1834 
 
 1931 
 
 2030 
 
 2131 
 
 2235 
 
 2342 
 
 2451 
 
 2562 
 
 2676 
 
 2792 
 
 28 1775 
 
 1874 
 
 1975 
 
 2079 
 
 2186 
 
 2295 
 
 2407 
 
 2522 
 
 2639 
 
 2759 
 
 2882 
 
 3007 
 
 30 1902 
 
 2008 
 
 2116 
 
 2228 
 
 2342 
 
 2459 
 
 2579 
 
 2702 
 
 2828 
 
 2956 
 
 3087 
 
 3222 
 
 32 2029 
 
 2142 
 
 2258 
 
 2376 
 
 2498 
 
 2623 
 
 2751 
 
 2882 
 
 3016 
 
 3153 
 
 3293 
 
 3436 
 
 34 2156 
 
 2276 
 
 2399 
 
 2525 
 
 2654 
 
 2787 
 
 2923 
 
 3062 
 
 3205 
 
 3350 
 
 3499 
 
 3651 
 
 36 2283 
 
 2410 
 
 2540 
 
 2673 
 
 2810 
 
 2951 
 
 3095 
 
 3242 
 
 3393 
 
 3547 
 
 3705 
 
 3866 
 
 38 2410 
 
 2543 
 
 2681 
 
 2822 
 
 2967 
 
 3115 
 
 3267 
 
 3422 
 
 3582 
 
 3744 
 
 3911 
 
 4081 
 
 40 2536 
 
 2677 
 
 2822 
 
 2970 
 
 3123 
 
 3279 
 
 3439 
 
 3602 
 
 3770 
 
 3941 
 
 4117 
 
 4295
 
 260 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 BRITISH COLUMBIA LOG SCALE continued 
 
 a DIAMETER IN INCHES 
 
 i 
 
 B 
 
 
 
 
 
 
 
 
 
 
 
 
 3 50 
 
 51 
 
 52 
 
 53 
 
 54 
 
 55 
 
 66 
 
 67 
 
 58 
 
 59 
 
 60 
 
 61 
 
 ft. 
 1 112 
 
 117 
 
 121 
 
 126 
 
 131 
 
 136 
 
 141 
 
 147 
 
 152 
 
 157 
 
 163 
 
 168 
 
 10 1120 
 
 1166 
 
 1214 
 
 1262 
 
 1312 
 
 1362 
 
 1414 
 
 1466 
 
 1519 
 
 1574 
 
 1629 
 
 1685 
 
 12 1343 
 
 1399 
 
 1457 
 
 1515 
 
 1574 
 
 1635 
 
 1696 
 
 1759 
 
 1823 
 
 1888 
 
 1955 
 
 2022 
 
 14 1567 
 
 1633 
 
 1699 
 
 1767 
 
 1837 
 
 1907 
 
 1979 
 
 2052 
 
 2127 
 
 2203 
 
 2280 
 
 2359 
 
 16 1791 
 
 1866 
 
 1942 
 
 2020 
 
 2099 
 
 2180 
 
 2262 
 
 2346 
 
 2431 
 
 2518 
 
 2606 
 
 2696 
 
 18 2015 
 
 2099 
 
 2185 
 
 2272 
 
 2361 
 
 2452 
 
 2545 
 
 2639 
 
 2735 
 
 2832 
 
 2932 
 
 3033 
 
 20 2239 
 
 2332 
 
 2428 
 
 2525 
 
 2624 
 
 2725 
 
 2827 
 
 2932 
 
 3039 
 
 3147 
 
 3258 
 
 3370 
 
 22 2463 
 
 2566 
 
 2670 
 
 2777 
 
 2886 
 
 2997 
 
 3110 
 
 3225 
 
 3343 
 
 3462 
 
 3583 
 
 3707 
 
 24 2687 
 
 2799 
 
 2913 
 
 3030 
 
 3148 
 
 3269 
 
 3393 
 
 3519 
 
 3646 
 
 3777 
 
 3909 
 
 4044 
 
 26 2911 
 
 3032 
 
 3156 
 
 3282 
 
 3411 
 
 3542 
 
 3676 
 
 3812 
 
 3950 
 
 4091 
 
 4235 
 
 4381 
 
 28 3135 
 
 3265 
 
 3399 
 
 3535 
 
 3673 
 
 3814 
 
 3958 
 
 4105 
 
 4254 
 
 4400 
 
 4561 
 
 4718 
 
 30 3359 
 
 3499 
 
 3641 
 
 3787 
 
 3936 
 
 4087 
 
 4241 
 
 4398 
 
 4558 
 
 4721 
 
 4886 
 
 5055 
 
 32 35S3 
 
 3732 
 
 3884 
 
 4039 
 
 4198 
 
 4359 
 
 4524 
 
 4691 
 
 4862 
 
 5036 
 
 5212 
 
 5392 
 
 34 3807 
 
 3965 
 
 4127 
 
 4292 
 
 4460 
 
 4632 
 
 4807 
 
 4985 
 
 5166 
 
 5350 
 
 5538 
 
 5729 
 
 36 4030 
 
 4198 
 
 4370 
 
 4544 
 
 4723 
 
 4904 
 
 5089 
 
 527S 
 
 5470 
 
 5665 
 
 5864 
 
 6066 
 
 38 4254 
 
 4432 
 
 4612 
 
 4797 
 
 4985 
 
 5177 
 
 5372 
 
 5571 
 
 5774 
 
 5980 
 
 6190 
 
 6403 
 
 40 4478 
 
 4665 
 
 4855 
 
 5049 
 
 5247 
 
 5449 
 
 5655 
 
 5864 
 
 6077 
 
 6294 
 
 6515 
 
 6740 
 
 62 
 
 63 
 
 64 
 
 65 
 
 66 
 
 67 
 
 68 
 
 69 
 
 70 
 
 71 
 
 72 
 
 73 
 
 ft. 
 1 174 
 
 180 
 
 186 
 
 192 
 
 198 
 
 204 
 
 210 
 
 217 
 
 223 
 
 230 
 
 237 
 
 243 
 
 10 1742 
 
 1800 
 
 1859 
 
 1919 
 
 1980 
 
 2042 
 
 2105 
 
 2169 
 
 2233 
 
 2299 
 
 2366 
 
 2433 
 
 12 2091 
 
 2160 
 
 2231 
 
 2303 
 
 2376 
 
 2450 
 
 2526 
 
 2602 
 
 2689 
 
 2759 
 
 2839 
 
 2920 
 
 14 2439 
 
 2520 
 
 2603 
 
 26S7 
 
 2772 
 
 2859 
 
 2947 
 
 3036 
 
 3127 
 
 3219 
 
 3312 
 
 3407 
 
 16 2787 
 
 2880 
 
 2975 
 
 3071 
 
 3168 
 
 3267 
 
 3368 
 
 3470 
 
 3573 
 
 3678 
 
 3785 
 
 3893 
 
 18 3136 
 
 3240 
 
 3347 
 
 3454 
 
 3564 
 
 3676 
 
 3789 
 
 3903 
 
 4020 
 
 4138 
 
 42r,S 
 
 4380 
 
 20 3484 
 
 3600 
 
 3718 
 
 3838 
 
 3960 
 
 4084 
 
 4210 
 
 4337 
 
 4467 
 
 4598 
 
 4731 
 
 4867 
 
 22 3833 
 
 3960 
 
 4090 
 
 4222 
 
 4356 
 
 4492 
 
 4631 
 
 4771 
 
 4913 
 
 5058 
 
 5204 
 
 5353 
 
 24 4181 
 
 4320 
 
 4462 
 
 4606 
 
 4752 
 
 4901 
 
 5051 
 
 5205 
 
 5360 
 
 5518 
 
 5677 
 
 5840 
 
 26 4529 
 
 4680 
 
 4834 
 
 4990 
 
 5148 
 
 5309 
 
 5472 
 
 5638 
 
 5807 
 
 5977 
 
 6151 
 
 6327 
 
 28 4878 
 
 5040 
 
 5206 
 
 5374 
 
 5444 
 
 5717 
 
 5893 
 
 6072 
 
 6253 
 
 6437 
 
 6621 
 
 6813 
 
 30 5226 
 
 5401 
 
 5578 
 
 5757 
 
 5950 
 
 6126 
 
 6314 
 
 6506 
 
 6700 
 
 6897 
 
 7097 
 
 7300 
 
 32 5575 
 
 5761 
 
 5949 
 
 6141 
 
 6336 
 
 6534 
 
 6735 
 
 6939 
 
 7146 
 
 7357 
 
 7570 
 
 7787 
 
 34 5923 6121 
 
 6321 
 
 6525 
 
 6732 
 
 6943 
 
 7156 
 
 7373 
 
 7593 
 
 7816 
 
 8043 
 
 8273 
 
 36 62721 6481 
 
 6693 
 
 6909 
 
 7128 
 
 7351 
 
 7577 
 
 7807 
 
 8040 
 
 8276 
 
 8516 
 
 S760 
 
 38 6620 6841 
 
 7065 
 
 7293 
 
 7524 
 
 7759 
 
 7998 
 
 8240 
 
 S48C 
 
 sr:ic, 
 
 8989 
 
 9247 
 
 40 6968 7201 
 
 7437 
 
 7677 
 
 7920 
 
 8168 
 
 8419 
 
 8674 
 
 8933 
 
 9196 
 
 9462 
 
 9734
 
 TABLES RELATING TO PARTS III AND IV 261 
 
 VOLUME TABLE No. 1. WHITE PINE BY THE SCRIBNER 
 RULE 
 
 Breast 
 Diam. 
 Inches 
 
 Total Height of Tree Feet 
 
 60 
 
 60 
 75 
 90 
 100 
 120 
 140 
 160 
 
 70 
 
 70 
 
 85 
 100 
 115 
 135 
 160 
 185 
 210 
 240 
 270 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 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 
 
 80 
 100 
 115 
 135 
 155 
 180 
 210 
 240 
 270 
 310 
 350 
 390 
 440 
 490 
 540 
 
 95 
 115 
 135 
 155 
 180 
 200 
 240 
 270 
 310 
 350 
 390 
 430 
 480 
 540 
 600 
 660 
 720 
 
 
 
 
 
 
 
 
 
 
 
 
 : 
 
 iso 
 
 210 
 230 
 270 
 310 
 350 
 390 
 440 
 480 
 540 
 600 
 660 
 720 
 790 
 850 
 920 
 990 
 
 '270 
 310 
 350 
 390 
 440 
 490 
 540 
 600 
 660 
 730 
 800 
 870 
 940 
 1020 
 1100 
 1180 
 1270 
 1360 
 1450 
 1550 
 1650 
 1750 
 
 
 
 
 
 ;;;; 
 
 
 
 
 
 440 
 460 
 550 
 600 
 670 
 740 
 810 
 890 
 970 
 1040 
 1130 
 1210 
 1300 
 1400 
 1500 
 1600 
 1700 
 1800 
 1900 
 
 
 
 
 '680 
 750 
 830 
 910 
 990 
 1070 
 1150 
 1240 
 1330 
 1420 
 1520 
 1630 
 1750 
 1870 
 1980 
 2100 
 
 
 
 
 
 
 
 
 
 940 
 1020 
 1100 
 1190 
 1280 
 1370 
 1470 
 1580 
 1690 
 1800 
 1920 
 2040 
 2170 
 2300 
 
 1320 
 1420 
 1530 
 1640 
 1750 
 1860 
 1980 
 2100 
 2220 
 2360 
 2500 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Based on 3000 trees cut in New York, the Lake States, 
 and Canada, cut as a rule into 16-foot logs. These scaled 
 with due allowance for crook and breakage, but not for 
 decay. Original.
 
 262 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 2. RED PINE, IN BOARD FEET, BY THE 
 MINNESOTA SCRIBNER RULE 
 
 (Trees under 130 Years Old) 
 
 Diameter 
 S 
 
 Total Height in Feet 
 
 Inches 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 7 
 
 17 
 
 24 
 
 
 
 
 8 
 
 29 
 
 38 
 
 'SO 
 
 - 
 
 
 9 
 
 44 
 
 63 
 
 
 81 
 
 '94 
 
 10 
 
 61 
 
 72 
 
 88 
 
 104 
 
 119 
 
 11 
 
 80 
 
 92 
 
 110 
 
 130 
 
 148 
 
 12 
 
 100 
 
 114 
 
 136 
 
 159 
 
 180 
 
 13 
 
 120 
 
 138 
 
 160 
 
 189 
 
 214 
 
 14 
 
 140 
 
 164 
 
 189 
 
 222 
 
 250 
 
 15 
 
 
 190 
 
 220 
 
 257 
 
 292 
 
 16 
 
 
 
 252 
 
 296 
 
 340 
 
 17 
 
 
 
 
 334 
 
 394 
 
 18 
 
 
 
 
 372 
 
 450 
 
 VOLUME TABLE No. 3. RED PINE, IN BOARD FEET, BY THE 
 MINNESOTA SCRIBNER RULE 
 
 (Trees over 200 Years Old) 
 
 Diameter 
 
 
 Breast 
 
 Total Height in Feet 
 
 High 
 
 
 Inches 
 
 70 
 
 80 
 
 90 
 
 100 
 
 10 
 
 85 
 
 105 
 
 
 
 11 
 
 102 
 
 126 
 
 147 
 
 
 12 
 
 122 
 
 150 
 
 177 
 
 
 13 
 
 144 
 
 176 
 
 210 
 
 
 14 
 
 168 
 
 208 
 
 246 
 
 
 15 
 
 193 
 
 240 
 
 284 
 
 
 16 
 
 220 
 
 275 
 
 323 
 
 383 
 
 17 
 
 250 
 
 311 
 
 370 
 
 435 
 
 18 
 
 282 
 
 349 
 
 417 
 
 490 
 
 19 
 
 317 
 
 390 
 
 468 
 
 551 
 
 20 
 
 355 
 
 433 
 
 523 
 
 616 
 
 21 
 
 396 
 
 480 
 
 582 
 
 685 . 
 
 22 
 
 
 530 
 
 646 
 
 755 
 
 23 
 
 
 584 
 
 715 
 
 830 
 
 24 
 
 
 
 790 
 
 905 
 
 25 
 
 
 
 867 
 
 986 
 
 26 
 
 
 
 951 
 
 1075 
 
 27 
 
 
 '.'.'. 1041 1166
 
 TABLES RELATING TO PARTS III AND IV 263 
 
 The preceding tables from Minnesota timber cut into 
 16-foot logs and scaled straight and sound. By H. H. 
 Chapman. 
 
 VOLUME TABLE No 4. WHITE PINE IN FEET BOARD 
 MEASURE 
 
 (From State Forester of Massachusetts) 
 
 Diameter 
 
 
 Breast 
 
 Total Height of Tree Feet 
 
 High 
 
 
 Inches 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 5 
 
 10 
 
 
 
 
 
 
 
 
 6 
 
 15 
 
 20 
 
 30 
 
 
 
 
 
 
 7 
 
 20 
 
 30 
 
 40 
 
 50 
 
 65 
 
 
 
 
 8 
 
 25 
 
 35 
 
 50 
 
 65 
 
 85 
 
 
 
 
 9 
 
 30 
 
 45 
 
 60 
 
 80 
 
 105 
 
 iis 
 
 '( ' 
 
 
 10 
 
 40 
 
 55 
 
 75 
 
 95 
 
 125 
 
 145 
 
 
 
 11 
 
 
 65 
 
 90 
 
 115 
 
 145 
 
 170 
 
 200 
 
 230 
 
 12 
 
 
 75 
 
 105 
 
 135 
 
 165 
 
 200 
 
 230 
 
 260 
 
 13 
 
 
 85 
 
 120 
 
 155 
 
 190 
 
 235 
 
 260 
 
 295 
 
 14 
 
 
 100 
 
 140 
 
 175 
 
 215 
 
 265 
 
 300 
 
 335 
 
 15 
 
 
 115 
 
 160 
 
 200 
 
 245 
 
 300 
 
 340 
 
 375 
 
 16 
 
 
 
 180 
 
 230 
 
 275 
 
 335 
 
 380 
 
 420 
 
 17 
 
 
 
 
 260 
 
 310 
 
 370 
 
 425 
 
 470 
 
 18 
 
 
 
 
 295 
 
 350 
 
 410 
 
 475 
 
 530 
 
 19 
 
 
 
 
 335 
 
 390 
 
 455 
 
 530 
 
 600 
 
 20 
 
 
 
 
 380 
 
 435 
 
 505 
 
 580 
 
 660 
 
 21 
 
 
 
 
 
 480 
 
 550 
 
 635 
 
 720 
 
 22 
 
 
 
 
 
 520 
 
 595 
 
 680 
 
 780 
 
 23 
 
 
 
 
 
 565 
 
 640 
 
 730 
 
 835 
 
 24 
 
 
 
 
 
 600 
 
 690 
 
 780 
 
 890 
 
 25 
 
 
 
 
 
 645 
 
 740 
 
 830 
 
 940 
 
 26 
 
 ' 
 
 
 
 
 
 
 885 
 
 995 
 
 Gives yield of trees from foot stump to 4 inches in 
 the top as sawed into round or waney-edged, or both round 
 and square-edged, lumber. In the smallest sizes of trees 
 appreciably more may be obtained by cutting to a smaller 
 size in the top.
 
 64 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 5. WHITE PINE IN CORDS 
 (From State Forester of Massachusetts) 
 
 Diameter 
 
 
 Breast 
 High 
 
 Total Height of Tree Feet 
 
 Inches 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 5 
 
 .03 
 
 
 
 
 
 
 
 6 
 
 .03 
 
 .04 
 
 .05 
 
 
 
 
 ; 
 
 7 
 
 .04 
 
 .05 
 
 .07 
 
 .09 
 
 
 
 
 8 
 
 .05 
 
 .07 
 
 .09 
 
 .11 
 
 .13 
 
 
 
 9 
 
 .07 
 
 .09 
 
 .11 
 
 .13 
 
 .16 
 
 
 
 10 
 
 
 .11 
 
 .13 
 
 .16 
 
 .19 
 
 .22 
 
 
 11 
 
 
 .13 
 
 .16 
 
 .19 
 
 .23 
 
 .26 
 
 .30 
 
 12 
 
 
 .15 
 
 .19 
 
 .22 
 
 .27 
 
 .31 
 
 .35 
 
 13 
 
 
 .17 
 
 .22 
 
 .26 
 
 .31 
 
 .36 
 
 .40 
 
 14 
 
 
 
 .25 
 
 .30 
 
 .34 
 
 .41 
 
 .45 
 
 15 
 
 
 
 .28 
 
 .34 
 
 .40 
 
 .46 
 
 .51 
 
 Includes volume of tree above ^ foot from ground and 
 up to 4 inches diameter in the top. 
 
 VOLUME TABLE No. 6. SPRUCE IN CUBIC FEET 
 
 Breast 
 Diam- 
 eter 
 
 Total Height of Tree Feet 
 
 Inches 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 CO 
 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 
 4.9 
 6.3 
 7.8 
 9.8 
 12.0 
 
 5.3 
 
 6.9 
 8.6 
 10.8 
 13.5 
 16.0 
 18.5 
 22. 
 
 5.8 
 7.6 
 9.5 
 12.0 
 150 
 18.0 
 21. 
 24. 
 28. 
 31. 
 
 6.5 
 
 8.5 
 10.6 
 13.4 
 16.5 
 19.7 
 23. 
 27. 
 30. 
 34. 
 38. 
 43. 
 47. 
 52. 
 56. 
 
 '9.6 
 12.0 
 15.0 
 18.2 
 22. 
 25. 
 29. 
 33. 
 37. 
 41. 
 46. 
 50. 
 55. 
 60. 
 
 
 
 
 14 
 17 
 20 
 23 
 27 
 31 
 36 
 40 
 44 
 49 
 54 
 59 
 65 
 72 
 79 
 87 
 96 
 
 
 
 
 '21 
 25 
 29 
 34 
 38 
 43 
 47 
 52 
 58 
 64 
 70 
 77 
 84 
 92 
 100 
 
 '27 
 32 
 36 
 41 
 46 
 51 
 56 
 62 
 69 
 76 
 82 
 88 
 95 
 104 
 
 '34 
 39 
 44 
 49 
 55 
 61 
 67 
 74 
 81 
 87 
 93 
 100 
 108 
 
 '63 
 70 
 77 
 85 
 93 
 98 
 105 
 114 
 123 
 
 '-' 
 
 
 
 
 
 
 
 
 

 
 TABLES RELATING TO PARTS III AND IV 265 
 
 Table No. 6 gives volume of tree from ground to tip 
 exclusive of branches. Includes bark, which is about 12^ 
 per cent of the total volume. Based on 2500 trees cut in 
 Maine, New Hampshire, and New York, calipered each 4 
 feet, computed separately, and averaged. Original. 
 
 This table may without great modification be applied to 
 other soft wood species, regard being had to the remarks on 
 tree form on pages 167 173 of this volume. Balsam fir, 
 however, is believed to be pretty uniformly somewhat 
 slimmer than spruce, having, as would appear from the 
 results of a study on fir made by Mr. Zon of the United 
 States Forest Service, 8 per cent less volume for the same 
 breast diameter and height. 
 
 VOLUME TABLE No. 7. SPRUCE IN FEET, BOARD 
 MEASURE 
 
 Breast 
 
 
 Diam- 
 
 Total Height of Tree Feet 
 
 eter 
 
 
 Inches 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 90 
 
 7 
 
 20 
 
 20 
 
 20 
 
 25 
 
 25 
 
 
 
 
 
 
 8 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 
 
 
 
 g 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 
 
 
 
 10 
 
 40 
 
 45 
 
 50 
 
 60 
 
 65 
 
 70 
 
 80 
 
 
 
 
 11 
 
 
 55 
 
 65 
 
 70 
 
 80 
 
 90 
 
 105 
 
 iis 
 
 
 
 12 
 
 
 65 
 
 75 
 
 85 
 
 100 
 
 110 
 
 120 
 
 135 
 
 i-50 
 
 
 13 
 
 
 75 
 
 CO 
 
 100 
 
 115 
 
 125 
 
 140 
 
 155 
 
 170 
 
 
 14 
 
 
 
 105 
 
 120 
 
 135 
 
 150 
 
 165 
 
 180 
 
 195 
 
 
 15 
 
 
 
 120 
 
 135 
 
 155 
 
 170 
 
 ISO 
 
 205 
 
 220 
 
 
 16 
 
 
 
 
 155 
 
 170 
 
 185 
 
 205 
 
 225 
 
 250 
 
 sis 
 
 17 
 
 
 
 
 170 
 
 190 
 
 210 
 
 230 
 
 250 
 
 275 
 
 350 
 
 18 
 
 
 
 
 185 
 
 210 
 
 235 
 
 255 
 
 280 
 
 310 
 
 390 
 
 19 
 
 
 
 
 205 
 
 235 
 
 260 
 
 290 
 
 320 
 
 350 
 
 430 
 
 20 
 
 
 
 
 235 
 
 265 
 
 295 
 
 325 
 
 355 
 
 385 
 
 470 
 
 21 
 
 
 
 
 
 300 
 
 330 
 
 360 
 
 390 
 
 425 
 
 510 
 
 22 
 
 
 
 
 
 330 
 
 360 
 
 395 
 
 430 
 
 465 
 
 550 
 
 23 
 
 
 
 
 
 360 
 
 400 
 
 435 
 
 470 
 
 510 
 
 600 
 
 24 
 
 
 
 
 
 400 
 
 440 
 
 480 
 
 515 
 
 555 
 
 650 
 
 Based on 2500 trees scaled in 16-foot log lengths up to 
 6 inches in diameter by the Maine rule and discounted 
 from 5 to 10 per cent. Purports to give the yield in edged 
 lumber of average spruce trees in economical woods and 
 mill practice,
 
 266 
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLtTME TABLE No. 8. SPRUCE IN CORDS 
 
 Breast 
 Diameter 
 
 Total Height of Tree Feet 
 
 Inches 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 6 
 
 .04 
 
 .05 
 
 .05 
 
 .06 
 
 
 
 
 
 
 7 
 
 .06 
 
 .06 
 
 .07 
 
 .08 
 
 .09 
 
 
 
 
 
 8 
 
 .07 
 
 .08 
 
 .09 
 
 .10 
 
 .12 
 
 .13 
 
 
 
 
 9 
 
 Of> 
 
 .10 
 
 .12 
 
 .13 
 
 .14 
 
 .16 
 
 
 
 
 10 
 
 .11 
 
 .12 
 
 .14 
 
 .16 
 
 .17 
 
 .19 
 
 .20 
 
 .22 
 
 
 11 
 
 
 .15 
 
 .17 
 
 .19 
 
 .20 
 
 .22 
 
 .24 
 
 .26 
 
 .28 
 
 12 
 
 
 .18 
 
 .20 
 
 .22 
 
 .24 
 
 .26 
 
 .28 
 
 .30 
 
 .32 
 
 13 
 
 
 .21 
 
 .23 
 
 .25 
 
 .27 
 
 .30 
 
 .32 
 
 .34 
 
 .37 
 
 14 
 
 
 
 .26 
 
 .29 
 
 .31 
 
 .34 
 
 .36 
 
 .39 
 
 .42 
 
 15 
 
 
 
 
 .32 
 
 .35 
 
 .38 
 
 .40 
 
 .43 
 
 .47 
 
 16 
 
 
 
 
 .36 
 
 .39 
 
 .42 
 
 .45 
 
 .48 
 
 .52 
 
 17 
 
 
 
 
 .40 
 
 .43 
 
 .46 
 
 .50 
 
 .54 
 
 .59 
 
 18 
 
 
 
 
 .45 
 
 .48 
 
 .50 
 
 .55 
 
 .59 
 
 .64 
 
 19 
 
 
 
 
 .49 
 
 .52 
 
 .56 
 
 .60 
 
 .65 
 
 .70 
 
 20 
 
 
 
 
 .52 
 
 .57 
 
 .62 
 
 .66 
 
 .72 
 
 .77 
 
 Table No. 8 derived from Table No. 6 by deducting 
 a fair allowance for waste in stump, also volume of top above 
 4 inches diameter, and dividing by 96, usual number of cubic 
 feet, solid wood, in a piled cord. The values in this table 
 are very closely confirmed by a table for second growth 
 spruce based on 711 trees that was made up in 1903 by 
 Mr. T. S. Woolsey of the United States Forest Service. 
 
 This table may be used for balsam fir, but in general with 
 some deduction. For the amount of this deduction see 
 the preceding page.
 
 TABLES RELATING TO PARTS III AND IV 267 
 
 YIELD OF HEMLOCK BARK 
 
 Where the tanbark industry is large and well organized, 
 2240 Ibs. of dried bark constitute one cord. One thou- 
 sand feet of hemlock timber, log scale, yields cord 
 usually, up to a cord in some cases. Small, thrifty hem- 
 lock, if closely utilized at the saw, as in parts of New 
 England, yields about cord per M. 
 
 VOLUME TABLE No. 9. HEMLOCK, BY THE SCRIBNER RULE 
 (From Bulletin No. 152, U. S. Dept. Agriculture, by E. H. Frothingham) 
 
 Diam- 
 eter 
 
 Total Height of Tree Feet 
 
 Diam- 
 eter 
 
 breast- 
 high 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 'bark 6 
 of top 
 
 Inches 
 
 Feet Board Measure 
 
 Inches 
 
 8 
 
 5 
 
 7 
 
 13 
 
 20 
 
 25 
 
 
 
 
 6 
 
 9 
 
 8 
 
 14 
 
 22 
 
 29 
 
 35 
 
 40 
 
 
 
 6 
 
 10 
 
 12 
 
 22 
 
 32 
 
 40 
 
 47 
 
 52 
 
 
 
 6 
 
 11 
 
 16 
 
 29 
 
 42 
 
 51 
 
 60 
 
 67 
 
 75 
 
 
 6 
 
 12 
 
 20 
 
 37 
 
 53 
 
 64 
 
 76 
 
 84 
 
 93 
 
 
 7 
 
 13 
 
 
 46 
 
 65 
 
 78 
 
 94 
 
 100 
 
 110 
 
 
 7 
 
 14 
 
 
 56 
 
 77 
 
 95 
 
 110 
 
 130 
 
 140 
 
 
 7 
 
 15 
 
 
 65 
 
 90 
 
 110 
 
 130 
 
 150 
 
 160 
 
 
 8 
 
 16 
 
 
 
 110 
 
 130 
 
 160 
 
 180 
 
 190 
 
 200 
 
 8 
 
 17 
 
 
 
 120 
 
 150 
 
 180 
 
 210 
 
 220 
 
 240 
 
 8 
 
 18 
 
 
 
 140 
 
 180 
 
 210 
 
 240 
 
 260 
 
 280 
 
 8 
 
 19 
 
 
 
 160 
 
 200 
 
 240 
 
 280 
 
 300 
 
 320 
 
 9 
 
 20 
 
 
 
 180 
 
 230 
 
 280 
 
 310 
 
 340 
 
 360 
 
 9 
 
 21 
 
 
 
 200 
 
 260 
 
 310 
 
 350 
 
 380 
 
 410 
 
 9 
 
 22 
 
 
 
 220 
 
 290 
 
 350 
 
 390 
 
 430 
 
 470 
 
 10 
 
 23 
 
 
 
 
 330 
 
 380 
 
 440 
 
 480 
 
 520 
 
 10 
 
 24 
 
 
 
 
 360 
 
 420 
 
 490 
 
 540 
 
 580 
 
 10 
 
 25 
 
 
 
 
 390 
 
 460 
 
 530 
 
 600 
 
 650 
 
 10 
 
 26 
 
 
 
 
 430 
 
 510 
 
 580 
 
 660 
 
 720 
 
 11 
 
 27 
 
 
 
 
 470 
 
 550 
 
 640 
 
 720 
 
 790 
 
 11 
 
 28 
 
 
 
 
 500 
 
 590 
 
 690 
 
 780 
 
 870 
 
 11 
 
 29 
 
 
 
 
 540 
 
 640 
 
 750 
 
 850 
 
 940 
 
 11 
 
 30 
 
 
 
 
 570 
 
 680 
 
 800 
 
 920 
 
 1030 
 
 12 
 
 Based on 534 trees cut in the Lake States and scaled 
 from a 2-foot stump to diameter given in 16.3 foot log 
 lengths. Crook, breakage, and defect not allowed for.
 
 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 10. HEMLOCK IN BOARD FEET 
 (From Report N. H. Forest Commission for 1906-7) 
 
 Diameter 
 
 
 Breast 
 
 Total Height of Tree Feet 
 
 High 
 
 
 Inches 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 6 
 
 5 
 
 
 
 
 
 7 
 
 10 
 
 '26 
 
 'SO 
 
 '42 
 
 
 8 
 
 17 
 
 28 
 
 39 
 
 50 
 
 
 9 
 
 26 
 
 36 
 
 49 
 
 60 
 
 
 10 
 
 36 
 
 46 
 
 59 
 
 71 
 
 "86 
 
 11 
 
 47 
 
 58 
 
 72 
 
 86 
 
 103 
 
 12 
 
 60 
 
 72 
 
 86 
 
 103 
 
 123 
 
 13 
 
 
 88 
 
 104 
 
 124 
 
 148 
 
 14 
 
 
 107 
 
 125 
 
 147 
 
 173 
 
 15 
 
 
 126 
 
 148 
 
 172 
 
 204 
 
 16 
 
 
 148 
 
 171 
 
 200 
 
 240 
 
 17 
 
 
 
 197 
 
 233 
 
 281 
 
 Based on 317 second growth trees grown in New Hamp- 
 shire, cut with good economy (4^ to 6^ inches in the top) 
 and sawed into edged boards and scantling. Figures 
 derived from actual tally of the sawed lumber. 
 
 VOLUME TABLE No. 11. PAPER BIRCH IN CORDS 
 (Adapted from Report of N. H. Forest Commission for 1906-7) 
 
 Diameter 
 
 
 Breast 
 High 
 
 Used Length of Tree Feet 
 
 Inches 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 6 
 
 .02 
 
 .04 
 
 .05 
 
 .07 
 
 .08 
 
 7 
 
 .03 
 
 .05 
 
 .07 
 
 .08 
 
 .10 
 
 8 
 
 .04 
 
 .07 
 
 .09 
 
 .11 
 
 .13 
 
 9 
 
 .05 
 
 .08 
 
 .11 
 
 .13 
 
 .16 
 
 10 
 
 .05 
 
 .10 
 
 .13 
 
 .16 
 
 .19 
 
 11 
 
 .07 
 
 .12 
 
 .16 
 
 .19 
 
 .22 
 
 12 
 
 .08 
 
 .14 
 
 .19 
 
 .22 
 
 .26 
 
 13 
 
 
 .17 
 
 .22 
 
 .26 
 
 .30 
 
 14 
 
 
 .19 
 
 .25 
 
 .30 
 
 .34 
 
 15 
 
 
 .22 
 
 .29 
 
 .34 
 
 .38 
 
 Based on 427 trees cut to be sawed. Volumes given are 
 of used portion of tree only. Original figures by Forest 
 Service men in cubic feet converted into cords at the ratio 
 of 96 cubic feet solid per cord.
 
 TABLES RELATING TO PARTS III AND IV 269 
 
 VOLUME TABLE No. 12. RED OAK IN BOARD FEET 
 (From Report of N. H. Forest Commission for 1906-7) 
 
 Diameter 
 
 
 Breast 
 
 Used Length of Tree Feet 
 
 High 
 
 
 Inches 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 5 
 
 7 
 
 
 
 
 
 6 
 
 9 
 
 15 
 
 
 
 
 7 
 
 14 
 
 22 
 
 '29 
 
 '34 
 
 
 8 
 
 18 
 
 30 
 
 39 
 
 43 
 
 
 9 
 
 25 
 
 40 
 
 48 
 
 58 
 
 
 10 
 
 31 
 
 50 
 
 60 
 
 73 
 
 '99 
 
 11 
 
 37 
 
 63 
 
 74 
 
 90 
 
 118 
 
 12 
 
 44 
 
 78 
 
 89 
 
 110 
 
 143 
 
 13 
 
 54 
 
 93 
 
 107 
 
 132 
 
 174 
 
 14 
 
 65 
 
 109 
 
 126 
 
 160 
 
 208 
 
 15 
 
 
 124 
 
 149 
 
 190 
 
 243 
 
 16 
 
 
 143 
 
 173 
 
 225 
 
 288 
 
 17 
 
 
 163 
 
 201 
 
 262 
 
 330 
 
 18 
 
 
 181 
 
 232 
 
 308 
 
 
 19 
 
 
 202 
 
 265 
 
 356 
 
 
 20 
 
 
 
 223 
 
 300 
 
 405 
 
 
 Based on about 700 trees tallied through saw mills by 
 members of United States Forest Service. Trees from 50 
 to 80 years of age, cut off at from 5 to 9 inches at the top. 
 Lumber sawed round or waney-edged; 85 per cent of 
 the product 1^-inch boards surveyed as 1 inch; balance l- 
 inch plank. 
 
 Table may be used for other second growth hard wood 
 species when similarly cut and manufactured.
 
 270 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 13. PEELED POPLAR IN CORDS 
 (Adapted from Report of N. H. Forest Commission for 190&-7) 
 
 Diameter 
 
 
 Breast 
 High 
 
 Total Height of Tree Feet 
 
 Inches 
 
 50 
 
 60 
 
 70 
 
 80 
 
 5 
 
 .02 
 
 .02 
 
 
 
 6 
 
 .03 
 
 .04 
 
 .05 
 
 
 7 
 
 .05 
 
 .06 
 
 .07 
 
 .08 
 
 8 
 
 .06 
 
 .08 
 
 .10 
 
 .12 
 
 9 
 
 .08 
 
 .11 
 
 .13 
 
 .15 
 
 10 
 
 
 .13 
 
 .16 
 
 .18 
 
 11 
 
 
 
 .20 
 
 .24 
 
 12 
 
 
 
 .25 
 
 
 13 
 
 
 
 .30 
 
 
 Based on 289 trees cut for pulp wood. All diameter 
 measures except diameter breast high taken on the wood 
 surface after peeling off the bark. Original figures in 
 cubic feet, converted into cords at the ratio of 90 cubic 
 feet solid wood per cord. 
 
 TABLE 14. SECOND GROWTH HARD WOODS IN CORDS 
 
 Diam. 
 Breast 
 High 
 Inches 
 
 Total Height of Tree Feet 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 00 
 
 85 
 
 Number Trees per Cord 
 
 3-5 
 5-7 
 
 7-9 
 
 61 
 
 47 
 
 38 
 24 
 
 33 
 20 
 
 31 
 17 
 12 
 
 is 
 
 i4 
 
 10 
 
 '9 
 
 From study by Harvard Forest School on oak thinnings. 
 Wood used up to 2 inches in diameter. 80 cubic feet 
 solid wood per cord. 
 
 The study showed that when the bolts from the trees 
 3 to 5 inches in breast diameter were piled by themselves, 
 there were 250 bolts and 67 cubic feet in a cord; wood 
 from the 5- to 7-inch trees piled together gave 173 bolts 
 and 79 J cubic feet; from the 7- to 9-inch trees, 133 bolts 
 and 91 cubic feet.
 
 TABLES RELATING TO PARTS III AND IV 271 
 
 FORM HEIGHT FACTORS FOR SECOND GROWTH 
 HARD WOODS IN CORDS 
 
 (Utilized to 1 inch in diameter; 80 cubic feet solid wood per cord.) Sec- 
 tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of 
 Wood 
 
 Diameter 
 Breast High 
 
 Basal 
 Area 
 
 Total Height in Feet 
 
 40 
 
 50 
 
 60 
 
 Inches 
 
 Sq. Ft. 
 
 Form Height Factors 
 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 
 .196 
 .267 
 ,349 
 .442 
 
 .545 
 .660 
 .785 
 
 .26 
 .26 
 .27 
 
 .31 
 .31 
 .32 
 .33 
 .35 
 .37 
 .39 
 
 .36 
 .37 
 .38 
 .38 
 .40 
 .43 
 .45 
 
 SAME FOR CHESTNUT EXTRACT WOOD 
 
 (Smaller trees used to 5 inches; 90 cubic feet solid wood per cord.) Sec- 
 tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of 
 Wood 
 
 
 Total Height of Tree in Feet 
 
 Diameter 
 
 
 Breast 
 
 
 
 
 
 
 
 
 
 High 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 '90 
 
 .100 
 
 110 
 
 Inches 
 
 Form Height Factors 
 
 6 
 
 .20 
 
 .23 
 
 .28 
 
 
 
 
 
 
 9 
 
 .18 
 
 .21 
 
 .25 
 
 .30 
 
 
 
 
 
 12 
 
 .18 
 
 .21 
 
 .23 
 
 .27 
 
 .31 
 
 
 
 
 15 
 
 .17 
 
 .20 
 
 .22 
 
 .26 
 
 .29 
 
 .34 
 
 .38 
 
 
 18 
 
 
 .19 
 
 .22 
 
 .25 
 
 .28 
 
 .32 
 
 .36 
 
 
 21 
 
 
 .19 
 
 .21 
 
 .24 
 
 .27 
 
 .31 
 
 .34 
 
 
 24 
 
 
 .18 
 
 .21 
 
 .24 
 
 .27 
 
 .30 
 
 .33 
 
 
 27 
 
 
 .18 
 
 .21 
 
 .24 
 
 .27 
 
 .30 
 
 .32 
 
 .34 
 
 30 
 
 
 
 .20 
 
 .23 
 
 .26 
 
 .29 
 
 .31 
 
 .33 
 
 36 
 
 
 
 
 .22 
 
 .25 
 
 .28 
 
 .31 
 
 .33 
 
 45 
 
 
 
 
 
 .26 
 
 .28 
 
 .30 
 
 .32 
 
 If the cord is 4' X 5' X 8', deduct Vfc from above figures. 
 
 Above tables from "Biltmore Timber Tables," by 
 Howard Krinbill, copyrighted.
 
 272 A MANUAL FOR NORTHERN WOODSMEN 
 
 To use, caliper or estimate the breast diameter of the 
 tree or stand and get the total height. Then multiply 
 the basal area in square feet (see table on page 238) by 
 the proper factor in the table above. The product gives 
 the result in cords. Considerable stands of timber 
 should be divided into diameter groups. 
 
 Example 1. A 10-inch tree is 50 feet high. How much 
 cordwood is hi it? .545 (basal area) X .35 (form height 
 factor) = .19 cord; or 1 -=-.19 = 5j, number of such 
 trees required for a cord if closely utilized. 
 
 Example 2. A bunch of chestnut averaging 80 feet 
 tall and running 13 to 17 inches in diameter, to be cut 
 into extract wood, proves after calipering to have a total 
 basal area of 95 square feet. 95 X .29 (form height 
 factor in second table above) = 27.55, number of cords 
 in the stand. 
 
 VOLUME TABLE No. 16. HARD WOODS, IN BOARD 
 FEET, BY THE SCRIBNER RULE 
 
 (From R. A. Brotherton, Negaunee, Mich.) 
 
 Stump 
 Diameter 
 
 Number of Sixteen-Foot Logs 
 
 Inches 
 
 1 
 
 2 
 
 3 
 
 4 
 
 10 
 
 30 
 
 50 
 
 90 
 
 
 12 
 
 55 
 
 95 
 
 130 
 
 
 14 
 
 80 
 
 140 
 
 180 
 
 
 16 
 
 110 
 
 180 
 
 250 
 
 
 18 
 
 140 
 
 250 
 
 340 
 
 390 
 
 20 
 
 190 
 
 320 
 
 440 
 
 540 
 
 22 
 
 240 
 
 400 
 
 550 
 
 650 
 
 24 
 
 300 
 
 470 
 
 640 
 
 750 
 
 26 
 
 360 
 
 560 
 
 740 
 
 900 
 
 28 
 
 420 
 
 680 
 
 900 
 
 1100 
 
 30 
 
 500 
 
 820 
 
 1100 
 
 1350 
 
 Stumps average about 3 'feet high. One and two log 
 trees may either be short trees, or those that above a 
 certain height are faulty or defective. 
 
 Elm in the sizes above 18 inches yields about 10 per 
 cent more than the above figures.
 
 TABLES RELATING TO PARTS III AND IV 273 
 
 VOLUME TABLE No. 17. NORTHERN HARD WOODS (BIRCH, 
 BEECH AND MAPLE) BY THE SCRIBNER RULE 
 
 (Adapted from Bulletin No. 285, U. S. Forest Service, 
 by E. H. Frothingham) 
 
 Diameter 
 
 Number of 16-foot Logs 
 
 Diameter 
 inside 
 
 high 
 
 1 
 
 H 
 
 2 
 
 21 
 
 3 
 
 3i 
 
 4 
 
 bark of 
 top 
 
 Inches 
 
 Volume Board Feet 
 
 Inches 
 
 9 
 
 20 
 
 30 
 
 45 
 
 
 
 
 
 6 
 
 10 
 
 20 
 
 35 
 
 50 
 
 70 
 
 
 
 
 6 
 
 11 
 
 25 
 
 40 
 
 60 
 
 80 
 
 100 
 
 
 
 6 
 
 12 
 
 25 
 
 50 
 
 70 
 
 95 
 
 120 
 
 140 
 
 
 7 
 
 13 
 
 30 
 
 55 
 
 80 
 
 110 
 
 140 
 
 170 
 
 
 7 
 
 14 
 
 30 
 
 65 
 
 95 
 
 130 
 
 160 
 
 190 
 
 230 
 
 7 
 
 15 
 
 
 70 
 
 110 
 
 140 
 
 180 
 
 220 
 
 260 
 
 8 
 
 16 
 
 
 80 
 
 120 
 
 160 
 
 210 
 
 250 
 
 290 
 
 8 
 
 17 
 
 
 
 140 
 
 190 
 
 240 
 
 280 
 
 320 
 
 9 
 
 18 
 
 
 
 160 
 
 210 
 
 270 
 
 320 
 
 380 
 
 9 
 
 19 
 
 
 
 
 240 
 
 300 
 
 360 
 
 430 
 
 10 
 
 20 
 
 
 
 
 270 
 
 340 
 
 410 
 
 490 
 
 10 
 
 21 
 
 
 
 
 300 
 
 380 
 
 460 
 
 550 
 
 11 
 
 22 
 
 
 
 
 340 
 
 430 
 
 520 
 
 620 
 
 12 
 
 23 
 
 
 
 
 380 
 
 480 
 
 580 
 
 690 
 
 12 
 
 24 
 
 
 
 
 420 
 
 530 
 
 640 
 
 770 
 
 13 
 
 Based on 800 trees cut in the Lake States scaled from 
 taper measures in logs 16.3 feet long from a stump 1 foot 
 high to top diameters found in actual logging: figures 
 evened by curves. As no allowance was made for crook 
 and defect, considerable discount is necessary in most 
 timber. 
 
 NOTE. Comparison between the values in this table and the preceding 
 shows striking differences, and the text indicates how these arose, from dif- 
 ferences in tree form and soundness, lumbering practice, and methods of re- 
 cording and computing. The cruiser is under obligation before he applies 
 either in practice t9 understand these points, and he will do well to check 
 the table he uses with local practice and on local timber. That done, how- 
 ever, the tables will apply throughout the distribution of the species.
 
 274 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 18. LONGLEAF PINE. IN BOARD FEET, 
 BY THE SCRIBNER RULE 
 
 Diam- 
 
 Total Height of Trees Feet 
 
 Diam- 
 
 eter 
 
 
 eter 
 
 breast- 
 
 
 
 
 
 
 
 
 
 
 inside 
 
 high 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 bark 
 of top 
 
 Inches 
 
 Volume 
 
 Inches 
 
 7 
 
 5 
 
 10 
 
 15 
 
 
 
 
 
 
 
 6 
 
 8 
 
 10 
 
 20 
 
 25 
 
 
 
 
 
 
 
 6 
 
 9 
 
 20 
 
 30 
 
 40 
 
 50 
 
 
 
 
 
 
 6 
 
 10 
 
 25 
 
 40 
 
 55 
 
 70 
 
 
 
 
 
 
 6 
 
 11 
 
 35 
 
 50 
 
 70 
 
 90 
 
 110 
 
 
 
 
 
 6 
 
 12 
 
 
 65 
 
 90 
 
 115 
 
 135 
 
 
 
 
 
 6 
 
 13 
 
 
 80 
 
 110 
 
 135 
 
 165 
 
 195 
 
 
 
 
 6 
 
 14 
 
 
 95 
 
 130 
 
 160 
 
 200 
 
 230 
 
 
 
 
 7 
 
 15 
 
 
 115 
 
 150 
 
 190 
 
 2,30 
 
 270 
 
 310 
 
 
 
 7 
 
 16 
 
 
 
 175 
 
 220 
 
 260 
 
 310 
 
 350 
 
 
 
 7 
 
 17 
 
 
 
 200 
 
 250 
 
 295 
 
 350 
 
 400 
 
 450 
 
 
 7 
 
 18 
 
 
 
 225 
 
 280 
 
 330 
 
 390 
 
 450 
 
 500 
 
 
 8 
 
 19 
 
 
 
 250 
 
 310 
 
 370 
 
 440 
 
 500 
 
 560 
 
 620 
 
 8 
 
 20 
 
 
 
 
 350 
 
 420 
 
 490 
 
 560 
 
 630 
 
 700 
 
 8 
 
 21 
 
 
 
 
 390 
 
 470 
 
 550 
 
 620 
 
 700 
 
 780 
 
 8 
 
 22 
 
 
 
 
 440 
 
 520 
 
 610 
 
 690 
 
 780 
 
 860 
 
 9 
 
 23 
 
 
 
 
 490 
 
 580 
 
 670 
 
 770 
 
 860 
 
 950 
 
 9 
 
 24 
 
 
 
 
 
 640 
 
 740 
 
 850 
 
 950 
 
 1050 
 
 10 
 
 25 
 
 
 
 
 
 710 
 
 820 
 
 930 
 
 1040 
 
 1140 
 
 10 
 
 26 
 
 
 
 
 
 780 
 
 890 
 
 1010 
 
 1130 
 
 1240 
 
 11 
 
 27 
 
 
 
 
 
 840 
 
 960 
 
 1090 
 
 1220 
 
 1340 
 
 11 
 
 28 
 
 
 
 
 
 
 1050 
 
 1180 
 
 1310 
 
 1440 
 
 12 
 
 29 
 
 
 
 
 
 
 1140 
 
 1280 
 
 1410 
 
 1550 
 
 12 
 
 30 
 
 
 
 
 
 
 1230 
 
 1380 
 
 1520 
 
 1670 
 
 13 
 
 31 
 
 
 
 
 
 
 
 1480 
 
 1630 
 
 1780 
 
 13 
 
 32 
 
 
 
 
 
 
 
 1580 
 
 1740 
 
 1900 
 
 14 
 
 33 
 
 
 
 
 
 
 
 1690 
 
 I860 
 
 2030 
 
 15 
 
 34 
 
 
 
 
 
 
 
 
 1980 
 
 2160 
 
 16 
 
 35 
 
 
 
 
 
 
 
 
 2110 
 
 2200 
 
 17 
 
 36 
 
 
 
 
 
 
 
 
 2230 
 
 2340 
 
 18 
 
 
 
 
 
 
 
 Based on 614 trees cut in Alabama scaled as a rule in 
 16-foot logs. Height of stump equal diameter breast- 
 high. By Franklin B. Reed of the U. S. Forest Service. 
 Shortleaf pine, as shown by other work of the Service, 
 follows Longleaf closely.
 
 TABLES RELATING TO PARTS III AND IV 275 
 
 VOLUME TABLE No. 19. LOBLOLLY PINE. BY THE 
 SCRIBNER RULE 
 
 (Ashe in Bulletin No. 24, N. C. Geological and Economic Survey) 
 
 Diam- 
 
 Total Height of Tree Feet 
 
 Diam- 
 
 eter 
 breast- 
 
 
 
 eter 
 inside 
 
 
 
 
 
 
 
 
 
 
 
 
 high 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 bark 
 at top 
 
 Inches 
 
 Contents Board Feet 
 
 Inches 
 
 8 
 
 5 
 
 13 
 
 21 
 
 27 
 
 
 
 
 
 
 
 
 5 
 
 9 
 
 12 
 
 22 
 
 32 
 
 42 
 
 52 
 
 
 
 
 
 
 
 6 
 
 10 
 
 18 
 
 30 
 
 42 
 
 55 
 
 65 
 
 
 
 
 
 
 
 6 
 
 11 
 
 25 
 
 40 
 
 54 
 
 68 
 
 81 
 
 93 
 
 
 
 
 
 
 6 
 
 12 
 
 32 
 
 50 
 
 66 
 
 83 
 
 99 
 
 110 
 
 130 
 
 140 
 
 150 
 
 
 
 7 
 
 13 
 
 40 
 
 60 
 
 81 
 
 100 
 
 120 
 
 140 
 
 160 
 
 170 
 
 180 
 
 
 
 7 
 
 14 
 
 
 70 
 
 97 
 
 120 
 
 150 
 
 180 
 
 200 
 
 220 
 
 240 
 
 
 
 8 
 
 15 
 
 
 
 110 
 
 140 
 
 170 
 
 210 
 
 230 
 
 260 
 
 290 
 
 
 
 8 
 
 16 
 
 
 
 120 
 
 160 
 
 200 
 
 240 
 
 270 
 
 300 
 
 330 
 
 
 
 8 
 
 17 
 
 
 
 
 190 
 
 230 
 
 270 
 
 310 
 
 350 
 
 380 
 
 
 
 8 
 
 18 
 
 
 
 
 220 
 
 270 
 
 310 
 
 360 
 
 400 
 
 440 
 
 
 
 9 
 
 19 
 
 
 
 
 
 300 
 
 360 410 
 
 460 
 
 500 
 
 53Q 
 
 
 
 
 20 
 
 
 
 
 
 
 410 i 470 
 
 520 
 
 570 
 
 610 
 
 
 9 
 
 21 
 
 
 
 
 
 
 460 
 
 530 
 
 590 
 
 640 
 
 690 
 
 
 10 
 
 22 
 
 
 
 
 
 
 510 
 
 600 
 
 660 
 
 720 
 
 780 
 
 
 10 
 
 23 
 
 
 
 
 
 
 570 
 
 660 
 
 740 
 
 810 
 
 870 
 
 
 10 
 
 24 
 
 
 
 
 
 
 620 
 
 730 
 
 820 
 
 900 
 
 960 
 
 1020 11 
 
 25 
 
 
 
 
 
 
 
 810 
 
 910 
 
 990 
 
 1060 
 
 11301 11 
 
 26 
 
 
 
 
 
 
 
 890 
 
 990 
 
 1090 
 
 1170 
 
 1240 : 11 
 
 27 
 
 
 
 
 
 
 
 970 
 
 1090 
 
 1190 1280 
 
 1350 12 
 
 28 
 
 
 
 
 
 
 
 1060 1180 
 
 1290 ! 1390 
 
 1470; 12 
 
 29 
 
 
 
 
 
 
 
 1150 1280 
 
 1400 1500 
 
 1590 13 
 
 30 
 
 
 
 
 
 
 
 1240 1380 
 
 1510 
 
 1620 
 
 1710; 13 
 
 31 
 
 
 
 
 
 
 
 .... 1500 
 
 1630 
 
 1750 
 
 1860 13 
 
 32 
 
 
 
 
 
 
 
 
 1610 
 
 1750 
 
 1880 
 
 1980 14 
 
 33 
 
 
 
 
 
 
 
 
 1720 
 
 1870 
 
 2010 
 
 2130 14 
 
 34 
 
 
 
 
 
 
 
 
 1840 
 
 2000 
 
 2140 
 
 2250 15 
 
 35 
 
 
 
 
 
 
 
 
 
 2130 
 
 2270 
 
 2380 15 
 
 36 
 
 
 
 
 
 
 
 
 
 2270 
 
 2400 
 
 2510 15 
 
 Based on measurement of about 3000 trees scaled in 
 16.3 foot log lengths (with some shorter logs to avoid waste) 
 from a stump 1 or 1.5 foot high to top diameters stated. 
 Allowance made for normal but not excessive crook, and 
 not for defect or breakage. With the same outside dimen- 
 sions younger trees yield slightly less than old ones : 40 to 
 45 year old trees yield about 10% less than above figures.
 
 276 A MANUAL FOR NORTHERN WOODSMEN 
 
 NOTES ON WESTERN VOLUME TABLES 
 
 The tables which follow are representative and the 
 most reliable in existence; all are in use in work of impor- 
 tance. No one, however, either East or West, should 
 harbor the idea that such tables will work his salvation. 
 
 Few will require caution as to the difference between 
 log scale and saw product. It is well understood that de- 
 fect has to be specially allowed for. The big part break- 
 age plays in the yield of Coast timber was emphasized in 
 earlier pages. 
 
 The fact that trees may have been scaled for a volume 
 table by a scale rule different from the one by which 
 timber in question is actually to be scaled will be con- 
 sidered of consequence only if the two rules vary enough 
 to signify among the inevitable errors of estimating. If 
 that is the case a comparison should be worked out, not 
 a difficult undertaking. Then varying practice in appli- 
 cation of the scale rule itself might make noticeable 
 difference. The general conclusion is that, before trust- 
 ing any volume table on responsible work, the cruiser 
 had better test it to see how it fits his timber and practice. 
 
 Further, it is indispensable, when such tables are relied 
 on, that the exact nature of the table itself should be un- 
 derstood and field practice governed accordingly. Three 
 different kinds of tables are, in fact, represented. 
 
 In No. 23, for lodgepole pine, total height of the tree 
 is used as the basis of height classification. Some men 
 will find it strange to work hi that dimension; it is habitual 
 with others, however. The general reliability of tables 
 of this kind was discussed on pages 170 and 171, and it 
 is necessary here to add only a suggestion on the head of 
 timber utilization. When the table in question was made 
 up, the logs were scaled to a diameter of 6 inches at the 
 top. If actual utilization in a given locality falls short 
 of that, a very few measurements on down trees will 
 enable a man to make proper deduction. If, for instance, 
 actual utilization of lodgepole pine should fall one log 
 length lower than the standard, a 6-inch 16-foot log,
 
 TABLES RELATING TO PARTS III AND IV 277 
 
 scaling 18 feet by the Scribner rule, may be deducted 
 from the tabular values. It is not a large percentage of 
 sizable timber. If logs are cut and scaled in longer lengths 
 than 16 feet, adjustment may be made on somewhat the 
 same plan, as explained on pages 172 and 173. This 
 last adjustment may be made in any kind of table. 
 
 In most of the western tables total height is neglected 
 and the trees are classified by number of merchantable 
 log lengths. That follows the usual practice in western 
 cruising, practice connected apparently with the great 
 height of the timber. There are, however, two types of 
 tables in this class those in which the timber is scaled 
 up to a single fixed diameter and those in which the top 
 diameter varies with actual utilization. Nos. 28 and 22, 
 tables for Washington hemlock and for yellow pine of 
 the Southwest, illustrate these two types. 
 
 The chances of error in connection with tables of the 
 type of No. 22 (leaving out of account now individual 
 variation of form) may be illustrated as follows: A 
 tree 31 inches in breast diameter with five 16-foot logs is 
 given a volume of 1410 feet and the figure is based (see 
 table 21) on utilization to a 13-inch top limit. If very 
 close utilization should secure another log length above 
 that, the fact would not greatly concern an estimator 
 because it would be so small in volume proportionally. 
 Even if one less log were taken out than the table con- 
 templates, it would amount to but 97 feet, 7 per cent of 
 the tabular volume. What is of more importance, how- 
 ever, is that the height at which the .tree reaches 13 
 inches diameter be estimated correctly. Should this 
 height be set a log length too low and the tree scored down 
 as of four logs instead of five, the value derived from the 
 table would be 1230 feet instead of 1410, 13 per cent too 
 little. An error of equal amount results if the tree is 
 scored a log too long. 
 
 Tables of the type of No. 28, scaling the logs up to a 
 small diameter uniform in all sizes of timber, present an 
 appearance of greater accuracy, but as a matter of fact 
 much larger errors than the above may arise from care-
 
 278 A MANUAL FOR NORTHERN WOODSMEN 
 
 less use of such tables. A chief reason is that men tend 
 strongly to tally timber as yielding the log lengths to 
 which they are accustomed in practice, which in the case 
 of large trees departs widely from the theoretical utiliza- 
 tion. Thus, a 36-inch 5-log hemlock is given in table 28 
 as having 3430 feet of timber. In logging, however, 
 somewhere about 128 feet in log lengths would be got out 
 of it. If, then, a cruiser tallied it as a 4-log tree, his table 
 would give him 2530 feet, over 26 per cent less than the 
 true volume. That might indeed in a given case just about 
 make due breakage and defect allowance, but such a re- 
 sult accidentally arrived at is no justification of the practice. 
 The user of these tables, then, of whatever description, 
 must realize their exact nature and govern his field work 
 accordingly. Judgment also must supplement their use, 
 
 
 Diameter Breast High 
 
 
 
 
 
 Diameter at Top 
 
 Contents by 
 
 
 
 
 of Log 
 
 Decimal 
 
 Tree No. 
 
 Outside 
 Bark 
 
 Inside 
 Bark 
 
 (32 Feet) 
 
 Rule 
 
 
 Inches 
 
 Inches 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 Feet 
 
 1 
 
 27 
 
 23 
 
 19 
 
 16 
 
 13 
 
 10 
 
 
 1,110 
 
 2 
 
 38 
 
 32 
 
 26 
 
 23 
 
 20 
 
 15 
 
 
 2,590 
 
 3 
 
 53 
 
 45 
 
 36 
 
 32 
 
 27 
 
 21 
 
 
 5,030 
 
 4 
 
 84 
 
 74 
 
 62 
 
 57 
 
 51 
 
 46 
 
 36 
 
 19,570 
 
 5 
 
 
 23 
 
 18 
 
 15 
 
 11 
 
 
 
 850 
 
 6 
 
 
 23 
 
 20 
 
 18 
 
 16 
 
 is 
 
 12 
 
 1,750 
 
 7 
 
 26 
 
 24 
 
 20 
 
 17 
 
 14 
 
 8 
 
 
 1,290 
 
 8 
 
 39 
 
 36 
 
 31 
 
 28 
 
 24 
 
 17 
 
 
 2,760 
 
 9 
 
 46 
 
 43 
 
 36 
 
 31 
 
 26 
 
 19 
 
 io 
 
 4,870 
 
 10 
 
 51 
 
 48 
 
 41 
 
 37 
 
 32 
 
 24 
 
 12 
 
 7,040 
 
 11 
 
 
 48 
 
 43 
 
 39 
 
 34 
 
 25 
 
 11 
 
 7,690 
 
 12 
 
 
 48 
 
 40 
 
 37 
 
 32 
 
 21 
 
 11 
 
 6,760 
 
 13 
 
 
 30 
 
 27 
 
 25 
 
 21 
 
 12 
 
 
 2,790 
 
 14 
 
 
 30 
 
 25 
 
 23 
 
 19 
 
 12 
 
 
 2,310 
 
 15 
 
 
 74 
 
 63 
 
 60 
 
 46 
 
 41 
 
 
 17,090 
 
 16 
 
 
 .73 
 
 54 
 
 48 
 
 45 
 
 40 
 
 
 13,280 
 
 and some men, having arrived at direct, first-hand grasp 
 of timber quantity, find tables of use only incidentally. 
 
 On pages 196 to 197 volume tables produced by scal- 
 ing logs decreasing by a regular taper, as if trees were 
 conical in form, were referred to as in wide use in Oregon
 
 TABLES RELATING TO PARTS III AND IV 279 
 
 and Washington. In the application of these to standing 
 timber somewhat the same difficulties are met as above, 
 while others arise due to the fact that only a very unusual 
 tree throughout its merchantable length has a true taper. 
 Normal and also unusual relations in northwestern trees 
 are illustrated above. The inference is easy that tables 
 of the kind mentioned are best left to the use of experts. 
 
 The first four of the above sets of figures, for Douglas 
 fir, represent normal form. The body of the tree is seen 
 to have less taper than either the butt log or the top; the 
 larger the tree's diameter the faster the taper normally, 
 and that shows in the butt log particularly. On this last 
 fact rests the practice of cruisers of taking base diameter 
 pretty high usually and frequently discounting the diam- 
 eter ascertained by measure. Their effort really is to 
 line the basal diameter with that at the top of the first 
 log and those above it. 
 
 Trees No. 5 and 6 are representative of quick and slow 
 taper, or what amounts to the same thing, of short and 
 tall timber. On the same base diameter one tree has 
 twice the contents of the other. No. 6 is a tree of very 
 unusual taper, however. 
 
 Other northwestern species, with the exception of 
 cedar, have form in general similar to fir, but a much 
 thinner bark, as Nos. 7 to 10, for hemlock and noble fir, 
 illustrate. Very heavy taper high up in the trees is also 
 shown here. The bearing of this last fact on the appli- 
 cability of a straight-taper volume table is illustrated 
 below from tree No. 10 in the series. (See also discussion on 
 pages 196 and 197.) The error in one case is 3 per cent, the 
 other 15 per cent. This last error is seen to be incurred 
 by inclusion in the reckoning of a log that contains only 
 2 per cent of the volume of the tree, and that likely to be 
 broken up in felling. The practice of commercial cruisers 
 in neglecting the contents of trees above a diameter equal 
 about half the base diameter is thus rationalized. 
 
 Contents of 4 lower logs, actual taper 6880 feet 
 
 Contents of 4 lower logs, regular taper 6660 feet 
 
 Contents of 5 logs, actual taper 7040 feet 
 
 Contents of 5 logs, regular taper 5960 feet 
 
 Contents of fifth log 160 feet
 
 280 A MANUAL FOR NORTHERN WOODSMEN 
 
 The remaining figures illustrate variation of form and 
 irregularity. Nos. 11 and 12, having the same diameter 
 breast high and also at the top of the logs used, are yet 
 13 per cent apart in contents, while the second pair of 
 matched trees differ by 19 per cent, of the average value 
 in each cas*e. The taper of the body of these trees is 
 regular, however; the variation is in the butt and top 
 log sections, the former being far more significant. Trees 
 Nos. 15 and 16 show some real irregularity, though noth- 
 ing extreme. Much wider departures from type than 
 any of these could in fact be chosen. 
 
 In conclusion, a contrast will be drawn between present 
 commercial methods and the use of volume tables. In 
 the construction of these it is customary to throw out 
 swell butt and other abnormality of form, and, that 
 done, the tables derive strength from the law of averages. 
 Single trees may depart from the type and a certain 
 amount of variation goes with age, but the table, based 
 on a large number of trees and applied to large numbers, 
 if that is done in the same way the measures behind the table 
 were taken, gives results that are trustworthy within 
 reasonable limits. Present-day commercial estimates may 
 be equally correct, but that depends on a different thing 
 on the ability of the cruiser to size up each tree as 
 seen, on the basis of his training of every description.
 
 TABLES RELATING TO PARTS III AND IV 281 
 
 VOLUME TABLE No. 20. WESTERN WHITE PINE, IN 
 BOARD FEET. BY THE SCRIBNER RULE 
 
 (From Bulletin No. 36, U. S. Forest Service) 
 
 Diam- 
 eter 
 
 Number of Sixteen-Foot Logs 
 
 
 breast- 
 
 
 
 
 
 
 
 
 
 
 Basis 
 
 high 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 
 Inches 
 
 Volume Board Feet 
 
 Trees 
 
 8 
 
 40 
 
 60 
 
 85 
 
 105 
 
 
 
 
 
 
 7 
 
 9 
 
 45 
 
 70 
 
 95 
 
 120 
 
 
 
 
 
 
 40 
 
 10 
 
 55 
 
 85 
 
 110 
 
 140 
 
 165 
 
 
 
 
 
 65 
 
 11 
 
 65 
 
 95 
 
 125 
 
 160 
 
 190 
 
 
 
 
 
 76 
 
 12 
 
 75 
 
 110 
 
 145 
 
 180 
 
 215 
 
 245 
 
 
 
 
 104 
 
 13 
 
 
 125 
 
 165 
 
 200 
 
 240 
 
 280 
 
 
 
 
 76 
 
 14 
 
 
 145 
 
 190 
 
 230 
 
 270 
 
 320 
 
 360 
 
 
 
 107 
 
 15 
 
 
 165 
 
 215 
 
 260 
 
 310 
 
 360 
 
 400 
 
 
 
 86 
 
 16 
 
 
 185 
 
 235 
 
 290 
 
 340 
 
 400 
 
 450 
 
 
 
 80 
 
 17 
 
 
 
 255 
 
 320 
 
 380 
 
 450 
 
 510 
 
 570 
 
 
 104 
 
 18 
 
 
 
 275 
 
 350 
 
 420 
 
 500 
 
 570 
 
 640 
 
 
 111 
 
 19 
 
 
 
 295 
 
 380 
 
 460 
 
 550 
 
 630 
 
 720 
 
 
 117 
 
 20 
 
 
 
 320 
 
 410 
 
 500 
 
 600 
 
 690 
 
 790 
 
 880 
 
 115 
 
 21 
 
 
 
 
 430 
 
 540 
 
 650 
 
 760 
 
 870 
 
 980 
 
 103 
 
 22 
 
 
 
 
 460 
 
 580 
 
 710 
 
 830 
 
 960 
 
 1080 
 
 94 
 
 23 
 
 
 
 
 480 
 
 620 
 
 760 
 
 910 
 
 1050 
 
 1190 
 
 83 
 
 24 
 
 
 
 
 510 
 
 660 
 
 820 
 
 980 
 
 1140 
 
 1300 
 
 81 
 
 25 
 
 
 
 
 
 710 
 
 890 
 
 1060 
 
 1240 
 
 1410 
 
 69 
 
 26 
 
 
 
 
 
 760 
 
 950 
 
 1140 
 
 1330 
 
 1520 
 
 64 
 
 27 
 
 
 
 
 
 810 
 
 1010 
 
 1220 
 
 1430 
 
 1630 
 
 65 
 
 28 
 
 
 
 
 
 
 1080 
 
 1300 
 
 1530 
 
 1750 
 
 40 
 
 29 
 
 
 
 
 
 
 1150 
 
 1390 
 
 1630 
 
 1870 
 
 23 
 
 30 
 
 
 
 
 
 
 1220 
 
 1470 
 
 1730 
 
 1990 
 
 28 
 
 31 
 
 
 
 
 
 
 
 1550 
 
 1830 
 
 2110 
 
 14 
 
 32 
 
 
 
 
 
 
 
 1630 
 
 1930 
 
 2230 
 
 9 
 
 33 
 
 
 
 
 
 
 
 1710 
 
 2030 
 
 2360 
 
 14 
 
 34 
 
 
 
 
 
 
 
 
 2140 
 
 2490 
 
 6 
 
 35 
 
 
 
 
 
 
 
 
 2250 
 
 2630 
 
 6 
 
 36 
 
 
 
 
 
 
 
 
 2360 
 
 2770 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 1791 
 
 From timber grown in northern Idaho. 
 
 Trees scaled to a top diameter inside bark of 6 to 8 
 inches. Height of stump 2 to 3 feet. All trees scaled 
 as though sound. Loss by breakage was 4 per cent. 
 Loss due to invisible rot was 5 per cent.
 
 282 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 21. WESTERN YELLOW PINE IN 
 BOARD FEET, BY THE SCRIBNER RULE 
 
 (From Bulletin No. 36, U. S. Forest Service) 
 
 Diam- 
 eter 
 breast- 
 high 
 
 Inches 
 
 Height of Tree-Feet 
 
 Diam- 
 eter of 
 
 ^d*- 
 bark 
 
 Inches 
 
 Basis 
 Trees 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 12 
 
 50 
 
 60 
 
 70 
 
 80 
 
 
 
 
 
 
 8.3 
 
 
 13 
 
 60 
 
 80 
 
 90 
 
 100 
 
 
 
 
 
 
 8.5 
 
 23 
 
 14 
 
 70 
 
 90 
 
 110 
 
 120 
 
 146 
 
 150 
 
 
 
 
 8.7 
 
 48 
 
 15 
 
 90 
 
 110 
 
 130 
 
 150 
 
 170 
 
 180 
 
 166 
 
 
 
 8.9 
 
 91 
 
 16 
 
 110 
 
 130 
 
 160 
 
 180 
 
 200 
 
 220 
 
 230 
 
 240 
 
 
 9.2 
 
 117 
 
 17 
 
 130 
 
 160 
 
 180 
 
 210 
 
 230 
 
 260 
 
 280 
 
 290 
 
 310 
 
 9.4 
 
 142 
 
 18 
 
 160 
 
 180 
 
 210 
 
 240 
 
 270 
 
 300 
 
 320 
 
 350 
 
 370 
 
 9.6 
 
 136 
 
 19 
 
 180 
 
 210 
 
 250 
 
 280 
 
 310 
 
 350 
 
 380 
 
 410 
 
 430 
 
 9.9 
 
 135 
 
 20 
 
 210 
 
 250 
 
 '280 
 
 320 
 
 360 
 
 400 
 
 440 
 
 470 
 
 500 
 
 10.1 
 
 104 
 
 21 
 
 240 
 
 280 
 
 320 
 
 370 
 
 410 
 
 460 
 
 500 
 
 540 
 
 580 
 
 10.4 
 
 127 
 
 22 
 
 280 
 
 310 
 
 360 
 
 410 
 
 470 
 
 520 
 
 570 
 
 620 
 
 670 
 
 10.G 
 
 135 
 
 23 
 
 
 350 
 
 410 
 
 470 
 
 520 
 
 590 
 
 640 
 
 700 
 
 760 
 
 10.9 
 
 103 
 
 24 
 
 
 390 
 
 450 
 
 520 
 
 590 
 
 660 
 
 720 
 
 780 
 
 850 
 
 11.1 
 
 105 
 
 25 
 
 
 430 
 
 500 
 
 580 
 
 650 
 
 730 
 
 800 
 
 880 
 
 950 
 
 11.3 
 
 85 
 
 26 
 
 
 470 
 
 550 
 
 630 
 
 720 
 
 800 
 
 890 
 
 980 
 
 1070 
 
 11.6 
 
 93 
 
 27 
 
 
 
 610 
 
 690 
 
 790 
 
 880 
 
 980 
 
 1080 
 
 1190 
 
 11.9 
 
 83 
 
 28 
 
 
 
 660 
 
 760 
 
 860 
 
 960 
 
 1080 
 
 1190 
 
 1310 
 
 12.1 
 
 63 
 
 29 
 
 
 
 
 820 
 
 930 
 
 1040 
 
 1170 
 
 1300 
 
 1440 
 
 12.4 
 
 51 
 
 30 
 
 
 
 
 880 
 
 1000 
 
 1130 
 
 1270 
 
 1420 
 
 1570 
 
 12.7 
 
 42 
 
 31 
 
 
 
 
 940 
 
 1070 
 
 1220 
 
 1380 
 
 1550 
 
 1720 
 
 12.9 
 
 21 
 
 32 
 
 
 
 
 1010 
 
 1150 
 
 1310 
 
 1490 
 
 1680 
 
 1870 
 
 13.2 
 
 28 
 
 33 
 
 
 
 
 
 1230 
 
 1410 
 
 1610 
 
 1820 
 
 2020 
 
 13.5 
 
 22 
 
 34 
 
 
 
 
 
 1310 
 
 1510 
 
 1740 
 
 1960 
 
 2180 
 
 13.9 
 
 22 
 
 35 
 
 
 
 
 
 1390 
 
 1620 
 
 1870 
 
 2110 
 
 2330 
 
 14.3 
 
 17 
 
 36 
 
 
 
 
 
 1470 
 
 1720 
 
 1990 
 
 2260 
 
 2500 
 
 14.7 
 
 13 
 
 37 
 
 
 
 
 
 
 1810 
 
 2120 
 
 2410 
 
 2660 
 
 15.2 
 
 6 
 
 38 
 
 
 
 
 
 
 1900 
 
 2250 
 
 2550 
 
 2820 
 
 15.8 
 
 4 
 
 39 
 
 
 
 
 
 
 
 2390 
 
 2690 
 
 2980 
 
 16.4 
 
 5 
 
 40 
 
 
 
 
 
 
 
 2530 
 
 2840 
 
 3150 
 
 17.0 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 1822 
 
 Measurements by T. S. Woolsey, Jr., in Arizona. 
 
 Trees scaled to 8-inch top inside bark straight and 
 sound. Allow 3 to 15 per cent for defects. The so-called 
 " black jack " variety requires a further reduction of 
 about 12 per cent, having a smaller volume than the older 
 " yellow pine."
 
 TABLES RELATING TO PARTS III AND IV 
 
 VOLUME TABLE No. 22. WESTERN YELLOW PINE, BY 
 THE SCRIBNER RULE 
 
 Same trees classified by 16-foot log lengths 
 
 Diam- 
 
 Number of 16-foot Logs 
 
 
 eter 
 
 
 
 breast- 
 high 
 
 1 
 
 2 3 
 
 * 
 
 5 
 
 6 
 
 Basis 
 
 Inches 
 
 Volume Board Feet 
 
 Trees 
 
 13 
 
 50 
 
 80 
 
 
 
 
 
 22 
 
 14 
 
 60 
 
 100 
 
 140 
 
 190 
 
 
 
 47 
 
 15 
 
 70 
 
 120 
 
 160 
 
 210 
 
 
 
 93 
 
 16 
 
 80 
 
 140 
 
 180 
 
 240 
 
 
 
 119 
 
 17 
 
 100 
 
 160 
 
 210 
 
 270 
 
 
 
 142 
 
 18 
 
 120 
 
 190 
 
 240 
 
 310 
 
 380 
 
 
 140 
 
 19 
 
 140 
 
 220 
 
 270 
 
 350 
 
 430 
 
 
 138 
 
 20 
 
 160 
 
 250 
 
 310 
 
 400 
 
 490 
 
 
 108 
 
 21 
 
 
 290 
 
 360 
 
 450 
 
 550 
 
 
 128 
 
 22 
 
 
 330 
 
 410 
 
 500 
 
 610 
 
 
 136 
 
 23 
 
 
 380 
 
 460 
 
 560 
 
 680 
 
 
 101 
 
 24 
 
 
 420 
 
 520 
 
 630 
 
 760 
 
 
 108 
 
 25 
 
 
 470 
 
 580 
 
 700 
 
 840 
 
 
 86 
 
 26 
 
 
 530 
 
 640 
 
 780 
 
 920 
 
 ioeo 
 
 95 
 
 27 
 
 
 580 
 
 710 
 
 860 
 
 1010 
 
 1150 
 
 85 
 
 28 
 
 
 630 
 
 790 
 
 950 
 
 1100 
 
 1250 
 
 5 
 
 29 
 
 
 
 870 
 
 1040 
 
 1200 
 
 1360 
 
 54 
 
 30 
 
 
 
 960 
 
 1130 
 
 1300 
 
 1470 
 
 43 
 
 31 
 
 
 
 1050 
 
 1230 
 
 1410 
 
 1590 
 
 25 
 
 32 
 
 
 
 1140 
 
 1340 
 
 1530 
 
 1710- 
 
 28 
 
 33 
 
 
 
 1240 
 
 1460 
 
 1660 
 
 1830 
 
 21 
 
 34 
 
 
 
 1340 
 
 1580 
 
 1780 
 
 1960 
 
 21 
 
 35 
 
 
 
 
 1710 
 
 1910 
 
 2090 
 
 14 
 
 36 
 
 
 
 
 1830 
 
 2040 
 
 2220 
 
 12 
 
 37 
 
 
 
 
 1950 
 
 2160 
 
 2340 
 
 5 
 
 38 
 
 
 
 
 2060 
 
 2280 
 
 2450 
 
 3 
 
 39 
 
 
 
 
 2160 
 
 2400 
 
 2560 
 
 3 
 
 40 
 
 
 
 
 2260 
 
 2520 
 
 "2670 
 
 2 
 
 
 
 
 
 
 
 
 1844 . 
 
 The values in this table are materially higher than 
 those of other Forest Service tables for the same species 
 made in California and Oregon.
 
 284 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 23. LODGEPOLE PINE, IN BOARD 
 FEET, BY THE SCRIBNER RULE 
 (From Bulletin No. 36, U. S. Forest Service) . 
 
 Diam- 
 eter 
 
 Total Height of Tree Feet 
 
 Basis 
 
 high 
 Inches 
 
 50 
 
 60 
 
 70 . 
 
 80 
 
 90 
 
 100 
 
 Trees 
 
 10 
 
 50 
 
 65 
 
 75 
 
 90 
 
 105 
 
 125 
 
 495 
 
 11 
 
 60 
 
 75 
 
 90 
 
 105 
 
 125 
 
 155 
 
 478 
 
 12 
 
 75 
 
 90 
 
 105 
 
 125 
 
 150 
 
 185 
 
 296 
 
 13 
 
 90 
 
 105 
 
 125 
 
 145 
 
 180 
 
 215 
 
 146 
 
 14 
 
 105 
 
 125 
 
 145 
 
 170 
 
 215 
 
 250 
 
 120 
 
 15 
 
 
 140 
 
 170 
 
 200 
 
 250 
 
 285 
 
 113 
 
 16 
 
 
 160 
 
 195 
 
 230 
 
 285 
 
 315 
 
 60 
 
 17 
 
 
 
 225 
 
 260 
 
 315 
 
 350 
 
 44 
 
 18 
 
 
 
 250 
 
 290 
 
 350 
 
 385 
 
 25 
 
 19 
 
 
 
 275 
 
 320 
 
 380 
 
 420 
 
 17 
 
 20 
 
 
 
 300 
 
 345 
 
 415 
 
 460 
 
 14 
 
 Figures by Tower and Redington from trees cut in 
 Gallatin County, Montana. Trees scaled in logs 10 to 
 16 feet long up to 6 inches in top. 
 
 YIELD OF LODGEPOLE PINE IN RAILROAD TIES 
 
 (From Study by Students of University of Washington) 
 
 Diam- 
 eter 
 breast- 
 high 
 
 Inches 
 
 Average Number Obtained per Tree 
 
 Hewn Ties 
 
 Sawed Ties 
 
 Tall 
 over 80' 
 
 Medium 
 60-80' 
 
 Short 
 under Qff 
 
 Tall 
 over 80' 
 
 Medium 
 60-80' 
 
 Short 
 under 60' 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 1.7 
 3.0 
 4.0 
 4.9 
 5.5 
 6.0 
 6.4 
 6.7 
 6.9 
 7.1 
 7.2 
 
 1.5 
 2.7 
 3.5 
 4.0 
 4.4 
 4.7 
 5.0 
 5.0 
 5.0 
 
 1.1 
 
 1.8 
 2.2 
 2.5 
 2.7 
 2.9 
 
 0.9' 
 1.9 
 3.0 
 3.9 
 4.6 
 5.1 
 5.5 
 5.9 
 6.1 
 6.3 
 
 0.8 
 1.7 
 2.6 
 3.3 
 3.8 
 4.2 
 4.2 
 4.2 
 
 0.7 
 1.2 
 1.8 
 2.2 
 2.5 
 
 Results from 267 trees cut in eastern Oregon : Hewn ties 
 from timber not less than 8^ inches in diameter, made 
 7 inches thick; sawed ties, 6 by 8 inches; both kinds, 8 feet 
 long. Average height of 10-inch trees, 68 feet; of 15-inch 
 trees, 85 feet; of 20-inch trees, 93 feet.
 
 TABLES RELATING TO PARTS III AND IV 285 
 
 VOLUME TABLE No. 24. WESTERN LARCH, IN BOARD FEET. 
 BY THE SCRIBNER RULE 
 
 (From Bulletin No. 36, U. S. Forest Service) 
 
 Diam- 
 eter 
 breast- 
 high 
 
 Inchea 
 
 Number of 16-Foot Logs 
 
 Diam- 
 eter 
 of top 
 inside 
 bark 
 
 Inches 
 
 Basis 
 Trees 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 11 
 
 95 
 
 140 
 
 
 
 
 
 
 3 
 
 12 
 
 105 
 
 155 
 
 
 
 
 
 7.3 
 
 15 
 
 13 
 
 120 
 
 165 
 
 220 
 
 
 
 
 7.4 
 
 31 
 
 14 
 
 135 
 
 185 
 
 240 
 
 
 
 
 7.5 
 
 93 
 
 15 
 
 155 
 
 205 
 
 270 
 
 
 
 
 7.6 
 
 114 
 
 16 
 
 175 
 
 230 
 
 295 
 
 380 
 
 
 
 7.7 
 
 119 
 
 17 
 
 195 
 
 260 
 
 325 
 
 415 
 
 
 
 7.8 
 
 128 
 
 18 
 
 220 
 
 285 
 
 365 
 
 455 
 
 
 
 7.9 
 
 100 
 
 19 
 
 240 
 
 315 
 
 400 
 
 490 
 
 
 
 8.0 
 
 93 
 
 20 
 
 265 
 
 345 
 
 435 
 
 535 
 
 645 
 
 
 8.1 
 
 127 
 
 21 
 
 
 380 
 
 475 
 
 585 
 
 705 
 
 
 8.1 
 
 86 
 
 22 
 
 
 415 
 
 520 
 
 635 
 
 775 
 
 
 8.1 
 
 89 
 
 23 
 
 
 450 
 
 560 
 
 695 
 
 840 
 
 ioos 
 
 8.2 
 
 80 
 
 24 
 
 
 485 
 
 605 
 
 745 
 
 905 
 
 1085 
 
 8.2 
 
 79 
 
 25 
 
 
 525 
 
 655 
 
 805 
 
 975 
 
 1180 
 
 8.2 
 
 52 
 
 26 
 
 
 565 
 
 700 
 
 865 
 
 1055 
 
 1275 
 
 8.2 
 
 32 
 
 27 
 
 
 605 
 
 755 
 
 930 
 
 1130 
 
 1375 
 
 8.3 
 
 32 
 
 28 
 
 
 650 
 
 805 
 
 995 
 
 1210 
 
 1470 
 
 8.3 
 
 35 
 
 29 
 
 
 
 855 
 
 1060 
 
 1295 
 
 1565 
 
 8.4 
 
 17 
 
 30 
 
 
 
 910 
 
 1130 
 
 1385 
 
 1670 
 
 8.5 
 
 21 
 
 31 
 
 
 
 
 1205 
 
 1465 
 
 1770 
 
 8.7 
 
 12 
 
 32 
 
 
 
 
 1280 
 
 1560 
 
 1875 
 
 8.8 
 
 10 
 
 33 
 
 
 
 
 1360 
 
 1650 
 
 1975 
 
 9.0 
 
 4 
 
 34 
 
 
 
 
 1440 
 
 1745 
 
 2085 
 
 9.2 
 
 8 
 
 35 
 
 
 
 
 1525 
 
 1845 
 
 2190 
 
 9.4 
 
 1 
 
 36 
 
 
 
 
 1600 
 
 1945 
 
 2295 
 
 9.6 
 
 5 
 
 37 
 
 
 
 
 1685 
 
 2040 
 
 2395 
 
 9.8 
 
 3 
 
 38 
 
 
 
 
 1770 
 
 2145 
 
 2505 
 
 10.0 
 
 2 
 
 39 
 
 
 
 
 1850 
 
 2240 
 
 2610 
 
 10.2 
 
 
 40 
 
 
 
 
 1930 
 
 2340 
 
 2715 
 
 10.4 
 
 
 
 
 
 
 
 
 
 
 1391 
 
 Above table by L. Margolin from timber cut in Flat- 
 head County, Montana. Trees scaled without allowance 
 for breakage and defect, which in this timber amounted 
 to 5 per cent. In addition 5 per cent or more should be 
 allowed for " butts " left if logs are driven.
 
 286 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 25. ENGELMANN SPRUCE, IN BOARD 
 FEET, BY THE SCRIBNER RULE 
 
 (From Bulletin No. 36, U. S. Forest Service) 
 
 Diam- 
 
 
 Diam- 
 
 
 eter 
 breast- 
 high 
 
 Height of Tree Feet 
 
 eter 
 of top 
 inside 
 bark 
 
 Basia 
 
 
 
 
 
 
 
 
 
 
 Inches 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 Inches 
 
 Trees 
 
 8 
 
 15 
 
 20 
 
 30 
 
 
 
 
 
 
 
 6.2 
 
 8 
 
 9 
 
 15 
 
 25 
 
 35 
 
 50 
 
 70 
 
 
 
 
 
 6.3 
 
 19 
 
 10 
 
 20 
 
 30 
 
 45 
 
 60 
 
 80 
 
 
 
 
 
 6.4 
 
 19 
 
 11 
 
 25 
 
 40 
 
 55 
 
 70 
 
 90 
 
 iio 
 
 
 
 
 6.5 
 
 35 
 
 12 
 
 30 
 
 50 
 
 65 
 
 85 
 
 110 
 
 135 
 
 
 
 
 6.6 
 
 45 
 
 13 
 
 40 
 
 60 
 
 80 
 
 100 
 
 130 
 
 160 
 
 
 
 
 6.7 
 
 44 
 
 14 
 
 50 
 
 70 
 
 95 
 
 120 
 
 150 
 
 185 
 
 220 
 
 
 
 6.8 
 
 51 
 
 15 
 
 60 
 
 80 
 
 110 
 
 140 
 
 170 
 
 210 
 
 250 
 
 
 
 6.9 
 
 37 
 
 16 
 
 70 
 
 95 
 
 125 
 
 160 
 
 190 
 
 240 
 
 280 
 
 340 
 
 
 7.0 
 
 61 
 
 17 
 
 
 110 
 
 140 
 
 180 
 
 220 
 
 270 
 
 320 
 
 380 
 
 
 7.1 
 
 57 
 
 18 
 
 
 125 
 
 160 
 
 200 
 
 250 
 
 300 
 
 360 
 
 430 
 
 
 7.1 
 
 55 
 
 19 
 
 
 
 180 
 
 225 
 
 280 
 
 330 
 
 400 
 
 470 
 
 
 7.2 
 
 45 
 
 20 
 
 
 
 205 
 
 250 
 
 310 
 
 360 
 
 440 
 
 520 
 
 600 
 
 7.2 
 
 43 
 
 21 
 
 
 
 230 
 
 280 
 
 340 
 
 400 
 
 480 
 
 560 
 
 650 
 
 7.3 
 
 41 
 
 22 
 
 
 
 250 
 
 310 
 
 370 
 
 440 
 
 520 
 
 610 
 
 700 
 
 7.4 
 
 29 
 
 23 
 
 
 
 
 340 
 
 400 
 
 480 
 
 560 
 
 660 
 
 760 
 
 7.4 
 
 21 
 
 24 
 
 
 
 
 370 
 
 430 
 
 520 
 
 600 
 
 710 
 
 820 
 
 7.5 
 
 21 
 
 25 
 
 
 
 
 
 470 
 
 560 
 
 650 
 
 760 
 
 880 
 
 7.5 
 
 10 
 
 26 
 
 
 
 
 
 500 
 
 600 
 
 700 
 
 820 
 
 950 
 
 7.6 
 
 11 
 
 
 
 
 
 
 
 
 
 
 
 
 652 
 
 From trees cut in Colorado and Utah measured by 
 H. D. Foster. Stump height l|-3 feet.
 
 TABLES RELATING TO PARTS III AND IV 287 
 
 VOLUME TABLE No. 26. DOUGLAS FIR OF THE COAST 
 BY THE SCRIBNER DECIMAL RULE 
 
 (U. S. Forest Service) 
 
 Diameter 
 
 
 Number of Thirty-two-Foot Logs 
 
 at Stump 
 Outside 
 
 Average 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Bark 
 
 
 H 
 
 2 
 
 21 
 
 3 
 
 31 
 
 4 
 
 4* 
 
 5 
 
 6j 
 
 6 
 
 61 
 
 7 
 
 Inches 
 
 Volume Board Feet in Tens 
 
 18 
 
 40 
 
 28 
 
 34 
 
 41 
 
 50 
 
 58 
 
 
 
 
 
 
 
 
 20 
 
 50 
 
 32 
 
 39 
 
 47 
 
 56 
 
 65 
 
 
 
 
 
 
 
 
 22 
 
 62 
 
 
 44 
 
 53 
 
 66 
 
 78 
 
 92 
 
 
 
 
 
 
 
 24 
 
 77 
 
 
 49 
 
 60 
 
 75 
 
 88 
 
 102 
 
 
 
 
 
 
 
 26 
 
 91 
 
 
 55 
 
 68 
 
 84 
 
 '.IS 
 
 112 
 
 122 
 
 
 
 
 
 
 28 
 
 105 
 
 
 01 
 
 76 
 
 95 
 
 110 
 
 124 
 
 130 
 
 
 
 
 
 
 30 
 
 125 
 
 
 GO 
 
 84 
 
 106 
 
 124 
 
 141 
 
 157 
 
 
 
 
 
 
 32 
 
 145 
 
 
 
 92 
 
 115 
 
 138 
 
 162 
 
 182 
 
 
 
 
 
 
 34 
 
 169 
 
 
 
 100 
 
 1 2.-> 
 
 149 
 
 176 
 
 203 
 
 
 
 
 
 
 36 
 
 195 
 
 
 
 120 
 
 138 
 
 164 
 
 192 
 
 '227 
 
 247 
 
 
 
 
 
 38 
 
 228 
 
 
 
 
 
 183 
 
 212 
 
 253 
 
 278 
 
 
 
 
 
 40 
 
 270 
 
 
 
 
 
 
 228 
 
 280 
 
 313 
 
 
 
 
 
 42 
 
 312 
 
 
 
 
 
 
 246 
 
 306 
 
 342 
 
 385 
 
 437 
 
 
 
 44 
 
 365 
 
 
 
 
 
 
 208 
 
 332 
 
 374 
 
 120 
 
 462 
 
 
 
 46 
 
 425 
 
 
 
 
 
 
 280 
 
 358 
 
 403 
 
 454 
 
 494 
 
 
 
 48 
 
 480 
 
 
 
 
 
 
 
 388 
 
 133 
 
 187 
 
 534 
 
 592 
 
 
 50 
 
 535 
 
 
 
 
 
 
 
 420 
 
 468 
 
 528 
 
 581 
 
 644 
 
 
 52 
 
 588 
 
 
 
 
 
 
 
 450 
 
 502 
 
 566 
 
 598 
 
 680 
 
 730 
 
 54 
 
 ' 645 
 
 
 
 
 
 
 
 480 
 
 530 
 
 595 
 
 654 
 
 722 
 
 774 
 
 56 
 
 705 
 
 
 
 
 
 
 
 
 
 630 
 
 697 
 
 771 
 
 830 
 
 58 
 
 765 
 
 
 
 
 
 
 
 
 
 008 
 
 744 
 
 821 
 
 
 60 
 
 830 
 
 
 
 
 
 
 
 
 
 711 
 
 790 
 
 872 
 
 942 
 
 62 
 
 900 
 
 
 
 
 
 
 
 
 
 760 
 
 838 
 
 926 
 
 1009 
 
 64 
 
 972 
 
 
 
 
 
 
 
 
 
 80,8 
 
 886 
 
 985 
 
 1082 
 
 66 
 
 1048 
 
 
 
 
 
 
 
 
 
 S04 
 
 953 
 
 1066 
 
 1171 
 
 68 
 
 1133 
 
 
 
 
 
 
 
 
 
 
 1030 
 
 1147 
 
 1261 
 
 .70 
 
 1226 
 
 
 
 
 
 
 
 
 
 
 1118 
 
 1225 
 
 1345 
 
 72 
 
 1310 
 
 
 
 
 
 
 
 
 
 
 1198 
 
 1312 
 
 1420 
 
 74 
 
 1413 
 
 
 
 
 
 
 
 
 
 
 1285 
 
 1390 
 
 1486 
 
 76 
 
 1515 
 
 
 
 
 
 
 
 
 
 
 1364 
 
 1465 
 
 1556 
 
 Based on 1394 trees measured in logging operations in 
 Lane County, Oregon. Diameters, taken outside bark, 
 on the stump, which was ordinarily about 4 feet high, are 
 closely comparable with the diameter at breast height. 
 Trees scaled without deduction for defect or breakage, to 
 a point 10 inches in diameter at the top, unless unmer- 
 chantable to this point. The majority of the logs were 
 24 feet long, though the length varied from 16 to 36 feet.
 
 288 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 27. DOUGLAS FIR OF THE INTERIOR 
 IN BOARD FEET, BY THE SCRIBNER RULE 
 
 (From Bulletin No. 36, U. S. Forest Service) 
 
 Diam- 
 
 
 Diam- 
 
 
 eter 
 breast- 
 high 
 
 Total Height of Tree Feet 
 
 eter 
 of top 
 inside 
 bark 
 
 Basis 
 
 
 
 
 
 
 
 Inches 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 Inches 
 
 Trees 
 
 8 
 
 20 
 
 30 
 
 
 
 
 
 6.2 
 
 1 
 
 9 
 
 30 
 
 40 
 
 60 
 
 
 
 
 6.3 
 
 7 
 
 10 
 
 40 
 
 60 
 
 70 
 
 
 
 
 6.5 
 
 4 
 
 11 
 
 60 
 
 70 
 
 90 
 
 iio 
 
 
 
 6.6 
 
 23 
 
 12 
 
 70 
 
 90 
 
 110 
 
 130 
 
 
 
 6.7 
 
 53 
 
 13 
 
 90 
 
 110 
 
 130 
 
 160 
 
 190 
 
 
 6.8 
 
 57 
 
 14 
 
 100 
 
 130 
 
 150 
 
 180 
 
 220 
 
 
 6.9 
 
 51 
 
 15 
 
 120 
 
 150 
 
 170 
 
 210 
 
 250 
 
 
 7.0 
 
 55 
 
 16 
 
 140 
 
 170 
 
 200 
 
 240 
 
 290 
 
 
 7.2 
 
 59 
 
 17 
 
 150 
 
 190 
 
 230 
 
 270 
 
 320 
 
 
 7.3 
 
 51 
 
 18 
 
 170 
 
 220 
 
 250 
 
 300 
 
 360 
 
 400 
 
 7.4 
 
 64 
 
 19 
 
 190 
 
 240 
 
 280 
 
 330 
 
 400 
 
 450 
 
 7.5 
 
 57 
 
 20 
 
 210 
 
 270 
 
 320 
 
 370 
 
 440 
 
 500 
 
 7.6 
 
 55 
 
 21 
 
 230 
 
 300 
 
 350 
 
 410 
 
 480 
 
 550 
 
 7.8 
 
 57 
 
 22 
 
 250 
 
 330 
 
 380 
 
 450 
 
 530 
 
 600 
 
 7.9 
 
 50 
 
 23 
 
 
 360 
 
 420 
 
 490 
 
 580 
 
 650 
 
 8.0 
 
 45 
 
 24 
 
 
 390 
 
 450 
 
 540 
 
 630 
 
 710 
 
 8.2 
 
 40 | 
 
 25 
 
 
 420 
 
 490 
 
 580 
 
 690 
 
 770 
 
 8.3 
 
 
 26 
 
 
 450 
 
 530 
 
 630 
 
 750 
 
 830 
 
 8.5 
 
 31 
 
 27 
 
 
 480 
 
 580 
 
 680 
 
 810 
 
 900 
 
 8.6 
 
 22 
 
 28 
 
 
 520 
 
 620 
 
 730 
 
 870 
 
 970 
 
 8.8 
 
 12 
 
 29 
 
 
 
 670 
 
 790 
 
 940 
 
 1040 
 
 8.9 
 
 9 
 
 From timber cut in Wyoming and Idaho measured by 
 Messr. Redington and Peters.
 
 TABLES RELATING TO PARTS III AND IV 
 
 VOLUME TABLE No. 28. WASHINGTON HEMLOCK BY THE 
 
 SCRIBNER DECIMAL RULE 
 (By E. J. Hanzlik of U. S. Forest Service) 
 
 Diameter 
 
 
 Number of Thirty-two-Foot Logs 
 
 Breast: 
 High 
 
 Average 
 
 
 
 
 
 
 
 
 
 
 
 Outside 
 
 
 U 
 
 2 
 
 21 
 
 3 
 
 3J 
 
 4 
 
 4J 
 
 5 
 
 5J 
 
 Bark 
 
 
 
 
 
 
 
 
 
 
 
 Inches 
 
 Volume Board Feet in Tens 
 
 12 
 
 14 
 
 16 
 
 21 
 
 
 
 
 
 
 
 
 13 
 
 20 
 
 17 
 
 23 
 
 28 
 
 32 
 
 
 
 
 
 
 14 
 
 26 
 
 18 
 
 26 
 
 31 
 
 37 
 
 '44 
 
 
 
 
 
 15 
 
 32 
 
 19 
 
 29 
 
 35 
 
 42 
 
 49 
 
 
 
 
 
 16 
 
 39 
 
 21 
 
 32 
 
 39 
 
 47 
 
 55 
 
 
 
 
 
 17 
 
 46 
 
 23 
 
 35 
 
 43 
 
 52 
 
 61 
 
 
 
 
 
 18 
 
 53 
 
 26 
 
 
 47 
 
 58 
 
 68 
 
 78 
 
 
 
 
 19 
 
 62 
 
 
 42 
 
 52 
 
 64 
 
 76 
 
 87 
 
 
 
 
 20 
 
 70 
 
 
 46 
 
 57 
 
 71 
 
 84 
 
 96 
 
 
 
 
 21 
 
 80 
 
 
 50 
 
 62 
 
 77 
 
 91 
 
 104 
 
 
 
 
 22 
 
 90 
 
 
 54 
 
 67 
 
 84 
 
 100 
 
 112 
 
 iio 
 
 
 
 23 
 
 100 
 
 
 57 
 
 73 
 
 90 
 
 108 
 
 122 
 
 148 
 
 
 
 24 
 
 111 
 
 
 
 80 
 
 96 
 
 116 
 
 130 
 
 156 
 
 
 
 25 
 
 122 
 
 
 
 86 
 
 104 
 
 124 
 
 139 
 
 165 
 
 
 
 26 
 
 134 
 
 
 
 92 
 
 112 
 
 133 
 
 148 
 
 174 
 
 
 
 27 
 
 146 
 
 
 
 100 
 
 120 
 
 141 
 
 158 
 
 184 
 
 
 
 28 
 
 158 
 
 
 
 106 
 
 128 
 
 149 
 
 167 
 
 193 
 
 226 
 
 
 29 
 
 170 
 
 
 
 113 
 
 139 
 
 158 
 
 177 
 
 204 
 
 237 
 
 
 30 
 
 183 
 
 
 
 121 
 
 147 
 
 168 
 
 186 
 
 214 
 
 248 
 
 
 31 
 
 197 
 
 
 
 
 156 
 
 177 
 
 197 
 
 226 
 
 260 
 
 
 32 
 
 212 
 
 
 
 
 165 
 
 186 
 
 208 
 
 238 
 
 274 
 
 
 33 
 
 228 
 
 
 
 
 173 
 
 195 
 
 219 
 
 250 
 
 
 
 34 
 
 245 
 
 
 
 
 181 
 
 204 
 
 229 
 
 263 
 
 305 
 
 353 
 
 35 
 
 264 
 
 
 
 
 190 
 
 213 
 
 242 
 
 278 
 
 323 
 
 376 
 
 36 
 
 284 
 
 
 
 
 
 222 
 
 253 
 
 293 
 
 343 
 
 404 
 
 37 
 
 304 
 
 
 
 
 
 231 
 
 266 
 
 310 
 
 366 
 
 436 
 
 38 
 
 326 
 
 
 
 
 
 240 
 
 280 
 
 330 
 
 393 
 
 477 
 
 39 
 
 346 
 
 
 
 
 
 250 
 
 294 
 
 351 
 
 424 
 
 519 
 
 40 
 
 368 
 
 
 
 
 
 259 
 
 308 
 
 378 
 
 460 
 
 561 
 
 Based on 1440 trees, in both pure and mixed stands, 
 measured at logging operations at various points in west- 
 ern Washington. A stump height equal breast diameter 
 allowed. Trees scaled in 16-foot log lengths (with trim- 
 ming allowance) to a diameter inside bark of 8 inches. 
 No deduction for defect or breakage. 
 
 Actual utilization a little over 80 per cent of above 
 figures. 
 
 The true firs are formed very nearly like hemlock.
 
 290 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLES No. 29. WASHINGTON RED CEDAR 
 BY THE SCRIBNER DECIMAL RULE 
 
 TALL TIMBER 
 
 Diameter 
 Breast 
 High 
 
 First 32' Log 
 
 Second 32' Log 
 
 If 
 
 fl 
 
 3 
 
 "3 3 
 
 11 
 
 ' o 
 
 
 
 
 
 
 
 Outside 
 Bark 
 
 Top 
 Diam 
 
 Scale 
 
 %& 
 
 Top 
 .Diam 
 
 Scale 
 
 %of 
 Total 
 
 r 
 
 | S 
 
 Feet 
 
 16 
 
 11 
 
 140 
 
 70 
 
 7 
 
 *60 
 
 30 
 
 
 
 200 
 
 18 
 
 12 
 
 160 
 
 70 
 
 8 
 
 70 
 
 30 
 
 
 
 230 
 
 20 
 
 13 
 
 190 
 
 61 
 
 10 
 
 120 
 
 39 
 
 
 
 310 
 
 22 
 
 14 
 
 230 
 
 62 
 
 11 
 
 140 
 
 38 
 
 
 
 370 
 
 24 
 
 16 
 
 320 
 
 67 
 
 12 
 
 160 
 
 33 
 
 
 
 480 
 
 26 
 
 17 
 
 370 
 
 59 
 
 13 
 
 190 
 
 30 
 
 ii(J) 
 
 
 630 
 
 28 
 
 18 
 
 430 
 
 55 
 
 14 
 
 230 
 
 30 
 
 10 
 
 
 780 
 
 30 
 
 19 
 
 480 
 
 53 
 
 15 
 
 280 
 
 31 
 
 11 
 
 
 900 
 
 32 
 
 21 
 
 610 
 
 56 
 
 16 
 
 320 
 
 29 
 
 12 
 
 
 1090 
 
 34 
 
 22 
 
 670 
 
 51 
 
 17 
 
 370 
 
 28 
 
 13 
 
 ii(i) 
 
 1300 
 
 36 
 
 23 
 
 750 
 
 50 
 
 18 
 
 430 
 
 28 
 
 14 
 
 12(i) 
 
 1490 
 
 38 
 
 24 
 
 810 
 
 48 
 
 19 
 
 480 
 
 28 
 
 15 
 
 10 
 
 1690 
 
 40 
 
 25 
 
 920 
 
 47 
 
 20 
 
 560 
 
 29 
 
 16 
 
 11 
 
 1940 
 
 42 
 
 27 
 
 1100 
 
 49 
 
 21 
 
 610 
 
 27 
 
 17 
 
 11 
 
 2220 
 
 44 
 
 28 
 
 1160 
 
 46 
 
 23 
 
 750 
 
 29 
 
 18 
 
 12 
 
 2500 
 
 46 
 
 29 
 
 1220 
 
 44 
 
 24 
 
 810 
 
 29 
 
 19 
 
 13 
 
 2700 
 
 48 
 
 30 
 
 1310 
 
 42 
 
 25 
 
 920 
 
 30 
 
 20 
 
 14 
 
 3000 
 
 50 
 
 31 
 
 1420 
 
 42 
 
 26 
 
 1000 
 
 30 
 
 21 
 
 15 
 
 3300 
 
 The above and following table are based on field 
 measurements of about 1200 sound and normal trees 
 grown in fully stocked mixed stands in the Puget Sound 
 region, at elevations from 200 to 1000 feet, by A. G. Jack- 
 son of the U. S. Forest Service. Scaled from taper meas- 
 urements in 32-foot logs to diameters stated. Data 
 arranged to promote timber grading. 
 
 Cedar scaled in short lengths, if at the same time it is 
 sound, of good form, and fully utilized, will yield more 
 than these values. On the other hand the tree is so 
 largely subject to swell butt, rot and breakage, that tables 
 must be used with great caution and often discarded 
 altogether.
 
 TABLES RELATING TO PARTS III AND IV 291 
 
 SHORTER TIMBER 
 
 Diam- 
 eter 
 
 First 32' Log 
 
 Second 32' Log 
 
 St 
 
 !< 
 
 ll 
 
 High 
 Outside 
 Bark 
 
 Top 
 Diam. 
 
 Scale 
 
 % of 
 Total 
 
 Top 
 Diam. 
 
 Scale 
 
 % of 
 Total 
 
 "S-5 
 3 Q 
 H 
 
 
 
 H 
 
 Feet 
 
 16 
 
 10 
 
 120 
 
 70 
 
 6 
 
 50 
 
 30 
 
 
 
 170 
 
 18 
 
 11 
 
 140 
 
 70 
 
 7 
 
 60 
 
 30 
 
 
 
 200 
 
 20 
 
 12 
 
 160 
 
 70 
 
 8 
 
 70 
 
 30 
 
 
 
 230 
 
 22 
 
 13 
 
 190 
 
 68 
 
 9 
 
 90 
 
 32 
 
 
 
 280 
 
 24 
 
 14 
 
 210 
 
 69 
 
 10 
 
 120 
 
 31 
 
 
 
 330 
 
 26 
 
 15 
 
 280 
 
 67 
 
 11 
 
 140 
 
 33 
 
 
 
 420 
 
 28 
 
 17 
 
 370 
 
 70 
 
 12 
 
 160 
 
 30 
 
 
 
 530 
 
 30 
 
 18 
 
 430 
 
 63 
 
 13 
 
 190 
 
 28 
 
 10(i) 
 
 
 680 
 
 32 
 
 19 
 
 480 
 
 61 
 
 14 
 
 230 
 
 29 
 
 12(1) 
 
 
 790 
 
 34 
 
 20 
 
 560 
 
 58 
 
 15 
 
 280 
 
 32 
 
 10 
 
 
 960 
 
 36 
 
 22 
 
 670 
 
 57 
 
 17 
 
 370 
 
 31 
 
 11 
 
 
 1180 
 
 
 23 
 
 750 
 
 55 
 
 18 
 
 430 
 
 33 
 
 12 
 
 
 1340 
 
 40 
 
 24 
 
 810 
 
 55 
 
 19 
 
 480 
 
 32 
 
 13 
 
 
 1480 
 
 42 
 
 25 
 
 920 
 
 50 
 
 20 
 
 560 
 
 31 
 
 15 
 
 11(4) 
 
 1830 
 
 44 
 
 27 
 
 1100 
 
 52 
 
 21 
 
 610 
 
 29 
 
 16 
 
 12(1) 
 
 2110 
 
 46 
 
 28 
 
 1160 
 
 48 
 
 23 
 
 750 
 
 31 
 
 17 
 
 11 
 
 2420 
 
 48 
 
 29 
 
 1220 
 
 47 
 
 24 
 
 810 
 
 31 
 
 18 
 
 12 
 
 2620 
 
 50 
 
 30 
 
 1310 
 
 45 
 
 25 
 
 920 
 
 32 
 
 19 
 
 13 
 
 2900 
 
 The trees in this table are really of good length. Meas- 
 urements on short mountain timber are not available. 
 
 Cedar Shingle Bolts. Very defective trees, the break- 
 age of logging operations, and sometimes the whole 
 usable contents of trees above about 20 inches in breast 
 diameter are largely utilized in this form. The bolts are 
 cut 52 inches long and the larger pieces split; they are 
 then piled and measured in the cord 8X4 feet. In 
 present practice from 18 to 25 bolts make a cord which 
 careful measurement has shown to contain of solid wood 
 about 70 per cent of its outside contents. A cord is 
 equivalent to from 500 to 700 feet log scale, less in the 
 smaller sizes of timber.
 
 292 A MANUAL FOR NORTHERN WOODSMEN 
 
 VOLUME TABLE No. 30. SUGAR PINE IN CALIFORNIA 
 BY THE SCRIBNER DECIMAL RULE 
 
 (U. S. Forest Service) 
 
 
 Number of Sixteen-Foot Logs 
 
 M J4 
 
 -a 
 
 
 Diameter 
 
 
 e 
 
 
 Breast- 
 high 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 c ,52 fc" 1 
 
 si* 
 
 11 
 
 Inches 
 
 Volume Board Feet in Tens 
 
 Inches 
 
 
 12 
 
 9 
 
 15 
 
 22 
 
 
 
 
 
 
 
 
 
 8 
 
 
 14 
 
 10 
 
 17 
 
 24 
 
 
 
 
 
 
 
 
 
 8 
 
 'i 
 
 16 
 
 10 
 
 l f ) 
 
 27 
 
 39 
 
 
 
 
 
 
 
 
 g 
 
 2 
 
 18 
 
 13 
 
 20 
 
 30 
 
 43 
 
 
 
 
 
 
 
 
 9 
 
 7 
 
 20 
 
 17 
 
 25 
 
 37 
 
 50 
 
 65 
 
 79 
 
 
 
 
 
 
 9 
 
 28 
 
 22 
 
 
 31 
 
 43 
 
 57 
 
 74 
 
 89 
 
 
 
 
 
 
 9 
 
 23 
 
 24 
 
 
 40 
 
 53 
 
 67 
 
 83 
 
 100 
 
 i22 
 
 
 
 
 
 g 
 
 35 
 
 26 
 
 
 50 
 
 64 
 
 78 
 
 96 
 
 113 
 
 136 
 
 
 
 
 
 9 
 
 35 
 
 28 
 
 
 63 
 
 78 
 
 92 
 
 110 
 
 128 
 
 152 
 
 
 
 
 
 10 
 
 44 
 
 30 
 
 
 80 
 
 94 
 
 108 
 
 125 
 
 144 
 
 170 
 
 189 
 
 
 
 
 10 
 
 53 
 
 32 
 
 
 
 113 
 
 127 
 
 145 
 
 163 
 
 192 
 
 218 
 
 
 
 
 10 
 
 50 
 
 34 
 
 
 
 135 
 
 149 
 
 166 
 
 187 
 
 217 
 
 247 
 
 
 
 
 10 
 
 38 
 
 36 
 
 
 
 100 
 
 173 
 
 191 
 
 213 
 
 246 
 
 279 
 
 310 
 
 
 
 11 
 
 36 
 
 38 
 
 
 
 IS"! 
 
 200 
 
 220 
 
 245 
 
 278 
 
 313 
 
 346 
 
 
 
 11 
 
 40 
 
 40 
 
 
 
 210 
 
 I.'-") 
 
 253 
 
 280 
 
 313 
 
 349 
 
 386 
 
 
 
 11 
 
 41 
 
 42 
 
 
 
 240 
 
 261 
 
 _'ss 
 
 319 
 
 354 
 
 390 
 
 427 
 
 463 
 
 
 11 
 
 43 
 
 44 
 
 
 
 271 
 
 295 
 
 ;,-, 
 
 359 
 
 398 
 
 435 
 
 473 
 
 515 
 
 
 12 
 
 39 
 
 46 
 
 
 
 aiw 
 
 3:50 
 
 365 
 
 401 
 
 445 
 
 482 
 
 523 
 
 567 
 
 
 12 
 
 31 
 
 48 
 
 
 
 337 
 
 366 
 
 105 
 
 446 
 
 493 
 
 532 
 
 575 
 
 623 
 
 
 12 
 
 43 
 
 50 
 
 
 
 
 401 
 
 446 
 
 493 
 
 544 
 
 586 
 
 630 
 
 681 
 
 749 
 
 12 
 
 41 
 
 52 
 
 
 
 
 438 
 
 iyi 
 
 544 
 
 598 
 
 642 
 
 686 
 
 740 
 
 818 
 
 12 
 
 56 
 
 54 
 
 
 
 
 472 
 
 532 
 
 597 
 
 653 
 
 698 
 
 742 
 
 801 
 
 885 
 
 13 
 
 36 
 
 56 
 
 
 
 
 
 575 
 
 652 
 
 711 
 
 756 
 
 800 
 
 862 
 
 953 
 
 13 
 
 25 
 
 58 
 
 
 
 
 
 619 
 
 709 
 
 769 
 
 814 
 
 860 
 
 923 
 
 1022 
 
 13 
 
 25 
 
 60 
 
 
 
 
 
 660 
 
 764 
 
 829 
 
 872 
 
 921 
 
 987 
 
 1090 
 
 14 
 
 28 
 
 62 
 
 
 
 
 
 704 
 
 820 
 
 886 
 
 930 
 
 983 
 
 1051 
 
 1159 
 
 14 
 
 25 
 
 64 
 66 
 
 
 
 
 
 
 876 
 933 
 
 943 
 1000 
 
 990 
 1053 
 
 1046 
 1109 
 
 1116 
 1181 
 
 1227 
 1297 
 
 14 
 14 
 
 27 
 11 
 
 68 
 
 
 
 
 
 
 989 
 
 1058 
 
 1115 
 
 1173 
 
 1250 
 
 1366 
 
 15 
 
 9 
 
 70 
 
 
 
 
 
 
 1048 
 
 1117 
 
 1177 
 
 1239 
 
 1319 
 
 1434 
 
 15 
 
 17 
 
 73 
 
 
 
 
 
 
 
 1176 
 
 1240 
 
 1305 
 
 1388 
 
 1502 
 
 15 
 
 6 
 
 74 
 
 
 
 
 
 
 
 1235 
 
 1303 
 
 1370 
 
 1456 
 
 1570 
 
 16 
 
 2 
 
 76 
 
 
 
 
 
 
 
 1296 
 
 1368 
 
 1435 
 
 1523 
 
 1639 
 
 16 
 
 6 
 
 78 
 
 
 
 
 
 
 
 1358 
 
 1431 
 
 1500 
 
 1590 
 
 1707 
 
 16 
 
 4 
 
 80 
 
 
 
 
 
 
 
 1420 
 
 1497 
 
 1565 
 
 1659 
 
 1778 
 
 16 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 910 
 
 Average stump heights 1.3 to 3.1 feet. 
 Logs scaled in commercial lengths as cut.
 
 SECTION III 
 MISCELLANEOUS TABLES AND INFORMATION 
 
 1. RULES FOR AREA AND VOLUME OF DIFFERENT 
 
 FIGURES 294 
 
 2. WEIGHT OF MATERIALS 296 
 
 3. HANDY EQUIVALENTS 297 
 
 4. NUMBER OF PLANTS PER ACRE WITH DIFFERENT 
 
 SPACING 297 
 
 5. COMPOUND INTEREST TABLE 298 
 
 6. TIME IN WHICH A SUM WILL DOUBLE 298 
 
 7. TABLE OF WAGES AT GIVEN RATES PER MONTH . . 299 
 
 8. THE BILTMORE STICK 301
 
 RULES FOR AREA AND VOLUME OF DIFFERENT 
 FIGURES 
 
 Area of Square. Multiply the length of side by itself, 
 or, as is said, " square " it. 
 
 Area of Rectangle. Multiply the base by the altitude. 
 
 FIGURE A 
 
 Area of Parallelogram. (Figure A.) Multiply base a b 
 by altitude b c, not by b d. If b d and the angle at d are 
 known, b c may be found by the formula 
 
 be = bd X sine of angle at d. 
 
 Area of Triangle. (Figure B.) Multiply base a b by 
 altitude c d and divide by 2. 
 
 Area of Triangle with 3 Sides Given. (Figure B.) Add 
 the 3 sides together and divide the sum by 2. From this 
 half sum take each side in succession. Multiply the half 
 sum and the remainders all together and take the square 
 root. The formula is 
 
 V|(i*-a)(i-6)(J* c) 
 
 Circle. Circumference equals diameter X 3.1416. 
 Area of Circle. (Figure C.) Square the diameter, 
 multiply by 3.1416, and divide by 4.
 
 MISCELLANEOUS TABLES AND INFORMATION 295 
 
 Right-Angled Triangle. The 
 square of the hypothenuse of a 
 right-angled triangle equals the 
 sum of the squares on the other 
 two sides, or, in the figure, 
 
 AB* + AC 2 = BC 2 , 
 01 O + N = M. 
 
 By means of this rule, when any 
 two sides of a right-angled triangle 
 are given, the third can be 
 found. 
 
 Volume of Cylinder. (Figure E.) 
 of the base by the altitude. 
 
 Volume of Cone. (Figure F.) Multiply the area of the 
 base by one-third of the height. 
 
 
 
 ^Ss,// 
 
 A 
 
 
 B 
 
 
 N 
 
 
 FIGURE D 
 
 .) Multiply the area 
 
 FIGURE E 
 
 FIGURE F 
 
 Volume of Prism whether Eight or Oblique. (Figure 
 G.) Multiply area of base by the vertical height. 
 
 Volume of Pyramid. (Figure H.) Multiply base by 
 one-third of the height. 
 
 To Measure the Contents of a Box or Solid with Sides 
 at Right Angles to One Another. Multiply length by 
 breadth by height. If the dimensions are in feet the result 
 will be the contents in cubic feet.
 
 296 A MANUAL FOR NORTHERN WOODSMEN 
 
 WEIGHT OF MATERIALS 
 
 A cubic foot of water weighs 62i Ibs. 
 
 A cubic foot of cast iron weighs about 450 Ibs. 
 
 A cubic foot of wrought iron or steel weighs about .... 480 Ibs. 
 
 Woods when thoroughly seasoned weigh per cubic foot 
 about as follows. Absolute drying in a kiln will lessen 
 these figures about 10 per cent. Green wood is from 50 
 to 80 per cent heavier. 
 
 White pine, white spruce, balsam fir, aspen 27 Ibs. 
 
 Red spruce, hemlock, poplar 30 Ibs. 
 
 Pitch pine, Norway pine, black spruce, white maple .... 31-35 Ibs. 
 White birch, red maple, tamarack, white ash, yellow birch, 
 
 red oak 40-45 Ibs. 
 
 Beech, sugar maple about 48 Ibs. 
 
 White oak, black birch about 52 Ibs. 
 
 A cord of green spruce pulp wood weighs about 4500 Ibs. ; 
 fir and white pine a little more. A cord of dry spruce pulp 
 wood weighs 3000 to 3500 Ibs. Pine, fir, and poplar are 
 somewhat lighter if in exactly the same moisture condition. 
 
 Green hard wood by the cord varies greatly in weight. 
 A cord of white birch spool- wood weighs 6000 to 7000 Ibs. ; 
 sugar maple and yellow birch are 10 per cent heavier; soft 
 maple, ash, basswood, and poplar are somewhat lighter 
 than white birch. For green split cord wood 4000 to 6000 
 Ibs. are the usual limits of weight. Medium dry birch, 
 beech, and maple, split, 66 per cent solid in the pile, weighs 
 about 3000 Ibs. to the cord. 
 
 A thousand feet of old growth spruce logs, Andros- 
 coggin scale, weighs about 6000 Ibs., and this is probably 
 the lower limit for green soft-wood lumber, while southern 
 yellow pine at 8000 to 10,000 Ibs. is the limit in the other 
 direction. Between these limits there is wide variation by 
 reason of scale and quality. 
 
 Seasoning decreases the weight of timber by 30 to 50 
 per cent as a rule, and at the same time increases its 
 strength by 50 to 100 per cent.
 
 MISCELLANEOUS TABLES AND INFORMATION 297 
 
 HANDY EQUIVALENTS 
 
 There are 160 square rods in an acre. 
 
 A square acre is 208.71 feet on a side. 
 
 118 feet is approximately the radius of a circular acre, 
 83 feet of a half acre, and 59 feet of a quarter acre. 
 
 There are 5280 feet in a mile. 
 
 A meter contains 39.37 inches ; a kilometer is .62 mile. 
 
 A liter contains 61 cubic inches, nearly the contents 
 of a quart. 
 
 A hectare contains 2.47 acres. 
 
 A gram weighs 15.432 grains, Troy weight. 
 
 A kilogram or kilo contains 2.2 Ibs avoirdupois. 
 
 There are 231 cubic inches in a U. S. liquid gallon. 
 
 There are 2150.42 cubic inches in a U. S. struck bushel. 
 
 A horsepower is the work done in lifting 33,000 pounds 
 1 foot in 1 minute. A flow of 528 cubic feet of water per 
 minute with 1 foot fall generates one horsepower. 
 
 A miner's inch is the flow of water through an orifice 
 1 inch square under a head (in some States) of 6 inches. 
 In California 50 miner's inches equal 1 cubic foot per 
 second, equal 1.9835 acre feet per day, nearly an inch an 
 hour. In some States 40 miner's inches equal this flow. 
 
 NO. OF PLANTS PER ACRE WITH 
 DIFFERENT SPACING 
 
 Spacing 
 
 No. 
 
 3 X 3 ft. 
 
 4840 
 
 4X4 
 
 2720 
 
 5X5 
 
 1740 
 
 6X6 
 
 1210 
 
 7X7 
 
 890 
 
 8X8 
 
 680 
 
 9X9 
 
 538 
 
 10 X 10 
 
 436
 
 298 A MANUAL FOR NORTHERN WOODSMEN 
 
 COMPOUND INTEREST TABLE 
 
 Amount of $1 principal after any number of years and at 
 given rates percent 
 
 Yrs. 
 
 2% 
 
 24% 
 
 3% 34% | 4% 1 4i% 
 
 5% 
 
 5i% 
 
 6% 
 
 1 
 
 1.020 
 
 1.025 
 
 1.030 1.035 1.040 1.045 
 
 1.050 
 
 1.055 
 
 1.060 
 
 2 
 
 1.040 
 
 1.051 
 
 1.061 1.071 1.082 1.092 
 
 .103 
 
 1.113 
 
 1.124 
 
 3 
 
 1.061 
 
 1.077 
 
 1.093 1.103 .125 .141 
 
 .158 
 
 1.174 
 
 1.191 
 
 4 
 
 .082 
 
 1.104 
 
 1.126 1.148 .170 .193 
 
 .216 
 
 1.239 
 
 1.262 
 
 5 
 
 .104 
 
 1.131 
 
 1.159 , 1.188 .217 .246 
 
 .276 
 
 1.307 
 
 1.338 
 
 6 
 
 .126 
 
 1.160 
 
 1.194 ! 1.229 .265 1.302 
 
 .340 
 
 1.379 
 
 1.419 
 
 7 
 
 .149 
 
 1.189 
 
 1.230 1.272 .316 1.361 
 
 .407 
 
 1.455 
 
 1.504 
 
 8 
 
 .172 
 
 1.218 
 
 1.267 1.317 .369 1.422 
 
 .478 
 
 1.535 
 
 1.594 
 
 9 
 
 .195 
 
 1.249 
 
 1.305 1.363 .423 1.486 
 
 .551 
 
 1.619 
 
 1.660 
 
 10 
 
 1.219 
 
 1.280 
 
 1.344 1.411 .480 1.553 
 
 .629 
 
 1.708 
 
 1.791 
 
 11 
 
 1.243 
 
 1.312 
 
 1.384 1.460 .540 1.623 
 
 710 
 
 1.802 
 
 1.898 
 
 12 
 
 1.268 
 
 1.345 
 
 1.426 1 1.511 .601 1.696 
 
 .796 
 
 1.901 
 
 2.012 
 
 13 
 
 1.294 
 
 1.379 
 
 1.469 i 1.564 .665 4.772 
 
 .886 
 
 2.006 
 
 2.133 
 
 14 
 
 1.320 
 
 1.413 
 
 1.513 ! 1.619 .732 1.852 
 
 1.980 
 
 2.116 
 
 2.261 
 
 15 
 
 1.346 
 
 1.448 
 
 1.55S 1.675 .801 1.935 
 
 2.079 
 
 2.233 
 
 2.397 
 
 16 
 
 1.373 
 
 1.485 
 
 1.605 1.734 .873 2.022 
 
 2.183 
 
 2.355 
 
 2.540 
 
 17 
 
 1.400 
 
 1.522 
 
 1.653 1.795 .948 2.113 
 
 2.292 
 
 2. 485 
 
 2.693 
 
 18 
 
 1.428 
 
 1.560 
 
 1.702 1.853 2.026 2.209 
 
 2.407 
 
 2.622 
 
 2.854 
 
 19 
 
 1.457 
 
 1.599 
 
 1.754 ! 1.923 2.107 2.308 
 
 2.527 
 
 2.766 
 
 3.026 
 
 20 
 
 1.486 
 
 1.639 
 
 1.806 1.990 2.191 12.412 
 
 2.653 
 
 2.918 
 
 3.207 
 
 25 
 
 1.641 
 
 1.854 
 
 2.094 2.363 2.666 3.005 
 
 3.386 
 
 3.813 
 
 4.292 
 
 30 
 
 1.811 
 
 2.098 
 
 2.427 2.807 3.243 3.745 
 
 4.322 
 
 4.984 
 
 5.744 
 
 35 
 
 2.000 
 
 2.373 
 
 2.814 3.334 3.946 4.667 
 
 5.516 
 
 6.514 
 
 7.686 
 
 40 
 
 2.208 
 
 2.685 
 
 3.262 3.959 4.801 5.816 
 
 7.040 
 
 8.513 
 
 10.286 
 
 45 
 
 2.438 
 
 3.038 
 
 3.782 ! 4.702 5.841 J7.248 
 
 8.985 
 
 11.127 
 
 13.765 
 
 8 
 
 2.692 
 
 3.437 
 
 4.384 j 5.585 7.107 19.033 
 
 11.467 
 
 14.542 
 
 18.420 
 
 TIME IN WHICH A SUM WILL DOUBLE 
 
 Rate 
 
 
 
 Per cent 
 
 Simple Interest 
 
 Compound Interest 
 
 2 
 
 50 years 
 
 35 years 
 
 24 
 
 40 years 
 
 28 years 1 month 
 
 3 
 
 33 years 4 months 
 
 23 years 54 months 
 
 t 
 
 28 years 7 months 
 25 years 
 22 years 2} months 
 20 years 
 
 20 years 24 months 
 17 years 8 months 
 15 years 9 months 
 14 years 2* months 
 
 9 
 
 18 years 7 months 
 16 years 8 months 
 
 12 years 114 months 
 11 years 11} months 
 
 Note in above tables that a sum at compound interest doubles when rate 
 of interest X number of years equals (very nearly) 71. With this remem- 
 bered many problems in compound interest can be solved mentally.
 
 MISCELLANEOUS TABLES AND INFORMATION 299 
 
 TABLE OF WAGES, AT GIVEN RATES PER MONTH 
 OF TWENTY-SIX DAYS 
 
 
 
 
 
 
 1 
 
 
 D 
 
 $15 
 
 $16 
 
 $17 
 
 $18 
 
 $19 $20 
 
 $21 
 
 1 
 
 0.58 
 
 0.62 
 
 0.66 0.69 
 
 0.73 0.77 
 
 0.81" 
 
 2 
 
 1.15 
 
 1.23 
 
 1.31 
 
 1.38 
 
 1.46 ! 1.54 
 
 1.62 
 
 3 
 
 1.73 
 
 1.85 
 
 1.96 
 
 2.08 
 
 2.19 
 
 2.31 
 
 2.42 
 
 4 
 
 2.31 
 
 2.46 
 
 2.62 
 
 2.77 
 
 2.92 
 
 3.08 
 
 3.23 
 
 5 
 
 2.88 
 
 3.08 
 
 3.27 
 
 3.46 
 
 3.65 
 
 3.85 
 
 4.04 
 
 6 
 
 3.46 
 
 3.69 
 
 3.92 
 
 4.15 
 
 4.38 
 
 4.62 
 
 4.85 
 
 7 
 
 4.04 
 
 4.31 
 
 4.58 
 
 4.85 
 
 5.12 
 
 5.38 
 
 5.65 
 
 8 
 
 4.62 
 
 4.92 
 
 5.23 
 
 5.54 
 
 5.85 
 
 6.16 
 
 6.46 
 
 9 
 
 5.19 
 
 5.54 
 
 5.88 
 
 6.23 
 
 6.58 
 
 6.92 
 
 7.27 
 
 10 
 
 5.77 
 
 6.15 
 
 6.54 
 
 6.92 
 
 7.31 
 
 7.69 
 
 8.08 
 
 11 
 
 6.35 
 
 6.77 
 
 7.19 
 
 7.62 
 
 8.04 
 
 8.46 
 
 8.88 
 
 12 
 
 6.92 
 
 7.38 
 
 7.85 
 
 8.31 
 
 8.77 
 
 9.23 
 
 9.69 
 
 13 
 
 7.50 
 
 8.00 
 
 8.50 
 
 9.00 
 
 9.50 
 
 10.00 
 
 10.50 
 
 14 
 
 8.08 
 
 8.62 
 
 9.15 
 
 9.69 
 
 10.23 
 
 10.77 
 
 11.31 
 
 15 
 
 8.65 
 
 9.23 
 
 9.81 
 
 10.38 
 
 10.96 
 
 11.54 
 
 12.12 
 
 16 
 
 9.23 
 
 9.85 
 
 10.46 
 
 11.08 
 
 11.69 
 
 12.31 
 
 12.92 
 
 17 
 
 9.81 
 
 10.46 
 
 11.12 
 
 11.77 
 
 12.42 
 
 13.08 
 
 13.73 
 
 18 
 
 10.38 
 
 11.08 
 
 11.77 
 
 12.46 
 
 13.15 
 
 13.85 
 
 14.54 
 
 19 
 
 10.96 
 
 11.69 
 
 12.42 
 
 13.15 
 
 13.88 
 
 14.62 
 
 15.35 
 
 20 
 
 11.54 
 
 12.31 
 
 13.08 
 
 13.85 
 
 14.62 
 
 15.38 
 
 16.15 
 
 21 
 
 12.12 
 
 12.92 
 
 13.73 
 
 14.54 
 
 15.35 
 
 16.16 
 
 16.96 
 
 22 
 
 12.69 
 
 13.54 
 
 14.38 
 
 15.23 
 
 16.08 
 
 16.92 
 
 17.77 
 
 23 
 
 13.27 
 
 14.15 
 
 1504 
 
 15.92 
 
 16.81 
 
 17.69 
 
 18.58 
 
 24 
 
 13.85 
 
 14.77 
 
 15.69 
 
 16.62 
 
 17.54 
 
 18.46 
 
 19.38 
 
 25 
 
 14.42 
 
 15.38 
 
 16.35 
 
 17.31 
 
 18.27 
 
 19.23" 
 
 20.19 
 
 26 
 
 15.00 
 
 16.00 
 
 17.00 
 
 18.00 
 
 19.00 
 
 20.00 
 
 21.00 
 
 D 
 
 $22 
 
 $23 
 
 $24 
 
 $25 
 
 $26 
 
 $27 
 
 $28 
 
 1 
 
 0.85 
 
 0.88 
 
 0.92 
 
 0.96 
 
 1.00 
 
 1.04 
 
 1.08 
 
 2 
 
 1.70 
 
 1.77 
 
 1.85 
 
 1.92 
 
 2.00 
 
 2.07 
 
 2.15 
 
 3 
 
 2.54 
 
 2.65 
 
 2.77 
 
 2.89 
 
 3.00 
 
 3.11 
 
 3.23 
 
 4 
 
 3.38 
 
 3.53 
 
 
 3.84 
 
 4.00 
 
 4.15 
 
 4.31 
 
 5 
 
 4.23 
 
 4.42 
 
 4.62 
 
 4.81 
 
 5.00 
 
 5.19 
 
 5.38 
 
 6 
 
 5.08 
 
 5.30 
 
 5.54 
 
 5.77 
 
 6.00 
 
 6.23 
 
 6.46 
 
 7 
 
 5.92 
 
 6.19 
 
 6.46 
 
 6.73 
 
 7.00 
 
 7.27 
 
 7.54 
 
 8 
 
 6.77 
 
 7.08 
 
 7.38 
 
 
 8.00 
 
 8.30 
 
 8.62 
 
 9 
 
 7.61 
 
 7.96 
 
 8.31 
 
 8.65 
 
 9.00 
 
 9.34 
 
 9.69 
 
 10 
 
 8.46 
 
 8.85 
 
 9.23 
 
 9.61 
 
 10.00 
 
 10.38 
 
 10.77 
 
 11 
 
 9.30 
 
 9.93 
 
 10.15 
 
 10.57 
 
 11.00 
 
 11.42 
 
 11.84 
 
 12 
 
 10.15 
 
 10.62 
 
 11.08 
 
 11.54 
 
 12.00 
 
 12.46 
 
 12.92 
 
 13 
 
 11.00 
 
 11.50 
 
 12.00 
 
 12.50 
 
 13.00 
 
 13.50 
 
 14.00 
 
 14 
 
 11.84 
 
 12.38 
 
 12.92 
 
 13.46 
 
 14.00 
 
 14.54 
 
 15.08 
 
 15 
 
 12.69 
 
 13.27 
 
 13.85 
 
 14.42 
 
 15.00 
 
 15.58 
 
 16.15 
 
 16 
 
 13.54 
 
 14.15 
 
 14.77 
 
 15.38 
 
 16.00 
 
 16.61 
 
 17.23 
 
 17 
 
 14.38 
 
 15.03 
 
 15.70 
 
 16.34 
 
 17.00 
 
 17.65 
 
 18.31 
 
 18 
 
 15.23 
 
 15.91 
 
 16.62 
 
 17.31 
 
 18.00 
 
 18.68 
 
 19.38 
 
 19 
 
 16.07 
 
 16.79 
 
 17.54 
 
 18.27 
 
 19.00 
 
 19.72 
 
 20.46 
 
 20 
 
 16.92 
 
 17.69 
 
 18.46 
 
 19.23 
 
 20.00 
 
 20.76 
 
 21.54 
 
 21 
 
 17.77 
 
 18.56 
 
 19.38 
 
 20.19 
 
 21.00 
 
 21.80 
 
 22.61 
 
 22 
 
 18.61 
 
 19.46 
 
 20.31 
 
 21.15 
 
 22.00 
 
 22.84 
 
 23.69 
 
 23 
 
 19.46 
 
 20.34 
 
 21.23 
 
 22.11 
 
 23.00 
 
 23.88 
 
 24.77 
 
 24 
 
 20.30 
 
 21.22 
 
 22.16 
 
 23.08 
 
 24.00 
 
 24.91 
 
 25.85 
 
 25 
 
 21.15 
 
 22.12 
 
 23.08 
 
 24.04 
 
 25.00 
 
 25.95 
 
 26.92 
 
 26 
 
 22.00 
 
 23.00 
 
 24.00 
 
 25.00 
 
 26.00 
 
 27.00 
 
 28.00
 
 300 A MANUAL FOR NORTHERN WOODSMEN 
 
 TABLE OF WAGES AT GIVEN RATES PER MONTH 
 OF TWENTY-SIX DAYS continued 
 
 D 
 
 $29 
 
 $30 
 
 $31 
 
 $32 
 
 $35 
 
 $40 
 
 $45 
 
 1 
 
 1.12 
 
 1.15 
 
 1.19 
 
 1.23 
 
 1.35 
 
 1.54 
 
 1.73 i 
 
 2 
 
 2.23 
 
 2.30 
 
 2.38 
 
 2.46 
 
 2.69 
 
 3.08 
 
 3.46 ! 
 
 3 
 
 3.34 
 
 3.46 
 
 3.58 
 
 3.69 
 
 4.04 
 
 4.62 
 
 5.19 i 
 
 4 
 
 4.46 
 
 4.62 
 
 4.77 
 
 4.92 
 
 5.38 
 
 6.15 
 
 6.92 
 
 5 
 
 5.58 
 
 5.77 
 
 5.96 
 
 6.15 
 
 673 
 
 7.69 
 
 8.65 
 
 6 
 
 6.69 
 
 6.92 
 
 7.15 
 
 7.38 
 
 8.07 
 
 9.23 
 
 10.39 
 
 7 
 
 7.80 
 
 8.08 
 
 8.35 
 
 8.61 
 
 9.42 
 
 10.77 
 
 12.12 
 
 8 
 
 8.92 
 
 9.23 
 
 9.53 
 
 9.85 
 
 10.77 
 
 12.31 
 
 13.85 
 
 9 
 
 10.04 
 
 10.38 
 
 10.73 
 
 11.08 
 
 12.11 
 
 13.84 
 
 15.58 
 
 10 
 
 11.15 
 
 11.54 
 
 11.92 
 
 12.31 
 
 13.46 
 
 15.38 
 
 17.31 
 
 11 
 
 12.27 
 
 12.69 
 
 13.12 
 
 13.54 
 
 14.81 
 
 16.92 
 
 19.04 
 
 12 
 
 13.38 
 
 13.85 
 
 14.32 
 
 14.77 
 
 16.15 
 
 18.46 
 
 20.77 
 
 13 
 
 14.50 
 
 15.00 
 
 15.50 
 
 16.00 
 
 17.50 
 
 20.00 
 
 22.50 
 
 14 
 
 15.61 
 
 16.15 
 
 16.70 
 
 17.23 
 
 18.84 
 
 21.54 
 
 24.23 
 
 15 
 
 16.73 
 
 17.31 
 
 17.88 
 
 18.46 
 
 20.19 
 
 23.07 
 
 25.96 
 
 16 
 
 17.84 
 
 18.46 
 
 19.07 
 
 19.69 
 
 21.54 
 
 24.61 
 
 27.70 
 
 17 
 
 18.96 
 
 19.62 
 
 20.27 
 
 20.92 
 
 22.88 
 
 26.15 
 
 29.43 
 
 18 
 
 20.07 
 
 20.77 
 
 21.47 
 
 22.15 
 
 24.23 
 
 27.69 
 
 31.16 
 
 19 
 
 21.19 
 
 21.92 
 
 22.65 
 
 23.38 
 
 25.57 
 
 29.23 
 
 33.89 
 
 20 
 
 22.30 
 
 23.08 
 
 23.85 
 
 24.62 
 
 26.92 
 
 30.77 
 
 34.62 
 
 21 
 
 23.42 
 
 24.23 
 
 25.04 
 
 25.85 
 
 28.27 
 
 32.31 
 
 36.35 
 
 22 
 
 24.53 
 
 25.38 
 
 26.23 
 
 27.08 
 
 29.61 
 
 3.3.84 
 
 38.08 
 
 23 
 
 25.65 
 
 26.54 
 
 27.42 
 
 28.31 
 
 30.96 
 
 35.38 
 
 39.81 
 
 24 
 25 
 
 26^6 
 27*8 
 
 27.69 
 28.85 
 
 28.61 
 29.81 
 
 29.54 
 30.77 
 
 32.31 
 33.65 
 
 36.92 
 38.46 
 
 41.54 
 43.27 
 
 26 
 
 29.00 
 
 30.00 
 
 31.00 
 
 32.00 
 
 3500 
 
 40.00 
 
 45.00 
 
 D 
 
 850 
 
 $60 
 
 $70. 
 
 $75 
 
 $80 
 
 $90 
 
 $100 
 
 1 
 
 1.92 
 
 2.31 
 
 2.69 
 
 2.88 
 
 3.08 
 
 3.46 
 
 3.85 
 
 2 
 
 3.85 
 
 4.62 
 
 5.38 
 
 5.77 
 
 6.15 
 
 6.92 
 
 7.69 
 
 3 
 
 5.77 
 
 6.92 
 
 8.08 
 
 8.65 
 
 9.23 
 
 10.38 
 
 11.54 
 
 4 
 
 7.69 
 
 9.23 
 
 10.77 
 
 11.54 
 
 12.31 
 
 13.85 
 
 15.38 
 
 5 
 
 9.61 
 
 11.54 
 
 13.46 
 
 14.42 
 
 15.38 
 
 17.31 
 
 19.23 
 
 6 
 
 11.54 
 
 13.85 
 
 16.15 
 
 17.11 
 
 18.46 
 
 20.77 
 
 23.08 
 
 7 
 
 13.46 
 
 16.15 
 
 18.84 
 
 19.19 
 
 21.54 
 
 24.23 
 
 26.92 
 
 8 
 
 15.38 
 
 18.46 
 
 21.54 
 
 23.08 
 
 24.62 
 
 27.69 
 
 30.77 
 
 9 
 
 17.31 
 
 20.77 
 
 24.23 
 
 25.96 
 
 27.69 
 
 31.16 
 
 34.61 
 
 10 
 
 19.23 
 
 23.08 
 
 26.92 
 
 28.85 
 
 30.77 
 
 34.62 
 
 38.46 
 
 11 
 
 21.15 
 
 25.38 
 
 29.61 
 
 31.73 
 
 33.84 
 
 38.08 
 
 42.31 
 
 12 
 
 23.08 
 
 27.69 
 
 32.31 
 
 34.61 
 
 36.92 
 
 41.54 
 
 46.15 
 
 13 
 
 25.00 
 
 30.00 
 
 35.00 
 
 37.50 
 
 40.00 
 
 45.00 
 
 50.00 
 
 14 
 
 26.92 
 
 32.31 
 
 37.69 
 
 40.38 
 
 43.08 
 
 48.46 
 
 53.85 
 
 15 
 
 28.85 
 
 34.61 
 
 40.38 
 
 43.27 
 
 46.15 
 
 51.92 
 
 57.69 
 
 16 
 
 30.77 
 
 36.92 
 
 43.08 
 
 46.15 
 
 49.23 
 
 55.38 
 
 61.54 
 
 17 
 
 32.69 
 
 39.23 
 
 45.77 
 
 49.04 
 
 52.31 
 
 58.85 
 
 65.38 
 
 18 
 
 34.61 
 
 41.54 
 
 48.46 
 
 51.92 
 
 55.38 
 
 62.31 
 
 69.23 
 
 19 
 
 36.54 
 
 43.84 
 
 51.15 
 
 54.81 
 
 58.46 
 
 65.77 
 
 73.08 
 
 20 
 
 38.46 
 
 46.15 
 
 53.85 
 
 57.69 
 
 61.54 
 
 69.23 
 
 76.92 
 
 21 
 
 40.38 
 
 48.46 
 
 56.54 
 
 60.58 
 
 64.61 
 
 72.69 
 
 80.77 
 
 22 
 
 42.31 
 
 50.77 
 
 59.23 
 
 63.46 
 
 67.69 
 
 76.15 
 
 84.61 
 
 23 
 
 44.23 
 
 53.08 
 
 61.92 
 
 66.35 
 
 70.77 
 
 79.61 
 
 88.46 
 
 24 
 
 46.15 
 
 55.38 
 
 64.62 
 
 69.23 
 
 73.85 
 
 83.08 
 
 92.31 
 
 25 
 
 48.08 
 
 57.69 
 
 67.31 
 
 72.12 
 
 76.92 
 
 86.54 
 
 96.15 
 
 26 
 
 50.00 
 
 60.00 
 
 70.00 
 
 75.00 
 
 80.00 
 
 90.00 
 
 100.00
 
 THE BILTMORE STICK 
 
 301 
 
 THE BILTMORE STICK 
 
 This implement, employed to ascertain the diameter of 
 standing timber when held at arm's length tangent to the 
 trees to be measured, was briefly described on page 163. 
 Relations between tree, stick, and eye when the stick is 
 in use are made clear in the figure, the circle representing 
 a section of a tree -breast high, B X the Biltmore stick, 
 A T the distance from the stick to the eye, and M a 
 radius vertical to the line of sight passing on one side of 
 the tree. With this for a pattern it is clear how the woods- 
 man, after having determined A T as a matter of practice, 
 can plot circles of different diameters, draw tangents to 
 them from A, and ascertain by measurement in each case 
 B C, the proper stick graduation. 
 
 The geometry of the matter is that of similar right- 
 angled triangles, and consideration will show the soundness 
 of the formula appended, from which may be derived 
 
 AT(AT+D) 
 
 the value of B C for circles of any size and for any arm 
 reach. When .the latter, A T, has been determined by 
 trial, the formula becomes simpler. Thus with A T = 25 
 
 BC 
 
 25 D 
 
 or, for D = 10 inches 
 
 V25 (25 + D) 
 250 250 
 
 V625 + 250 29.58 
 
 = 8.45 inches. 
 
 Values of B C for tree diameters from 6 to 60 inches and 
 distances of 23 to 27 inches have been worked out and 
 are published in the- "Proceedings of the Society of Amer- 
 ican Foresters " for 1914, page 48.
 
 302 A MANUAL FOR NORTHERN WOODSMEN 
 
 The Forest Service has employed the Biltmore stick in 
 measuring large timber on the Pacific Coast and else- 
 where, and the tests applied have shown reasonable 
 accuracy. A careful analysis of sources of error 1 has devel- 
 oped the following: 
 
 (a) Tilting the stick and holding it other than vertical 
 to the line of sight to the trees' center are practices to be 
 guarded against, but if reasonable care is used in manipula- 
 tion, errors are negligible. 
 
 (6) In applying values derived from plots or tables to 
 the stick itself, regard must be had to its thickness. The 
 stick may well be beveled, or a steel spline may be inserted 
 into it to carry the graduations. 
 
 (c) Errors arising from measuring a tree the narrow or 
 the wide way are greater than with the c'aliper; hence 
 cross measures are the more desirable. 
 
 (d) It is very easy in practice to vary the distance 
 between the stick and the eye, and this introduces error 
 that is material, though in continued work successive 
 errors tend to balance. 
 
 (e) Men of ordinary height have a constant tendency 
 to measure tree diameter not breast high, but higher, near 
 the eye level. 
 
 To conclude, the Biltmore stick requires to be practi- 
 cally tested before use and constant care in application. 
 More liable to error than the caliper, in ordinary timber 
 it works less rapidly as well. While serviceable in its 
 field, its general use is not to be recommended. 
 
 1 Bruce at previous reference.
 
 CENTRAL UNIVERSITY LIBRARY 
 
 University of California, San Diego 
 
 DATE DUE 
 
 UtC 171983 
 
 
 JuN * 2 RC1 
 
 
 JUN27IQPT 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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