a. LIBKi FACULTY OF FORESTRY UNIVERSITY OF TORONTO A MANUAL FOR NORTHERN WOODSMEN A MANUAL FOR NORTHERN WOODSMEN BY AUSTIN GARY Recently Assistant Professor of Forestry in Harvard University REVISED EDITION CAMBRIDGE HARVARD UNIVERSITY PRESS 1918 FIRST EDITION COPYRIGHT, 1909 BT 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 GARY One thousand copies issued in January, 1918 Til PRINTED AT THE HARVARD UNIVERSITY PRESS CAMBR1DQB, MAM., U.S.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 t nited 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. I'UKI \< I Thr lunik, however, is not materially increased in hulk, 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 mm. in whatever section they are, and whatever may UfM 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 viii CONTENTS PART U. FOREST MAPS PAGE SECTION I. THE TRANSIT 73 1. Adjustments 73 2. Care of the Transit 3. Stadia Measurement 4. Uses of the Transit 80 5. Summary 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 Vin. ADVANTAGES OF A MAP SYSTEM . . . 133 PART III. LOG AND WOOD MEASUREMENT SECTION I. CUBIC CONTENTS 137 SECTION II. CORD WTOOD RULE 138 SECTION III. NEW HAMPSHIRE RULE 'l.ss SECTION IV. BOARD MEASURE 139 General 139 ner and Decimal Rules 141 Spaulding or Columbia River Rule 141 Duylr Rule 141 Maim- Rule 142 New Brunswick Rule 144 Quelx-c Rule 145 8. Tli.-ory of Sale Rules and Clark's International Log Rule 145 SECTION V. NEW YORK STANDARD RULE 147 \ I S( \; OKI I'usi iid US SECTION VII. MILL TAI . 1 ,1 VHI. COBD 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 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 X CONTENTS PAGE 1*. CLARK'S INTERNATIONAL RULE 254 13. SPAULDINO RULE or COLUMBIA RIVER 255 1 1 Human COLUMBIA RULE 258 15. VOLUME TABLES A. Eastern 1. White Pine by the Scribner Rule 261 «, 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 «7. Douglas Fir «,f tin- Interior 288 28. Washington H.-mU-k in Board Measure . . . 289 «9. Washington Red Cedar in Board Measure . . 290 SO. California Sugar Pine in Board Measure ... 292 SECTION III. MisceUaneou* Tables and Information 1. Ruuoi rot AREA AND VOLUME or DIFFERENT . . 294 KJOHT or MATERIALS I HANDY EQUIVALENTS *;>: CONTENTS XI PAGE 4. NUMBER OP 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 1 in SIKYKYOR'S COMPASS I. I !.. Instrument \dju>tinrnt> «>f the Compass Keepiiur the CompUB in Order Si. IIOM II 'I'm: MAGNETIC NEEDLE 7 II. M I:\.SIKKMKNT OF DISTANCE i. UK Surveyor's Chain . Tape 10 3. Marking I 'ins 4. Chaining Practice . . 5. Measuring Inaccessible Lines 6. Stadia Measurement 7. Units of Distance and Area SECTION IV. SURVEYING PRACTICE 1. (tunning a Compass Line (Backsight, Picketing, Needle) 20 2. Try-Li. M-S 22 3. Marking Lines and Corners 23 4. Original Surveys ;:nd Kesurveys ! 5. Age of Spots or Blazes 26 6. Notes 28 7. Party and Cost 28 SECTION V. COMPUTATION AND OFFICE WORK .... 31 averse 31 37 3. Plotting 40 '• ' i l'>i \i;i\«, OP LINKS 43 \ll. < K OHIAIMV. MM. MI:I;IDIVX .... 51 SECTION VI 11 THE UNITED STATES PUBLIC LAND SURVEYS 60 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 bearing. 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. b. 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 la doubled and at the same time made more apparent, ough mastery of this principle will generally enable one to think out the proper method of adjusting all parts of any sun-eying 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 itial. 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 tjie 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 il 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- l»le time should lie in the north and south direction. Balancing Needle. The needle is commonly balanced «>n the pivot I iy a fine brass wire wound around the south • •M.I. It ehaiiiri' ,,f latitude is made, the balance will be dcstro\r.l. ami 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 FOB 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 thi*t 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 Inn- through with accuracy, and a transit or solar instru- ment must I*- us, .I 1 See page 21. Ul 1» 115 110 106 100 100 Weit fl LINES or EQUAL MAGNETIC DECLINATION AND or EQUAL ANJ United States Coaa 80 75 c, CHANGE IN THE UNITED STATES FOR 1915. (From Report of i.d Geodetic Survey.) 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 FOB 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 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 J to J inch wide and No. 30 to IW thick. \\ider 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 timl>cr land surveyor. Some precaution must be taken with steel tapes. \Yheii in use, they should be kept out at full length and never be 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. Fir,. 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 1(1 A MANUAL FOR NORTHERN WOODSMEN as x. Set up at 6 and, turning off a right angle, set a stake r in the range a x. Then ab = bc. 5. Method by 26° 34' Angle. (B) Proceed as before, making the angle b a c = 26° 34' ; then a 6 = 2 6 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 6 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 6, take the bearing of c 6 and thus get the angle a b c. In the table of tangents (I (* look up the tangent of this angle. Then ab FIG. C FIG. D FIG. E 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 o c or 6 c, whichever is easier. Then a b 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 CO0 at c, run out c b to an equal distance. Then, if the work has been done accurately, 6 is in the line and ab = ac=bc. 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 1 FIG. G 6. STADIA MEASUREMENT A substitute for chaining, which has to some extent been employed in forest land surveying and which deserves 18 \ 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- pass sights. 2. Distances over very steep ground can be measured more accurately and quickly than by use 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 A TELESCOPIC SIGHT SURVEYING PRACTICE 19 should be so s'paced 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 33 J 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. £0 A MANUAL FOB 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- t<-r 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 iiurveyor is assured that tlirre 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 com- jKtssman 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 when 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 lint*. 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'. iTrial Line 5ch. 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 ri^lit angles to the try-line, at different points along it. the di-t;in., J/?.4f Oxford Co., Ma/ne Sepf.25 /90S. £-/ne ory//?a//yrv/?by£.Ba//artfJn/794, has been btozedorer some s/'/rce.Auf never resi/ryeyed. £.5. Dearborn, rear cAa/n. Hare traced down and proved Me 4asf ///re of the towns/r//? to a //'/re OfSpo ts running wesf supposed forests soi/ftr //'/&. . Searc/r a/o/?g ffr/s •sAotvs W/ftl/n Zorods a spruce and a6/'rch wiffi very o/d 6/azes w6/c/7/?rove as near i '3 Mer//i#5 ca/7 be cou/tfedfo be ///years o/d. Ab/aze of Me age j's a/so fbt//?d 3 rods fo the eastward. JVo s/o/? seen of ffte or/^/fja/ Cor/ye ~ noted as oe//70~ //? a fr/rc/?. forage ofrte S/?0fc easf and ' wssf a/?d //? /tie ///re com/ng sot/ft Sefa cedar pas f andsfo/ies. 77r/s /s /'/? f/af s/ort/ce /and and 3 rvds from Fs/ar?d fb/rd fo the easfwa/rf. AfarAetfffie/Tasf 0/7 MW. TJ /?. 4 ; on ME. T4- ft-4- ,Of75. TStf.3, a/so 'U.J.B. &0S. " The w/fncss trees, a/so marted J.J.B. WOS, Ore a cedar 5t&nc//rtg M /0"£ /O ///?As from trie/tost; a/rotAer- S.S0*£ /3 ///7/fS, as/truce •S.30°Wsfranafr/'a////K /Y.83°)Y. af r/y/?f a/y/es fo/fie /?& 5 bne After 8Srods -found anof/rer or/g/'/ra/ 6/aze 2O //nAs to trie /-*- teO ft is ing ontv fne fieighf ofar/'dge w/?/ch fa//s off /?rec//)/fous/y £ rods fo the South. Or/g/va/ f/'/nter 6/onr/? down a/rd roffe* /?&re affd 5o/ne rods aAead. f-> sffor tfy0 corner Of secf/ons -3S & 36 ntarAed on /V.W "S A'? 35. " on M£. "s.Af°36~.", on 5. "T.S ft.3" MarAed /f and the w/tness frees t/.J.ff. /3Of? \^ 30 A MANUAL FOK NORTHERN WOODSMEN f Woodstock, Mass., AfyZO, S907 Survey made for C/ark Lumber Co of fair fbrtcr Lot SOCa/te/ Dccl.ofneed/e as near as know //'Jm/S^Sc&i, Begin at (/#7 test- corner cf /of" afj'uncf/o/r ofsfo/?e wa//s sr?arA//r? recoqn/z dfjo f?c/ar/&s of tfre /ot Thence — Bear/no; Dtst N/0*E 84?' Along >va//fv //s end 917' through pine f/mter bo ft? sties mffr /ro 5/gn ofproper/y fi,tn/) fine, fo a roffesr fence rvnn/nff easfer/y. Tne cfe&ds ca///mj for a//'ne runn/ngr "//7 a nor/fier/y cf/recf/o/r" / 6(azecf the. //n& ffrrovg/r onrfre range offne >va// anrfsef a/xxt ancfsfones af/rs norfn enrf. This is on /edgy ground Wirh a drop off SO feer wesf. S79'3S'£. /OS*' Along fhe o/d fence //ne. -Sma// 6rooA runs War 68O ft fo 5 £ Corner of ff?e /of-/y/r?ff north, as /ndtcafec/ 6>y range ofo/d farm wa/frur? /'n fron? fne nor/A fo fl?/spo/nt Set a stone b/ock on 'end 'and 'surrounded ' /f w/fhsfones Set several heaps ofsfones a/o/rg fne //ne. A//0°£ 3SO' On range of farm wa// 'mentioned 'and roi/gn/y a/0™7 ^e bound offhecirtfi/y, /n -swam/ty /and 'after 2oo'. Ser stakes a/ona fhe //ne each 2OO 'andaffhe end a post with heap of s rones. S80°£ JO' At right ang/es fo the range //ne fo Cohasse 6roo/c. Tn/s distance is the one (Jroa'sJ ca//ed for /n fhe deed and/sfhe on/y n?ea/?s of f/x/ny /he /asf named corner Off the norrh and south //ne . S3S'£ /76"} 5SJ%£ 3/9\ Along Cohasse brooA as /?er ca// of c/eea". 580°£ 33S Across brook, tf?en 0/7 south border of f/'e/d //? /tosses- si on of owners north, to ivesf 5/de offr/ghway. 7h/s point /s 7/6 fr 5Oirfher/y fron? the forks of fhe h/ghway, the deedcat/fng for "about 40 rods "Sef/yosr ands/ones. S26*W /68 Down h/ghway to br/dge over Co/jasse brook as ca//ed S^O'30'£ ZSO for /n deed S40'30'£ /33' S£6W 712 In the swamp c/ose to foot of the r/dae 5/?V 185 Offset freoitenf/y to get exact area of the "hard to/id* 536>W 720 H/7/ch was conveyed 'tn ffie deed To stone wo//, fhe s7?5 .-,,-.'- recognized south bound of fhe /of #$£*_ 296 Along wa//, up a /yrec/p'fous -sfope N7Q*3O'H 1066 Alor& fhe wa//fo p/ace of 6eg'nn/ng 7* asur*. Wh*. foe terms offfa deeds as near as the/ can be /nfcr/ore/eof jHHtAmntr vq.a •SJObar of Me Axa/ty JOyears one/ fom///ar */M '6 bnd transfers SgMagW ».-• . Wtf-and says tfietxafofr eymes as /tear at /» Anom *//A fAe wr- «r*to«** Tt*e* 'parftes one/ foe ti fff/x>SSCUioa. Locahon, Mtcrvforc.food The V*»*v/ "Tf» -AtefontAa s«1s sur*tyed"c.L Co /SO7 "and a/so »nV> my/rnttab 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 FOB 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 tiorth 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 comes 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. 9° 30' 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 S4 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 "975163 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. NY hen 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 depart 11 iv Tli us, suppose that four courses of the above survey have COMPUTATION AND OFFICE WORK 35 v^ ^ O & : : 3 5 2 i It 0) s W S 8 : : : 1^ 06 i ! : 0 rom nor I from w 1 flj *c3 IO -H CO 'S *^ m 02* d : : : 6 O cc fc 1 O O 00 S|S Q S 2 2 2 §3 s is^ | ^•^ 3 •sa ur 6 W H £ £ £ ""it "~ i-H II | earing »O O O O 00000 O iO O ^ OS CD CO (N CO ^H "-§15 •s'ff p m JS-g ^ II s HI 0 a a •+. 0} < P3 0 Q H II ^ KW S 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 X and east of the starting point, much further north than east; hence a course somewhat west of south E 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 •"•'-H-S-- >• 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. V21.022-f7.172 = 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. 2. AREA 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 -f- 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 = -\A'(5 ~ a) (s ~ &) (s ~ c)» where a, b, 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 Gross 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 BCD Et and secondly that the figure b B C D E c 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 ra, the altitude of the trapezoid b B C c, is the Jatitude 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 -f 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 •f 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 1293.95 324.32 324.32 2)969.63 484.81 sq. ch. Area = 48.48 acres. S. 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 lim-s 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 FIG. 1 FIG. 2 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 thati kind, if one is required, is best devised for each forest! region or property. Maps may be rendered plainer by the judicious use ofj ON THE BEARING OF LINES 43 topographic symbols. A number that are in common use and generally agreed upon are given herewith. Railroad ^ — | >__| — | — t Highway • Wood Road ------^-^-- Trail ^- -^__-~ Stone Wall oo^coococXxXXXEoc^ Fence Telephone Line ...... i Field or Prairie >-ffc ^,, ^ ^,,,, Ml Open Swamp ^^^^J^^* -".._ .tu \l, «•». . Dam - I - 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 correct^ 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° 207 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° 2(X 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° 1(X 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 declination. 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. mple : A land line in the Adirondacks was run out j in 1800 on the magnetic meridian. What course should be set in 1910 U 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 (Jan. 1) Maine N'theul Maine S'thweel New Hamp. Ver- mont Mass. East Mass. West 1750 12 05W 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 55 8 10 7 03 6 44 7 00 5 31 1780 12 05 8 10 6 47 6 28 6 50 5 19 171JO 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 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 1POO 19 02 14 ?1 12 31 12 08 12 34 10 59 1910 19 45W 15 06W 13 16W 12 57W 13 21W 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 0 52 1800 6 19 4 51 5 28 2 13 2 08 0 37 1810 6 38 5 08 5 34 2 13 2 09 0 31 1820 7 05 5 34 5 50 2 24 2 22 0 37 1830 7 40 6 07 6 17 2 46 2 47 0 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 JV? 10 25 10 48 7 37 7 25 5 07 1910 12 40W 11 11W 11 31W 8 12W 8 07W 5 45W 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 17bO 4 04 1770 3 bl 1780 3 C6 17LO 2 50 1800 2 45 3 13E 4 44E 5 54E 1810 2 fQ 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 I860 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 0 37E 2 35 4 44 9 06 3 47 1890 7 14 0 02W 1 57 4 05 8 21 2 58 1900 7 49 0 42 1 24 3 36 7 52 2 20 1910 8 33W HOW 1 08E 3 25E 7 57E 2 05E Year Man. 1) Michigan South Wisconsin Minnesota North Minnesota South 0 / 0 / 0 t 0 / 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 I860 2 46 7 49 10 27 11 20 1870 2 04 7 14 9 59 10 54 1880 1800 1 17 0 32E 6 25 5 36 8 33 10 22 y 32 KOO 0 02W 5 01 7 58 8 57 1910 0 27W 4 51E 8 03E 9 OOE ON THE BEARING OF LINES 47 ABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- TION IN THE UNITED STATES (From U. S. Coast and Geodetic Survey Reports) *i Washington D.C. Maryland (Baltimore) Virginia East (Richmond) M IS.Q 1*1 > 1 •| Sj North Caro- lina East (Newbern) North Caro- lina West (Salisbury) 1750 1 41W 305W 1 13W 0 18W 1 31E 1760 1 02 226 0 37 008E 0 18E 208 1770 028 1 52 005W 042 050 242 1780 001W 1 25 0 20E 11 17 3 12 1790 0 19E 1 05 038 33 200E 35 334 1800 0 28 056 047 46 2 15 44 3 48 1810 028 056 047 51 220 44 3 52 1820 0 19E 1 05 038 46 2 15 35 3 48 1830 001W 1 25 0 20E 33 200 1 16 3 33 1840 028 1 52 005W 11 1 37 050 3 10 1850 1 02 226 0 36 0 45 1 05 0 17E 240 1860 1 41 3 05 1 12 0 10E 030E 0 19W 206 1870 2 21 3 45 1 51 029W 0 12W 058 1 29 1880 300 424 229 1 09 051 1 35 051 1890 3 36 500 306 1 46 1 28 2 14 0 13E 1900 4 11 535 3 40 222 206 251 023W 1910 4 51W 6 15W 4 13W 2 53W 2 39W 3 25W 0 47W 'oS A S3 , .- ^ A c|3 S3 — -§^2 £^"0 ej_g'c3 S o 04 C II 111 M3| •&§ 11 5^5 3^1 fas§ ww •c»l -2£fl K'fi si If "53 o II 1750 204E 3 16E 2 27-E 500E 500E 252E 1760 241 3 53 3 04 5 37 5 30 3 28 1770 3 15 4 29 3 40 6 13 555 403 1780 3 44 501 4 12 6 44 6 15 434 1790 406 5 26 4 37 7 11 6 26 502 1800 4 19 5 44 4 55 7 32 6 30 5 24 7 54E 1810 424 553 504 7 45 6 26 539 8 13 1820 4 19 553 504 7 50 6 15 5 47 8 24 1830 406 5 44 4 55 7 45 555 5 46 828 1840 3 44 5 26 437 731 530 538 8 24 1850 3 15 501 4 12 7 12 500 522 8 13 1800 2 41 4 29 3 40 6 45 4 28 500 7 57 1870 203 3 53 3 04 6 13 3 53 432 731 18SO 1 25 3 14 225 534 3 16 3 54 6 55 1890 047 239 1 50 457 2 48 3 15 6 21 1900 0 HE ?08 1 19 4 29 2 10 249 5 58 1910 0 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) *l Tennessee East (Chat- tanooga) Tennessee West (Hun- tingdon) Kentucky East (Lexington ) Kentucky West (Princeton) Louisiana (Alexandria) Texas East (Houston) Texas Mid- dle (San Antonio) 1750 0 / 0 / 0 / 0 / 0 / 0 / 0 / 1760 1770 1780 1790 1800 507E 422E 632E 804E 1810 5 16 431 650 8 25 1820 5 16 724E 431 6 59 841 855E 1830 507 7 24 422 6 59 8 49 9 10 937E 1840 449 7 16 404 6 50 848 9 19 9 48 1850 424 6 59 339 632 840 9 19 9 53 1860 352 635 307 607 824 9 12 9 48 1870 3 16 605 231 537 802 856 937 1880 236 529 1 53 457 7 26 829 9 19 1890 201 453 1 15 420 6 53 7 56 852 1POO 1 30 424 041 3 51 633 7 44 8 43 1910 1 12E 4 18E 0 19E 3 36E 6 50E 8 05E 9 09E 1 a III 111 II 13 || nsas East Imporia) III Ij'j rt d '-S > j < oo SS5S- £* ~£ X, - 1750 0 / 0 / 0 / 1 1760 1770 1780 1790 1800 8 13E L810 836 1 V() 851 1003E 11 39EH IS.il ) 1046E 900 10 13 11 57 | 1840 11 00 859 10 13 1207 1 1850 11 08 851 10 15E 1004 11 34E 1224E 1207 1 L800 11 07 834 1006 946 11 28 12 23 11 59 || 1870 11 00 8 14 951 924 11 12 12 12 11 41 i ISM, 1048 738 9 33 844 10 45 11 54 11 10 1 is' o 1024 701 9 07 802 1007 11 21 1031 | 1POO 1010 10 18 Hi f,OK ': :;s 8 42 8 55E 738 7 4(iE 9 50 10 08E 11 (K 11 27E 10 14JI 10 2Sll| ON THE BEARING OF LINES 49 'ABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- TION IN THE UNITED STATES (From U. S. Coast and Geodetic Survey Reports) Sd ^5 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 0 / 1760 1770 1780 1790 1800 1810 1820 1830 1840 1306E 1809E 1853E 1850 1527E 13 06 16 26E 1431E 1737E 1827 19 18 1860 15 27 ' 12 57 16 26 14 21 17 37 18 36 19 36 1870 15 18 1239 16 16 14 02 17 27 1836 19 45 1880 1450 1207 15 50 13 31 1700 1821 1934 1890 14 20 11 25 15 17 1243 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 18 17E 20 02E •£ c § a *• 3 be ^ M « O S-* S^T sT all G _^.> IS II? til !i §1 JH § S.H o 2.^ § So '£& £ !>J ia 5. ^ s > ^ M hHW IT s^s »£ IB § jfc 0^ o 1750 1760 1770 1780 17 19E 1790 17 52 1800 18 27 1605E 1810 1904 16 43 1820 19 41 17 22 1830 20 16 1801 1840 2049 18 38 1850 1551E 16 45E 18 OOE 21 16E 21 19 19 15E 19 12 1860 1870 15 59 1559 16 58 17 02 18 30 18 45 21 37 21 52 21 45 22 06 19 40 19 58 19 41 20 06 1880 15 47 16 54 18 45 21 56 22 19 2009 20 24 1890 1524 1636 18 39 2206 2238 20 11 2032 1900 1910 15 19 1543E 1637 17 08E 1851 1931E 2222 23 OOE 2258 23 40E 2026 21 07E 2050 21 33E 50 A MANUAL FOR NORTHERN WOODSMEN TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEf'I.TN TION IN THE UNITED STATES (From U. S. Coast and Geodetic Survey Reports) Sd ^3 California South (Los Angeles) California Middle (San Jose) California North (Redding) 111 |«g ill III Utah (Salt Lake) i - 1750 1760 1770 • 1780 1024E 1337E 1407E 1790 10 58 1403 1435 1800 11 32 1432 1504 1810 1207 1501 15 34 1820 1239 1530 1604 1830 1309 15 57 1633 1840 1336 16 22 1701 1850 13 57 16 45 17 26 17 20E 16 16E 16 25E 1860 14 13 1705 1747 1736 1637 1636 1870 14 24 1720 1806 17 41 16 52 1640 1880 1433 17 28 18 15 17 44 1700 16 30 1890 1436 1732 1820 1738 1702 1620 1900 14 52 1751 1839 1749 17 17 16 28 1910 15 35E 18 32E 19 22E 18 27E 17 58E 17 03E ^ o ~ 3* 5 " ^ 1750 1760 1770 1780 1790 1800 1810 is JO 1880 1840 1850 1347E 1607E 12 43E . 13 26E 13 33E I860 1350 16 15 1247 1333 i:: it 13 46 16 16 1243 13 34 IS 17 l.i 10 1880 1604 12 29 13 22 i.; 10 1800 1300 1540 1203 1302 13 25 1900 1010 1253 15 39 16 10E 11 59 12 29E 13 0:' 13 36E 1 .-{ 1 1 U 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 not 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. \Vhen 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- 52 A MANUAL FOB NORTHERN WOODSMEN REFLECTOR Zeta 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 utxiut April 10, and is, there- fore, the proper star to use at that date and for some two or! three months before and after. Great Polaris Delta North Pole pela ON OBTAINING THE MERIDIAN 53 Six months later the star Zeta (ft, 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- siojx'iiL', Zeta (f) Ursa? 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 : For Zeta Urs. Maj. For Delta Cass. (1910 J1920 (1930 1910 1920 1930 6.5 10.6 14.7 7.1 m n. 11.0 14.9 annual increase .41 min. annual increase .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 \u -stern 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 wrire for some time, then leave it in a direction con- trary to its former motion ; thus indicating the time 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 yerticality 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 wood, 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 wrest 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 theplumb 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 l>e, keep tlie star on the plumb line until it npprars to remain stationary, thus indicating that it has retched 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 min., 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 .-H «> OCO-*-*U5 CDt^000005 )rH COCOOTf05 10-H (NCO^IOCO r^osdcvjco ict^od ICJ (NININCNCSJ .. t^ OOOS^INTW 101 O«ocoqt>. 1 *O CO Is- 00 O *— i CM ^ KNCMlN (NCOCOCOCO •> kccdco'r^oo ooos'd-H COTj{:£ 1921 add 1922 add 1923 add »* {2! 1925 add 1926 add 1927 add 1Q9R /add 1928 ( add 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. 0.7 minute 0.9 minute 2.5 minutes 4.0 minutes up to March 1 0.1 minute on and after March 1 1.6 minutes 3.1 minutes 4.5 minutes 5.9 minutes up to March 1 2.0 minutes on and after March 1 3.3 minutes 4.6 minutes 5.9 minutes 7.2 minutes up to March 1 3.3 minutes on and after March 1 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 th<- 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 ation 0.10 in in. 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- trad 0.10 min. /or 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 VIII THE UNITED STATES PUBLIC 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 surveyed or pa tented, 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, Ix'ginning 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 o\«r it the number of the township within which such section may be. Fifth. \Vlu-rc the exterior lines of the townships which may be sulnlivided into sections or half-sections exceed or do not ex- tend fix miles, the excess or deficiency .shall l>" 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 he 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 ujwm trees, and meas- ured with chains, containing two {Arches 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 t 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 snail 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 I Foiled 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 e.staUishment of standard parallels conforming to parallels of latitude, initiated from the principal meridian at vals of 24 miles and extended east and west of the same. 'lit ml. 'Flic establishment of guide meridians conforming to true meridians, initiated II]M>II the base line and successive standard UNITED STATES PUBLIC LAND SURVEYS (>!> parallels at intervals <.f 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 43,040 acres, as nearly as may l>e, and designated townships. Such townships shall l>e subdivided into thirty-six tracts, called sections, each of which shall contain (540 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 ran of the townships, to the east or west, beginning with No. 1, at 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 1 Standard 9 a £. Parallel 1 I Base \ - Principal Meridian Standard Parallel ft | ;§ i C to B ~B 1 E 1 1 S Standard Parallel FIRST SUBDIVISION OP LAND 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 lin«-. Thus the sixth township north of a base line in the fourth range east of a principal meridian is designated as township (> north, range 4 east. Each township contains UNITED STATES PUBLIC LAND SURVEYS DO 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. G 5 4 3 2 1 7 8 9 10 11 12 18 17 1C 15 14 13 19 20 21 22 23 24 30 29 28 27 26 25 31 32 33 34 35 3G X. W. J£ N. E. J4 160 acres 160 acres of S.W. H 80 acres of S.W. 80 acres N.W. % ofS.E. 40 acres 40 acres of S.E. s 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 f>f> 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 l«-t tn-N inscribed on the faces give the location, and this in the case of section corners is also indicated by notches cut in tin- cd^rs or by grooves on faces. These notches, on account of their durability, are of much service in idonti- 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. Township 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 FOR 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 Corners 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 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, 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, ana 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 i, 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 H. 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 FOR 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 OP 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 20.0 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. When 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 Diff. 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 for 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. ejev. 7.25 'are found in the tables. 99.47X1.81 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. £. 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 hold vor- 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. Road tho boa ring for a check, and measure the line. Proceed in this way until all tho angles have been turned and all tho sidos 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/c/ vSto. //?/: Anq/e Observed 0ear//7Cf Computed Bear/'ry D/'sfartce, o N8/°£ W8/°£ J/8.63ff; 1 269° &' A/8°/5'W M8°/9'W 48. /9 " 2. 9J°32 M7S°45E /V75°49'£ 300.53 " 3 8S°/2' S9°30'E S9°23'E /83.60 " 4 Sl°28' S79°tfW S733W 8/S.96" J 86°J6' A/7*45W A/7*47'W /34.8S" o 3/°/3' M8/°£ 515.63' 48.19' 2> 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, 84 A MANUAL FOB NORTHERN WOODSMEN along with the amount of the deflection. Notes may be kept as follows : Instr. at Deflection Angle Observed Bearing Computed Bearing Distance 0 N. 81° E. N. 81° E. 518.63 ft. 1 89° 19T,. 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 tliis way until the survey is completed. If the survey is a closed one, when the transit is finally set up again at the initial jx>int, the azimuth of the first line should be the same as it was at the beginning. THE TRANSIT Notes may be kept as follows: Line Azimuth Bearing Distance A — B 162° 12' HO" 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. W.W.CooA, last Bear/'/rg r.A. Remarks o-/ 1-0 3-2. 3-4- S-4- S-6 7-6 7-3 9-G 9-/0 10-3 2.30 2.30 6./6 J2S /./O 6.S2 S.30 6 JO Q.JS 3.SO 9. SO 2.30ch ffcodfi on /A ect/c. -2* /09" 5.30- 6./0" 8./S" 3.30" 9.SO" Sfa.O J~6. S c/ra/ns So. on //• as •S/rotv/? 6y Survey of 6ovmfary These courses a/o/y SovMr stye onto shoulder com/ny fro/7 Af£ 2.45 on Mis course 6rooA crosses 75s/ 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, briiii^ tin- tube undrr the axis of the telescope by means of the lateral THE LEVEL 89 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 FOB 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 THK LMVK1, 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 (^ Prvfi/e offbrAftoaJ Se^/a/907 $&&5?ocr\ 6/0 0.S. H.f. /%5. £/ev. «&P £tev Descr/prtort &M3 /2.B3 3438 ^2.7S O 38 2S.a 1 6.6 aa.4- a 3.0 32. 0 7T/P, /.43 33.SS Of? sfumjo // 1/./8 44.73 3 6./ 38.6 +6S1 E.7 42.0 4 3.7 410 S S.E 39.5 6 //£ 33.6 TPz S.& 39.// Boulder a 3.48 #39 7 /o^ 3^4- \ 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 yi 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 tin- trijxxl. Levelling is employed by woodsmen in constructing dams and ascertaining the area of flowngo, 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 (b) in the figure, and beside it, occupying half the orifice of the tube, is a mirror set at •i if/ an angle of 45°. Directly over the wire and mirror is a spirit tube (c), shown inclined in the f ^rure. -^ ^ 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 l£ 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- A MANUAL FOR NORTHERN WOODSMEN ination. 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 ON MOUNTAIN TRAILS Slope Length of step ascending Length of step descending 0° 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 M when nothing seems to go right. Keeping the count also is a source of frequent error. Woods travel is too uneven COMPASS AM) PACING 97 as a rule to allow a pedometer lo 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 Outlet Section Lines Compaes 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 close 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 alwrays in the north and south position. A brass ruler with vertical sights attached serves both to sight with and to draw lines junl 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 of ROUND LAKE Washington Co. Maine C. A. Gary 1907 Area 343 Acres . Scale of Feet 500 1000 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 \svll 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 }, 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. (b) 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 r g- f- •b , | e (c) By setting up the board on any desired point on the •.lion- ;i^ }', oii. n!« d l)\ 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 for the Temperature of the Air. An inch difference in pressure at a temperature 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- BAROGRAPH 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 ah*, 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 2j 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 from damage, also from extreme heat and rapid changes of temperature. 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 T 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 column 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 6 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. b 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 stall on barometer or the record of a barograph. The barograph sheet reproduced herewith shows for the \\orking hours of that Friday a steady fall of pressure. At (5.30 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 29.100. 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.oyT2 4 6 BIOX// 2 468 lOftTZ 4 6 8 \OXII2 468 10er 0/7 /? ///Mixed a/rds/torf. fiotfom rotyfy 2.9. 17S /03S /7S Canada fray road 0/7 easy /artd 2.9. /93 /0/S 37S Dow/r eas/' /y w /ar^e/ff/yed^royY/fifo eatye of swampy /and 29.26O SSO ISO Towrrsfr/p ///?e ffosfeps £asf of ^.m/e marA Bar 9.3S (TA. 6s°J tt.aao 930 Bar Camp //A. M. (I A. 69J 29. E8O Barcyrap/r //, 29. /7S STRAIGHT TBAVEKSE ACROSS SECTION. ELEVATIONS BY BAROMETER CORRECTED BY BAROGHAPH 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. Tin- 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. oroughly cut about 1890 for gprucc saw logs Explored 1900 TIMBER SHEET Cutting since that date marked by section lining •vr. 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 main 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, hi 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. 13£ 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 IDCbi 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 bni.shy 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 acre 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, so as 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 WOOD MEASUREMENT PART m. 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 . U5 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 VQ. MILL TALLIES 151 SECTION VQI. CORD MEASURE . 157 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 J inch are taken as of the inch above, and fractions of 4 inch and less are disregarded. 138 A MANUAL FOB 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 m 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 Spauldlng, 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 writh 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 taper, 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 Pacific 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 inches, 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, i 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 of 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 £-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 point 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, ^-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 ^ _ ci Top Diam. i] 8 and Mill No. Sawed alive and Mill No. Sawed alive fi 02 Gang Scale by Maine Log Rule ffl a a 6 in. 30 26 20 18 24 20 7 in. 41 36 29 25 34 31 8 in. 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 1 i 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 92 111 130 149 170 190 211 232 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. 8i in. 37% 21-24 ft. 12 in. 11% 25-28 ft. 9} 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 arc 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. Clark1 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 1^ 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 ij 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 to 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 (D2 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 g*f inch kerf add 1.3 per cent. For A inch kerf subtract .5 per cent. For I inch kerf subtract 9.5 per cent. For f6 inch kerf subtract 13.6 per cent. For | inch kerf subtract 17.4 per cent. For ^ 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 1^ 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 equal 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. 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 2j per cent on the scale or the timber. On 30-foot logs, it means Ij 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 eftcct 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 Length of Logs in Feet Diam. of Hole 10 12 14 16 18 20 Inches Board Feet 2 5 6 7 8 9 10 3 9 11 13 15 16 18 4 14 17 20 23 25 28 5 20 24 28 32 36 40 6 27 33 38 44 49 55 7 36 43 50 57 65 72 8 45 54 63 72 81 90 9 56 67 78 89 100 112 10 67 81 93 107 120 133 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 J-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 the 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, sawed 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 Top Diam. 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 39 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 HI Same logs but grouped according to mid diameter outside bark. Length of Log — Feet Mid Diana. 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 wore 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 2J 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 fth-otvn 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 i 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 TV "Racic iviameter Surface Measure liasis 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 17 feet 75 logs 9 inches 22 feet 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 FOR NORTHERN WOODSMEN Log diameter taken at top end, inside bark. Saw kerf J 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 this 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 Ij 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 J 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, welUtrimmed 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 90 158 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. l 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 wood 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 161 SECTION II. INSTRUMENTAL HELPS 162 SECTION HI. 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 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 1 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 in steady work on timber of ordinary dimensions. y Si J..'.i, ',,'.,',:: iti i! .1 11 >4 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. BARK 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 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 : 1 COUNTER 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 ij inches wide, containing a longi- tudinal slot about | 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 eye 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. VOLUMK TABLES AND TREE FORM 167 Example: Standing SO feet from a tree, the angle to tin- top is found to be 31 ° and that to the base 8$°, of depression. From the tables the tangent of 31° is found to be .6001); multiplying this by 80 gives 48 feet for the height of the tree above the level of the eye. Again the tangent of S$° is found from the tables to be .1495 and this multiplied by SO 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 4j 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 1G9 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 274-275, 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 101, 20$, and 277. VOLUMK TABLKS AM) TKKK 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 TIMUKK 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 52 56 64 72 84 92 12 60 68 80 88 96 108 13 72 80 92 100 112 125 14 85 100 110 125 140 155 15 100 115 130 145 160 175 16 130 143 155 175 190 17 142 158 175 190 210 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 No. Observed Heights Deduced Scale Total Diam. Trees Height Each Scale 8" 85 51-47-50-54-59 50' 50' 4250' 9 70 50-47-52-48-56-57 55 70 41,00 10 70 tl'.i -if, 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 \ \ Deduced s* - -f ( Su¥ ht •e_ f^K / / / \/ ' 8 9 10 11 12 ia 14 15 1C 17 18 19 20 21 22 23 24 25 26 27 2 Diameter Breast High —Inches form existed as to call for differentiation of treatment. Instru- ments employed, caliper and Faustmaiin's hypsouieter. 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 in 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 in 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, VII, VIII, IX, 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 IV Plot VIII Plot III Plot IX Plot II Plot X Plot I 125 paces 178 A MANTJAL 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, eacn 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 of? 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 :irc 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 tne 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 run so as to cross the ridges at as nearly right angles as is possible. Co..Cheboygan._._ Sta.tQ.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 arid tallies each kind under the proper heading. 180 A MANUAL FOR NORTHERN WOODSMEN Examination Lot... 1. Made by. Sec — 29 May, 1908.. C.L. 12-1 12-2 13-1 13-2 13-3 14-1 14-2 14-3 15-1 15-2 15-3 16-1 16-2 16-3 16-4 Maple Bass Beech Hemlock II n 48 160- II 19 64 H a in 180 400 1 an fh Illll 450 1 50 in 440 1 110 1 ho HI HI 'Ml 216 1320 III 380 II 72 140 K tt 1 Hit 1 III 864 ?,5W 1 so II /I 1 576 540 HI 432 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 calij>er 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 us 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 hah* 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 £th 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 |i 1 ! Ji 1 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 sm.-ill 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 atmosnhp.rfl a.nd thp la.v of thp land Knth liavp nn pffpr>t r»n 184 A MANUAL FOR NORTHERN WOODSMEN 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 TIMBI:R KSTIMATING 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 6, 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 9Sl " 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 * 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 Se<> 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 niches 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 4 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 1 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 hi 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 11)1 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 Locality.. T. 5_R.18^.W..E..L.S.rMaine_ Type^Hardwood. Slope. Date_Sepf .. 17+1901 Sheet No. A. 41 P.B.H. Spruce Dead Fir White Birch Beech Hard Maple Pine Popl. 2 in. sin N . 3 " car. 4 « H. • • • 5 " 1ST. 6 " D3.. . 7 " tl . w . 8 " . &a. .. 9 " . . pa:. . M. • 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. 6. 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 TIMIJKU INTIMATING l!).'J Carefully training in this way, a man will find himself able to guess within 2 feet of the .09. 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 inches 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 2j 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. /" Sp Logs Sp.Pa/jo nr Cedar P/r?e HardWood 4-4-00 3 -.3 /6-ls //? -300 9-1200 28-4- 8-/80O 2 8-/ Soff wo ~>ds on f/af- 3~400 7-1 1-100 /and, Sfo f?y buj- 3-SOO 7-1 34-4 Smootfy /oggwg. IO-20OO 7-JB 24-3 4-100 Abundan f re/yrocfi/cf=- 3 ~/30O 2 9-/.3 /or? of fi r; w/thyruce 8 -WOO 7-1 12-IJL 2-300 & occasfo 7a /p we v? //-ISOO 23-Zk 8-1 o/x/?/ng^ 8 - tOOO 37-3 3 -8OO S3 -2 £3 £asf6C roofs //7 2-30O 3 -7OO 6-6 4-.3 mixed growth S-900 2555*7 S.4C. 470 /33' /33' 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 1 PRACTICE OF TIMIJKU KSTI MATING 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 are 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. 9. 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 ' , "1" Total 1st 32-foot log 31 1420 33 2nd 32-foot log 28 1160 27 3rd 32-foot log 4th 32-foot log 5th 32-foot log 25 20 14 920 560 230 21 14 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 107 constructed on principles that have very seldom l>een employed elsewhere. After basal diameter, taper per 32-foot l 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, 2^ 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, ll/2 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 16 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 "Rir fVdar D & D HPTTI Q Down Fir Hem. Cedar 2-6 M 2 1-.7 .8 1-1.5 1-5 M 1 1 111 1-2.3 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 200 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 ncrrs- 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 Unit 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 half 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 cornpassman 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 % °f 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 1C 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 j>er tviit. of (h(> scaled contents in lumber in the grades of No. 2 Clear and better. PRACTICE OF TIMBER ESTIMATING 203 No. 2 (or Merchantable] logs shall ho not less than 16 feet long and which, having defects which prevent their grading No. 1, in the judgment of the sealer, will he 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 applying 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. £ 3 Logs or 96 Feet 4 Logs or 128 Feet Butt a d Logs a Logs Diam. a ft Inches k 2 1 Contents B. M £ - 3 § Contents B. M £ £ 5 re i A Q £ £ s £ L^ tf - 3 28 4230 40 33 27 25 5128 83 27 22 18 4 25 3714 43 33 24 21 4330 37 2S 21 14 5 22 3234 46 33 «1 17 3610 42 2'.) 19 10 37 6 19 2790 50 32 18 13 2979 47 30 17 (Hi 7 16 2386 r,r, 32 11 8 13 2029 60 31 ()'.» 9 10 1729 66 2S (Hi 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 thr 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 been 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 riot 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 in some size groups, with which he may check published volume tables. Or old devices and short cuts1 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 In --I 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 il I )i- ':ii,rr 0' 10' 20' 30' 40' 60' (X 10' 20' 3CX 40' 5(X 0° 100.0 100.0 100.0 100.0 100.0 1000 16° 92.4 92.3 92.1 01.9 91.8 91.6 1° 100.0 lOO.Oi 99.9 99.9 99.9 99.9 17° 91.5 11.8 91.1 «.)1.0 «10.S 90.6 2° 99.9 90.8 99.8 99.8 99.8 99.8 18° 90.4 89.9 8H.8 89.6 3° 99.7 99.7 99.7 99.6 99.6 99.6 19- 89.4 S8.9 88.7 88.5 4° 99.5 99.5 99.4 99.4 99.3 99.3 20" 88.3 88.1 87.9 87.7 87.5 87.3 5° 99.2 99.2 99.1 91). 1 99.0 99.0 121° 87.2 87. 0 86.6 86.4 80.2 6° 98.9 98.9 98.8 98.7 98.6 98.6 22° 86.0 85.8 85.4 85.2 84.9 7° 98.5 98.4 98.4 98.3 98.2 98.1 84.7 84.6184.3 M.l s:-;. 9 83.7 8° 98.1 98.0 97.9 97.8 97.7 97.6 24° 183.5 ;.0 S2.8|82.6 82.4 9° 97.5 97.5 97.4 97.3 97.2 97.1 B5° 82.1 si. «.i SI. 7 M. 5 81. 2 81.0 10° 97.0. 96.9 96.8 96.7 96.6 96.5 26° 80.8 so.r, so.:; so.l 79.9 7'.). 6 11° 96.4 96.3 96.1 96.0 95.9 95.8 27° 79.4 79.2 78.9 78.7 78.4 78.2 12° 95.7 95.6 95.4 95.3 95.2 95.1 28° 78.0 77.7 77.5 77.2 77.0 76.7 13° 94.9 94.8 94.7 94.5 94.4 94.3 29° 76.5 76.2 76.075.7 75.5 75.2 14° 94.2 94.0 93.9 93.7 93.6 93.4 30° 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' 40' 50' 1' 2' 3' 4' 5' 6' 7' 8' 9/ 0° 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 .09 .12 .14 .18 .20 .23 .26 2° 3.49 3.78 4.07 4.36 4.65 4.94 .03 .06 .09 .121.14 .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 7.53 7.82 8.11 8.40 .03 .06 .09 .12 .14 .17 .20 .23 .26 5° 8.68 8.97 9.25 9.54 9.83 10.11 .03 .06 .08 .11 .14 .17 .20 .23 .25 6° 10.40 10.68 10.96 11.25 11.53 11.81 .03 .06 .081.11 .14 .17 .20 .23 .25 7° 12.10 12.3S 12.66 12.94 13.22 13.50 .03 .on OS .11 .14 .17 .20 .22 .25 8° 9° 13.78 15.45 14.06 14.341 14.62 15.73|l6.00 16.28 14.90 15.17 16.55 16.83 .03 .06 .08.11 .03 .06 .08 11 .14 .14 .17 .17 .19 .19 .22 .22 .25 .25 10° 17.10 17.37117.65 17.92 18.19 18.46 .03 .05 .08 .11 .14 .16 .19 .22 .24 11° 18.73 19.00 19.27 19.54 19.80 20.07 .03 .05 .08 .11 .13 .16 .19 .21 .24 12° 20.34 20.8020.8721.13 21.3921.66 .031.05 .08 .11 .13 .16 .18 .21 .24 13° 21.92 22.1822.4422.70 22.96 23.22 .03 .<>.-) .08 .10 .13 .16 .18 .21 .23 14° 23.47 2:5.7:5 2M.99 24.21 24.49 24.75 .03|.05 .(IS .10 .13 .15 .18 .20 .23 15°. 25.00 25.25 25.50 25.75 26.00 26.25 .03 .05 .07 .10 .13 .15 .17 .20 .23 16° 26.50 26.74 26.99 27.23 27.48 27.72 .02 .05 .07 .10 .12 .15 .17 .20 .22 17° 27.96 J28.20 28.44 ,28. (is 2S.92 29.15 .02 .051.07 .10 .12 .14 .17 .19 .21 18° 29.39 29.6229.8630.0930.32 30.55 .02 .05 .07 .09 .12 .14 .16 .19 .21 19° 50.7,8 31.01 31.21 31.47 31.69 31.92 .02 .(15 .07 .09 .11 .14 .16 .18 .21 20° 32.14 32.3632.58 32. SO 33.02 33.24 .02 .01 .07 .09 .11 .13 .15 .18 .20 21° 33.46 33.67 33.S9 34.10 34.31 34.52 .02 .04 .or, .os .11 .13 .15 .17 .19 22° 34.73 34.9435.15135.36135.56 35.76 .02 .01 .or, (is .10 .12 .14 .16 .19 23° S5.97 36.17 36.37 36.57 36.77 36.96 .02 .01 .06 .OS .10 .12 .14 .16 .18 24° 37.16 37.35 37.54 37.74 37.93 38.11 .02 .04 .06 .OS .09 .11 .13 .15 .17 25° ;s.:;o 38. 49)38.67 3S.S6 39.0-1 39.22 .02 .04 .06 07 .09 .11 .13 .15 .17 26° •59.10 39. 5S 39. 76 39. 93 40.11 40.28 .02 .04 .05 .07 .09 .11 .12 .14 .16 27° 40.45 40.62 40.79 40. 96 41.12 41.29 1.02 .03 .05 .07 .08 .10 .12 .13 .15 28° 41.15 11.61 41.77 41.93 12.09 42.25 .05 .06 .08 .10 .11 .13 .14 29° 12.10 12.5C) 42.71 12.86 13.01 43.16 .02 .03 .05 .06 .OS .09 .11 .12 .14 80° -I3.:;o 14.01 01 03 04 .06 .07 .09 .10.11 .13 1 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 BAG. The cosine, cosecant, and cotangent of triangle ABC are as follows : BAG are respect- ively the sine, secant, and tangent of CAD, the complement of BAG. Represented as ratios, the functions of the angle A in the right-angled Cosine A = AB_ AC BG Tangent A = — Secant A = 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, 6, c the opposite sides, of any oblique triangle ; then . 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, 6, c £, C, c Area A B c Area A B, C Area C = 180° - (A + B) 6ain 7? sin A sin A b sin /I a C = 180° - (A + B) a sin C sin yl a2 sin B sin C 2 sin A i (/I + 5) = 90° - -J C a-6 tan -A- ( A Tl\ tin * (A \ TC\ a + b A = i (/I + B) + i (/I - B) cos £ (/i — B) sin ^ (/I — B) Area = £ a b sin C Let s = 4 (a + 6 + c) Then -in A i 4/(5 ~ 6) (^ - c) be be fnn i /< — /53. 5877 15 7 0 9925 1219 9851 2437 9776 3656 9702 4875 9627 6013 83 0 15 9920 1262 9840 2524 9760 3786 9680 6048 9600 6390 45 30 9914 1305 9829 2611 9743 3916 9658 5221 9572 6526 30 45 0.9909 0.1349 1.9817 0.2697 2.9726 0.4046 3.9635 0.5394 4.9543 0.6743 15 8 0 9903 1392 9805 2783 9708 4175 9611 5561 9513 6959 82 0 15 9897 1435 9793 2870 9690 4305 9586 5740 9483 7175 45 30 9890 1478 9780 2956 9670 4434 9561 5912 9451 7390 30 45 9884 1521 9767 3042 9651 4564 9534 6085 9418 7606 15 9 0 9877 1564 9754 3129 9631 4693 9508 6256 9384 7822 81 0 15 9870 1607 9740 3215 9610 4822 9480 6430 9350 8037 46 30 9863 1650 9726 3301 9589 4951 9451 6602 9314 8252 30 45 9856 1693{ 9711 3387 9567 5080 9422 6774 9278 8467 15 10 0 9848 1736 9696 3473 9544 5209 9392 6946 9240 8682 80 0 15 0.9840 0.1779 1.9681 0.3559 2.9521 0.5338 3.9362 0.7118 4.9202 0.8897 45 30 9833 1822 968S 3645 9498 5467 9330 7289 9163 9112 30 45 9825 1S05 9849 3730 9474 65% 9298 7461 9128 9326 16 11 0 9816 1908 9633 3816 9449 5724 9265 7632 9081 9540 79 0 15 9808 1951 9616 3902 9424 5853 9231 7804 9039 9755 46 30 9799 1994 9598 3987 9398 5981 9197 7975 8996 9968 30 45 9790 2036 9581 4073 9371 6109 9162 «146 8952 1.0182 16 12 0 9781 2079 9563 4158 9344 6237 9126 8316 8907 0396 78 0 15 9772 3122 9545 4244 9317 6860 9089 8487 8862 0609 45 30 9763 2ii;4 9526 4329 9289 6493 9052 8658 8815 0822 30 45 0.9753 0.2207 1.9507 0.4414 2.9260 0.6621 3.9014 0.8828 4,8767 1.1035 15 13 0 '.1744 2250 9487 4499 6231 6749 6976 8998 8719 1248 77 0 15 9734 2299 9468 4584 9201 6876 8935 9168 8669 1460 45 30 9734 2334 9447 4669 9171 7003 8895 Jtt'lS 8618 1C.72 30 45 9713 2377 9427 4754 9140 7131 8854 9507 8567 1884 15 14 0 9703 2419 M06 4838 9109 7258 8812 9677 76 0 15 0899 9888 9077 7385 8769 9846 8462 2308 45 30 0681 9868 5008 9044 7511 8726 1.0016 81. 7 2519 80 45 1670 9341 5092 9041 7f.3s 8682 0184 8352 2730 IB 15 0 MM 2868 9819 5176 8978 7766 8637 0353 B896 •.:in i 75 0 !»,,, Lat. Dep. Lat. Ucp. "LaT Dep. Lat. Dep. Lat. Dint. 1 Di«t. 2 Dist. 3 Diet. 4 ~~Di8t. 5 uourso I UAVMHSK TABU': 215 Dint. G Dist. 7 1 1 Dist. 8 Dist. 9 L 10 'Course Lat. Dep. Lat. j !>• p. lLat. Dep. Lat. I),-,,. Lat. !),„. o i'r, '5.9999 0.02G2 6.99990.0305 0.0349 0.039: 9.9999 30 9998 9'.i'.»7i 061 Ij 9997 9997 0873 30 45 9<>95 0786 9H1M 091 G 9993 1047 9992 U71 9991 1309 15 1 0 9991 1047 9989 9988 1396 1571 1745 89 0 15 9986 1309 99S3 1:VJ7 1746 9979 11IG3 9976 45 30 9979 1571 1882 2094 9966 2618 30 45 9972 1882 Din 17 21 as 1)963 2443 2748 15 2 0 9963 I'd'. (4 9957 2143 9951 2792 9945 3141 3490 88 0 15 9954 236(1 9114(1 274S 3141 9923 46 30 9948 2617 9933 8053 9924 3490 9914 3H2G 9905 43(12 30 45 5.9931 0.2879 6.9919 0.3358 7. 991 is 0.3838 0.4318 5 0.4798 15 3 0 9918 8140 91)04 9890 4187 4710 5284 87 0 15 9904 3402 9887 3968 9871 4535 9855 r>i(>2 9839 46 30 9888 3GG3 9869 4273 9851 4884 6494 9813 6105 30 45 9872 3924 9850 4578 5232 97SG (1540 15 4 0 9854 4186 9829 9806 5581 9781 9766 6976 8G 0 15 9836 4447 9808 6188 9780 5929 9763 6671 9725 7411 30 4708 97S4 5492 9753 9723 70(11 9692 78 if. 30 45 9794 49G8 9700 57H7 H725 9891 7453 9657 8281 15 5 0 9772 5229 9734 (1101 9G% 8972 9658 7844 9619 8716 86 0 15 5.9748 0.5490 6.9708 o.r»4or, 7.9G64 0.7320 S. 9(122 0.8235 .9580 0.9150 45 30 9724 5751 9678 G709 963'.' 9586 8626 9540 9585 30 45 9698 G011 9848 7013 9597 8015 9547 9017 9497 1.0019 15 G 0 15 9(571 9643 8272 6532 9817 9584 7: '.1 7 9562 7(121 9f/_T, 8362 8709 9507 9466 9408 9798 9452 9406 0453 0887 84 0 45 30 9G14 6792 9550 7U24 ; 9486 9056 9421 1.01SK 9357 1320 30 45 9584 7052 9516 9445 9403 5378 0578 9307 1754 16 7 0 Or,53 7312 9478 9404 9750 9329 9255 21S7 83 0 15 30 95L>0 9487 7572 7832 9440 9401 8834 9137 931G 1.0096 0442 92S( 9230 1358 1747 9200 9144 26201 45 3053 30 45 5.9452 0.8091 G.93G1 0.944o"7.92(; 8633 6628 731080 0 15 r>.9()42 1.0677 6.8883 1.2456 7.872:? 1.4285 8.8564 1.6015 9.8404 17794 4r, 30 8995 0934 8728 2756 8660 4579 8493 6401 8325 8224 30 45 8947 1191 8772 8067 8596 41 122 S421 6787 8245 Sf,r>2 15 11 0 8898 1449 8714 3357 8530 5266 8346 7173 8163 9081 79 0 15 8S47 1705 8655 :;65G 8403 5G07 8271 7558 8079 9509 45 30 8795 1962 8596 3D56 83'. >4 5949 8193 7943 79H2 9937, 30 45 8743 2219 8533 4255 832 1 6291 8114 8328 7'.t05 2.03G4 15 12 0 8689 2475 8470 4554 8033 8712 7815 0791 78 0 15 8634 2731 8406 4852 8178 8974 7951 9096 7723 1218 45 30 8578 298(5 8341 5151 8104 7315 7867 94s() 7630 1644 30 45 5.8521 1.3242 6.8274 1.5449 7.8027 1.7G.-,G 8.7781 1.98G3 9.7534 2.2070 15 13 0 8462 3497 8206 5747 71 !.",() 7996 7693 2. 0246 7137 2-41C, 77 0 15 8403 3752 8137 6044 7870 8836 7604 0628 21 '20 45 30 8342 4007 8066 6341 7790 8676] 7513 1010 7237 8345 30 45 8281 4261 7994 6638 7707 9015 7421 1392 7134 8769 15 14 0 8218 4515 7U2 1 6936 7624 9354 7327 1773 7030 419276 0 15 8154 47J9 7846 7231 7538 9692 7231 2164 4615 45 30 8089 5023 7770 7627 7452 2.0030 7133 2534 8816 503s 30 45 8023 5276 7693 7822 7364 0368 7034 2914 6705 54f.(i 15 15 0 7956 5529 7615 8117 7274 0706 6933 3294 6593 re o Dep. Lat, Dep. Lat. Dep.| Lat. Dep. Lat. Dep. L«t. ^ rm re A Dist. 6 Dist. 7 Dist. 8 Dist. 9 Dist. 10 JUUlOC 216 TRAVERSE TABLE Diet. 1 Dist. 2 Dist. 3 Diet. 4 Dist. 5 Course Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1515 0.9648 0.2630 1.9296 0.5261 2.8944 0.7891 3.8591 1.0521 4.8239 1.3152 74 45 30 9636 2672 92731 6345 8909 8017 8545 0090 8182 3362 30 45 9625 2714 9249 5429 8874 8143 8498 0858 8123 3572 15 16 0 9613 2756 9225 5513 8838 8269 8450 1023 8063 3782 74 0 15 9600 2798 9201 5597 8801 8395 8402 1193 8002 3991 45 30 9588 2840 9176 5680 8765 8520 8353 1361 794 4201 30 45 9576 2882 9151 5764 8727 8646 8303 1528 7879 4410 15 17 0 9563 2924 9126 5847 8689 8771 8252 1695 7815 4619 73 0 15 9550 2965 9100 5931 8651 8896 8201 1862 7751 4827 45 30 9537 3007 9074 6014 8612 9021 8149 2028 7686 6035 30 45 0.9524 0.3049 1.9048 0.6097 2.8572 0.9146 3.8096 1.2195 4.7620 1.5243 15 18 0 9511 3090 9021 6180 8532 9271 8042 2361 7553 5451 72 0 15 9497 3132 8994 6263 8491 9395 7988 2527 7485 ii678 45 30 9483 3173 8966 6346 8450 9519 7933 2692 7416 5865 30 45 9469 3214 8939 6429 8408 9(543 7877 2858 7347 6072 16 19 0 9455 3256 8910 6511 8366 K7I ;7 7821 3023 7276 6278 71 0 15 9441 3297 8882 6594 8323 9891 7764 3188 7204 6485 45 30 9426 3338 8853 6676 8279 1.0014 7706 3352 7132 6690 30 45 9412 3379 8824 6758 8235 0138 7647 3517 7059 6896 15 20 0 9397 3420 8794 6840 8191 0261 7588 3081 6985 7101 70 0 15 0.9382 0.3461 1.8764 0.6922 2.8146 1.0384 3.7528 1.3845 4.6910 1.7306 45 30 9367 3502 8733 7004 8100 0506 7467 4008 6884 7510 30 45 9351 3543 8703 7086 8054 0629 7405 4172 675" 7715 15 21 0 9336 3584 8672 7167 8007 0751 7343 4335 6679 7918 69 0 15 9320 3624 8640 7249 7960 0873 7280 4498 0000 8122 45 30 9304 3666 8608 7330 7913 0995 7217 4660 6521 8325 30 45 9288 3706 8576 7411 7864 1117 7152 4822 6440 8528 15 22 0 9272 3746 8544 7492 7816 1238 7087 4984 6359 8730 68 0 15 9255 3786 8511 7573 7766 1359 7022 6140 6277 8931, 45 30 9239 3827 8478 7654 7726 1481 6955 5307 6194 9134 30 45 0.9222 0.3867 1.8444 0.7734 2.7666 1.1601 3.6888 1.5468 4.6110 1.9336 15 23 0 9205 3907 8410 7815 7615 1722 6820 5029 002" 953" 67 0 15 9188 3947 8376 7895 7564 1842 6752 5790 5940 9737 46 30 9171 3987 8341 7975 7512 1962 6682 5950 5853 9937 30 45 9153 4027 8306 8055 7459 2082 6612 6110 5760 2.0137 15 24 0 9135 4067 8271 8135 7406 '2-20-2 6542 6569 5677 0337 66 0 15 9118 4107 8235 8214 7353 2322 6470 04'2'J 5588 0530 45 30 9100 4147 8199 8294 7299 2441 6398 6588 M9,x 073T 30 45 9081 4187 8163 8373 7214 2500 6326 6746 6407 0933 15 25 0 9063 4226 8126 8452 7189 2679 6252 6905 5315 1131 65 0 15 0.9045 0.4266 1.8089 0.8531 2.7034 1.2797 3.6178 1.7063 4.5223 2.1328 45 30 9020 4305 8052 8610 7078 2915 6103 7220 5129 1621 30 45 9007 4344 8014 8689 7021 3033 6028 7378 6035 1722 5 26 0| 8988 4384 7976 8767 6964 3151 5952 7535 4940 1919 64 0 15 8909 4423 7937 8846 6906 3269 5875 7692 4844 '2114 45 30 8949 4462 7899 8924 6848 33S6 5797 7848 4747 2310 30 45 8930 4501 7860 9002 6789 3503, 5719 8004 4649 2505 15 27 0 8910 4540 7820 9080 6730 3«J20 5640 8160 4550 2700 63 0 15 8890 4579 7780 9157 6671 8786 6661 8315 4451 2894 45 30 8870 4617 7740 9235 6610 8862 5480 8470 4351 3087 30 45 0.8S50 0.4656 1.7700 09312 2.6550 1.3968; 3.5400 .S«!2.p> 4.4249 2.3-281 15 28 (i 4695 7660 B8M 6488 HIM 5318 87711 4147 3474 62 0 16 MM 4733 7618 9466 <;4-_>7 4200 6286 8933 4046 45 30 8788 4772 757os 1580 2691 5527 1879 9474 45 30 5024 3925 41i>4 7912 3365 1900 2535 5887 1706 9875 30 45 4919 4165 4072 8192 3225 2220 2375 6247 1531 4.027f 15 24 0 4813 4404 3948 8472 3084 2639 2219 1355 0674 66 0 15 4706 4643 3823 8750 2941 2858 2059 6965 1171 1072 45 30 4598 4882 3697! 9029 2797 3175 1897 7322 0996 1469 30 45 4489 5120 35701 9306 2661 3493 1733 7679 CM 4 1866 15 25 0 4378 5357 :U!2 9583 2606 3809 1568 8036 0631 2262 66 0 15 5.4267 2.5594 6.3312 2 9800 7.2356 3.4125 8.1401 ;.,s39i 9.0446 4.2657 45 30 4155 5831 3181 3.0136 2207 4441 1233 8746 0259 3051 30 45 4042 6007 :;i;ii) 04ii 2056 4756 1063 91001 0070 3445 15 26 0 3928 6302 2916 0686 1904 6070 0891 945:; 8.9879 3837 64 0 15 3812 6537 2781 0900 1750 5.383 0719 «.isi)6 9687 4229 45 30 3096 0772 2646 12:;4 151)5 5696 064 1 4.01T.8 9493 4620 30 45 3579 7006 2509 1507 1438 6008 0509 5010 15 27 (I 3460 7239 2:170 1779 12S1 6319 0191 0859 9101 63 0 15 3341 7472 2231 2051 1121 6630 0012 1209 8902 6787 45 30 3221 7705 2091 2,322 0961 6940 7.9831 1557 8701 6175 30 45 5.3099 2.7937 6.1949 .'5.2593 7.0799 3.7249 7.9649 4.1905 8.8499 4.6661 16 28 0 2977 8168 1806 2803 0636 7558 9466 2262 6947 62 0 15 2853 8399 1662 3132 6471 7866 9280 2599 8089 7332 45 30 2729 8630 1517 .'5401 0305 M7.3 9094 2944 7882 7716 30 46 2604 8859 1371 3669 0138 8479 8905 .3289 7673 8099 15 29 0 2477 9089 122:5 .39:57 6.9970 8786 8716 3683 7462 8481 SI 0 16 2350 9317 1075 42( 13 9090 8976 7250 8862 46 80 2221 9545 0925 4470 9394 4318 7036 9242 30 45 2092 977:; 0774 4735 9456 9697 8118 4669 6820 ! it ;•_'•_• 15 30 0 19G2 3.0000 0622 6000 4.0000 7942 6000 6603 5.0000 30 0 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. | Lat. Dist. 6 Dist. 7 Dist. 8 Dist. 9 Dist. 10 Jourse 218 TRAVERSE TABLE finnrqp Dist. 1 Dist. 2 Dist. 3 Dist. 4 Dist. 5 uoursc Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep, 30 15 0.8638 0.5038 1.7277 1.0075 2.5915 1.5113 3.4653 2.0151 4.3192 2.5189 59 45 30 8616 5075 7223 0151 5849 5226 4465 0302! 3081 5377 30 45 8594 5113 7188 0226 5782 5339 4376 0452 2970 5565 15 31 0 8572 5150 7142 0301 5715 5451 4287 0602 2858 5752 59 0 15 8549 5188 7098 0375 5647 5563 4196 0751 2746 5939 45 30 8526 5225 7053 0450 5579 5675 4106 0900 2632 6125 30 45 8504 5262 7007 0524 5511 5786 4014 1049 2518 6311 15 32 0 8480 5299 6961 0598 5441 5898 3922 1197 2402 6496 58 0 15 8457 5336 6915 0672 5372 6008 3829 1345 2286 6681 45 30 8434 5373 6868 0746 5302 6119 3736 1492 2170 6865 30 45 0.8410 0.5410 1.6821 1.0819 2 5231 1.6229 3.3642 2.1639 4.2052 2.7049 15 33 0 8387 5446 6773 0893 5160 6339 3547 1786 1934 7232 57 0 15 8363 5483 6726 0966 5089 6449 3451 1932 1814 7415 45 30 8339 5519 6678 1039 5017 6558 3355 2077 1694 7597 30 45 8315 5556 6629 1111 4944 6667 3259 2223 1573 7779 15 34 0 8290 5592 6581 1184 4871 6776 3162 2368 1452 7960 56 0 15 8266 5628 6532 1256 4798 6884 3064 2512 1329 3140 45 30 8241 5664 6483 1328 4724 G992 2965 2656 1206 8323 30 45 8216 5700 6433 1400 4649 7100 2866 2800 1082 8500 18 35 0 8192 5736 6383 1472 4575 7207 2766 2943 0958 8679 55 0 15 0.8166 0.5771 1.6333 1.1543 2.4499 1.7314 3.2666 2.3086 4.0832 2.8857 45 30 8141 5807 6282 1614 4423 7421 251J5 3228 0706 9035 30 45 8116 5842 6231 1685 4347 7527 2463 3370 0579 9212 15 36 0 8090 5878 6180 1756 4271 7634 2361 3511 0451 9389 54 0 15 8064 5913 6129 1826 4193 7739 2258 3652 0322 9565 45 30 8039 5948 6077 1896 4116 7845 2154 3793 0193 9741 30 45 8013 5983 6025 1966 4038 7950 2050 3933 0063 9916 15 37 0 7986 6018 5973 2036 3959 8054 1945 4073 3.9932 3.009153 0 15 7960 6053 5920 2106 3880 8159 1840 4212 9800 0365 45 30 7934 6088 5867 2175 3801 8263 1734 4350 9668 0438 30 45 0.7907 0.6122 1.5814 1.2244 2.3721 1.8367 3.1628 2.4489 3.9534 3.0611 15 38 0 7880 6157 5760 2313 3640 8470 1520 4<;-_><; 9400 0783 52 0 15 7853 6191 5706 2482 3560 8573 1413 4764 9266 0966 45 30 7826 6225 5652 2450 3478 8675 1304 4901 9130 1128 30 45 7799 6259 5598 2518 3397 8778 11951 5037 8994 1296 15 39 0 7771 6293 5.543 2586 3314 8880 1086 5173 8857 1466 51 0 15 7744 6327 5488 2654 3232 8981 0976 5308; 8720 1635 45 30 7716 6361 5432 2722 3149 9082 0865 5443 8581 1804 30 45 7688 6394 5377 2789 3065 9183 0754 5578 8442 1972 15 40 0 7660 6428 5321 2856 2981 9284 0642 5512 8302 2139 50 0 15 0.7632 0.6461 1.5265 1.2922 2.2897 1.9384 3.0529 2.5845 3.8162 3.2306 45 30 7604 6494 5208 2989 2812 9463 0416 5978 8020 •_'472 30 45 7576 6528 6151 3055 2727 9583 0303 6110 7878 15 41 0 7547 6561 5094 3121 2641 9682 0188 6242 7735 2803 49 0 15 7518 6593 5037 3187 2555 9780 0074 6374 7692 2967 48 30 7490 6626 4979 3252 2469 9879 2.9958 6505 744S 3131 30 45 7461 6659 4921 3318 2382 9976 9642 6636 7303 3294 15 42 0 7431 6891 4863 3888 2294 2.0074 9726 <>7Ur. 7157 8467 48 0 15 7402 6724 4-04 3447 2207 0171 9609 6896 7iM1 3618 46 30 7373 6756 4746 3512 2118 0268 9491 7024 6864 3780 30 10 0.7343 0.6788 1.4686 1.3576 2.2030 _>.o;;r,i 2.9873 2.7152 S.i'TH: 15 43 0 7314 6820 4627 3C40 1041 0460 9264 7280 6668 4100 47 0 15 7284 6852 4567 3704 1851 0555 9186 7-107 6419 4259 30 7254 6884 4507 3767 1761 OI151 9015 7684 6268 4418 30 45 7224 0010 4447 8880 1C.71 0745 8898 7661 6118 4676 US 44 0 7198 li'.»47 4387 3893 UWO 0840 8774 7786 6967 4t; o 15 7KJ3 0978 4896 3966 1 ix'i 091*4 7912 30 7133 TOOK 4268 4018 1308 1027 8680 8086 6663 6046 30 tf TUB THKI 4904 4080 1806 1120 8407 8161 16 45 0 7071 7071 1 1 r_- 1218 1218 8284 B284 15 0 Lat Dep. Lat. Lat. Dep. Lat. DeP. Lat. Dint. 1 Di.st. -2 Dist. 3 | Dist. 4 Dirt. 6 Course TRAVKHSi; TABU-: 219 Dist. 6 t. 7 Diat. 8 Dist. 9 Gourse Lat. Dep. Dep. Lat. 1.,,,. Lat. Dap. Dep. . 5.1880 4.0:!ir_' 1 53H B.6884 5.0377 fill 45 3< in; is 0452 0314 0603 7547 0754 30 45 1064 01 ITS 0158 571(1 niio:; 7347 6011 5941 1121 15 31 0 1430 0902 0002 6058 8573 1203 7145 6717 1504 ;7.» 0 16 1295 1120 5.9844 6314 8393 6491 1877 80 1158 1350 9085 SJl 1 1800 6738 2250 30 45 1021 1573 9525 8028 2097 053:. 5081 15 32 0 0883 1795 701)4 7844 6324 7«.n: 4801 2982 58 0 15 0744 9201 7353 7658 6111 8025 3361 45 30 0003 2238 9037 7011 7471 2884 5906 8357 4339 30 45 5.0462 3.2458 5.8873 6.728! 4.3278 4.SOSS 8.4104 5, 10!)7 16 3? 0 0320 2678 8707 SI 25 7094 3571 4404 67 0 15 0177 8540 8901 3629 4S21 45 30 0033 3110 8372 8636 0711 4155 91174 3389 5 I'M 30 45 4.9888 3334 8203 8890 6518 4440 4832 3147 5557 16 34 0 9742 3552 8033 9144 47.T, 4613 0327 2904 59 11 66 0 15 9595 3708 786J 9396 0127 5024 4393 2659 6281 45 30 9448 3984 7689 9048 593) 5812 4171 0977 2413 6641 30 45 9299 4200 7616 9900 5732 5i;oo 3948 1300 7000 15 35 0 9149 4415 7341 1.0150 5632 5886 3724 1022 1915 7358 55 0 15 4.8998 3.4629 5.7105 4.0400 6.5331 4.6172 7.3498 5.1943 8.1664 6.7716 45 30 SS47 4842 6988 004!) 5129 6456 3270 1412 8070 30 45 8<;.!>4 5055 6810 0897 4920 6740 3042 2582 1157 8425 15 3G 0 S5 1 1 6031 1145 4721 7023 2812 2901 0902 8779 64 0 15 8387 5479 645] 1392 4510 7305 25SO 3218 0044 9131 45 30 8231 0270 1688 4309 7586 2347 3534 0386 94SL 30 45 8075 5899 6088 1883 4100 7866 2113 3849 0125 9832 10 37 0 7918 0109 5904 2127 3891 8145 1877 4193 7.98M 6.0182 53 0 15 77(10 6318 5720 2371 3680 8424 1040 4470 9000 0529 45 30 7601 6526 5536 2013 3468 8701 1402 4789 9335 0876 30 45 4.7441 3. 0733 ! 4.2S55 6.3255 4.8977 7.1102 5.5100 7.9069 6.1222 15 38 0 7281 6940 5101 ::nm; 3041 9253 0921 5410 8801 15tK 52 0 15 7119 714(1 4972 3337 0079 5718 8532 1909 45 30 6956 7351 4783 8576 2009 9801 0435 6026 8201 2251 30 45 6793 7555 4599 3815 2391 5.0074 0190 03M3 7988 2692 15 39 0 6629 7759 4400 4052 2172 0340 6.9943 6639 7715 2932 51 0 15 6464 7962 4207 4289 1951 0010 9696 6943 7439 3271 45 30 6297 8165 4014 4525 1730 0886 9440 7247 7162 3608 30 45 0131 8366 3819 4701 1507 1166 011)0 7550 6884 3944 15 40 0 59C3 8567 3023 4995 1284 1423 8944 7851 0(04 4279 50 0 15 4.5794 3.8767 5.3426 4.5229 6.1059 5.1690 6.8691 5.8151 7.6323 6.4612 45 30 6624 8987 3228 5401 0832 1966 8437 8450 6041 4945 30 45 5454 9100 3030 6693 0605 2221 8181 8748 5276 15 41 0 5283 9314 2830 5924 0377 2486 7924 9045 5471 500(1 49 0 15 5110 9661 2629 6154 0147 2748 7666 9341 5184 6935 45 30 4937 9757 2427 5.9916 3010 7400 9638 489) 6282 30 45 4703 9953 2224 01.12 9685 3271 7145 9929 4601 6588 15 42 0 4589 4.0148 2020 6839 9452 3530 GSS3 ',0222 4314 0913 48 0 15 4413 0342 1815 7000 9217 3789 6620 4022 7237 45 30 4237 0535 KM 19 7291 8982 4047 0803 3728 7559 30 46 4.4059 4.072S j.l 403 4.7510 5.8746 "..430! ;.f,osi) '..1002 6.7880 15 43 0 3881 0920 1 l!>r, 7740 8508 4560 5822 13SO 3135 8200 47 0 15 3702 1111 OUStl 7903 S270 4S15 5553 1666 2837 45 30 3522 1301 07T6 8185 8030 5HOS 8835 30 45 3342 1491 0666 8400 5018 2236 P151 15 44 0 3100 1680 0354 7547 5573 4711 2519 ID: 'A 9466 46 0 15 2978 1807 01411 SS45 7304 5823 4467 2801 1630 9779 45 30 2796 2066 4.91)28 1)0(4 70(!0 6073 4193 1326 7.0091 30 45 2611 2241 D713 92S1 6815 3917 1019 0401 IB 45 0 2426 2426 9477 9497 6569 6569 3040 8640 0711 0711 45 0 Dep. Lat. D^pT ~LatT Dep. Lat. Dep. Lat. Dep. Lat. •nurcp Dist. 6 Dist. 7 Dist. 8 Dist. 9 | Dist. 10 ;OUr be 220 A MANUAL FOR NORTHERN WOODSMEN LOGARITHMS OF NUMBERS No. 0 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 0569 0607 0645 0682 0719 0755 12 0792 0828 0864 0899 0934 0969 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 2480 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 5658 5670 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5S99 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 (ttl'O 43 6335 6345 6355 6365 6375 6385 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 6665 6675 6684 6693 6702 6712 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 (581)3 49 6902 6911 6920 6928 6U37 6946 6955 6964 6972 6981 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7007 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7 1 ;.L' 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 723fi 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7318 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 No. 0 1 2 3 4 5 6 7 8 9 TAIJLI-:S UI;LAII.\<; TO PARTS I AND n 221 LOGARITHMS OF NUMHKKS No. 0 1 2 3 4 5 6 7 8 9 55 7404 7412 7419 7427 7435 7443 7461 7459 7466 7474 56 7482 7490 7497 7505 7513 7520 7536 7643 7551 57 7559 7566 7574 7:>x<.) 7597 7604 7612 7619 7627 58 7634 7642 7649 7657 7664 7(172 7679 7686 7694 7701 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 60 7782 7789 7796 7S03 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7903 7910 7917 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 63 7993 8000 8007 8014 8021 sous 8035 8041 S048 S055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 S254 67 8261 8267 8274 S2SO 8287 8293 8299 8306 8312 S3 19 68 8325 8331 833.x 8344 8351 8357 X3<>:* X370 8376 83X2 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8-1 -15 70 8451 8457 8463 8470 8476 8488 8494 8500 8506 71 8513 8519 SoL'5 8531 8637 S5-13 8549 8555 8561 8567 72 8573 8579 S5S5 8591 8597 8603 S<;0<> 8615 8621 8627 73 8633 8639 8645 8651 8657 8663 S669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 76 8808 8814 8820 8831 8837 8842 8848 8854 8S59 77 SS65 8871 SS7C) 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 SU3S 8943 8949 8954 8960 8965 8971 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 82 9138 OH 3 9149 9154 9159 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 7340 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 91 9590 9595 9600 9605 9609 9614 DC, H) 9624 <><>2S 9633 92 9638 9643 9647 6952 9657 9661 9666 9671 U()75 9680 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9632 9S3<5 9841 9845 9850 9854 9S50 98«3 97 9868 9872 9877 9881 9890 9894 9899 9903 990S 98 9912 9917 9921 9926 W30 9943 9948 9952 99 9956 9961 9965 9969 9974 9987 '.!!>!> 1 9996 No. 0 1 2 3 4 5 i 6 7 8 9 222 A MANUAL FOR NORTHERN WOODSMEN LOGARITHMIC SINES, COSINES, Angle Sin. D.I' Cos. D.r Tan. D.r Cot. 0° 0' 00 10.0000 00 00 90° 0' 0° 10' 0° 20' 0° 30' 0° 40' 0° 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 .0 J 7.4637 .7648 .9409 8.0658 .1627 301.1 176.1 124.9 96.9 79 2 2.5363 .2352 .0591 1.9342 .8373 89° 50' 89° 40' 89° 30' 89° 20' 89° 10' 1° 0' 8.2419 fifi Q 9.9999 8.2419 67 0 1.75H1 89° (X 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 37 g .6911 .6331 .5819 .5362 .4947 88° 50' 88° 40' 88° 30' 88° 20' 88° 10' 2° 0' 8.5428 04 o 9.9997 o 8.5431 34 8 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 04 Q .9997 .9996 .9996 .9995 .9995 .1 .0 .1 .0 1 .5779 .6101 .6401 .6682 .6945 32.2 30.0 28.1 26.3 24 9 .4221 .3899 .3599 .3318 .3055 87° 50' 87° 40' 87° 30' 87° 20' 87° 10' 3° 0' 8.7188 oq c 9.9994 1 8.7194 23 5 1.2SO<> 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 IOC .9993 .9993 .9992 .9991 .9990 .0 .7429 .7652 .7865 .8067 .8261 22.3 21.3 20.2 19.4 18 5 . .2571 .2348 .2135 .1933 .1739 86° 50' 86° 40' 86° 30' 86° 20' 86° 10' 4° 0' 8.8436 177 9.9989 o 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 15.2 147 .9989 .9988 .9987 .9986 .9985 '.1 .1 2 .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 .1 8.9420 143 1.0580 85° 0' 5° 10' 5° 20' 6° 30' 5° 40' 5° 50' .9545 .9682 .9816 .9945 9.0070 13.7 13.4 12.9 12.5 •too .9982 .9981 .9980 .9979 .9977 .1 .1 .1 .2 .1 .9563 .9701 .9836 .9966 9.0093 13.8 13.5 13.0 12.7 12 3 .0437 .0299 .0164 .0034 0.9907 84° 50' 84° 40' 84° 30' 84° 20' 84° 10' 6° 0' 9.0192 no 9.9976 j 9.02 Hi 12 0 0.9784 84° 0' 6° 10' 6° 20' 6° 30' 6° 40' 6° 50' .(Kill .0426 .0539 .0648 .0755 11.5 11.3 10.9 10.7 in 4 .9975 .9973 .9972 .9971 .9969 .2 .1 .1 .2 1 .0336 .0453 .0567 .0678 .0786 11.7 11.4 11.1 10.8 10 5 .9664 .9547 .9433 .9322 .'.'21 1 83° 50' 83° 40' 83° 30' 83° 20' 83° 10' 7° 0' 9.<)Sf> » in 2 «>.«I«.M;S 9.0S91 10 4 O.'.HOit 83° 0' 7° 10' 7° 20' 7° 30' .<)«.»<) 1 .1060 .1157 9.9 9.7 .9966 ,9964 .9963 .2 .1 .0090 1096 .1194 10.1 9.8 .9005 £904 ,8808 82° 50' 82° 40' 82° 30' Cos. D.r Sin. D.r Cot. D.r Tan. Angle TABLES KKLATIM; TO I-AIMS i .\.\i> 223 TANGENTS, AND COTAN( ; 1 Angle Sin. D.I' Cos. D.I' Tan. D.I' Cot. 7° 30' 7° 40' 7° 50' 9.1157 .1252 .1345 9.5 9.3 9 1 9.9963 .9961 .9959 .2 .2 I 9.1194 .1386 9.7 9.4 9 3 O.SSOC, .8709 .8615 82° 30' SIT 20' 82° 10' 8° 0' 9.1436 8 9 9.9968 2 9.1478 9 1 O.N522 82° 0' 8° 10' 8° 20' 8° 30' 8° 40' 8° 50' . 1 5'2-, .1612 .1697 .1781 .1863 8.7 8.5 8.4 8.2 .9956 .9964 [9962 .9950 .9948 .2 .2 .2 .2 ,1669 .1746 .1915 8.9 8.7 8.6 8.4 8 2 .8431 .8342 .8169 .SONS 81° 50' 81° 40' 81° 30' 81° 20' 81° 10' 9° 0' 9.1943 8.0 9.119-Hi 9.1997 8 1 o.s:> 81° 0' 9° 10' 9° 20' 9° 30' 9° 40' 9° 50' .2022 .2100 .2176 .2251 .2324 7.9 7.8 7.6 7.5 7.3 .9944 .9942 .9940 .9938 .9936 .2 .2 .2 .2 .2 .2078 .2158 !2236 .2313 .2389 8.0 7.8 7.7 7.6 .7922 .7842 .7764 .7687 .7611 80° 50' 80° 40' so w ,M)J 20' 80° 10' 10° 0' 9.2397 7.3 9.9934 .2 9.2463 7.4 0.7537 80° 0' 10° 10' 10° 20' 10° 30' 10° 40' 10° 50' .2468 .2538 .2606 .2674 .2740 7.1 7.0 6.8 6.8 6.6 .9931 .9929 .9927 .9924 .9922 .3 .2 .2 .3 .2 12609 .2680 .2750 .2819 7.3 7.3 7.1 7.0 6.9 .7464 .7391 .7320 .7250 .7181 79° 50' 79° 40' 79° 30' 79° 20' 79° 10' 11° 0' <>.2S()t> 6.6 9.W u» .3 9.2XX7 6.8 0.7113 79° 0' 11° 10' 11° 20' 11° 30' 11° 40' 11° 50' .2870 .2934 .2997 .3058 .3119 6.4 6.4 6.3 6.1 6.1 .9917 .9914 .9912 .9909 .9907 .2 .3 .2 .3 .2 .2953 .3020 .3085 .3149 .3212 6.6 6.7 6.5 6.4 6.3 .7047 .6980 .6915 .6851 .(5788 78° 50' 78° 40' 78° 30' 78° 20' 78° 10' 12° 0' 9.3179 6.0 9.9904 .3 9.3275 6.3 0.0725 78° 0' 12° 10' 12° -20' 12° 30' 12° 40' 12° 50' .3238 .3296 .3353 .3410 .3466 5.9 5.8 5.7 5.7 5.6 .9901 .9899 19896 J9893 .9890 .3 .2 .3 .3 .3 .3336 .3397 .3517 .3576 6.1 6.1 6.1 5.9 5.9 .6603 .6542 .6483 .0424 77° 50' 77° 40' 77° 30' 77° 20' 77° 10' 13° 0' 9.3521 5.5 9.9887 .3 9.3634 5.8 or>:;r>r> 77° 0' 13° 10' 13° 20' 13° 30' 13° 40' 13° 50' .3575 .3629 .3682 .3734 .3786 5.4 5.4 5.3 5.2 5.2 .9884 .9881 .9878 .9875 .9872 .3 .3 .3 .3 .3 .3691 13748 .3804 .3859 .3914 5.7 5.7 5.6 5.5 5.5 .6309 .6252 .6196 .6141 .6086 76° 50' 76° 40' 76° 30' 76° 20' 76° 10' 14° 0' 9.3837 5.1 9.9S69 9.396S O.4 0.6032 76° 0' 14° 10' 14° 20' 14° 30' 14° 40' 14° 50' .3887 .3937 .3986 .4035 .4083 5.0 4.9 i.9 4.8 .9866 [9863 .9869 .9866 .9863 .3 .4 .3 .3 .4021 .4074 .4127 .4178 !4230 5.3 5.3 5.1 5.2 .5979 .5926 .5873 .5822 .5770 75° 50' 75° 40' 75° 30' 75° 20' 75° 10' 15° 0' 9.4130 9.9849 0.5719 75° 0' 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' Cot. 15° 0' 9.4130 4 7 9.9849 3 9.4281 5 0 0.5719 75° 0' 15° 10' 15° 20' 15° 30' 15° 40' 15° 50' .4177 .4223 .4269 .4314 .4359 4.6 4.6 4.5 4.5 4 4 .9846 .9843 .9839 .9836 .9832 .3 .4 .3 .4 4 .4331 .4381 .4430 .4479 .4527 5.0 4.9 4.9 4.8 4 3 .5669 .5619 .5570 .5521 .5473 74° 50' 74° 40' 74° 30' 74° 20' 74° 10' 16° 0' 9.4403 4 4 9.9828 3 9.4575 4 7 0.5425 74° 0' 16° 10' 16° 20' 16° 30' 16° 40' 16° 50' .4447 .4491 .4533 .4576 .4618 4.4 4.2 4.3 4.2 4 1 .9825 .9821 .9817 .9814 .9810 .4 .4 .3 .4 4 .4622 .4669 .4716 .4762 .4808 4.7 4.7 4.6 4.6 4 5 .5378 .5331 .5284 .5238 .5192 73° 50' 73° 40' 73° 30' 73° 20' 73° 10' 17° 0' 9.4659 4 1 9.9806 4 9.4853 4 5 0.5147 73° 0' 17° 10' 17° 20' 17° 30' 17° 40' 17° 50' .4700 .4741 .4781 .4821 .4861 4.1 4.0 4.0 4.0 3 9 .9802 .9798 .9794 .9790 .9786 .4 .4 .4 .4 4 .4898 .4943 .4987 .5031 .5075 4.5 4.4 4.4 4.4 4 3 .5102 .5057 .5013 .4969 .4925 72° 50' 72° 40' 72° 30' 72° 20' 72° 10' 18° 0' 9.4900 3 9 9.9782 4 9.5118 4 3 0.4882 72° 0' 18° 10' 18° 20' 18° 30' 18° 40' 18° 50' .4939 .4977 .5015 .5052 .5090 3.8 3.8 3.7 3.8 3 6 .9778 .9774 .9770 .9765 .9761 .4 .4 .5 .4 4 .5161 .5203 .5245 .5287 .5329 4.2 4.2 4.2 4.2 4 1 .4839 .4797 .4755 .4713 .4671 71° 50' 71° 40' 71° 30' 71° 20' 71° 10' 19° 0' 9.5126 3 7 9.9757 5 9.5370 4 1 0.4630 71° 0' 19° 10' 19° 20' 19° 30' 19° 40' 19° 50' .5163 .5199 .5235 .5270 .5306 3.6 3.6 3.5 3.6 3 5 .9752 .9748 .9743 .9739 .9734 .4 .5 .4 .5 4 .5411 .5451 .5491 .5531 .5571 4.0 4.0 4.0 4.0 40 .4589 .4549 .4509 .4469 .4429 70° 50' 70° 40' 70° 30' 70° 20' 70° 10' 20° 0' 9.5341 3 4 9.9730 5 9.5611 3 9 0.4389 70° 0' 20° 10' 20° 20' 20° 30' 20° 40' 20° 50' .5375 .5409 .5443 .5477 .5510 3.4 3.4 3.4 3.3 3 3 .9725 .9721 .9716 .9711 .9706 .4 .5 .5 .5 4 .5650 .5389 .5727 .5766 .5804 3.9 3.8 3.9 3.8 3 8 .4350 .4311 .4273 .4234 .4196 69° 50' 69° 40' 69° 30' 69° 20' 69° 10' 21° 0' 9.5543 3 3 9.9702 5 9.6842 3 7 0.4158 89° 0' 21° 10' 21° 20' 21° 30' 21° 40' 21° 50' .5576 .5609 .5641 .5673 .5704 3.3 3.2 3.2 3.1 .9697 .9692 .9687 .9682 .9677 .5 .5 .5 .5 5 .5879 .5917 .5954 .5991 .6028 3.8 3.7 3.7 3.7 .4121 .4083 .4046 .4009 .3972 68° 50' 68° 40' 68° 30' 68° 20' 68° 10' 22° 0' l).57:i<> 3.2 72 5 'UMW-l 0.3936 68° 0' 22° 10' 22° 20' 22° 30' .5767 .5798 .5828 3.1 8.1 3.0 .9667 .9661 .9656 .6 .5 .C.IOO .6136 .6172 3.6 3.6 3.6 .3900 .3864 .3828 67° 50' 67° 40' 67° 30' Cos. D.I' Sin. D.I' Cot. D.I' Tan. Angle TABLES KKLATI.M; TO I-AKTS i AND n 225 TANGENTS, AND COTANGENTS Angle Sin. D.I' Cos. D.I' Tan. D.I' Cot. 22° 30' 22° 40' 22° 50' 9.5828 .5859 .5889 3.1 3.0 3 0 9.9656 .9651 .9646 .5 .5 6 9.6172 .6208 .6243 3.6 3 6 0.3828 .3792 .3757 67° 30' 67° 20' 67° 10' 23° 0' 9.5919 2 9 9.9640 5 9.6279 3 5 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 g .9635 .9629 .9624 .9618 .9613 .6 .5 .6 .5 6 .6314 16348 !6383 .6417 .6452 3.4 3.5 3.4 3.5 3 4 .3686 .3617 .3548 66° 50' 66° 40' 66° 30' 66° 20' 66° 10' 24° 0' 9.601)3 2 g 9.9007 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 .9(502 .9596 .9590 .9584 .957'.) .6 .6 .6 .5 g .6520 .6553 .6587 .6620 .6654 3.3 3.4 3.3 3.4 3 3 .34 SO .3447 .3413 .3380 .3346 65° 50' 65° 40' 65° 30' 65° 20' 65° 10' 25° 0' 9.6259 2 7 9.9573 Q 9.6687 3 3 0.3313 66° 0' 25° 10' 25° 20' 25° 30' 25° 40' 25° 50' .6286 .6313 .6340 .6366 .6392 2.7 2.7 2.6 2.6 2 6 .9567 .9561 .9555 .9549 .9543 .6 .6 .6 .6 6 .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 Q 9.9537 7 9.6882 3 2 0.3118 64° 0' 26° 10' 26° 20' 26° 30' 26° 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 6 .6914 .6946 .6977 .7009 .7040 3.2 31 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 2 5 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 6 9.7257 3 0 0.2743 62° 0' 28° 10' 28° 20' 28° 30' 28° 40' 28° 50' .6740 .6763 .6787 .6810 .6833 2.3 2.4 2.3 2.3 2 3 .9453 .9446 .9439 .9432 .9425 .7 .7 .7 .7 7 .7287 .7317 .7348 .7378 .7408 3.0 3.1 3.0 3.0 30 .2713 .2683 .2652 .2622 J2592 61° 50' 61° 40' 61° 30' 61° 20' 61° 10' 29° 0' 9.6856 2 2 9 .941S 7 9.743S 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 .7 .7 .7467 .7497 .7526 .7556 3.0 2.9 3.0 2.9 .2503 .2474 .21 14 .2115 60° 50' 60° 40' 60° 30' 60° 20' 60° 10' 30° 0' 9.6990 9.9375 .8 8.7614 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 2 2 9.9375 7 9.7614 3 0 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 2.8 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 2 i 9.9331 g 9.7788 2 g 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 g .2184 .2155 .2127 .2098 .2070 58° 50' 58° 40' 58° 30' 58° 20' 58° 10' 32° 0' 9.7242 2.0 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 g .7986 .8014 .8042 .8070 .8097 2.8 2.8 2.8 2.7 2 8 .2014 .1986 .1958 .1930 .1903 57° 50' 57° 40' 57° 30' 57° 20' 57° 10' 33° 0' 9.7361 1 9 9.9236 g 9.8125 2 8 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 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 9 9.S452 2 7 6.154S 55° 0' 35° 10' 35° 20' 35° 30' 35° 40' 35° 50' .7604 .7622 .7640 .7657 .7675 .8 .8 . .7 .8 7 .9125 .9116 .9107 .9098 .9089 .9 .9 .9 .9 9 .8479 .8506 .8633 .8559 £686 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 g <».'J()S() 1 0 9.8613 2 6 0.1387 54° 0' 36° 10' •M" 'JAY 36° 30' :{«•" H)' 36° 50' .7710 .7727 .7744 .7761 .7778 .7 .7 .7 .7 7 .9070 .9061 .9052 .9042 .'.»<):;:', .9 .9 1.0 .9 1 0 .8639 .sr.tif, .8692 .8718 .8745 2.7 2.6 2.6 2.7 2 6 .1361 .1334 .1308 .1282 53° 50' 53° 40' 63* :«»' 53° 20' 53° 10' 37° 0' <|.77«.)5 6 9 H.H771 26 0.1229 53° 0' 37° 10' 37° 20' 37° 30' .7811 .7828 .7844 .7 .6 .«'«)! \ .9004 .8900 1.0 .9 .8797 .8824 .8850 2.7 2.6 .1203 .1 1, r, .1150 52° 50' Cos. D.I' Sin. D.I' Cot. D.I' Tan. Angle TABLES RELATING TO PARTS I AND 11 227 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 0 9.8850 2.6 2.6 2 6 0.1150 . 1 124 .1098 52° 30' /il" L'O' 52° 10' 38° 0' <>.7S'.»:> 1 7 D.SSMio 1 0 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 .S<)55 .SIM 5 £93$ .8925 .8915 1.0 1.0 1.0 1.0 1 0 .8954 .8980 .9006 .9032 .9058 2.6 2.6 2.6 2.6 " il .1046 .1020 .0994 .0968 .0942 51° 50 51° 40' 51° 30' 51° 20' 51° 10' 39° 0' 9.7989 1 5 «>.S.<)f><)7 2 5 0.0303 47° 0' 43° 10' 43° 20' 43° 30' 43° 40' 43° 50' .8351 .8365 .8378 .s:;:u .8405 1.4 L.3 1.3 1.4 1 3 .8629 .8618 .8608 .xs'M .S5X2 1.1 1.2 1.2 1.2 .9722 .9747 .9772 .9798 .9823 2.5 2.5 2.6 2.5 2 5 .0278 .0253 .0228 .0202 .0177 46° 50' 46° 40' 46° 30' 46° 20' 46° 10' 44° 0' 9.8418 1 3 9.9848 2 6 0.0152 46° 0' 44° 10' 44° 20' 44° 30' 44° 40' 44° 50' 45° 0' .8431 .si|! .8457 .8469 .8482 9.8495 1.3 1.2 1.3 1.3 .8657 .8520 .8507 9.8495 1.2 L3 1.2 L3 1.2 .9874 .9924 .9949 .9975 0.0000 2.5 2.5 2.5 2.6 2.5 .0126 .0101 .0076 .0051 o.oooo 45° 50' 45° 40' 45° 30' 45° 20' 45° 10' 45° 0' Cos. D.I' Sin. D.r Cot. D.r Tan. Angle 228 A MANUAL FOR NORTHERN WOODSMEN I-H O )*O IQ i-< O O5 x t- co »o «* ro CN ^ O " T}^T}<- xxxxxxxxx iOC5.t>.t>.t>.XX O5O5O5C3C3SOO5OJO xxxxxxxxx cooicoc O5Ot>. xxxxxxx x x x' x x x x' x' x' -H x x x x x x x x x xxxxxxxxx x' x' x x' x' x' x' x' x' xxxxxxxxx xxxxxxxxx XiMCOOCOt^OCCO t^t-t^t^^r^N't^t^ xxxxxxxxx r» t- 1- 1>. t>. N. r-. i> t> x" x' x' x x' x x x x' xxxxxxxxx (NCOOOOt^OCOt^O xxxxxxxxx xxxxxxxxx xxxxxxxxx t^coxccxcor^— no OOCOt>O-*t^i-c* lOiOiOiOiOiOiOiOiO CNCOCOCOCOCOCOCOfN OOSOSOOO iOiOOCO5OcO xxxxxxxxx xxxxxxxxx xxxxxxxxx 0 1/3 iO »O iq U3 O i« x x' x' x' x' 06 x' x' x' SC^iOt^OSdCOiOcO ^^ocot^ococo XXXOOSOOOO x' x x' x' x x' x' x' x' xxxxxxxxx 1 CMt^lNXCOXCOXCO xxxxxxxxx cococococococococo xx'x'xxx'xx'x' xxxxxxxxx xxxxxxxxx CO CO CO CO CO CO_ CO CO CO x' x x' x' x x' x' x x xxxxxxxxx 1 Oo O 00 O5 O ^H CO OCO«DOO'-iCOCOOO COiOh»O71^*COOOO OOOSO7lCCTfiOOOO 88oOOOOOO OOOOOOOOOOOOOOOOOO xooooxoosooic; Ci C SJ 0 Ci 0 C-- C. ST. s 1^ (M «O ^ CO ^H CD O < 06 06 oo oo' 06 oo' oo' oo' oo' oooooooooooooooooo oooooooooooooooooo lOOOOOO ._ -. ) OS OS OS OS OS OS 06 oo' oo' oo oo' oo' oo' oo' oo' os os os a> os os os os os 06 06 oo' oo' oo' oo' oo' oo' oo' oooooooooooooooox 10 10 -f re 7i OOOSOSOSO3CSOOO l> t^ t>-_ Is-- 1>- 1>. 00 00 00 06 oo' oo' oo' oo' oo' oo' 06 oo' Or-H^H^-I^H-H'M'M'M OOOOOOOOOOOOOOOOOO oo' 06 oo' oo' oo' oo' oo' oo' oo' CO 00 OS OS CS OS O O O oo" oo' oo' oo' oo' oo' oo 06 oo' OO^H^H— <^-*717;) GO 00 00 00 00 00 00 00 00 oooooooooooooooooo OOGOOOOOOOOOOOODOO oooooooooooooooooo «q «o coo oo" 06 oo' oo' 06 oo' oo' oo' oo' oooooooooooooooooo OOOOOOOOOOOOOOOOOO COCOCOCDCOCOCOCOCO GOGOGOOOGOOOOOOOOO oooooooooooooooooo X X X X X X X X X X oooooooooooooooooo oooooooooooooooooo O^H^-i 1C 1C >O CDt^l^OOOOOOOSO OOOOOSOO T)T l>: t>.' (^ oo' OO' 00 00 OO' oooooooooooooooooo OOOOQOOOOOOOQOQQOO >OcC>OOO5OiNM^»O OS O> OS d O O O O O tJ !>' t>I (>' oo' 00 00 OO' 00 ooooocoooooooooooo oooooooooooooooooo I-H IN eo TJ< 10 «o t^ oo os o WCCMCOCOCCCOCOCO <* 10 «o r>- oo GJ o »-< IN co ^ 10 o t>- oo os o -^ T}< •* •* ^ IQ 10 iO »O >O iO »O »O »O IO 33(> 69° 10' -.'()' .10742 .11031 .9942 .9939 50' 40' 40' 50' .2363 .2391 .9717 .9710 20' 10' 10' 20' .3611 .3638 .9325 .<>:', 15 50' 40' :;<)' 40' 50' .11320 .11609 .llX'.t.S .9936 .9932 .9929 30' 20' 10' 14° 10' 20' 2419 2447 2476 .9703 <><;<><> 9689 76° 50' 40' 30' 40' 50' .3665 3692 3719 «)2S3 30' 20' 10' 7° .12187 .9925 83° 30' L'f>0 1 9681 30' 22° 3746 l»272 68° 10' 20' .m 711 .12764 .9922 .9918 50' 40' 40' 50' 2532 2560 96* 1 •M5I57 20' 10' 10' 20' 3773 3800 !!2»il 50' 40' 30' .13053 .9914 30' 15° 25SX 9669 75° 30' 3827 «)231» 30' Cos. Sin. A. Cos. Sin. A. Cos. Sin. A. TABLES RELATING TO PARTS I AM) II NATURAL SINES AND COSINES - continued A. Sin. Cos. A. Sin. Cos. A. Sin. Cos. 30' .3827 .0239 30* 30° .5000 .8660 60°' 30' .60XX .7934 30' 40' 50' .3854 .3881 .9228 .9216 20' 10' 10' ?0' .5025 .5050 .X646 .8631 50' 40' 40' 50' .6111 .6134 .7916 17808 20' 10' 23° .3907 .9205 67° 30' .5075 .8616 30' 38° .6157 .7880 52° 10' 20' .3934 .3961 .9194 .9182 50' 40' 40' 50' .5100 .5125 .8601 .8587 20' 10' 10' 20' .til SO .6202 .7X62 .7844 50' 40' 30' .3987 .9171 30' 31° .5150 .8572 59° 30' .6225 .7826 30' 40' 50' .4014 .4041 .9159 .9147 20' 10' 10' 20' .5175 .5200 .8557 .8542 50' 40' 40' 50' .624X .6271 .7808 .7790 20' 10' 24° .4067 .9135 66° 30' .5225 .8526 30' 39° .6293 .7771 51° 10' 20' .4094 .4120 .9124 9112 50' 40' 40' 50' .5250 .5275 .8511 .8496 20' 10' 10' ?0' .6316 .6338 .7753 .7735 50' 40' 30' .4147 .9100 30' 32° .5299 .8480 58° 30' .6361 .7716 30' 40' 50' .4173 .4200 .9088 .9075 20' 10' 10' ?0' .5324 .5348 .8465 .8450 50' 40' 40' 50' .6383 .6106 .7698 .7679 20' 10' 25° .4226 .9063 66° 30' .5373 .8434 30' 40° .6428 .7660 50° 10' 20' .4253 4279 .9051 9038 50' 40' 40' 50' .6398 .5422 .8418 .8403 20' 10' 10' 90' .6450 .6472 .7642 .7623 50' 40' 30' .4305 .9026 30' 33° .5446 .8387 57° 30' .6494 .7604 30' 40' 50' .4331 .4358 .9013 .9001 20' 10' 10' ?0' .5471 .5495 .8371 .8355 50' 40' 40' 50' .6517 .Ii53« .7585 .7566 20' 10' 26° .4384 .8988 64° 30' .5519 30' 41° .6561 .7547 49° 10' 20' .4410 4436 .8975 8962 50' 4O' 40' 50' .5544 .5568 .8323 .8307 20' 10' 10' 90' .6583 .6604 .7528 .7509 50' 40' 30' .4462 .8949 30' 34° .5592 .8290 66° 30' .6626 .7490 30' 40' 50' .4488 .4514 .8936 .8923 20' 10' 10' ?0' .5616 .5640 .8274 .8258 50' 40' 40' 50' .6648 .6670 .7470 .7451 20' 10' 27° .4540 .8910 63° 30' .5664 .8241 30' 42° .6691 .7431 48° 10' 20' .4566 4592 .8897 8884 50' 40' 40' 50' .5688 .5712 .8225 .8208 20' 10' 10' ?0' .6713 .6734 .7412 .7302 50' 40' 30' .4617 .8870 30' 35° .5736 .8192 55° 30' .6756 .7373 30' 40' 50' .4643 .4669 .8857 .8843 20' 10' 10' ?0' .5760 .57X3 .8175 ,S 1 f)X 50' 40' 40' 50' .6777 .6799 .7353 .7333 20' 10' 28° .4695 .8829 62° 30' .5X07 .8141 30' 43° .6820 .7314 47° 10' 20' .4720 4746 .8816 8802 50' 40' 40' 50' .5831 .5854 .8124 .xl 07 20' 10' 10' ?0' .6X41 6862 .7294 .7274 50' 40' 30' .4772 .8788 30' 96° .5878 .8000 54° 30' .6X84 .7254 30' 40' 50' .4797 .4823 .8774 .8760 20' 10' 10' 20' .5901 .5925 .X07M .8056 50' 40' 40' 50' .6905 6926 .7234 .7214 20' 10' 29° .4848 .8746 61° 30' .5948 .8039 30' 44° .6947 .7193 46° 10' 20' .4874 4899 .8732 8718 50' 40' 40' 50' .5972 .5995 .X021 .8004 20' 10' 10' ?0' .6967 .69XS .7173 .7153 50' 40' 30' .4924 .8704 30' 37° .6018 .79X6 53° 30' .7009 .7133 30' 40' 50' .4950 .4975 .8689 .8675 20' 10' 10' 20' .6041 .6065 .7969 .7951 50' 40' 40' 50' .7030 .7050 .7112 .7092 20' 10' 30° .5000 .8660 60° 30' .6088 .7934 30' 48° .7071 .7071 46° Cos. Sin. A. Cos. Sin. A. Cos. Sin. A. 232 A MANUAL FOR NORTHERN WOODSMEN NATURAL TANGENTS AND COTANGENTS A. Tan. Cot. A. Tan. Cot. A. Tan. Cot. 75° 50' 40' 30' 20' 10' 74° 50' 40' 30' 20' 10' 73° 50' 40' 30' 20' 10' 72° 60' 40' 30' 20' 10' 71° 60' 40' 30' 20' 10' 70° 50' 40' 30' 20' 10' 69° 50' 40' 30' 20' 10' 68° 50' 40' 30' A. 0° 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 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' 85° 50' 40' 30' 20' 10' 84° 50' 40' 30' 20' 10' 83° 50' 40' 30' 30' 40' 50' 8° 10' 20' 30' 40' 50' 9° 10' 20' 30' 40' 50' 10° 10' 20' 30' 40' 50' 11° 10' 20' 30' 40' 50' 12° 10' 20' 30' 40' 50' 13° 10' 20' 30' 40' 50' 14° 10' 20' 30' 40' 50' 15° .1317 .1346 .1376 7.5958 7.4287 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 .014545 343.7737 171.8854 114.5887 85.9398 68.7501 .2711 .2742 .2773 .2805 .2836 3.6891 3.6470 3.6059 3.5650 H.5261 .1405 7.1154 .1435 .1465 .1495 .1524 .1554 .1584 .1614 .1644 .1673 .1703 .1733 6.9682 6.8269 6.6912 6.5606 6.4348 .017455 57.2900 .2867 3.4874 .02036 .02328 .02619 .02910 .03201 49.1039 42.9641 38.1885 34.3678 31.2416 .2899 .2931 .2962 .2994 .3026 3.4495 3.4124 3.3759 3.3402 3.3052 6.3138 6.1970 6.0844 5.9758 5.8708 5.7694 .03492 28.6363 .3057 3.2709 .03783 .04075 .04366 .04658 .04949 26.4316 24.5418 22.9038 21.4704 20.2056 .3089 .3121 .3153 .3185 .3217 .3249 3.2371 3.2041 3.1716 3.1397 3.1084 .1763 5.6713 .1793 .1823 .1853 .1883 .1914 .1944 5.5764 5.4845 5.3955 5.3093 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 .3378 .3411 3.0475 3.0178 2.9887 2.9600 2.9319 5.1446 .1974 .2004 .2035 .2065 .2095 .2126 5.0658 4.9894 4.9152 4.8430 4.7729 06993 14.3007 .3443 2.9042 07285 07578 07870 08163 08456 13.7267 13.1969 12.7082 12.2505 11.8262 .3476 .3508 .3541 .3574 .3607 .3640 2.8770 2.8502 2.8239 2.7980 2.7725 4.7046 .2156 .2186 .2217 .2247 .2278 .2309 .2339 .2370 .2401 .2432 .241)2 4.6382 4.5736 4.5107 4.4494 4.3897 08749 11.4301 2.7475 09042 09335 09629 09923 10216 11.0594 10.7119 10.3854 10.0780 9.7882 .3673 .3706 .3739 .3772 .3805 .3839 2.722S 2.6985 2.6746 2.6511 2.6279 4.3315 4.2747 4.2193 4.1653 4.1126 4.0611 10510 9.5144 2.C.051 10805 11099 11394 11688 11 983 9.2553 9.0098 8.7769 8.5555 s.:Mf>() .3872 3900 3939 3973 •lOOf1, 2.5S2C) 2-5005 j 5:;sc. 2.5172 2.49C.O .219:5 .2524 .2555 .25SI) .2617 .2648 .2679 4.0108 urn fr 3.9136 3.8667 i.820S J.77*i() 3.7321 i 227X 8.1443 •1010 2.4751 1 2574 12869 13165 7.9630 7.7704 7.5968 •107-J 4108 4142 2.4545 2.4342 2.4142 Cot. Tan. A. Cot. Tan. A. Cot. Tan. TABLES KKLATI.M; TO I>AKTS 233 NATURAL TANGENTS AND COTANGENTS A. Tan. Cot. A. Tan. Cot. A. Tan. Cot. 30' .4142 2.4142 30' 30° .5774 1.7321 60° .7673 30' 40' 50' .4176 .4210 2.3945 2.3750 20' 10' 10' BO' .5812 .5851 1.7205 1.7090 50' 40' 40* 50' .7720 .7766 1.2964 1 .2876 20' 10' 23° .4245 2.355!) 67° HO' 1.6977 30' 38° J813 1.2799 52° 10' 20' 30' .4279 .4314 .4348 2.3369 2.:u S3 2.2998 50' 40' 30' 40' 50' 31° .5930 .5969 .6009 1.6864 1.8763 1.6643 20' 10' 59° 10' 20' 30' .7860 .71107 .7954 1 .2723 1.2647 1 .257:.' 50' 40' 30' 40' 50' .4383 .4417 2.2817 2.2637 20' 10' 10' 20' .6048 .6088 1.6534 1.6426 50' 40' 40' 50' .8002 1.2497 1.2423 20' 10' 24° .4452 2.2460 66° 30' .6129 1.6319 ax 39° 1 .2349 61° 10' 20' .4487 .4522 2.2286 2.2113 50' 40' 40' 50' .6168 .020S 1.6212 1.6107 20' 10' 10' ?0' .SM() .8195 1.2276 1.2203 50' 40' 30' .4557 2.1943 30' 32° .6249 1.6003 68U 30' .8243 1.2131 30' 40' 50' .4592 .462S 2.1775 2.1609 20' 10' 10' ?0' .6289 .6330 1.6900 1 579S 50' 40' 40' 50' .8292 .8342 1 .2059 1.1988 20' 10' 25° .4663 2.1445 65° 30' .6371 1 .5697 30' 40° .*:;'. M 1.1918 50° 10' ?0' .4699 .4734 2.1283 2.1123 50' 40' 40' 50' .6412 .6453 1.5597 1.5497 20' 10' 10' 20' .8441 .8491 1.1 S47 1.1778 50' 40' 30' .4770 2.0965 30' 33° .6494 1.5399 57° 30' .8541 1.1708 30' 40' 50' .4806 .4841 2.0809 2.0655 20' 10' 10' ?0' .6536 6577 1.630] 1 5204 50' 40' 40' 50' .8591 .K042 1.1640 1.1571 20' 10' 26° .4877 2.0503 64° 30' .6619 1.5108 30' 41° .8693 1.1504 49° 10' 20' .4913 4950 2.0353 2.0204 50' 40' 40' 50' .6661 .6703 1.5013 1.4919 20' 10' 10' 20' .8744 .8796 1.1436 1.1369 50' 40' 30' .4986 2.0057 30' 34° .6745 1.4826 56° 30' .8847 1.1303 30' 50' .5059 1.9768 20' 10' 10' 20* .6787 .6830 1.4733 1.4641 50' 40' 50' .8899 .8952 1.1237 1.1171 20' 10' 27° .5095 UW26 63° 30' .6873 1.4550 30' 42° .<:()()4 1.1106 48° 10' 20' .5132 .5169 1.9486 1.9347 50' 40' 40' 50' .6916 .6959 1.4460 1.4370 20' 10' 10' 20' .9057 .9110 1.1041 1.0977 50' 40' 30' .5206 1.9210 30' 35° .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 1.0850 1.0786 20' 10' 28° .5317 1.8807 62° 30' .7133 1.4019 w 43° 1.0724 47° 10' 20' .5354 .5392 1.SG70 1.8546 50' 40' 40' 50' .7177 .7221 1.3934 1 .3S4S 20' 10' 10' 20' .'.)i:;r, l.OlitU 1 .0599 50' 40' 30' .5430 1.8418 30' 36° .7265 1.3764 64° 30' .9460 1 .0538 30' 40' 50' .5467 ..->.-,().-, 1.8291 1.8165 20' 10' 10' ?0' .7310 .7355 1.3680 1.3597 50' 40' 40' 50' .9545 .9601 1 .01, , 1.0416 20' 10' 29° .;,.-,):; 1.8040 61° 30' .7400 1 :;r>l 1 30' 44° .9667 1.0355 46° 10' 20' .5581 .5619 1.7917 1.7796 50' 40' 40' 50' .7445 .7490 1.3432 1.3351 20' 10' 10' ?0' .9713 .9770 1.0295 1.0235 50' 40' 30' .5658 1.7675 30' 37° .7536 1.3270 53° 30' .9827 1.0176 30' 40' 50' .5696 .5735 1.7556 1.7437 20' 10' 10' ?0' .7581 .7627 1.311)0 l :;i 1 1 50' 40' •10' 50' 9SX4 9042 1.0117 L0068 20' 10' 30° .5774 1.7321 60° 30' .7673 1.3032 30' 45° 1.0000 1.0000 46° 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 OB BASAL AREAS 238 3. CORD WOOD RULE 239 4. NEW HAMPSHIRE RULE 240 5. NEW YORK STANDARD RULE 242 v 6. SCRIBNER LOG RULE, LEGAL, IN MINNESOTA . . . 243 7. DECIMAL RULE OF THE U. S. FOREST SERVICE . . . 244 vr 8. DOYLE RULE 246 9. MAINE Loo 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 t 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. WTestern 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 . . 2!M) 30. California Sugar Pine in Board Measure . . . 292 ^ CO C< 1-1 O 00 i-i'^Hl^OCC - ^i^^^H^Hc^iOr^Oir-icoior^ rH i-l rH T-H rH CO «O t- ( O 8 3 I SWIS§£832| -||g o — ! t- co d c i-iCMW*«O«Dl-OOC. 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OOt^cOCC'OTf^COCOIN'M^HO co r-i »t t>- O co o c; 01 1.0 oo >-i TJ< t>. «O I-H T-I r-< M (N for^O'rx — >-.-. — y -^ re — r. i- re c i - ' — CO O t ' -* • — 5CS1C^»OCNOO»O»— 'G0'f*^*t>-<»f icocoTjno«ocot^r>.cioosO5O r^ co C5 O ^ -t^t>'t^oooooooooso)O>O3OO •^t^OWOC5C^u300^^I-OCOOC5-t-t^-OOOOOOO5O5OCiOOO^'-i'-'IM 'OQ'OO'OQ'OO'OO'OO'OO'OO'OO'OO'OQ'OO'OO'OO'OC 32! iOClOO Tt-ooo»oo^c»c5eoi*»oio«t^ooooo5OQ'-Hc;icoco^>o2 <^Ht^' IZZt O CD O O '-C ^H ^ CO 00 T»ococoi^f-oo< 5 ^^: 248 A MANUAL FOR NORTHERN WOODSMEN 8 1! ic^csi O3'OOOC^>-cOOCl-5£'OC'JC^i-«OOOl - ooroo--. r^oBosoS — ci ^_^H^H_^rt^H_^l^Hri- ,^H^^i^H^F_f_^^H^;SSjJc^C45I| t^QOOso-'Mfct<'rio — 01 rt — ' ) O5O5O 250 A MANUAL FOR NORTHERN WOODSMEN PROVINCE OF QUEBEC Table of Contents of Saw Logs, Boom and Dimension Timber in Feet Board Measure LENGTH DIAMETER IN INCHES 4 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 10 11 16 22 31 40 46 55 69 82 92 110 128 147 170 192 12 8 11 12 18 24 34 44 50 60 75 90 100 120 140 160 185 210 13 9 12 13 19 26 37 48 54 ,65 81 97 108 130 152 173 200 227 14 10 13 14 21 28 40 51 58 70 87 105 117 140 163 187 216 245 15 11 14 15 22 30 42 55 62 75 94 112 125 150 175 200 231 262 16 12 15 16 24 32 45 59 67 80 100 120 133 160 187 213 247 280 17 17 25 34 48 62 71 85 106 127 142 170 198 227 262 297 18 18 27 36 51 66 75 90 112 135 150 180 210 240 277 315 19 19 28 38 54 70 79 95 119 142 158 190 222 253 293 332 20 20 30 40 57 73 83 100 125 150 167 200 233 267 308 350 21 21 31 42 59 77 87 105 131 157 175 210 245 280 324 367 22 22 33 44 62 81 92 110 137 165 183 220 257 293 339 385 23 23 34 46 65 84 96 115 144 172 192 230 268 307 355 402 24 24 36 48 68 88 100 120 150 180 200 240 280 320 370 420 25 25 37 50 71 92 104 125 156 187 208 250 292 333 385 437 26 26 39 52 74 95 108 130 162 195 217 260 303 347 401 455 27 27 40 54 76 99 112 135 169 202 225 270 315 360 416 472 28 28 42 56 79 103 117 140 175 210 233 280 327 373 432 490 29 . . . . 29 43 58 82 106 121 145 181 217 242 290 338 387 447 507 30 30 45 60 85 110 125 150 187 225 250 300 350 400 462 525 31 31 46 62 88 114 129 155 194 232 258 310 362 413 478 542 32 . . . . 32 48 64 91 117 133 160 200 240 267 320 373 427 493 560 33 33 49 66 93 121 137 165 206 247 275 330 385 440 509 577 34 34 51 68 96 125 142 170 212 225 283 340 397 453 524 595 35 •• •• 35 52 70 99 128 146 175 219 262 292 350 408 467 540 612 36 36 54 72 102 132 150 180 225 270 300 360 420 480 ->55 630 37 . . . . 37 55 74 105 136 154 185 231 277 308 370 432 493 570 647 38 38 50 76 108 139 158 190 237 285 317 380 443 507 586 665 39 59 57 78 111 143 162 195 244 292 325 390 455 520 601 682 40 10 00 SO 114 147 167 200 250 300 333 400 467 533 617 700 TABLES RELATING TO PARTS III AND IV 251 PROVINCE OF QUEBEC Table of Contents of Saw Logs, Boom and I)iincn>ion Timber in Hoard Measure DIAMETER IN INCHES | 21 22 23 24 25 26 27 28 29 30 31 32 192 217 240 262 283 317 333 362 392 421 450 475 ft. 10 211 238 264 289 312 348 367 399 431 463 495 522 11 230 260 288 315 340 380 400 435 470 505 540 570 12 249 282 312 341 368 412 433 471 509 547 585 617 13 268 303 336 367 397 443 467 507 548 589 630 665 14 287 325 360 394 425 475 500 544 587 631 675 712 15 307 347 384 420 453 507 533 580 627 673 720 760 16 326 368 408 446 482 538 567 616 666 715 765 807 17 345 390 432 472 510 570 600 652 705 757 810 855 18 364 412 456 499 538 602 633 689 744 800 855 902 19 383 433 480 525 567 633 667 725 783 842 900 950 20 402 455 504 551 595 665 700 761 822 884 945 907 21 422 477 528 577 623 697 733 797 862 926 990 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 1140 24 479 542 600 656 708 792 833 906 979 1052 1125 1187 25 498 563 624 682 737 823 867 942 1018 1094 1170 1235 26 517 585 648 709 765 855 900 979 1057 1136 1215 1282 27 637 607 672 735 793 887 933 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 30 594 672 744 814 878 982 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 12:5_' 1332 1431 1530 1615 34 671 758 840 919 992 1108 1167 1269 1371 1473 1575 1662 35 690 780 864 945 1020 1140 1200 1305 1410 1515 1620 1710 36 709 802 888 971 1048 1172 1233 1341 1449 1557 1665 1757 37 728 823 912 997 1077 1203 1267 1377 14«8 1599 1710 iso.-, 38 747 845 936 1024 1105 1235 1300 1414 1527 1641 1755 39 767 867 960 1050 1133 1267 1333 1450 1567 1683 1800 1900 40 252 A MANUAL FOR NORTHERN WOODSMEN PROVINCE OF QUEBEC Table of Contents of Saw Logs, Boom and Dimension Timber in Feet Board Measure LENGTH DIAMETER IN INCHES 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 1425 1500 19 997 1029 1077 1124 1172 1235 1314 1393 1441 1504 1583 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 2278 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 2833 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 :u)x:s 38 1995 2058 2153 2548 2343 2470 2628 2787 3008 3167 39 2047 L' 1 1 L> 2210 2307 2405 2697 2860 2957 3087 HL'f>0 40 2100 •2 1 r,7 2267 2367 2467 2600 2767 3033 3167 3333 TABLKS KKLATIM; TO PARTS in AND iv NEW BRUNSWICK LOG RULE "S£ g.s Diameter at Top in Inches 11 12 13 14 15 16 17 18 19 20 21 22 23 24 12 60 72 84 98 112 128 149 172 196 225 247 272 297 324 14 70 84 98 114 131 149 174 200 228 262 288 317 336 380 16 80 96 111! 130 150 170 198 229 Ml 300 327 362 376 432 18 90 108 126 147 168 192 223 258 294 337 370 408 445 486 20 100 120 140 163 187 213 248 286 32G 375 411 453 495 540 21 105 126 147 171 196 223 261 301 343 393 432 476 519 569 22 110 132 179 205 234 27B 315 359 412 453 498 544 594 24 120 144 168 196 224 256 298 344 392 450 494 544 594 648 26 142 168 196 226 259 298 346 396 453 509 560 614 660 730 28 154 182 212 245 280 323 374 428 490 550 605 653 716 788 30 164 194 226 261 299 344 398 457 523 588 644 698 756 840 32 176 208 242 280 320 368 427 490 561 027 689 738 808 898 34 186 220 256 297 336 390 452 519 594 064 732 784 877 952 36 198 234 273 315 360 415 481 552 631 707 778 853 B81 1011 38 208 246 287 331 379 436 506 580 663 745 S9S 981 1065 40 220 260 303 350 400 461 534 612 701 786 864 94S in: ;r 1123 42 231 273 318 367 419 4S4 562 644 736 825 90S 995 1181 44 242 286 333 384 439 509 590 674 771 865 951 1042 L138 1235 46 252 298 347 401 531 613 703 804 903 992 1088 L188 1289 48 264 312 364 420 1S( 554 642 736 842 944 1038 1138 1242 1348 50 286 336 392 450515 596 690 788 1003 1104 1208 1430 UNDERSIZED LOGS A log measuring 7 inches at the top contains twice feet as its own length. A log measuring 8 inches, 2i times its length. A log measuring 9 inches, 3 times its length. A log measuring 10 inches, 4 times its length. many superficial 254 A MANUAL FOR NORTHERN WOODSMEN CLARK'S INTERNATIONAL LOG RULE 1 Length — Feet 1 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 90 100 110 120 130 140 150 160 175 185 195 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 j 275 295 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 1 350 370 20 150 170 195 215 235 255 275 300 320 345 365 390 410 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 2051 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 32 410 465 520 575 630 685 740 795 850 910 965 1025 1080 33 440 495 555 610 670 730 790 850 905 970 1030 109011150 34 470 530 ! 590 650 715 775 840 900 965 1030 10951160 1225 35 495 560 625 690 755 825 890 965 102511095 1160 1230 1300 36 525 595 665 735 800 875 945 1015*1085 1160 1230 13051375 37 560 630 705 775 850 9251000 1075 1150 1225 1300 1380 1455 38 39 590 665 620 1 705 745 820 895 785 1 865 945 975 1055 1030 1110 1135 1210 1295 1195 1280 1365 1375 1455 1535 1450 1535 1620 40 655 740 825 910 99510851170 1260 1345 1435 1525 16151705 41 690 780 870 960,1050111401230 1325 1415 1510 1605 1700 1795 42 725 820 915 1010 1100 1200 1295 1390 1490 15S5 1685 1785 1885 43 760 860 960 1060 1155 1260 1360 146011560 11565 1770 1870 1975 44 800 900 1005 1110 1215 1320 1425 1530 1635 17451855 19602070 45 835 945 1055 1H>0 IU70 13X0 1490 1600 1715J1825 1940 2050 2165 46 875! 990 1100 1215 1330 1445 1560 1675 1790 1910 2030 12145 22(55 47 915 1035 1150 1270 390 1510 1630 1750 1870 1995 IM'JO U1MO 2365 48 955 1080 1205 1325 1450 1575 1700 1830 1955 20S5 J210 23-10 2470 I TABLES RELATING TO PARTS III AND IV 255 SPAULDING LOG RULE OF COLUMBIA RIVER 5 DIAMETER IN INCHES 1 § i-J 10 11 12 13 14 15 16 17 18 19 20 21 22 ft 12 38 47 58 71 86 103 121 141 162 184 207 231 256 14 44 55 67 82 100 120 141 164 189 214 241 269 298 16 50 63 77 94 114 137 161 188 216 245 276 308 341 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 94 116 142 172 206 242 282 324 368 414 462 512 26 82 101 125 153 186 223 262 305 351 39S 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 34 107 132 164 200 243 291 342 399 459 521 586 654 725 36 113 140 174 212 258 308 362 422 486 552 620 692 768 38 120 148 183 224 272 325 382 446 513 5S2 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 SOS 895 44 138 172 212 260 314 376 442 516 594 674 758 846 938 46 145 179 222 272 329 394 463 540 621 705 793 SS5 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 ft. 12 282 309 337 see 396 427 459 492 526 561 597 634 14 329 360 393 427 462 498 535 574 613 654 696 739 16 376 412 449 488 528 569 612 656 701 748 796 845 18 423 463 505 54S 594 640 688 738 789 841 895 951 20 470 515 561 610 660 711 765 820 876 935 995 1056 22 517 566 617 671 726 782 841 902 964 1028 1094 1162 24 564 618 674 732 792 854 918 984 1052 1122 1194 1268 26 611 669 730 793 858 925 994 1066 1139 1215 1293 1373 28 658 720 786 854 924 996 1070 1148 1226 1308 1392 1478 30 705 772 842 915 990 1067 1147 1230 1314 1402 1492 1584 32 752 824 898 976 1056 1138 1224 1312 1402 1496 1592 1690 34 799 875 954 1037 1122 1209 1300 1394 1490 15S9 1691 1796 36 846 926 1010 1098 1188 1280 1376 1476 1578 lfiS2 1790 1902 38 893 978 1066 115S 1254 1351 1453 1558 1665 1776 1S90 2007 40 940 1030 1122 122C 1320 1422 1530 1640 1752 1870 1990 2112 42 987 1081 1178 1281 1386 1493 1606 1722 1840 1963 2089 2218 44 1034 1132 1234 1342 1452 1564 1682 1804 1928 2056 2188 2324 46 1081 1184 1291 140C 1518 1636 1759 1886 2016 2150 22S8 2430 48 1128 1236 1348 1464 1584 1708 1836 1968 2104 2244 2388 2536 50 1175 1287 1404 152£ 1650 1779 1912 2050 2191 2337 2487 2641 256 A MANUAL FOR NORTHERN WOODSMEN SPAULDING LOG RULE — continued 1 DIAMETER IN INCHES 1 35 36 37 38 39 40 41 42 43 44 45 46 tt. 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 2388 2518 2652 2788 2926 3077 3213 3360 36 2018 2138 2264 2394 2528 2666 2808 2952 3098 3258 3402 3558 38 2130 2257 2390 2527 2669 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 53 54 55 56 57 58 ft. 12 1239 1293 1348 1404 1461 1519 i578 1638 1700 1763 1827 1893 14 1445 1508 1572 1638 1704 1772 1841 1911 1983 2056 2131 220S 16 1652 1724 1797 1872 1948 2025 2104 2184 2266 2350 2436 2524 18 1858 1939 2022 2106 2191 2278 2367 2457 2550 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 2684 2801 2920 3042 3165 3291 3419 3549 3683 3819 395S 4101 28 2S90 3016 3144 3276 3408 3544 3682 3822 3'JOO 4112 42(52 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 3063 3819 3978 4139 4303 4471 4641 4816 4994 5176 5363 36 3716 3878 4044 4212 4382 4556 4734 4914 5100 52SS 5480 5678 38 3923 4094 4268 4410 4626 4S09 4997 5187 53S3 5582 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 0000 0232 6464 669S O'.MO 46 4749 4956 5166 53S2 5600 5S22 6049 6279 6516 075S 7003 7256 48 4950 5172 5392 5010 5844 6076 6312 Of>r>l> (iSIM) 7052 7304 7572 50 5162 5387 5616 5850 6087 6329 6575 6825 7083 7345 7612 7887 TABLES RELATING TO PARTS III AND IV 257 SPAULDING LOG RULE — continued 1 DIAMETER IN INCHES 59 60 61 62 63 64 65 66 67 68 69 70 tt. 12 1960 2028 2098 2169 2241 2315 2390 2467 2545 2625 2706 2789 14 2286 2366 2447 2530 2614 2700 278«.» 2S7S 2'.Mi'.l 3062 3157 3253 16 2613 2704 2707 2892 3086 31 Mi :i2s'.» 3500 3718 18 2940 3042 3147 3253 3361 :U72 .•$5X5 3700 3817 3'.»37 40-)'.) 4ix:< 20 3266 3380 3496 3615 3735 3858 3'J«3 4111 4241 4375 4510 4G4X 22 3592 3718 3846 3976 4108 4244 4381 4522 4005 4812 4961 5113 24 3920 4056 4196 4338 4482 4630 4780 4934 5090 5250 5412 5-,7,s 26 4246 4394 4545 4699 4855 0015 5179 5345 5514 ",C,X7 f>s»>3 <~M2 28 4572 4732 4894 5060 5228 5400 5578 5756 5<>;5s 6124 r,3i4 G50T. 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 (19X9 7210 7437 7667 7901 36 5880 6084 6294 6506 6722 6944 7170 7400 7634 7874 XI IX 830»» 38 6206 6422 6643 Gsfis 7096 7330 7568 7811 X05S S3 12 X">09 SS31 40 6532 6760 6992 7230 7470 7716 7966 X222 8482 8750 9020 9296 42 6858 7098 7342 7591 7843 8102 8364 8633 8906 9187 9471 9761 44 7184 7436 7692 7952 8216 S4SS 8762 9044 9330 9624 9922 46 7512 7774 8042 8314 8590 SS74 9161 9456 9755 48 7840 8112 8392 8676 X964 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 1^ 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. 1 DIAMETER IN INCHES 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 13 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 89 104 120 137 155 175 195 217 240 264 289 315 14 48 60 73 88 104 121 140 160 181 204 228 253 280 308 337 368 1! 55 62 ?? 84 94 101 113 119 134 139 150 100 ISO 183 206 207 233 233 202 201 293 290 326 32SL 360 3a2 396 380 434 421 473 20 69 86 105 126 149 173 200 229 259 292 326 362 400 440 482 526 22 76 94 115 138 164 191 220 252 285 321 358 398 440 484 530 578 24 83 103 126 151 178 208 240 274 311 350 391 134 480 52S 57S 631 26 89 112 136 164 193 220 260 297 337 379 424 471 520 572 620 683 28 96 120 147 176 208 243 280 320 303 408 456 507 5150 616 675 736 30 103 129 157 189 223 260 300 343 389 437 489 543 600 660 723 789 32 110 137 168 201 238 278 320 360 415 466 521 579 640 704 771 841 34 117 146 178 214 253 295 340 3S9 441 496 554 Ola 6SO 748 819 894 36 124 155 189 227 268 312 360 412 466 525 586 052 720 792 807 94 0 38 131 163 199 239 283 330 380 435 492 554 619 OSS 760 836 910 999 40 138 172 210 252 297 347 400 457 518 583 652 724 800 880 964 1051 /TABLES RELATING TO PARTS III AND IV BRITISH COLUMBIA LOG SCALE — continued E DIAMETER IN Iv 0 w 26 27 28 29 30 31 32 33 34 35 36 37 ft. 1 29 31 33 36 39 41 44 47 50 53 57 00 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 MM 541 580 020 661 704 748 793 840 16 457 495 535 576 019 603 70S 756 sot 855 906 18 514 557 602 648 696 740 797 8.10 905 961 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 1003 1133 1207 1282 1360 1440 26 743 805 869 936 1005 1077 1151 1228 1307 1386 1473 1560 28 800 867 930 1008 10S2 1160 1240 1322 1408 1 I'.H; 1586 1079 30 857 928 1003 1080 1160 1243 1328 1417 1508 1002 1700 1799 32 914 990 1070 1152 1237 1325 1417 1511 1609 1709 1813 1919 34 971 1052 1136 1224 1314 1408 1505 It •()»» 1709 1.S10 1920 2039 36 1028 1114 1203 1296 1392 1491 1594 1700 1810 2039 2159 38 1086 1176 1270 1368 1469 1574 1682 179.-, 1910 2030 2153 2279 40 1143 1238 1337 1440 1546 1657 1771 1889 2011 2137 2200 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 9SS 1040 1093 1148 1204 1201 1320 1379 1441 1503 16 1015 1071 1129 1188 1249 1312 1376 1441 150S 1577 1647 1718 18 H41 1205 1270 1337 1405 1475 1547 1021 1697 1774 1852 1933 20 1268 1339 1411 1485 1561 1039 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 2202 2305 2470 2577 26 1649 1740 1834 1931 2030 2131 2235 2342 2451 2502 2070 2792 28 1775 1874 1975 2079 2295 o-°,7 2522 2039 2759 2SS2 3007 30 1902 2008 2116 2228 2342 2459 2702 2828 2950 3087 3222 32 2029 2142 225S 2376 2498 2623 2751 2882 3016 3153 3293 3430 34 2156 2276 2399 2525 2654 27S7 2923 3002 3205 3350 3499 3051 36 2283 2410 2540 2673 2810 2951 3095 3242 3393 3547 3705 3SOO 38 2410 2543 2681 2822 2967 3115 3267 3422 35S2 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 1 DIAMETER IN INCHES 1 50 51 52 53 54 55 56 57 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 4406 4561 4718 30 3359 3499 3641 3787 3936 4087 4241 4398 4558 4721 4886 5055 32 3583 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 5278 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 2687 2772 2859 2947 3036 3127 3219 3312 3407 16 2787 2880 2975 3071 3168 3267 3368 3470 3573 3678 37Sf> 3893 18 3136 3240 3347 3454 3564 3676 3789 3903 4020 4138 4258 4380 20 3484 3600 3718 3838 3960 4084 4210 4337 4467 4598 4731 4 SOT 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 5038 5807 5977 6151 6327 28 4878 5040 5206 5374 5444 5717 5893 6072 0253 6437 6024 6813 30 5226 5401 5578 5757 5950 6126 6314 6506 6700 6897 701)7 7300 32 5575 5761 5949 6141 6336 6534 6735 6939 7146 7357 7570 7787 34 5923 6121 6321 Of>25 0732 (iOl 3 7156 7373 7593 7816 8043 8273 36 6272 6481 6693 ()«.»()<> 7128 7351 7577 7807 8040 S270 8516 8760 38 0020 6841 7065 7293 7524 7759 7998 8241) XI SO 873(J S9S9 9247 40 6968 7201 7437 7677 7920 8168 8419 8674 8933 9196 9462 9734 TAHLKS KKLATINC; To PABT8 III AM) IV VOLUME TABLE No. 1. WHITE PINE BY Till: RULE Breast Diam. Inches Total Height of Tree — Feet 60 70 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 75 '.10 100 120 140 160 V 70 85> 100 1 i.-, 136 160 i •>:, 210 240 270 80 100 tg 155 ISO 210 210 270 310 350 390 440 490 540 95 115 135 155 180 200 210 270 310 350 390 430 ISO 540 600 660 180 210 230 270 310 350 390 440 480 540 600 660 720 790 850 920 990 270 310 350 390 440 490 540 600 660 730 soo 870 910 1020 1100 1180 1270 1360 1450 1550 1650 1750 440 190 550 t>00 670 7^0 810 890 970 1040 1130 1210 1300 1400 1500 1600 1700 1800 1900 680 910 990 1070 1150 1210 1330 1420 1520 1630 1750 1870 1980 2100 940 1020 1100 1190 12SO L370 1470 1580 1690 1800 1920 2040 2170 2300 1 120 1530 1640 1750 1860 1980 2100 2220 •J3»X) 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. A MANUAL FOR NORTHERN WOODSMEN VOLUME TABLE No. 2. RED PINE, IN BOARD FEET, BY THE MINNESOTA SCRIBNER RUL$ (Trees under 130 Years Old) Diameter Breast Total Height in Feet High Inches 60 70 80 90 100 7 17 24 8 29 38 'SO 9 44 53 68 "si '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 10 317 390 468 551 20 355 433 523 616 21 396 480 582 OSS 22 530 646 755 23 584 715 830 24 790 905 25 867 986 26 951 1075 27 1041 11C.C, TABLES RELATING TO I'AHTS III \\D IV The preceding tables from Minnesota timber cut into 16-foot logs and scaled straight and sound. By H. II. 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 80 105 115 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 :i(M» 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 24 600 690 780 800 25 645 740 S30 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. 264 A MANUAL FOR NORTHERN WOODSMEN VOLUME TABLE No. 5. WHITE PINE IN CORDS (From State Forester of Massachusetts) Diameter Breast Total Height of Tree — Feet High Inches 30 40 50 60 70 80 SO 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 J 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 90 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. 88. 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 20 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 *«8 70 77 85 08 08 106 111 138 • TABLKS KI-;r,ATIN(; TO 1'AKTS III AM) IV ^(i.> Table No. 6 gives volume of tree from ground to tip exclusive of branches. Includes bark, which is about Hj per cent of the total volume. Based on 'J500 trees cut in Maine, New Hampshire, and New York, calipcml each 1 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 159-165 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 IHani- 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 9 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 IMS 150 13 75 90 100 115 125 140 155 170 14 . 105 120 135 150 165 180 195 15 . 120 135 155 170 ISO 205 220 16 155 170 185 205 225 250 3i5 17 170 190 210 230 250 275 350 18 185 210 235 255 280 310 390 19 m 205 235 260 290 320 350 430 20 265 295 325 355 385 470 21 300 330 360 390 425 510 22 330 360 395 430 465 550 23 \ 360 400 435 470 510 600 24 • ... 400 440 480 515 555 660 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 VOLUME 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 .09 .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 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. B^MLOCK, BY THE SCRIBNER RULE (From Bulletin No. 152, U. S. Dept. Agriculture, by E. H. Frothingham) Diam- Total Height of Tree — Feet Diam- eter eter breast- high 30 40 50 60 70 80 90 100 'bark6 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 B 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 flSO 10 25 390 460 530 (500 650 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. 268 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 *30 '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 (4j to 6j 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 Used Length of Tree — Feet High 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 HKLATING TO PARTS III AM) IV 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 'i5 7 14 22 '29 8 18 30 39 4:< 9 25 40 48 58 10 31 50 60 *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 IT:; 225 288 17 163 201 262 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 Ij-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 1906-7) 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 60 65 Number Trees per Cord 3-5 5-7 7-9 61 47 38 24 33 20 9 12 15 11 ii 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 1'AKTS 111 AND IV 271 FORM HEIGHT FACTORS FOR SECOND GROWTH HARD WOODS IN COHUS (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 60 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 21 .19 .21 .'2\ .27 ,81 .34 24 .18 .21 .24 .27 M .33 27 .18 .21 .24 .27 .30 .32 .34 30r .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 % from above figures. Above tables from "Biltmore Timber Tables," by Howard Krinbill, copyrighted. 272 A MANUAL FOB 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 hi 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 in it? .545 (basal area) X .35 (form height factor) = .19 cord; or 1 -f- .19 = 5}, 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 Number of Sixteen-Foot Logs Diameter 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 VOLUME TABLE No. 17. NORTH K UN HARD WOODS (BIRCH. BEECH AND MAPLE) BY THE SCRIBNER RULE (Adapted from Bulletin No. 285, U. S. Forest Servi- . , by E. H. Frothingham) Diameter breast- high Number of 16-foot Logs Diami-n-r inside hark of top 1 li 2 2J 3 3* 4 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 to understand these points, and he will do well to check the table ne uses with local practice ana 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. LONGLEAP PINE, IN BOARD FEET, BY THE SCRIBNER RULE Diam- eter breast- high Total Height of Trees — Feet Diam- eter inside bark of top 40 50 60 70 80 90 100 110 120 Inches Volume Inches 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 5 10 20 25 35 10 20 30 40 50 65 80 95 115 15 25 40 55 70 90 110 130 150 175 200 225 250 6 6 6 6 6 6 6 7 7 7 7 8 8 8 8 9 9 10 10 11 11 12 12 13 13 14 15 16 17 18 50 70 90 115 135 160 190 220 250 280 310 350 390 440 490 110 135 165 200 230 260 295 330 370 420 470 520 580 640 710 780 840 •• 195 230 270 310 350 390 440 490 550 610 670 740 820 890 960 1050 1140 1230 3i6 350 400 450 500 560 620 690 770 850 930 1010 1090 1180 1280 1380 1480 1580 1690 450 500 560 630 700 780 860 950 1040 1130 1220 1310 1410 1520 1630 1740 1860 1980 2110 2230 620 700 780 860 950 1050 1140 1240 1340 1440 1550 1670 1780 1900 2030 2160 2200 2340 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 THK SCRIBNER RULE (Ashe in Bulletin No. 24. N. C. Geological and Economic Survey) Diam- eter breast- high Total Height of Tree — Feet Diam- eter inside bark at top 40 50 60 70 80 90 100 110 120 130 140 Inches Contents — Board Feet Inches 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 5 12 18 25 32 40 13 22 30 40 50 60 70 21 32 42 54 66 81 97 110 120 27 42 55 68 83 100 120 140 160 190 220 5 6 6 6 7 7 8 8 8 8 9 9 9 10 10 10 11 11 11 12 12 13 13 13 14 14 15 15 15 52 65 81 99 120 150 170 200 230 270 300 330 93 110 140 180 210 240 270 310 360 410 460 510 570 620 130 160 200 230 270 310 360 410 470 530 600 660 730 810 890 970 1060 1150 1240 140 170 220 260 300 350 400 460 520 590 660 740 820 910 990 1090 1180 1280 1380 1500 1610 1720 1810 150 180 240 290 330 380 440 500 570 640 720 810 900 990 1090 1190 1290 1400 1510 1630 1750 1870 2000 2130 2270 .... .. . ''530 610 690 780 870 960 1060 1170 1280 1390 1500 1620 1750 1880 2010 2140 2270 2400 1020 1130 1240 1350 1470 1590 1710 1860 1980 2130 2250 23HO 2510 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 hi 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 inevi table 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 in 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 111 AM) 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 17.'*. 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 hi 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 15 i2 1,750 7 26 24 20 17 14 8 1,290 8 39 36 31 28 24 17 2,760 g 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 tnat 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 case. 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 PAKTs 111 A M> IV 281 VOLUME TABLE No. 20. WESTERN WHITE PINE, IN BOARD FEET, BY THE SCRIHNKR RULE (From Bulletin No. 36, U. S /ice) Diam- Number of Sixteen-Foot Logs eter breast- Hlt-si.s high 2 3 4 5 6 7 8 9 10 Inches Volume — Board Feet T«« 8 40 60 85 105 7 a 45 70 95 120 10 55 85 110 140 165 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 21 430 540 650 760 870 980 108 22 460 580 710 830 960 10M) 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 11 lit 1330 M 27 810 1010 1220 1430 ill-iii 65 28 1080 1300 1530 1750 40 29 1150 1390 Ki.'iO 1870 23 30 1220 1470 1730 1990 28 31 1550 1830 2110 14 32 1630 1930 2230 9 33 1710 2030 14 34 2140 2t!)0 6 35 22f>0 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- Diam- eter breast- Height of Tree-Feet eter of top in- oiria Basis high 81 QG bark Inches 40 50 60 70 80 90 100 110 120 Inches Trees 12 50 60 70 80 8.3 13 60 80 90 100 8.5 23 14 70 90 110 120 iio 150 8.7 48 15 90 110 130 150 170 180 190 . 8.9 91 16 110 130 160 180 200 220 230 240 9.2 117 17 130 160 180 210 230 260 280 290 sio 9.4 142 IS 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 10.6 135 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 283 VOLUME TABLE No. 22. WESTERN YELLOW PINE, BY THE SCRIHNKK RULE Same trees classified by 16-foot log lengths Diam- Number of 16-foot Logs eter breast- BatiiM high 1 2 3 4 5 a 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 1060 95 27 580 710 860 1010 1150 85 28 630 790 950 1100 1250 65 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 forc&st/- 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 60' Tall over 807 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 VOLUME TABLE No. 24. WESTERN LARCH. IN BOARD 1 BY THE SCRIIJNKK RULE (From Bulletin No. 36, U. ,S. . ice) Diam- eter breast- high Inches Number of 16-Foot Logs Diam- of top insi.l- bark Bwfc Trees 3 4 5 6 7 8 11 95 140 3 12 105 155 13 120 165 220 7.1 14 135 185 240 7.5 93 15 155 205 270 7 6 1 11 16 175 230 295 380 7.7 1 l'i 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 r>xr> 705 8.1 22 415 520 635 775 8.1 89 23 450 560 695 840 ioos 8.2 BO 24 486 605 745 905 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 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 38 1770 2145 2506 10.0 2 39 1850 2240 2<;io 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- eter breast- high Inches Height of Tree — Feet Diam- eter of top inside bark Inches Basis Trees 40 50 60 70 80 90 100 1.10 120 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 15 15 20 25 30 40 50 60 70 20 25 30 40 50 60 70 80 95 110 125 30 35 45 55 65 80 95 110 125 140 160 180 205 230 250 50 60 70 85 100 120 140 160 180 200 225 250 280 310 340 370 70 80 90 110 130 150 170 190 220 250 280 310 340 370 400 430 470 500 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.1 7.2 7.2 7.3 7.4 7.4 7.5 7.5 7.6 8 19 19 35 45 44 51 37 61 57 55 45 43 41 29 21 21 10 11 iio 135 160 185 210 240 270 300 330 360 400 440 480 520 560 600 600 650 700 760 820 880 950 220 250 280 320 360 400 440 480 520 560 600 650 700 340 380 430 470 520 560 610 660 710 760 820 '•'• ••'•' 652 From trees cut in Colorado and Utah measured by H. D. Foster. Stump height l|-3 feet. TABLES HELA TING TO PARTS III AND IV 287 VOLUME TABLE No. 26. DOUGLAS FIR OF THE COAST BY THE SCRIBNER DECIMAL Rl 1. 1. (U. S. Forest Service) Diameter at Stump Outside Bark Inches Average Number of Thirty-two-Foot Logs H 2 2} 8 3i 4 41 5 5J 6 61 7 Volume — Board Feet in Tens 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 40 50 62 77 91 105 125 145 169 195 228 270 312 365 425 480 535 588 645 705 765 830 900 972 1048 1133 1226 1310 1413 1515 28 32 34 39 44 49 r>5 (il 60 41 47 53 00 68 76 84 92 100 120 50 50 (50 75 84 95 100 115 125 13S 58 65 78 88 98 110 124 138 149 164 183 92 102 112 124 141 162 176 192 212 228 246 20S 2SO 122 136 157 182 203 227 253 2SO 306 332 35S 388 420 450 480 247 278 313 342 374 403 433 4 OS 502 530 730 774 830 888 942 1009 10S2 1171 1261 1345 1420 1486 1556 385 420 454 487 528 566 595 630 60S 711 760 SOS S04 437 462 494 534 581 598 654 697 744 790 838 886 953 1030 1118 1198 1285 1364 592 644 680 722 771 821 872 926 9S5 1066 1147 1225 1312 1390 1465 '%" 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 t 6.7 53 13 90 110 130 160 i90 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 38 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 111 AM) IV 289 VOLUME TABLE No. 28. WASHINGTON HEMLOCK BY THK SCRIBNER DECIMAL Rl I.J. (By E. J. Hanzlik of U. S. Forest S.T Diameter Number of Thirty-two-Foot Logs Breast, High Average Outside n 2 2} 3 31 4 4* 5 5i Bark Inches Volume — Board Feet in Tens 12 14 16 21 13 20 17 23 28 32 14 26 18 26 31 37 II 15 32 19 29 35 42 49 16 39 21 32 39 47 55 17 46 23 35 43 52 61 18 53 26 39 47 58 88 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 lio 23 100 57 73 90 108 122 148 24 111 80 96 116 130 150 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 33 228 173 195 219 250 288 34 245 181 204 229 263 305 353 35 264 190 213 242 278 323 376 36 284 222 253 293 343 404 37 304 231 266 310 966 436 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 hemlult will be the contents in cubic feet. 296 A MANUAL FOR NORTHERN WOODSMEN WEIGHT OF MATERIALS A cubic foot of water weighs 62$ 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, bass wood, 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 HANDY EQUIVALENTS There are 160 square rods in an am-. 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 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 content-, 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 SI principal after any number of years and at given rates percent Yrs. 2% 2i% 3% 3*% 4% 4*% 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 1.103 .113 1.124 3 1.061 1.077 .093 1.109 1.125 1.141 / 1.158 .174 1.191 4 1.082 1.104 .126 1.148 1.170 1.193 1.216 .239 1.262 5 1.104 1.131 .159 1.188 1.217 1.246 1.276 .307 1.338 6 1.126 1.160 .194 1.229 1.265 1.302 1.340 .379 1.419 7 1.149 1.189 .230 1.272 1.316 1.361 1.407 .455 1.504 8 .172 1.218 .267 1.317 1.369 1.422 .478 .536 1.594 9 .195 1.249 .305 1.363 1.423 1.486 .551 .619 1.690 10 .219 1.280 .344 1.411 1.480 1.553 .629 .708 1.791 11 .243 1.312 .384 1.460 1.540 1.623 710 .802 1.898 12 .268 1.345 .426 1.511 1.601 1.696 .796 1.901 2.012 13 .294 1.379 .469 1.564 1.665 1.772 .886 2.006 2.133 14 .320 1.413 .513 1.619 1.732 1.852 1.980 2.116 2.261 15 .346 1.448 .558 1.675 1.801 1.935 2.079 2.233 2.397 16 .373 1.485 1.605 1.734 1.873 2.022 2.183 2.355 2.540 17 .400 1.522 1.653 1.795 1.948 2.113 2.292 2.485 2.693 18 .428 1.560 1.702 1.853 2.026 2.209 2.407 2.622 2.854 19 .457 1.599 1.754 1.928 2.107 2.308 2.527 2.766 3.026 20 .486 1.639 1.806 1.990 2.191 2.412 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 7.248 8.985 11.127 13.765 50 2.692 3.437 4.384 5.585 7.107 9.033 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 2* 40 years 28 years 1 month 3 33 years 4 months 23 years 5$ months 3$ 28 years 7 months 20 years 2$ months 4 25 years 22 years 2i months 17 years 8 months 15 years 9 months 9 20 years 18 years 7 months 16 years 8 months 14 years 2$ months 12 years 11$ months 11 years 11 J months Note in above tables that a sum at compound interest doubles when rate <>f 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 ENFOBMATIOH TABLE OF WA«,,S..V,-V;| 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 i :,j 3 1.73 1.85 1.96 2.08 2.19 2.42 4 2.31 2.46 2.62 2.77 3.08 5 2.88 3.08 3 If, 6 3.46 3.69 3.92 •I I.', 7 4.04 4.31 4.58 5.65 8 4.62 4.92 6.16 6.46 9 5.19 5.54 5.88 6.23 6.58 6.92 10 5.77 6.15 ii :. I 6.92 7J9 8.08 11 6.35 6.77 7 111 7.62 8.04 s.ss 12 6.92 7.38 7.85 8.31 '.» »-,'.» 13 7.50 8.00 8.50 9.00 9.50 10.80 14 8.08 8.62 9.15 (».»;<» 10.23 10.77 15 8.66 9.23 9.81 10 38 10.96 n r> i 16 9.23 9.85 10.46 11.08 1 1 .f,<> 17 9.81 10.46 11.12 11.77 12.42 18 10.38 11.08 11.77 12.46 13.16 19 10.96 11.69 12.42 13.15 13.88 iir.2 20 11.54 12.31 13.08 13.85 21 12.12 12.92 13.73 14.64 15.35 Ml If, 16.06 22 12.69 13.64 14.38 15.23 KiOH lf>.<»2 23 13.27 14.15 15.04 15.92 KVX1 17 r.-.i 18.68 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 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 3 2.54 2.65 2.77 2.89 3.00 3.11 4 3.38 3.53 3.69 3.84 4.00 4.15 5 4.23 4.42 4.62 4.81 5.00 5.19 5.38 6 5.08 5.30 5.54 6.00 6.46 7 5.92 6.19 6.46 6.73 7.00 7. 1'7 7.54 8 6.77 7.08 7.38 7.69 8.00 8.30 8.62 9 7.61 7.96 8.31 8.65 1UK) 9.34 9.60 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 1 1 M 12 10.15 10.62 11.08 11.54 12.00 13 11.00 11.50 12.00 12.50 13.00 14.00 14 11.84 12.38 12.92 13.46 14.00 1 t :, 1 15.08 15 12.69 13.27 13.85 14.42 15.00 16 13.54 14.15 14.77 15.38 16.00 If, f,l 17 14.38 15.03 15.70- IQ.34 17.00 17.66 18 15.23 15.91 16.62 17.31 1S.(K) 18.68 19.38 19 16.07 16.79 17.54 18.27 19.00 19.72 20146 20 16.92 17.69 18.46 19.23 20.00 20i76 21 17.77 18.56 19.38 20.19 2LOO 21.80 22.61 22 18.61 19.46 20.31 21.15 22.00 22S4 23.69 23 19.46 20.34 21.23 22.11 23.00 23. HS 24 20.30 21.22 22.16 23.08 24. (K) 24.01 25.86 25 21.15 22.12 23.08 24.04 25.00 26.99 26 22.00 23.00 24.00 25.00 2SOO 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 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 4 4.46 4.62 4.77 4.92 5.38 6.15 6.92 5 5.58 5.77 5.96 6.15 6.73 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 33.84 38.08 23 25.65 26.54 27.42 28.31 30.96 35.38 39.81 24 26.76 27.69 28.61 29.54 32.31 36.92 41.54 25 27.88 28.85 29.81 30.77 33.65 38.46 43.27 26 29.00 30.00 31.00 32.00 35.00 40.00 45.00 D $50 360 $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 THE BILTMORK 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 pu:/ Relations between tree, stick, and eye when tin- stick is in use are made clear in the figure, the circle representing a section of a tree breast high, B X the liiltmore stick, A T the distance from the stick to the eye, and () M a radius vertical to the line of sight passing on one sidr of the tree. With this for a pattern it is clear how tin- 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 BC- 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 inches BC = V25 (25 + D) or, for D = 10 inches 250 250 8.45 niches. V625 + 250 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 l 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 hi 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 caliper; 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. LIBRARY FACULTY OF FORESTRY UNIVERSITY OF TORONTO SD 371 G3 1918 Gary, Austin A manual for northern woodsmen Rev. ed. GARY, Austin SD AUTHOR A manual f*OT» 371 TITLE woodsmen . Rev . ed . 1918 DATE ISSUED TO