3 1822 01088 2777
371
, C3
presented to the
UNIVERSITY LIBRARY
UNIVERSITY OF CALIFORNIA
SAN DIEGO
by
Mr. George Marshall
A MANUAL
FOR NORTHERN WOODSMEN
A MANUAL
FOR
NORTHERN WOODSMEN
AUSTIN CARY
Recently Assistant Professor of Forestry
in Harvard University
REVISED EDITION
CAMBRIDGE
HARVARD UNIVERSITY PRESS
1919
FIRST EDITION
COPYRIGHT, 1909
BY AUSTIN GARY
One thousand copies issued in January, 1909
One thousand copies issued in January, 1910
One thousand copies issued in July, 1911
Five hundred copies issued in August, 1915
REVISED EDITION
COPYRIGHT, 1918
BY AUSTIN CARY
One thousand copies issued in January, 1918
One thousand copies issued in March, 1919
PRINTED AT
THE HARVARD UNIVERSITY PR!
CAMBRIDGE, MASS., D. 8. A.
PREFACE
THE reception accorded this book since it was first
issued in 1909, particularly the appreciation expressed
by numerous woodsmen, has been gratifying. Letters
of commendation have been received from users in
all parts of the country. It is significant that the
first typographical error discovered (a wrong figure
in a logarithmic table) was pointed out by a ranger
on the largest tract of unsurveyed timber land in the
United States, in Idaho. The second correction was
sent in by a Canadian cruiser.
The incidents just mentioned illustrate the wide
distribution of the volume and explain the present
extension of it. As originally written, the book did
not aim at circulation west of the Lake states; but
from the first a large part of the demand for it came
from Westerners, chiefly those employed in the
United States Forest Service. Revisions have been
guided largely by this fact, and that is true especially
of the present and first considerable revision, for
aside from bringing the work up to date as concerns
appliances and methods which have come into use
since the first edition was written, the new matter
and tables which have been introduced are mainly
intended for the benefit of western woodsmen. As a
result, material additions have been made under the
heads Topographic Maps and Timber Estimating.
VI PREFACE
The book, however, is not materially increased in
bulk, nor has there been any change in its chief pur-
pose, which is to serve the men who are carrying the
load of actual timber work in this country. To these
men, in whatever section they are, and whatever may
have been their training, the author extends greeting.
CONTENTS
PART I. LAND SURVEYING
PAGE
SECTION I. THE SURVEYOR'S COMPASS
1. The Instrument 1
2. Adjustments of the Compass 4
3. Keeping the Compass in Order 6
SECTION II. THE MAGNETIC NEEDLE 7
SECTION III. MEASUREMENT OF DISTANCE 9
1. The Surveyor's Chain 9
2. The Tape 10
3. Marking Pins 11
4. Chaining Practice 11
5. Measuring Inaccessible Lines 15
6. Stadia Measurement ^17
7. Units of Distance and Area 19
SECTION IV. SURVEYING PRACTICE 19
1. Running a Compass Line (Backsight, Picketing,
Needle) 20
2. Try-Lines 22
3. Marking Lines and Corners 23
4. Original Surveys and Resurveys 26
5. Age of Spots or Blazes 26
6. Notes 28
7. Party and Cost 28
SECTION V. COMPUTATION AND OFFICE WORK .... 31
1. Traverse 31
2. Area 37
3. Plotting 40
SECTION VI. ON THE BEARING OF LINES 43
SECTION VII. ON OBTAINING THE MERIDIAN .... 51
SECTION VIII. THE UNITED STATES PUBLIC LAND
SURVEYS . 60
Vlll CONTENTS
PART II. FOREST MAPS
PAGE
SECTION I. THE TRANSIT 73
1. Adjustments . '. 73
2. Care of the Transit 77
3. Stadia Measurement 77
4. Uses of the Transit 80
5. Summary 87
SECTION II. THE LEVEL 87
1. Adjustments 88
2. Uses of the Level 90
SECTION III. THE HAND LEVEL AND CLINOMETER . . 93
SECTION IV. COMPASS AND PACING 94
SECTION V. THE TRAVERSE BOARD 98
SECTION VI. THE ANEROID BAROMETER 103
SECTION VII. METHODS OF MAP MAKING 113
1. Introductory . . . 113
2. Small Tracts 117
3. Large Tracts 121
A. With Land already subdivided 121
B. Based on Survey of Roads or Streams . . . 121
C. Subdivision and Survey combined 123
D. Western Topography. Use of Clinometer . 129
SECTION VIII. ADVANTAGES OF A MAP SYSTEM . . . 133
^PART III. LOG AND WOOD MEASUREMENT
SECTION I. CUBIC CONTENTS 137
SECTION II. CORD WOOD RULE 138
SECTION III. NEW HAMPSHIRE RULE 138
SECTION IV. BOARD MEASURE 139
1. General 139
2. Scribner and Decimal Rules .......... 141
3. Spaulding or Columbia River Rule 141
4. Doyle Rule . 141
5. Maine Rule 142
6. New Brunswick Rule 144
7. Quebec Rule 145
8. Theory of Scale Rules and Clark's International
Log Rule . . . 145
SECTION V. NEW YORK STANDARD RULE ..... 147
SECTION VI. SCALING PRACTICE 148
SECTION VII. MILL TALLIES . . 151
SECTION VIII. CORD MEASURE . 157
CONTENTS IX
PART IV. TIMBER ESTIMATING
PAGE
SECTION I. INTRODUCTION 161
SECTION II. INSTRUMENTAL HELPS 162
SECTION III. HEIGHT MEASUREMENT 165
SECTION IV. VOLUME TABLES AND TREE FORM ... 167
SECTION V. PRACTICE OF TIMBER ESTIMATING . . . 173
A. Small and Valuable Tracts 174
B. Larger and Less Valuable Tracts 186
1. Type and Plot System 187
2. The Strip System 188
3. Line and Plot System 192
C. Summary 195
D. Pacific Coast Methods 196
PART V. TABLES
SECTION I. Tables relating to Parts I and II
1. STADIA REDUCTIONS 211
2. SOLUTION OF TRIANGLES 212
3. TRAVERSE TABLES 214
4. LOGARITHMS OF NUMBERS 220
5. LOGARITHMIC SINES, COSINES, TANGENTS, AND CO-
TANGENTS 222
6. SUPPLEMENTARY TABLES OF SMALL ANGLES .... 228
7. NATURAL SINES AND COSINES 230
8. NATURAL TANGENTS AND COTANGENTS 232
9. SPECIMEN LETTERING : . . . 234
SECTION II. Tables relating to Parts III and IV
VOLUMES OF CYLINDERS (Locs) IN CUBIC FEET . . 236
AREAS OF CIRCLES OR BASAL AREAS 238
CORD WOOD RULE 239
NEW HAMPSHIRE RULE 240
NEW YORK STANDARD RULE 242
SCRIBNER LOG RULE, LEGAL IN MINNESOTA . . . 243
DECIMAL RULE OF THE U. S. FOREST SERVICE . . . 244
DOYLE RULE 246
MAINE LOG RULE 248
QUEBEC RULE 250
NEW BRUNSWICK RULE . . 253
X CONTENTS
PAGE
12. CLARK'S INTERNATIONAL RULE 254
13. SPATJLDING RULE OF COLUMBIA RIVER 255
14. BRITISH COLUMBIA RULE 258
15. VOLUME TABLES
A. Eastern
1. White Pine by the Scribner Rule 261
2, 3. Red (Norway) Pine by the Scribner Rule . . 262
4. White Pine as sawed in Massachusetts . . . 263
5. White Pine in Cords 264
6. Spruce in Cubic Feet 264
7. Spruce in Feet, Board Measure 265
8. Spruce in Cords 266
9. Hemlock by the Scribner Rule 267
10. Hemlock as sawed in New Hampshire . . . 268
11. White (paper) Birch in Cords 268
12. Red Oak as sawed in New Hampshire .... 269
13. Peeled Poplar in Cords 270
14. Second Growth Hard Woods in Cords .... 270
15. Form Height Factors for Southern Hard Woods 271
16, 17. Northern Hard Woods in Board Measure . 272, 273
18. Longleaf Pine in Board Measure 274
19. Loblolly Pine by the Scribner Rule .... 275
B. Western; Notes on Western Volume Tables .... 276
20. Western White Pine in Board Feet 281
21. Western Yellow Pine in Board Feet 282
22. Western Yellow Pine (16-foot log lengths) . . 283
23. Lodgepole Pine in Feet, Board Measure, and
in Railroad Ties 284
24. Western Larch in Board Measure 285
25. Engelmann Spruce in Board Measure .... 286
26. Douglas Fir of the Coast 287
27. Douglas Fir of the Interior 288
28. Washington Hemlock in Board Measure ... 289
29. Washington Red Cedar in Board Measure . . 290
30. California Sugar Pine in Board Measure ... 292
SECTION III. Miscellaneous Tables and Information
1. RULES FOR AREA AND VOLUME OF DIFFERENT
FIGURES . 294
2. WEIGHT OF MATERIALS 296
3. HANDY EQUIVALENTS . 297
CONTENTS XI
PAGE
4. NUMBER OF PLANTS PER ACRE WITH DIFFERENT
SPACING 297
5. COMPOUND INTEREST TABLE 298
6. TIME IN WHICH A SUM WILL DOUBLE 298
7. TABLE OF WAGES AT GIVEN RATES PER MONTH . . 299
8. THE BILTMORE STICK . . 301
PART I
LAND SURVEYING
PART I. LAND SURVEYING
SECTION I. THE SURVEYOR'S COMPASS
1. The Instrument li
2. Adjustments of the Compass 4
3. Keeping the Compass in Order 6*
SECTION II. THE MAGNETIC NEEDLE 1
SECTION III. MEASUREMENT OF DISTANCE
1. The Surveyor's Chain
2. The Tape 10
3. Marking Pins 11
4. Chaining Practice 11
5. Measuring Inaccessible Lines 15
6. Stadia Measurement 17
7. Units of Distance and Area 19
SECTION IV. SURVEYING PRACTICE 19
1. Running a Compass Line (Backsight, Picketing,
Needle) 20
2. Try-Lines
3. Marking Lines and Corners
4. Original Surveys and Resurveys
5. Age of Spots or Blazes
6. Notes 28
7. Party and Cost 28
SECTION V. COMPUTATION AND OFFICE WORK .... 31
1. Traverse 31
2. Area 37
3. Plotting 40<
SECTION VI. ON THE BEARING OF LINES 43
SECTION VII. ON OBTAINING THE MERIDIAN .... 51
SECTION VIII. THE UNITED STATES PUBLIC LAND
SURVEYS .
A MANUAL
FOR NORTHERN WOODSMEN
PART I. LAND SURVEYING
SURVEYING in forest land as compared with work done in
towns and on farms is carried out under unfavorable cir-
cumstances. In the first place, timber and brush growth
offer an obstruction to sighting; second, the work is often
done far from a well supplied base; third, the limits of
cost allowed are often the lowest practicable. These con-
ditions have a strong effect upon the methods employed,
and they also affect the choice of outfit. Equipment for
such work should not usually be expensive, it should be
as compact and portable as possible, and it should not
be so delicate or so complicated as to be likely to get
seriously out of order and so hold up a job.
SECTION I
THE SURVEYOR'S COMPASS
Compass and Chain are the instruments that at present
are most largely employed in forest land surveying, and
there is little doubt that they will continue to be so em-
ployed. The compass is one of the mainstays of the
practical woodsman. He should thoroughly understand
its capacities and limitations, and should have perfect
command of all parts of his own particular instrument.
1. THE INSTRUMENT
The essential parts of the surveyor's compass are a
magnetic needle for finding a meridian line, a horizontal
graduated circle for laying off angles from this meridian,
and sights attached for use in prolonging lines on the
ground.
2 A MANUAL FOR NORTHERN WOODSMEN
The needle in compasses used for surveying purposes is
commonly between four and six inches in length. It rests
by a jeweled bearing at its center upon a steel pivot screwed
into the compass plate, and, turning freely in the horizon-
tal plane, its ends traverse the graduated circle. The plane
of the sights passes through the center of the circle, and
cuts its circumference at two points marked N and S,
known as the north and south points of the instrument.
From these points the graduation of the circle runs 90° in
each direction to the points marked E and W. These
PLAIN SURVEYOR'S COMPASS
points on the face of the surveyor's compass are reversed
from their natural position for convenience in reading
bearings.
In using the compass, point the north end of the
circle forward along the line and read from the north
end of the needle.
A compass bearing is the direction from the observer at
THE SURVEYOR S COMPASS 3
the compass to any given object referred to the meridian.
It is read as so many degrees from the N or S direction,
up to 90°; as, N 10° W, S 88° 15' E. The graduations on
a surveyor's compass are commonly in half degrees, but it
is usual, if necessary, to set by estimation quarter degree,
or 15', courses. A bearing can be set, however, with a
surveyor's compass in first-class order, to about 5'.
A compass needle that is in good working order
takes some little time to settle, and its condition may be
told by the freedom and activity with which it moves.
Time can be saved in setting it by checking its motion
with the lifting screw. In its final settlement, however,
it must be left free. For important bearings, it is well to
let it settle two or more times independently.
A glass plate covers the compass box and two small
levels placed at right angles to each other are used to set
the instrument in the horizontal plane. It is very de-
sirable that the box of a compass employed for woods
work should be as nearly watertight as possible. In
general make-up, the instrument is subject to considerable
variation.
The plate of the Plain Surveyor's Compass is prolonged
in the north and south direction into arms on which the
sights are supported at a distance of twelve to sixteen
inches apart. The actual sighting is done through fine
vertical slits, and round apertures placed at intervals along
these are convenient for finding objects and for getting the
instrument approximately in line.
The Vernier Compass has the circle and the sights
upon separate plates which may be turned on one another
for 20° or more. Its advantage consists in the fact that
declination, or a change in declination, may be set off,
and the courses of an old survey set directly, or lines re-
ferred to the true rather than the magnetic meridian.
The Folding-Sight Compass possesses the advan-
tages of light weight and the utmost compactness, and is
therefore popular among woodsmen. The sights are set
upon the edge of the compass box, and fold down across
its face when not in use, the whole instrument with its
' mountings slipping into a leather case which may readily
4 A MANUAL FOR NORTHERN WOODSMEN
be carried in the pack or slung from the shoulder. A
folding-sight compass with too small a box and needle of
less than full length should not be employed on work of
importance, as it is impossible with such an instrument to
read bearings and set marks with accuracy.
Compasses are either mounted on a tripod or fitted for
attachment to a single staff called a Jacob-staff, which
the surveyor may make for himself, when needed, from a
straight sapling. The former is the firmer mounting and
better adapted to accurate work, but the latter is much
more portable, except on bare rocks is more quickly set up,
and is generally employed for the ordinary work of the
forest surveyor.
2. ADJUSTMENTS OF THE COMPASS
A compass in first-class order will meet the following
tests :
a. The plate must be perpendicular to the axis of the
socket.
6. The plane of the level bubbles must be perpendicular
to the same axis.
c. The point of the pivot must be in the center of the
graduated circle.
d. The needle must be straight.
e. The sights must be perpendicular to the plane of the
bubbles.
In these tests it is presupposed that the circle is accurately
graduated and that the plane of the sights passes through
the zero marks. These are matters that belong to the
maker of instruments, and in all modern compasses accu-
rate adjustment of them may be assumed.
The general principle of almost all instrumental adjust-
ments is the Principle of Reversion, whereby the error
is doubled and at the same time made more apparent.
Thorough mastery of this principle will generally enable
one to think out the proper method of adjusting all parts
of any surveying instrument. In the case of the compass
the above-named tests may be applied and the instrument
adjusted as follows. The order of the adjustments is
essential.
THE SURVEYOR S COMPASS 5
a. The plate is exactly vertical to the spindle in a new
compass, but the soft metal of most instruments is liable
in use to become bent. If that occurs to any considerable
degree, it will be shown by the needle and the bubbles.
The instrument should then be sent to the maker for repairs.
b. To make the plane of the level bubbles perpendicular
to the axis of the socket, level the instrument, turn it 180°,
and, if the bubbles are out, correct one half the movement
of each by means of the adjusting-screw at the end of the
bubble-case. Now level up again and revolve 180°, when
the bubbles should remain in the center. If they do not,
adjust for half the movement again and so continue until
the bubbles remain in the center of their tubes for all posi-
tions of the plate.
c. d. When the pivot is in the center of the circle and
the needle is straight, the two ends of the needle will cut
the circle exactly 180° apart in whatever position the in-
strument may be set. If the needle does not so cut, one
or both of these conditions is not fulfilled. If the differ-
ence between the two end readings is constant for all posi-
tions of the needle, then the pivot is in the center of the
circle but the needle is bent. If the difference in readings
is variable for different parts of the circle, then the pivot is
off center and the needle may or may not be straight.
To adjust the pivot, first find the position of the needle
which gives the maximum difference of end readings;
then, using the small brass wrench commonly supplied
with the compass, bend the pivot a little below the point at
right angles to the direction of the needle until one half
the difference in end readings is corrected. Repeat the
test and adjust again if necessary. When the needle cuts
opposite degrees, or when it fails to do that by a constant
quantity in all parts of the circle, the pivot point is in the
correct position.
With the above adjustment attended to, straighten the
needle. To do this, set the north end of the needle on some
graduation mark and bend the needle until the south end
cuts the circle exactly 180° from it.
e. To make the sights perpendicular to the plane of the
bubbles, level the instrument carefully, hang a plumb
6 A MANUAL FOR NORTHERN WOODSMEN
line some feet away, and then look through the sights upon
it. If the plumb line appears to traverse the forward slit
exactly, that sight is in adjustment. If not, file off the base
of the sight until the adjustment does come. Then revolve
the compass 180° and test the other sight in the same
manner.
3. KEEPING THE COMPASS IN ORDER
Sharpening Pivot. The pivot or center pin of a compass
much in use is liable to become dulled so that the needle
does not swing freely. To obviate this the needle should
always be raised off the pivot when the compass is being
carried. A much blunted pivot should be handed over to a
jeweller to be turned down in a lathe, but ordinary sharp-
ening can readily be accomplished by the surveyor him-
self with the aid of a fine whetstone and the small wrench
usually supplied with a compass, or a pair of pliers. The
pivot should be removed from the compass box and fixed
in the end of a small, split stick; the point may then be
sharpened by twirling it gently on the stone at an angle of
about 30° with its surface. When the point is made so
fine and sharp as to be invisible to the eye, it should be
smoothed by rubbing it on the surface of a soft, clean
piece of leather.
Remagnetizing Needle. Dulness of the needle may
be due to the fact that it has lost its magnetism and needs
to be recharged. For this purpose a permanent magnet is
required. The north end of the needle should be passed
several times along that pole of the magnet which attracts
it, and the south end passed similarly over the opposite
pole. The passes should be made from center to end of
the needle, and a circle described in bringing the two ends
successively into contact. In order to prevent the loss of
magnetism, the needle of a compass not in use for a con-
siderable time should lie in the north and south direction.
Balancing Needle. The needle is commonly balanced
on the pivot by a fine brass wire wound around the south
end. If change of latitude is made, the balance will be
destroyed, and the wire may be shifted to make adjustment.
Replacing Glass. In case of emergency, a piece of win-
THE MAGNETIC NEEDLE 7
dow glass may be cut down with a diamond and ground
on a grindstone to fit its setting. It may then be set in
place, with putty if possible, and the binding ring sprung
into place over it.
SECTION II
THE MAGNETIC NEEDLE
All compass surveying is based on the tendency of the
magnetic needle to point north and south. The direction
of the needle, however, is very far from being constant.
Secular Change. There is a belt of country crossing
the United States in a general north and south direction
through the states of Michigan, Ohio, and South Carolina
along which the needle at the present time points due north
toward the earth's pole. • This belt is called the agonic
line, or line of no variation. East of this line the needle
points westward of true north; west of this line it points
to the eastward of it. The direction from any place toward
the pole of the earth's revolution is for that place the true
meridian. The direction taken by the needle is the mag-
netic meridian. The angle between the two is called the
declination of the needle, west if the needle points west of
true north, east if the needle points east of it. The declina-
tion is greater the farther the agonic line is departed from,
amounting to more than 20° in the maritime provinces and
the Puget Sound country. The agonic line is not sta-
tionary but is moving slowly westward, as it seems to have
done constantly since the beginning of the last century.
The declination of the needle, therefore, is changing from
year to year and at a different rate in different parts of the
country.
These facts affect the work of the land surveyor impor-
tantly, and sections on the bearing of lines and on ascer-
taining the true meridian are given later on in this
volume.
Daily Change. The needle when free and undisturbed
swings back and forth each day through an arc amounting
commonly in the United States to about 10'. Early in the
morning, from four to six o'clock according to the season,
8 A MANUAL FOR NORTHERN WOODSMEN
the north end of the needle begins to swing to the east,
reaching its maximum position between eight and ten
o'clock in the forenoon. It then swings west to a maximum
westerly position reached from one to two o'clock p. M.
Then it swings slowly east again to a mean position reached
between six and eight p. M., at which point it remains
practically steady during the night.
The effect of this variation is such that if a surveyor
starts a line in the morning and runs one course all day, he
runs, not a straight line, but a long curve. This variation,
however, like the slight variation thut occurs during the
course of the year, is in woods work commonly disregarded.
Irregular Changes. The needle is subject occasionally
to sudden and irregular changes in direction. They some-
times occur during thunder storms, and at other times are
attributed to so-called magnetic storms, related perhaps
to the aurora borealis. Trouble from this source is not
often experienced by the surveyor, but it is a matter which
needs to be understood and watched for.
Local Attractions. All users of the compass are on
guard against the disturbance caused by iron in its vicinity,
in the form, for instance, of chains, axes, and steel rails.
In addition, there are in most countries regions of greater
or less extent where the needle is subject to irregularities.
These are due to iron ore or other magnetic material located
in the vicinity, or to unknown causes.
A local disturbance is indicated when the compass does
not read the same on the two ends of a line, and in compass
running error from this source is guarded against by keep-
ing careful watch of the backsight. Local disturbances
vary much in intensity. When very strong, they are readily
detected, and if confined in area present little difficulty to
the surveyor, who will clear out his line across them with
especial care, and either picket ! through or set the compass
by backsight. Slight disturbances are harder to detect.
If the area of disturbance is large, particularly if the ground
is broken, the compass cannot be depended on to carry a
line through with accuracy, and a transit or solar instru-
ment must be used.
1 See page 21.
MEASUREMENT OF DISTANCE 9
Electricity. A little caution is necessary in handling
the compass in order that the glass cover shall not be elec-
trified by the friction of cloth or the hand, so as to attract
the needle to its under surface. If, however, the glass does
become electric, the trouble may be removed by breathing
upon it, or by touching different parts of its surface with
the moistened finger.
Difference in Instruments. It is a well-known fact that
different instruments do not always give the same bearing
when read on the same marks at the same time. A differ-
ence of 15' is not uncommon.
Summary. The magnetic needle is thus seen to be sub-
ject to numerous variations and irregularities, and on that
account work with the needle compass cannot be expected
• to give the most accurate results. The instrument has
great advantages, however, and a very large field of legiti-
mate use. It gives an approximately true direction from a
detached point. Except on open ground, it furnishes the
quickest and cheapest means of turning an angle or pro-
longing a line. Most authoritative land surveys have
been made with the needle compass and their renewal is
best accomplished by use of the same instrument. The
special advantages of the compass in forest conditions and
its most effective use therein are discussed under the head
of SURVEYING PRACTICE.
SECTION III
MEASUREMENT OF DISTANCE
1. THE SURVEYOR'S CHAIN
The word "chain" in connection with land surveying is
used to represent two things: a distance of 4 rods or 66
feet, and an instrument for measuring distance. The
chain in use for general land surveying is 66 feet long and
divided into 100 links, but woodsmen working in rough
ground find the 33 foot or half chain with 50 links much
more convenient.
A chain for surveying purposes should be made of steel
wire, and its links should be brazed to prevent stretching
10 A MANUAL FOR NORTHERN WOODSMEN
by opening of the joints. Chains have every tenth link
marked by a brass tag, and these tags have one, two, three,
etc., teeth, so that the number of links may be readily and
accurately counted.
Chains change in length by use. The links may be bent
and the chain thus shortened, a matter which can readily
be adjusted by hammering; but more commonly a chain
increases in length from flattening of the links and wear
in the numerous joints. This may be corrected to a limited
extent by turning up the nuts which hold the handles.
Further effect may be had by taking out one or^more of the
rings which connect the links, or better still, by hammering
each link while it is held in a vise, and so distributing the
correction.
The chain is so liable to change in length that provision,
should be made for testing it frequently. An unused tape,
known to be of true length, kept at home or only taken
off on long jobs, is the best and most convenient safe-
guard.
2. THE TAPE
Steel tapes are in wide use for general surveying, but
not usually among woodsmen because of their liability to
breakage. They have, however, distinct advantages.
They are light, so as to be leveled readily when measure-
ment is being made on a slope. They do not stretch.
There are no links to get kinked and so cause a false
measure. A tape for field use should be made of steel
ribbon from i to J inch wide and No. 30 to 32 thick.
Wider and thinner tapes are a nuisance in woods
conditions.
Tapes are made of any length and graduated to suit the
work for which they are designed. One 66 or 33 feet long,
graduated to links, will best suit the needs of the timber
land surveyor.
Some precaution must be taken with steel tapes. When
in use, they should be kept out at full length and never be
doubled on themselves, for, if doubled, they are easily
kinked and broken. When done up, they should be wiped
clean and dry, and so cared for as to prevent rusting. A
MEASUREMENT OF DISTANCE 11
broken tape can generally be repaired on the ground if there
are at hand a punch, a piece of another tape, and some pins
to serve as rivets.
3. ]\IARKING PINS
Woodsmen frequently manufacture their own marking
pins of wood or wire. Those bought from dealers are
made of heavy iron wire, are some fifteen inches in length,
with one end sharpened and a ring turned in the other for
convenience in handling. Strips of cloth are tied in the
rings, so that they can be readily seen. It is most con-
venient to use eleven pins in chaining. One of them is
stuck at the starting point, the leading man takes ten,
and thus there is always one in the ground to start from
when the tallies are finished.
4. CHAINING PRACTICE
Chains are standardized in length at about ten pounds
pull with their full length supported. In woods work it is
generally necessary that the chain should be suspended
above the ground and not lie upon its surface. Care must
be taken, therefore, in accurate measurement, to give it
proper tension. What tension is proper for a suspended
chain, — in other words, what sag should be allowed to
compensate for the stretch of the chain under the greater
tension — may be determined on perfectly smooth and level
ground, and this is a valuable exercise for inexperienced
chainmen.
In order to get true chainage between points, the chain
should be kept straight and free from kinks. It must also
be kept in approximately true alignment, though a con-
stant error of 1° in that matter, equivalent to seven inches
error in setting pins each two rods of distance, shortens
the line by only nine and a half inches in the mile. Simi-
larly, the chain must be levelled so as to give distance in
a horizontal line, not following the contour of the ground.
In this last connection, that is, in getting distance correctly
on slopes and over rough ground, are met the greatest
difficulties in practical chaining. What is necessary is
first, to determine when the chain is level, and second, to
12 A MANUAL FOR NORTHERN WOODSMEN
carry the point occupied by the suspended end of the chain
vertically down to or up from the mark on the ground.
The use of plumb lines and plumbing rods for this pur-
pose is well known from standard works on surveying. It
is common woods practice to drop a pin from the head end
of the chain, and that practice, when a pin loaded near the
lower end is used, has been approved for United States
land surveys. Only one such pin is required in a set, as
after it is stuck in the ground another may be substituted
for it. Similarly, for the rear end of the chain, when it has
to be held above the ground, an ax held suspended beneath
the handle, with the bit turned across the line, enables one
to do quick and fairly accurate plumbing. For determin-
ing when the chain is level, a hand level or Abney clinom-
eter, such as is shown on page 93, may well be put in
the hands of the men. There is a strong tendency on the
part of unpracticed chainmen to hold the down-hill end of
the chain too low.
It is to be observed that all the above-mentioned sources
of error work in one direction, namely, to give too large a
valuation to the distance between two points. The young,
school-trained man particularly, with his aspiration after
exactness, is apt to undervalue these sources of error, and,
in consequence, not give land enough.
In view of all the facts and conditions, particularly be-
cause of the pressure for cheapness in this class of work,
many practical woods surveyors have concluded that it is
best and safest not to strive after too great mechanical
exactness, but to make a small constant allowance at the
rear end of the chain. On the other hand, the loose practices
of some old woodsmen, such as letting the chain run out
the length of a man's arm beyond the mark, have nothing
to be said in their defense.
The general method of procedure in chaining, to be
modified as circumstances may require, is as follows.
The two chainmen will be spoken of as head and rear
man. Commonly, the rear man is the better and more
experienced of the two, and is in general charge.
With one pin set at the starting point, the head man
takes his end of the chain or tape and ten pins and steps
MEASUREMENT OF DISTANCE
13
off in the direction of the line to be measured. Just before
the chain is all drawn out the rear man calls out " chain"
or " halt," and prepares to hold his end of the chain on
the mark. The rear man lines in the other, by the com-
pass ahead, by stakes left, or by the marks and bushing
TABLE SHOWING ERROR CAUSED BY CHAINING ALONG
GROUND OF DIFFERENT DEGREES OF SLOPE
Slope. Error.
Infect
per 100.
In degrees.
In feet
per mile.
In links
per chain.
2
U
1.0
.02
4
2J
4.3
.1
6
31
9.5
.2
8
«i
16.7
.3
9
fi
21.2
.4
10
51
26.1
.5
along the line. Kinks are shaken out, the chain is levelled,
and proper tension is applied. When all is ready and the
rear man has his handle firmly held on the mark, he calls
out " stick" to the leader who sets his pin at once and
calls " stuck." When the rear man hears this signal, and
not before, he pulls his pin and both men move quickly
forward, repeating the operation till the head man has
stuck his last pin or has reached the end of the line.
When the head man has stuck his last pin he calls
" tally." The rear man then drops his end of the chain,
counts the pins to make sure that none has been lost, and,
going forward, gives them to the head man who counts
them again. The tally is marked down and a stake left at
the point for reference in case of a lost pin or other cause
of debate in the next tally. Pins should be set plumb, and,
in general surveying practice, the point held to is the point
at which they enter the ground. In the brush and "down
stuff" of some woods lines, however, it is sometimes neces-
14 A MANUAL FOR NORTHERN WOODSMEN
sary to chain by the top, not the bottom, of the pins. No
jerking of the chain should be allowed. The rear man
should not stop the head man with a jerk. The head man
must pull steadily on the chain when measuring.
When chaining on slopes which are so steep that the
full length of the chain cannot be levelled at once, the
head man first draws the chain forward the whole length
and in line. He then drops the chain and his marking
pins and returns to a point where he can level a part of the
chain. This distance is measured and one of the rear man's
pins stuck at the point. The rear man then comes forward
and, taking the chain at the same point, holds it to the
mark while a second section is measured, and so on till the
end of the chain is reached, when the head man sticks one
of his own pins. It is not usually necessary to note the
lengths of the parts of the chain measured. Take care
only to measure to and from the same points in the chain
and not to lose the count by getting the marking-pins of
the two men mixed together.
Accuracy. The requirements of woods chainage vary
so widely, its difficulties are sometimes so great, and the
expense permissible for the work is often so restricted that
only guarded statements can be made as to obtainable
accuracy. When chainmen, measuring the same line
twice, agree almost exactly, it does not prove that they
have given correct chainage, for two other men on the
same line may get a result considerably variant. Really
correct chainage is to be obtained only by strict attention
to the sources of error mentioned above, their amount and
nature. In general, it may be said that on smooth and
level ground, free from obstructions, chaining may be
done with error of a very few feet in the mile. On land as
it runs, however, chainage accurate to within a rod in a
mile is generally called entirely satisfactory.
Summary. Good chaining consists in keeping the chain
of right length, in true alignment, vertical and horizontal,
and in proper stretching, marking, and scoring. It is a
very important part of all surveying which employs that
method of measuring distance, and has been badly neg-
lected in much woods work of the past. It needs and de-
MEASUREMENT OF DISTANCE
15
serves good men to carry it on, men who will get down to
the ground and take all needed pains in marking, level-
ing, and alignment. They should be brisk men, moving
quickly and doing their work in a prompt and business-
like manner. Much, too, depends on system, — on tally-
ing, passing pins, etc., from habit and in regular order.
Some men never will make good chainmen because they
will not take sufficient pains about details. A few in their
strict attention to these are liable to make gross blunders.
The man in general charge of surveying work must give
careful attention to this part of the business. Chainmen
must be trained in good methods and watched till they
are perfectly trustworthy, while careful consideration must
be given to sources of error and to possible improvements
in method.
5. MEASURING INACCESSIBLE LINES
Ponds, bogs, and bluffs, over which it is impossible to
chain, are met in the practice of nearly every surveyor, and
quick and accurate measurement across them constitutes
one of the problems which he has frequently to solve. Each
problem of that kind has to be solved in the field according
to the ground and circumstances. The methods commonly
employed in such cases are as follows:
1. Offset. Frequently a short offset squarely to left or
right will clear the obstacle.
FIG. A
2. Method by 45° Angle. (A) With the compass at a,
set a stake in the line at b across the obstruction, and,
turning off an angle of 45°, set another stake on that range
16 A MANUAL FOR NORTHERN WOODSMEN
as x. Set up at b and, turning off a right angle, set a
stake c in the range a x. Then a b = b c.
3. Method by 26° 34' Angle. (B) Proceed as before,
making the angle b a c = 26° 34' ; then a b = 2 b c, as
may be found in the table of tangents.
4. Method by 30° Angle. (C)
With compass at a set a stake
in line at b, and, turning off an
angle of 60°, set another stake
on that range, as x. Set up
at b and turn off a b c = 30°,
setting a stake c in the range
a x. Then a b = 2 a c.
6. Method by Tangents. (D) With the compass at a
set a stake at 6, also run out a perpendicular line and set
a stake at c visible from b at any convenient distance.
Measure a c. With the compass at b, take the bearing of
c b and thus get the angle a b c. In the table of tangents
look up the tangent of this angle. Then a b = — .
FIG. D
6. Method by Oblique Triangle. (E) The stake c may
be set at any convenient point visible from both a and b
and the angles at a and b measured. Measure also the side
a c or b c, whichever is easier. Then a 6 may be computed
as the side of an oblique triangle. For formulas neces-
sary, see pages 212-213.
7. Method by Traverse. (F) In the case of a large lake
or stream, several courses may be run along its banks, and
when the range of the line is again struck, as at e, the dis-
MEASUREMENT OF DISTANCE
17
tance a e may be computed by traverse. If a e runs N and
S, the distance a e will be the latitude of the traverse, or,
stated in other words, it will be the sum of
the products of the cosines of the several
courses into their respective distances. The
departure of such a traverse should be zero.
Thus, if e is not visible from a, or if it is not
convenient to take the range a e, e may be
set when the sum of the departures figures
up 0. This process of surveying a lake or
river shore is called " meandering." It is the
method pursued in the United States land
surveys on considerable bodies of water. The
same method may also be employed to get
round a precipitous hill or some other inac-
cessible object.
An example of the computation necessary
for solving a problem of this kind is given on
page 33.
8. Method by 60° Angles. (G) A precipitous bluff or
impassable swamp may occasionally be passed most read-
ily in the following manner. With
the compass at a, lay off a 60°
angle and run out a c, carefully
chaining. Next, making an angle
of 60° at c, run out c b to an equal
distance. Then, if the work has
been done accurately, b is in the
line and ab = a c = be.
In working by any of these
methods it is better, if possible,
to set b in range by the compass
from a rather than to rely for the range on any process of
figuring or angulation.
FIG. F
6. STADIA MEASUREMENT
A substitute for chaining, which has to some extent
been employed in forest land surveying and which deserves
18 A MANUAL FOR NORTHERN WOODSMEN
wider use, is stadia measurement, or the measurement of
distance by wires placed in the focus of a telescope and
the space which they cut off on a graduated rod. The
principles of this method are stated on page 77.
For this purpose a light telescope may be fitted to
the rear sight of the compass, as shown in the illustra-
tion, a level and vertical
circle being added if the
instrument is to be used
on rough ground. The
cost of such an instrument
complete is about the same
as that of a compass. Its
adjustments will readily
be understood from its
construction and from
consideration of the ad-
justments required for the
transit.
The advantages of this
instrument in land sur-
veying are as follows : —
1. Sights may be taken
on steeper ground, either
up or down hill, than can
be covered through com-
2. Distances over very
steep ground can be
measured more accurately
and quickly than by use
A TELESCOPIC SIGHT of the chain.
3. Distance across
gorges, swamps, and bodies of water can be obtained
directly and with ease.
4. It enables the surveyor himself to perform all the
particular work on a survey, and this on short jobs, or
wherever reliable chainmen cannot be had, may be a very
great advantage.
Stadia wires in an instrument used for land surveying
SURVEYING PRACTICE 19
should be so spaced that one foot on the rod will be cut off
when it is held at a distance of 66 feet, or, if the wires are
fixed, the rod may be graduated to correspond. For occa-
sional use in land surveying, the rod may best be made
of painted canvas, which, in case of need, may be tacked
on any pole that comes to hand.
The Stadia Hand Level is a simpler form of the instru-
ment, adapted to the measurement of the width of gorges
or ponds. It is readily carried in the pack, and, when in
use, may be held in the hand or mounted on a staff. The
ready range of this instrument is 200-300 feet.
7. UNITS OF DISTANCE AND AREA
7.92 inches =» 1 link.
25 links = 1 rod.
100 links = 66 feet = 1 chain.
320 rods = 80 chains = 1 mile.
160 square rods = 10 square chains = 1 acre.
640 acres = 1 square mile or section.
The vara, a measure of Spanish origin, prevails in Cali-
fornia and in Texas. The California vara is 33 inches.
The Texas vara is 33J inches, and 5645.376 square varas
make one acre.
In Louisiana and the Province of Quebec, the arpent,
an old French unit, is the measure of areas. This is .8449
acre.
The hectare = 10,000 square meters (meter = 39.37
inches) or 2.47 acres. This is also a French measure.
SECTION IV
SURVEYING PRACTICE
The starting point of a survey is generally settled for a
surveyor by outside controlling circumstances. When this
is recognized, the next thing to do may be to find out what
course to run by an observation for the true meridian, or
by finding the bearing of an old line. With the starting
point and course determined, the method of procedure is
about as follows.
20 A MANUAL FOR NORTHERN WOODSMEN
1. RUNNING A COMPASS LINE
Set up the compass at the point from which the line is to
start; level the plate; free the needle, and when it has
settled, set the course to be run. It is desirable on starting
a line to let the needle settle two or more times independ-
ently.
An assistant, called the rodman or flagman, then goes
ahead with a pointed rod or flag, and, following him, go
the axemen, clearing out the bushes and other obstruc-
tions in such a manner as to secure both a clear line of
sight and a path for the chain. The rodman may use an
axe. He guides himself at first by the compass sights, later
by signals from the compassman or by the range of the line.
The axemen guide their work by him.
When the rodman has gone ahead a convenient distance,
at signal from the compassman or acting on his own judg-
ment, he selects a spot for a second setting of the compass,
attention being paid both to firm setting and clear ground
for the instrument, and to facility in getting sight ahead.
On uneven ground summits commonly meet best this last
requirement.
When setting the rod, the rodman should face the com-
pass, holding the rod plumb and directly in front of him. He
sticks it as directed by the compassman, who assures him-
self at the time that everything about the instrument is
right. Before taking up the compass, the man in charge
of it sets a stake near by and in line to be used in backsight.
The needle is then lifted, and the compass taken up and
carried forward to be set up at the point marked by the
rodman. If a Jacob-staff is used instead of a tripod, the
compass should be set up ahead of the rod with its cen-
ter in line, the exact position of the foot of the staff being
of no consequence.
The compass is then levelled again with its N mark
ahead as before and the sights turned on the object left
at the starting point. The needle is then freed, and if,
when it settles, the bearing reads the same as before, the
surveyor is assured that there is no local disturbance, and
may proceed confidently. The rod and axemen soon learn
SURVEYING PRACTICE 21
to range for themselves, and lose no time waiting for the
set-up of the instrument. The chainmen keep behind the
instrument where they are out of the way. Each man
learns his exact duties, and all hands, particularly the corn-
passman and rodman, learn to work together.
Running by Backsight. The details of compass survey-
ing vary considerably in accordance with the accuracy re-
quired, cost allowed, and the make-up of the party doing
the work. If local attraction is suspected or, on short
lines, if great accuracy is required, obstructions are cleared
completely out of the line, and wrhen an assumed or trial
course has been started, it is prolonged by backsight en-
tirely, reference to the needle not necessarily being made.
In order to do this, either a rear rodman is employed or a
stake is set in line at each station occupied by the compass.
Picketing. The compass after the start, indeed, may not
be used at all, but straight stakes, preferably four to five
feet high and sharpened at both ends, may be ranged in
one after another along the line. This method of running
a line is frequently resorted to, and is called picketing.
To clear out in most woods a line open enough for con-
tinuous backsighting or picketing is an expensive process,
and, further, this method for long distances and uneven
ground is not to be relied on. If, in those circumstances,
close accuracy of alignment must still be had, resort must
be made to another class of instrument, a transit or solar,
which may carry the work out of the hands of the woods
surveyor.
Running by the Needle. Usually the compass will do
the work reasonably well and satisfactorily to all interested
parties, in which case the needle will be used at nearly
every setting. In all compass running it is well to carry a
light rod ahead, though that is sometimes dispensed with,
the compassman going up to a stake or even an axe set up
by the head axeman in line. When trees of some size are
run into, they are not commonly cut down, but the com-
passman notes, or has marked, the spot at which his line
of sight hits them, and, going forward, sets up beyond
them in the same range as nearly as he can. For back-
sighting it is not a great trouble to set stakes, but, in a
22 A MANUAL FOR NORTHERN WOODSMEN
country where local attraction is infrequent it is sufficient
precaution to watch the blazes and bushing back along the
line. In any case, time is saved by setting up the com-
pass approximately by the backsight before letting the
needle go free.
2. TRY-LINES
When two unconnected points are to be joined, it is usual
first to run a line without spotting, a try-line so called, and
if the desired point is not hit, to measure at right angles the
distance between the line run and the point aimed at, fig-
ure the angle of error, and rerun the line. The angle re-
quired is obtained from a table of tangents.
Thus suppose a try-line to have been run N 4° E 120
rods or 30 chains and to have hit 32 links east of the mark
aimed at. Dividing 32 by 3000 (the distance run in links)
gives .0107, and the angle of which this is tangent is
found in the table of natural tangents to be 37'. The com-
pass may therefore be set N 3° 23' E, and the line rerun.
Results near enough for most purposes may be had by
remembering that the tangent of 1° is .0175 (i. e., if feet in
100, or if links per chain) and that the tangents of small
angles are in proportion to the size of the angles. Thus
with the case above, the tangent of 1° being .0175 and
that of the angle required .0107, .0107 divided by .0175
equals .61 of 1°, or 37'.
a c i . ; L__i___|Trial Line
Sch. 10 ch. 15 ch. 20 ch. 25 ch. 30 ch.
DIAGRAM SHOWING THE METHOD BY OFFSET
Or instead of using the compass to rerun the line, its
position may be fixed by offset, that is, by measuring at
right angles to the try-line, at different points along it, the
distance required to place points in the desired range. For
this purpose stakes should be left in the try-line at equal
distances apart, say every 5 chains, and the length of each
offset may be figured by tangents or as a simple problem
in proportion.
SURVEYING PRACTICE £3
Thus with the case in hand. The tangent of the
angle between the try-line and the true line has been fig-
ured as .0107. This decimal multiplied by five chains
or 500 links gives 5| links, the offset from the 5-chain
point. Similarly 10 chains multiplied by .0107 gives 10.7
links, and so on until all the offsets have been computed.
By proportion the problem is even simpler. In the case
in hand the offset at the 15-chain mark should evidently be
half that at the finish, or 16 links. At the 5-chain mark it
is £ of it, or 5j links as found before. In the same way
offsets for any length of line and any error in closing may
be figured. When the points have been put in, the line
may be blazed through by eye, or with the aid of the
compass.
3. MARKING LINES AND CORNERS
Corners. Permanent corner marks are especially val-
uable in maintaining bounds and protecting property
rights; and the desirability of stone monuments, or, fail-
ing these, of earth mounds, iron rods, or charcoal, is not
to be disputed. Forest land is occasionally subject to
great mischances, as from clean cutting, wind, and fire, and
marks which can survive these have distinct and peculiar
value.
On the other hand, posts of durable wood, and trees that
are likely to remain in place a long time are generally
handiest, are easy to mark on, and frequently meet, better
than more elaborate and expensive marks, the ideas of
owners and the customs of the country. Supplemented
by blazed and marked witness trees, such markings for
corners are now in wide use on forest property and there
can be little doubt that their use will continue. Marks on
living trees should be placed in most cases on a peeled or
blazed surface of the wood, though bark marks, much dis-
torted it is true, have been known to remain legible for a
very long time.
Corners in every case should be plainly inscribed so that
any interested person may readily identify them. It is
usual in woods practice for the surveyor who establishes a
24 A MANUAL FOB NORTHERN WOODSMEN
corner to leave there his initials, or some mark peculiar to
him which will identify it as his work, together with the
year in which the survey was made. The same thing may
be done by a succeeding surveyor.
Practice in all these matters, however, varies a good deal
in different parts of the country. The methods presciibed
for use in the United States land surveys will be found on
later pages of this volume.
Lines. A property line in the forests of Germany is kept
cleared out several yards wide and blocks of cut stone are
deeply set along it near enough together so that one may be
seen from another. In addition, the range of a transit line
is inscribed upon them. This renders the property limit
prominent and durable, and, further, defines it to within a
quarter of an inch.
Such ideal marking is seldom to be looked for in this
country, but the ends to be aimed at, which in the fore-
going case were attained, should be in the mind of every
man who has to do with forest boundaries. A property
owner's interests are first, to have his bounds prominent so
that he and other parties may know where they are and so
that there will be no excuse for trespass ; second, to have
them durably marked for obvious reasons ; and third, to
have them so closely defined that all possible causes of
dispute may be avoided.
Stone walls, ditches, and fences are the common bounds
of property in settled and half-settled countries, and each
of these methods of delimitation has its grade of efficiency,
considered from the above points of view. In large forest
areas blazed trees are the means almost universally em-
ployed for the purpose. That system has been reasonably
satisfactory in the past. It would have been more so had
care and system always been employed in the marking and
more attention paid to renewal.
The directions for marking lines in timbered lands, as
contained in the " Manual of Instructions for the Survey
of the Public Lands of the United States," are as follows :
All lines on which are to be established the legal corner boun-
daries will be marked after this method, viz. : Those trees which
may be intersected by the line will have two chops or notches cut
SURVEYING PRACTICE 25
on the sides facing the line, without any other marks whatever.
These are called sight trees or line trees. A sufficient number of
other trees standing within 50 links of the line, on either side of
it, will be blazed on two sides diagonally or quartering toward the
line, in order to render -the line conspicuous, and readily to be
traced in either direction, the blazes to be opposite each other,
coinciding in direction with the line, where the trees stand very
near it, and to approach nearer each other toward the line, the
farther the line passes from the blazed trees.
Due care will ever be taken to have the lines so well marked
as to be readily followed, and to cut the blazes deep enough to
leave recognizable scars as long as the trees stand. This can be
attained only by blazing through the bark to the wood. Trees
marked less thoroughly will not be considered sufficiently blazed.
Where trees two inches or more in diameter occur along a line,
the required blazes will not be omitted.
Lines are also to be marked by cutting away enough of the
undergrowth of bushes or other vegetation to facilitate correct
sighting of instruments.
These directions are ample, have been tested by use, and
are practically the same as those issued for land survey
work in the Dominion of Canada. Plainly, however, they
are adapted to sparsely wooded land, for, in real timber
growth, blazed trees two rods away from the line would be
a source of confusion. In fact, the narrower a line is blazed,
so long as it is clear and durable, the better. A good
general rule to be applied in timber is to blaze those trees,
and only those, which a man can reach with his axe when
standing directly in the line.
A line in ordinary woods well blazed according to this
method is prominent, and reasonably durable, while the
quartering of the spots and special marking of the " line "
trees render it reasonably well defined. If decent care is
used in maintenance, and if when it has become dim or
doubtful it is thoroughly and carefully renewed, there need
be no great trouble or expense involved in that process,
and no trespass or dispute meanwhile. Certain identifica-
tion of the " line" trees of a previous authoritative survey
is a great help in renewal. In the United States system that,
is secured by notching those trees ; in the province of New
Brunswick they are blazed and the blazes hacked three
times upward. The same thing might be secured, and in
addition the work of the individual surveyor identified,
26 A MANUAL FOR NORTHERN WOODSMEN
by a personal mark, such as a stamp cut on the poll of the
blazing axe.
4. ORIGINAL SURVEYS AND RESURVEYS
The woods surveyor has two broad classes of work to do,
— the running of new lines, outlining property for sale or
administration, and the work of relocation. The first
class of work constitutes an original survey, which the sur-
veyor must carry out with due regard, on the one hand to
accuracy, on the other to cost. His ordinary duty here
consists of three parts: first, to duly outline and measure
the tract in question; secondly, to mark the bounds of it
in satisfactory fashion; third, to take notes of what he
does for record and the benefit of those who come after.
Resurveys. When a boundary has once been surveyed,
marked on the ground, and accepted, it becomes authorita-
tive, and the usual duty of the man who comes after is
simply to locate the work of the original surveyor. He
uses the compass commonly as the best means of finding
the old lines and corners. Hd may use the chain for the
same purpose, or to satisfy himself about area. But his
business, so far as the boundary itself is concerned, is to
find and remark the old one, not set up a new one ac-
cording to his notions of propriety. In relocating that
boundary the marks of the earlier surveyor are a more re-
liable guide than his notes : they must, however, be clearly
identified and not confused with those of irresponsible
parties. On the other hand, where monuments cannot be
found, reliable verbal testimony is admitted, while it has
further to be recognized that property boundaries may be-
come sanctioned by use or agreement, even though they
are crooked and astray from their original location.1
5. AGE OF SPOTS OR BLAZES
A subject of special interest to the forest surveyor is
the determination of the age of spots on trees. This means
1 For both legal and practical guidance in resurvey work, see
"Restoration of Lost or Obliterated Corners," by the Land
Office, and Hodgman's "Land Surveying."
SURVEYING PRACTICE
20 25 17 30 32 35 40 43
. BLAZE FIVE YEARS AFTER CUT WAS MADE : A, FRONT VIEW
SHOWING RIM OP CALLUS ; B, CROSS SECTION
C. BLAZE TWENTY-THREE YEARS AFTER CUT WAS MADE
28 A MANUAL FOR NORTHERN WOODSMEN
of identifying a surveyor's work is recognized by all the
courts. The handling of the problem in the field may be
made clearer by the accompanying figures, reproduced
from Circular No. 16, Division of Forestry, United States
Department of Agriculture.
6. NOTES
Notes should be full and exact so as to furnish for the
benefit of later comers a complete record of the work done.
In the case of resurveys they should be particularly clear
as to the old marks found, so that the evidence which gov-
erned in the resurvey may be a matter of record. This
rule holds especially in regard to starting points and
corners.
The date of a survey is an important thing to record
clearly, along with the meridian which was used, whether
magnetic, true, or one assumed for the occasion.
Notes should be so plainly and clearly written that any
fairly intelligent man can understand them. They should
be honest as well, not concealing actual errors. When the
lines of a survey do not close in exactly, it may not be worth
while to rerun them, but there ought at least to be no dodg-
ing of the facts. It is only an incompetent surveyor who
will not acknowledge his errors. Errors are normal and
to be expected. They grow out of imperfections in
method that are imposed on the surveyor by limitations
in the matter of expense. Errors are not to be confused with
mistakes or blunders.
The notes of a timber land survey should also be full as
regards topography. Such notes often give great assist-
ance in the relocation of lines and corners. They are also
of value to the owner and operator of such property.
7. PARTY AND COST
The great advantages of compass and chain surveying
for woods work are that it is sufficiently accurate for most
purposes, and that the cost involved is very moderate. Six
SURVEYING PRACTICE 29
/" Renew/ of souf/i tine of Tn/>., J/?.4, Oxford Co., Ma/ne Sept tt, /90s.
Line orig//?a//yrt//?fy£.Ba//art/ntf94, fas beer? 0/azedo/er some s/nce.iut
never
resurveyed. £.3. Dearborn, rear cAoin.
Hare traced dorm o/ra 'p/Tyrect 'tfte east ///re offtre tt>wns/rje> to a ///re
Ofspo
rove as
near c
s rfrerifys can be counted fr> be ///years o/d. Ab/aze of /Me
age is
also fvi/ffd 3 rods /o the eastward. M> 5/ff/? -seen offfie ory/rxr/
Corne.
~ noted as 6e//ro /# a &//T;/?.
f/7 rawe of-ffie spots east- and nesf a/Kt/ntte //fre com//705ovft
S£fa
cedar post- andstv/?&s. 7/r/s /j in f/af s/>re/ce /and and S rvds
from
Cs/ar7d Fond to the easfwa/tf. Afar/tea 'tfre/xaf o/rMW. 7~S/?.4;
Of? ME.
T4. /J4.j or? 5. T-5 ft.3 , a/so 'L/.J.B.&OS.'' The M/TrcsslrveSfa/so mortal
J.J.B.
19OS, am a cedar sts/Td/n^r tf/O°£ /O 6>rAs from tfie /oast, affotfrer
S.J0°£
/s//nto, a spruce s.3o°mo///?*s a. a fr'n* tf.45°n /s///rte.
From ffieposff&natr/a/ '///» /V83°W at ry/rt a/y/es to fire x*'* ^ brrc
After
esrods fotmd anot/rer ory/'/xr/ '6/aze 20 J/'/rAs to rte /efr. ffefur/redto
post a
vdnsr? tf.83°3O'rX
Rods
80
MarAed a b/rc/r rig ft f- of tine (*#+*•
KO
Rising ontv the freight- ofar/dae w/?/c/7 fa//s o/f />nx/p/foe/s/y
2. rods to the 3ot/fft. Or/g//7a/ t/'mter 6/0 nr/? down a/rd roffex fans
and some rods afiead. f~0v/7rf3ofSa//a/Ttfs spots c/ase toSfi&SHOffy.
i^y afidjo/??e spots t>y /i/mber/Tres? of/e/7 w/'a* S/ope 3.IY
210
Don/i a sfrvnas/ope -5. W O/d^pots /rare eee/7 Aav/ty to t/rf right
and flow o/re on a o/rch with ///r//ys over /f is jo /wAs ry/rt:
Off-set to if, ft'// in the /ine t>ac/c over the o/ds/>ots, and contr'ne/e
on same oear/n.<7-
840
Set a cedar 5tafi e mar/ted %M++
Z56
Watsr crosses tt> Soutfitvest-
17S
Lasf 40 rods tftroug/r swamp with main/yjot/nf ffrotvttr and no
SDO fs to oe see/7.
Old b/aze probao/y Sa//ards found now on a dead and down cedar.
Z95
Cross Canada /fay road.
320
A spof of Ba//ards age on a s/yrt/cejust oacA 2 rods 3oi/tfr ans
Spots of mucn /ess eye wh/ch come Sn/o rtrera/rtfe a feur svds
further 0/7. 0/azedthe tine ffrrvvaA s/m/pnf ^Sefa/nsffor
the corner Of -Secf/ons 3S & 36 mar/ted on /V.W "•S.M93S.
on //.£. "S.N036."> onS. "T.S ft.3" MarAed /f and the witness
frees ^.B. &OS?
\^ ,
30
A MANUAL FOR NORTHERN WOODSMEN
/^ WoodsfocA, Mass., tfayft, M07 Survey made for C/arA Lumber Co of
ftreir farter Lot- SO Ca/fed Dec/, ofneed/e as near as Anontr //.' 'Jm/towS'ctoin
Begin at
Souffn
vest- corner cf /of- at 'June fro/7 ofsfoae wa//s marA/'/y
recoqn/z
^/ bo
f/idar/es of f/re '/ofc Thence —
Bearing
0/sf.
NJO°E
847'
Along wa//to /f-s e#c/
19/7'
ffirot/qh p'fte fy'm^er 6otf?s/tf&s nrM /ro s/'f/r ofproper/y
(iota/)
//ne, to a roffs/r f&rce runnim? easfer/y. T/re deeds ca///m?
•for a /we ru/rn/'/y "Srr a norftter/y tf'necrwr" /Aibzec/
the. ///7 Conasse ArooSc.
77r/s c/isfance /s ffre one (3 rods) Catted for /n f/ie cfeed
and is f he on/y means of f/jf/ng f/re /as f named corner
Off the norfh and soufn //ne .
SJS°f
I7f\
SSJ>°£
3/9\
Along Cohasse brooA as /?es~ ca// of deed.
580°E
33S
Jcross 6rooA, ffren 0/r south border of f/e/d //? passes
siorr of owners norfh, to ivesf s/de of/r/jhway.
7/r/s/x>/nf/s 7/6 ff sotrffrerfy from ffre forks of fhe h/g/r#qy.
the deedca//>nff for "about 40 rods" Set- /xzsf- andsfones.
S&Tr
/68'
Down h/ohway to br/dge orer Cofasse broofi as ca//ed
S^O°3O'£
2SO
for /n deed
S40°30'£
/SS-
S£6W
7/2'
L//? the swamp c/ase fo foot of fne r/ctge
5 /aw
^ss'
Offset freauenf/y to get exacf area of the "hare/ tend
53a'w
720'
Hhtch was con i/eyed /n ffre deed To stone tva//,rt?e
szz'w
S62'-
recogn/zed South bound of the /of
/V84°W
296'
Along wa//, up a /yrec//)'fvi/s sfope
M73°JO'lV
1086
Along the rva// fo p/ac e of oeynnrna
This surrey
M/ows
ff/e terms oftfie deeds as near as ffre/ can be //rfer/refet?
jUtoArmsfi
ity,ar
•Sidenf of tfe Jxa//fy 3Ojear3 ana 'fy/rr///ar urM 'fs /bnd fmnsfers
ondoccu/xirK
'Hasp
Kent ancfiays ffotxaf/orr tyrges as near as />e Anom *r//tt fAf un-
derstendiiy o
'ttteol.
i^orf/es and facts of/x>ixssn>/r. /.ocaf/oa, ffterefore.food The
\uBMft */
ineino
-Aedonffa Sittr Surtr/ed"c.L Co /3O7 "and a/so Hifft myimfiafs
COMPUTATION AND OFFICE WORK 31
men form a usual party for line work in the northern woods,
and from one to three miles a day can commonly be run
with it, according to the ground and growth. The usual ex-
pense for such work ranges between $6 and $10 per mile.
A reliable transit line, on the other hand, cannot be cleared
out and run for twice those figures.
The work of the forest surveyor may be done for the fol-
lowing purposes, and the party required for each sort of
work, outside of maintenance, is noted in connection.
1. New work, for the purpose of sale or administration.
Party required : compassman, two chainmen, enough men,
commonly three, ahead of the compass, with axes and a
rod, to keep the rest of the party busy.
2. Resurvey, for the sake of reestablishing lines and
corners, also for getting area. Party : same as above ; or
it may be more economical in some circumstances not to
employ chainmen, but for the surveyor himself, with one
of his party, to go back and do the chaining.
3. Careful resurvey with the compass of old lines, no
chainage required. Party to correspond.
4. Remarking lines where no great difficulty is expected,
but where the lines need freshening. The man in charge
and two axemen form an economical party. A small fold-
ing sight compass may be used as needed.
Balance in the party is one element largely influencing
cost. The main thing is to have sufficient axemen to give the
rest of the party enough to do. Subsistence is an important
problem in some circumstances. A chainman can carry a
pack on his work, and frequently chainmen are employed
on long jobs in the backwoods to carry a portion -of the
supplies or outfit.
SECTION V
COMPUTATION AND OFFICE WORK
1. TRAVERSE
To " traverse" a line or route is to survey it by any
method that ascertains direction and distance. The cir-
32 A MANUAL FOR NORTHERN WOODSMEN
cuit of a farm's boundaries by compass and chain is a
traverse. So is the survey of a road by usual methods.
When a survey has been made in this fashion the notes
are for some purposes best worked up after a method
called " computing by traverse," the principles and appli-
cations of which are developed in the following paragraphs.
If a course is run out N 30° E 20 chains, a certain dis-
tance is made in a northerly direction, also a certain dis-
tance in a direction east. The distance made in the former
direction is called latitude ; in the latter, departure. In this
case it is north latitude and easterly departure. These
elements may be made evident on a plot by drawing a
meridian and base line through the starting point and
lines perpendicular to these from the point reached. These
distances are also to be obtained from traverse tables.
The same is true of a course run in any direction and
for any distance. Any course not run exactly east and west
makes northing or southing. The former is reckoned as
positive latitude, with the sign (+). The latter is negative
or (— ) latitude. Similarly, distance made in an easterly
direction is (+) departure; that made towards the west
(— ) departure. If several courses are run in succession,
the sum, algebraically reckoned, of their latitudes and
their departures gives the position of the point finally
attained.
This method of reckoning, using traverse tables for the
purpose, has a wide use in connection with land surveying.
The traverse table given on pages 214-219 furnishes the
elements for 15' courses, those usually employed in com-
pass work. The following is a simple problem illustrating
their use.
In running a section line due north, the surveyor conies
to a lake shore. Setting there a post, duly marked, he runs
round the lake near the shore by the following courses :
N 50° E 12 chains.
N 9° 30' E 20
N 40° W 9
S 80° W 6.81 "
Reckoning up his courses by the traverse table, he finds
COMPUTATION AND OFFICE WORK
33
that his E and W departures balance, hence he should be
in line. The difference between northing and southing
gives him the distance. He may then set a second post,
add the distance to his previous chainage, and proceed with
his survey.
COMPUTED TRAVERSE
Field Notes.
From Traverse Tables.
Bearing.
Distance.
Latitude.
Departure.
N.
S.
E.
W.
N. 50° E.
12.0 chains
7.71
9.19
N. 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
34
A MANUAL FOR NORTHERN WOODSMEN
the distribution. In any case the correction is applied so
as to help close the survey and not the reverse. This pro-
cess is called Balancing a Survey.
The field notes of a closed survey, the latitudes and de-
partures as they reckon out, and the same balanced, are
given herewith. The reckoning is also given, and all is in
convenient arrangement. The latitudes and departures
COMPUTING LATITUDES AND DEPARTURES
Course.
Course.
Course.
Course.
Course.
A — B
B — C
C — D
D— E
E — A
log sin
9.9386
9.7604
9.5340
9.9555
9.5163
log dist. =
1.3010
1.1790
1.0910
1.2109
1.3444
log dep. =
1.2396
0.9394
0.6250
1.1664
0.8607
Departure =
17.36
8.70
4.22
14.67
7.26
log cos =
9.6957
9.9125
9.9730
9.6340
9.9752
log dist, =
1.3010
1.1790
1.0910
1.2109
1.3444
log lat.
0.9967
1.0915
1.0640
0.8449
1.3196
Latitude =
9.92
12.35
11.59
7.00
20.87
in this case have been reckoned out not from the traverse
table, but from the table of logarithmic sines and cosines.
A little consideration, shows that the latitude of a course is
the cosine of its bearing multiplied by its distance, while
the departure is the product of the sine multiplied by the
distance. Now a table of sines and cosines gives values
to single minutes instead of for 15' bearings. Logarithmic
computation, too, shortens the process. This is, therefore,
the more convenient way of reckoning for transit work, or
for accurate compass surveying.
When all but the final course has been run, it is in
some circumstances desirable to ascertain what course
to set in order to hit the starting point. This, too, may
readily be done by means of the figured latitudes and
departures.
Thus, suppose that four courses of the above survey have
COMPUTATION AND OFFICE WORK
« *
S S
8 8
8 2 3 8 2
o Q w
36
A MANUAL FOR NORTHERN WOODSMEN
been run out and the latitude and departure computed, as
given. The result shows that the point reached is north
FIGURED LATITUDES AND DEPARTURES
Latitude.
Departure.
N.
S.
E.
W.
A — B
9.92
17.36
B — C
12.35
8.70
C — D
11.59
4.22
D— E
7.00
14.67
30.94
9.92
26.06
18.89
9.92
18.89
21.02
7.17
and east of the starting point, much further north than
east; hence a course somewhat west of south
must be set to reach it. In the figure E X
represents the latitude reached and A X the
departure.
Now to find the bearing of E A we have
tan. A E X =
.3411.
AX 7.17
WX~ 21.02
A E X from the table of tangents =18° 50'.
S 18° 50' W is therefore the bearing required.
S The length of E A may also be found, since
it is the hypothenuse of a right angled tri-
angle whose base and altitude are the latitude and de-
parture given.
22.21,
the distance required. That this value and that for the
angle differ somewhat from the true ones is due to the
errors of compass surveying.
In a similar way the course and distance of an inacces-
sible line may be computed or omissions supplied in notes.
COMPUTATION AND OFFICE WORK 37
That is a very undesirable thing to do, however, as it in-
fringes on the tests which serve to verify the work.
Rectangles. The woodsman in his land work has
most frequently to do with rectangular figures, and com-
putation of area is simple. If the average of the chained
east and west sides of a rectangular piece of land is 201
rods or 50.25 chains, and the north and south dimension
40 chains, the area equals 50.25 X 40 -r- 10 (the number of
square chains in an acre), or 201 acres. So with a rect-
angular piece of any dimensions.
Area by Triangles. The area of a triangle of known
base and altitude is half the product of these dimensions,
and an irregular figure when plotted may be cut into tri-
angles, the dimensions of each measured, and the areas
computed. The same process in case of necessity may
be performed on the ground.
When, as is frequently the case, it is easier to obtain the
three sides of a triangle than the base and altitude, the area
may be obtained from the formula
Area = V*(s — «) (* — 6) (* — c),
where a, 6, and c are the three sides and s is half their sum.
Or, lastly, an irregular figure when plotted may be re-
duced graphically to the triangular form and the area ob-
tained at one computation by either of the methods just
given.
The relations between units of distance and of area are
given on page 19.
By Offsets. In surveying around the borders of a body
of water, and in some cases when the exact border of a
property presents great difficulties, it is customary to run
as near the border as is practicable and to take rectangu-
lar offsets to it at selected intervals along the line. These
offsets should be measured to angles in the border, or
placed near enough together so that the border between
offsets may be considered a straight line. The area of
the figure between each two offsets may then be computed
by multiplying the distance along the base by half the
sum of the two offsets.
38
A MANUAL FOR NORTHERN WOODSMEN
Another way is to take the offsets at regular distances
along the base, 10 rods apart for instance. In that
case the rule for the area is : — Add together all the in-
termediate offsets and half the end offsets, and multiply
the sum by the constant interval between them.
By Cross Sectioning. The method of ruling off an area
on a map into squares of equal and known size is very
convenient, especially for irregular areas like bodies of
water. The whole squares can be counted up and the
fractions of squares estimated. In such cases it may be
best to do the ruling not on the map itself but on a de-
tached piece of tracing cloth or of paper. If the map is
opaque, the ruled tracing cloth may be laid over it and
held firmly till the work is done. If it is transparent, the
ruled sheet may be laid underneath.
By Planimeter. The area of any surface may be
quickly and accurately ascertained by an instrument called
the planimeter. That instrument is not, however, in the
hands of most woodsmen.
From Traverse. The area
enclosed by a balanced sur-
vey may be accurately com-
puted from the latitude and
departure of its courses.
The general scheme will be
grasped at once from the
figure, in which ABODE
represents the survey whose
notes are given on page 35,
e b is a meridian through its'
most westerly point, bB,cC,
d D, and e E are lines drawn
vertical to it from the angles,
and B m, D n, and E o are
parallel to it or vertical to c C
and d D. In this figure it is
evident in the first place that
the area of the figure b B C D E e minus the area of the
two triangles A E e and A B b equals the area of A B C D
E, and secondly that the figure b B C D E e is made up of
COMPUTATION AND OFFICE WORK 39
the three trapezoids b B C c, c C D d, and d D E e.
The area of these trapezoids and triangles is easily com-
puted from their dimensions. All that is necessary is to
express those dimensions clearly in terms of latitude and
departure.
One dimension of these figures, the altitude, is the lati-
tude of the course in question. Thus for the triangle A B b,
the altitude A b is the latitude of the course A B, and in
the same way e A, the altitude of the triangle A E e, is the
latitude of E A. These latitudes, it is to be noted, are
negative and, to correspond, the areas of A B b and of
E A e are to be deducted from b B C D E e to give the area
of A B C D E which we are after. B m, the altitude of
the trapezoid b B C c, is the latitude of the course B C and
is positive. D n and E o have the same relation to the two
succeeding courses.
The bases of these triangles and trapezoids are clearly
related to departure, b B is the departure of the course
A B, and A b Xb B = twice the area of A B b. b B +
c C, the two bases of the trapezoid b B C c, = twice the
departure of A B + the departure of B C. c C + d D
= the same expression as the last + the departure of B C
+ the departure of C D, which last, however, being west-
erly, is reckoned negatively. Now a general expression
for these values is double meridian distance, meridian dis-
tance being perpendicular distance from the meridian.
The D. M. D. of a course is the sum of the meridian dis-
tances of its two ends. For a course starting on the me-
ridian it equals the departure of the course. For any
succeeding course it equals the D. M. D. of the preceding
course plus the departure of that course plus the departure
of the new course, easterly departures being reckoned as
positive and westerly departures as negative.
A check on the reckoning of the D. M. D.'s is in the
last one, which should be numerically equal to the de-
parture of the last course.
These elements for convenient working out of the area
surrounded by a closed survey are embodied in the follow-
ing rule : — Twice the area of the figure enclosed by a sur-
vey is equal to the algebraic sum of the products of the
40
A MANUAL FOB NORTHERN WOODSMEN
D. M. D.'s of the several courses multiplied by the corre-
sponding latitudes, north latitudes being reckoned posi-
tively and south latitudes negatively. If the tract is kept
on the right in the course of the survey, the result comes
out with a minus sign.
An operation of this kind, starting with the balanced
latitudes and departures, may be conveniently arranged
as follows :
Course.
Lat.
Dep.
D. M. D.
+
Area.
Area.
A — B
— 9.95
+ 17.38
17.38
172.93
B — C
+ 12.32
+ 8.72
43.48
535.67
...
•C — D
+ 11.57
— 4.21
47.99
555.24
D— E
+ 6.97
— 14.65
29.13
203.04
...
E — A
— 20.91
- 7.24
7.24
151.39
1293.95 1 324.32
324.32 1
2)969.63
484.81 sq. ch.
Area = 48.48 acres.
3. PLOTTING
The computation of traverse, if it aids in testing the
accuracy of a survey, gives also data for plotting it with
ease and accuracy. Taking the initial point of the survey
as the starting point for a meridian and a base line vertical
to it, the position of the second point of the survey may be
fixed by measuring off its latitude on the vertical line, its
departure on the horizontal, and from these points drawing
lines parallel to the base and the meridian until they inter-
sect. The latitude of the second course may then be added
to that of the first and the two departures also added to-
gether, when the third point of the survey may be fixed in
the same way as before, and so on until the survey is
finished. The points thus fixed may then be joined by
lines representing the courses. The position of the points
in the above survey as taken from the balanced figures on
COMPUTATION AND OFFICE WORK
41
page 35 is given in the table, and below is a diagram
showing the method of plotting.
Point.
N.
s..
E.
W.
A
B
9.95
17.38
C
2.37
26.10
D
13.94
21.89
E
20.91
7.24
It is not, however, the most common practice to plot a
survey after this fashion. The more usual way is to
plot the angles and distances directly from the notes. To
do this select a point on the paper for the initial point of
the survey and draw a meridian through it in pencil. Then
by means of a protractor mark the bearing of the first
METHODS OP PLOTTING A SURVEY.
FIG. 1 BY LATITUDES AND DEPARTURES. FIG. 2 BY COURSES AND DISTANCES.
course and draw a line of indefinite length through it. On
this line lay off to scale the length of the course, thus
42 A MANUAL FOR NORTHERN WOODSMEN '
establishing the second corner. Through this draw another
meridian in pencil and proceed as before. If the survey
and the plotting are both perfect, the last course should
hit the initial point. If it does not so hit, there is error in
one or the other.
To plot one course from another by means of the figured
angles between them is not good practice, because by that
method errors accumulate.
THE ESSENTIAL INSTRUMENTS FOR PLOTTING
A straight edge, a scale, a protractor, a pair of dividers,
and a parallel ruler or a pair of triangles are the essentials
for ordinary plotting.
The lettering on a woodsman's map ought to be plain.
The size of the letters should be varied according to the
importance of the object designated. It is a good rule to
use erect letters in general, and slant capitals and italics in
connection with water.
The usual practice is to represent waters and swamps
with blue ink, contours with brown, and all other objects
with black. Common brown and blue inks, however, do
not blueprint well, so black is ordinarily used for tracings.
Various systems have been devised for representing the
character and density of timber growth. A system of that
kind, if one is required, is best devised for each forest
region or property.
Maps may be rendered plainer by the judicious use of
ON THE BEARING OF LINES 43
topographic symbols. A number that are in common use
and generally agreed upon are given herewith.
Railroad
Highway
Wood Road. . .
Trail .
Stone Wall ooo333coxx»ooca»»xcxx)0
Fence
Telephone Line ,,.,.,,,.
Field or Prairie -
Open Swamp
Dam . , . . —
TOPOGRAPHIC SYMBOLS
SECTION VI ,
ON THE BEARING OF LINES
The surveying work of the woodsman of the present day
is mostly of the nature of resurveys, or the subdivision
of tracts whose boundary lines are on the ground. To
ascertain correctly the present bearing of old lines is there-
fore a problem of great importance and one very fre-
quently met with.
1. Bearing Directly Observed. The best and surest
way to find that direction is the direct one of running a
piece of the line. For example, suppose a section of land
was run out in 1845 with lines stated to run north, east,
south, and west by the true meridian. The surveyor com-
ing on to retrace it in 1915 may pay no attention to the
north star or reference meridians, but finding the southwest
corner of the tract plain and running northerly find by trial
44 A MANUAL FOR NORTHERN WOODSMEN
that N 4° 20' E runs through the old spots. He figures
now that the courses he will have to run in order to repro-
duce the lines of the square are N 4° 20' E, S 85° 40' E,
S 4° 20' W, and N 85° 40' W. He may run them so or
turn the vernier of his compass 4° 20', so as to read N, E,
S, and W, like the compass of the original surveyor. In any
case he will not be able to reproduce the old line all around
exactly. Even if no errors are made in either survey the
daily variation of the needle will be pretty sure to cause
some divergence. In remarking the line he will follow as
closely as possible the marks of the old surveyor.
2. By Reference Meridian. The change in bearing of
old lines may often be ascertained by reading on a refer-
ence meridian. If the compass in use be so tested and if
the compass which did the work to be reviewed was tested
on the same marks at the time of the original survey, then
the difference in the two bearings will hold closely for a
considerable region around.
Example: On a county meridian in Pennsylvania in
1850 a surveyor's compass read N 2° 30' E and in the
neighborhood a line was run bearing S 55° E. In 1905
another compass on the meridian reads N 6° 20' E, show-
ing a change of 3° 50' in the time elapsed. Then S 51° W
E ought to reproduce the line.
3. By Tables. The following tables, derived from
publications of the United States Coast and Geodetic
Survey, are very convenient for determining change in
decimation. They give for many localities well distrib-
uted throughout the United States declination at ten-
year intervals as far back as it has been recorded. The
change found to have taken place at a given locality
between any two dates may then be applied through a con-
siderable region around it. It should be understood, how-
ever, that this means of determination does not obviate
the chances of error due to difference between instru-
ments. It is well known that two compasses on the
same line at the same time may not read exactly alike.
Example: A land line in the Adirondacks was run out
in 1800 on the magnetic meridian. What course should
be set in 1910 to reproduce it ?
ON THE BEARING OF LINES
45
TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC-
LINATION IN THE UNITED STATES
(From U. S. Coast and Geodetic Survey Reports)
Year Maine Maine
(Jan. 1) j N'theast ! S'thwest
New
Hamp.
Ver-
mont
Mass.
East
«a
1750
12 05 W
8 34W
8 02W
7 43W
7 46W
6 21W
1760
11 53
8 15
7 28
7 09
7 19
5 52
1770 11 53
8 10
7 03
6 44
7 00
5 31
1780
12 05
8 10
6 47
6 28
6 50
5 19
1790
12 26
8 15
6 42
6 23
6 50
5 17
1800
12 58
8 34
6 49
6 30
7 01
5 25
1810
13 38
9 02
7 06
6 47
7 20
5 54
1820
14 23
9 38
7 32
7 13
7 47
6 08
1830
15 12
10 18
8 11
7 48
8 22
6 41
1840
16 02
10 57
8 56
8 29
9 04
7 21
1850
16 58
11 38
9 46
9 13
9 48
8 05
1860
17 43
12 18
10 31
9 59
10 28
8 43
1870
18 13
12 48
11 08
10 39
11 01
9 17
1880
18 34
13 22
11 38
11 14
11 32
9 58
1890
18 44
13 51
12 03
11 39
12 02
10 25
1900
1910
19 02
19 45W
14 21
15 06 W
12 31
13 16W
12 08
12 57W
12 34
13 21W
10 59
11 42W
Year
(Jan. 1)
Rhode
Island
Conn.
N. Y.
East.
N. Y.
West
Penn.
East
Penn.
West
1750
7 04W
5 47W
7 35W
4 40W
4 47W
1760
6 37
5 18
6 53
3 57
4 01
1770
6 18
4 57
6 17
3 18
3 19
1780
6 08
4 45
5 50
2 46
2 44
1 16W
1790
6 08
4 43
5 34
2 24
2 21
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 52
10 25
10 48
7 37
7 25
5 07
1910
12 40W
11 11W
11 31W
8 12W
8 07W
5 45\V
46
A MANUAL FOR NORTHERN WOODSMEN
TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC-
LINATION IN THE UNITED STATES
(From U. S. Coast and Geodetic Survey Reports)
Year
(Jan. 1)
New
Jersey
Ohio
Indiana
Illinois
Iowa
Mich.
North
1750
4 43W
1760
4 04
1770
3 31
1780
3 06
1790
2 50
1800
2 45
3 13E
4 44E
5 54E
1810
2 fO
3 22
4 59
6 18
1820
3 06
3 22
5 04
6 33
10 09E
6 42E
1830
3 31
3 13
4 59
6 37
10 24
6 42
1840
4 04
2 53
4 44
6 33
10 30
6 28
1850
4 43
2 24
4 21
6 18
10 24
6 02
1860
5 22
1 50
3 50
5 54
10 09
5 25
1870
6 01
1 14
3 13
5 26
9 44
4 38
1880
6 41
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
(Jan. 1)
Michigan
South
Wisconsin
Minnesota
North
Minnesota
South
1750
0 ,
0 ,
0 /
0 /
1760
1770
1780
1790
1800
1810
1820
4 10E
8 34 E
10 27E
11 20E
1830
4 04
8 40
10 44
11 36
1840
3 46
8 34
10 50
11 42
1850
3 20
8 16
10 44
11 36
1860
2 46
7 49
10 27
11 20
1870
2 04
7 14
9 59
10 54
1880
1 17
6 25
9 17
10 22
1890
0 32E
5 36
8 33
9 32
1900
0 02W
5 01
7 58
8 57
1910
0 27W
4 51E
8 03E
9 OOE
ON THE BEARING OF LINES
47
TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA-
TION IN THE UNITED STATES
(From U. S. Coast and Geodetic Survey Reports)
ll
Washington
D.C.
Maryland
(Baltimore)
Virginia
East
(Richmond)
Virginia
West
(Lynchburg)
.S|
8-1 8
*£3
o
North Caro-
lina East
(Newbern)
North Caro-
lina West
(Salisbury)
1750
141W
305W
1 13W
0 /
o / 4
0 18W
1 31E
1760
1 02
2 26
037
008E
0 18E
208
1770
028
1 52
005W
0 42
0 50
2 42
1780
001W
1 25
0 20E
1 11
1 17
3 12
1790
0 19E
1 05
038
33
200E
135
3 34
1800
028
0 56
047
46
215
1 44
348
1810
028
0 56
0 47
51
2 20
1 44
3 52
1820
0 19E
1 05
038
46
2 15
1 35
3 48
1830
1840
001W
028
1 25
1 52
005W
33
11
200
137
1 16
0 50
3 33
3 10
1850
1 02
226
036
045
105
0 17E
240
1860
1 41
305
1 12
0 10E
030E
0 19W
206
1870
2 21
3 45
1 51
0 29W
0 12W
058
1 29
1880
3 00
4 24
2 29
1 09
0 51
1 35
0 51
1890
336
500
306
146
1 28
2 14
013E
1900
4 11
535
3 40
222
206
2 51
023W
1910
4 51W
6 15W
4 13W
2 53W
2 39W
3 25W
0 47W
^
.aSl
""fl
ijl
a ^"3
«J3'*
||
|fg
ll
111
M55
fl
M
5
fa fe
PI
w
^ 0
MM
S
| *
a? ^
£8
0
1750
o /
0 /
0 /
o ,
0 /
0 /
0 /
1760
1770
1780
17 19E
1790
1752
1800
18 27
1605E
1810
1904
16 43
1820
1941
17 22
1830
2016
1801
1840
2049
1838
1850
15 51E
16 45E
18 OOE
21 16E
21 19
19 15E
19 12
1860
1559
16 58
18 30
21 37
21 45
19 40
19 41
1870
1559
17 02
18 45
21 52
2206
19 58
2006
1880
1890
15 47
1524
16 54
1636
18 45
18 39
21 56
2206
22 19
2238
2009
20 11
20 24
2032
1900
1910
15 19
1543E
1637
17 08E
1851
1931E
22 22
23 OOE
22 58
23 40E
2026
21 07E
20 50
2133E
A MANUAL FOR NORTHERN WOODSMEN
TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA-
TION IN THE UNITED STATES
(From U. S. Coast and Geodetic Survey Reports)
K
PM^
California
South (Los
Angeles)
California
Middle
(San Jose)
California
North
(Redding)
III
Sgg
Nevada
West (Haw-
thorne)
Utah
(Salt Lake)
1750
0 /
1760
1770
1780
1024E
13 37E
1407E
1790
1058
1403
14 35
1800
11 32
1432
1504
1810
1207
15 01
1534
1820
1239
1530
1604
1830
1309
1557
1633
1840
13 36
16 22
1701
1850
13 57
1645
17 26
17 20E
16 16E
16 25E
1860
14 13
1705
17 47
1736
1637
16 30
1870
14 24
17 20
1806
17 41
1652
16 40
1880
14 33
17 28
18 15
1744
1700
16 30
1890
1436
1732
1820
1738
1702
16 20
1900
1452
17 51
1839
17 49
17 17
16 28
1910
15 35E
1832E
19 22E
18 27E
17 58E
17 03E
Ij
w
Colorado
West (Glen-
wood
Springs)
New Mexico
East
(Santa Rosa)
8 ~
'?' — -
fl
'A
111
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
13 47E
1607E
1243E
13 26E
13 33E
13 19E
1860
13 50
16 15
1247
13 33
13 44
1233
1870
13 46
16 16
12 43
13 34
13 47
13 40
1880
1331
1604
12 29
13 22
13 40
13 36
1890
1300
15 40
1203
1302
13 25
13 32
1900
1910
12 53
13 19E
1539
16 10E
11 59
12 29E
1302
13 36E
13 29
U 05E
13 44
14 25E
ON OBTAINING THE MERIDIAN 51
From the table for change of declination, and for the
locality eastern New York, the values 5° 28' and 11° 31'
are obtained, showing that the needle in the 110 years
swung 6° 03' to the westward. The desired bearing
therefore should prove to be N 6° E nearly.
SECTION VII
ON OBTAINING THE MERIDIAN
When for any reason it is necessary to determine a true
meridian, that is best obtained from the north star. This
star, easily identified by the range of the " pointers," is nol
exactly at the pole of the heavens, but in 1908 was 1° 11' 4"
from it. This angle is called the " polar distance" of the
star. It is decreasing at the rate of about one third of a
minute yearly.
The north star, like other stars, is thus circling around
the pole once in about 24 hours. When directly over or
under the pole it is said to be in culmination, upper or
lower as the case may be. The star is then in the meridian,
and bringing it down with plumb line or transit gives the
meridian directly.
When the north star is farthest from the meridian 'it is
said to be in elongation, east when the star is east of the
meridian, west when on the opposite side. A plane through
the observer, the zenith, and the north star when at elonga-
tion, prolonged downward to the horizon, makes an angle
with the meridian which is called the azimuth of the star
at that time. This angle may be obtained for any time and
position from tables, and setting off the angle, the true
meridian is found. Upon this meridian the needle can be
read or marks can be left for reference at any future time.
The operation of bringing down the star may be per-
formed either with the plumb line or, more accurately and
conveniently, with a well-adjusted transit. When the
transit is used it is necessary to illuminate the cross wires.
This may often be done by holding a lantern or candle
in front of the transit tube and a little to one side, when
the field should appear light with the cross hairs show-
A MANUAL FOR NORTHERN WOODSMEN
REFLECTOR
ing as dark lines. If light enough is not so obtained,
a tin reflector may be made of the design shown, or a
piece of tracing cloth or greased paper,
with a hole cut in it may be bound bell-
shape over the front of the instrument
with a string or rubber band.
Directions for obtaining the true merid-
ian which involve an accurate knowledge
of time are not adapted to the use of the
woodsman. The following directions do
not impose that very difficult requirement.
(From United States " Manual of Instructions for Sur-
vey of the Public Lands.")
To OBTAIN A MERIDIAN AT CULMINATION OF POLARIS
A very close approximation to a meridian may be had by re-
membering that Polaris very nearly reaches the meridian when
it is in the same vertical plane with the star Delta (5) in the con-
stellation Cassiopeia. The vertical
wire of the transit should be fixed
upon Polaris, and occasionally brought *
down to the star Delta, to observe its
approach to the same vertical line. *
When both stars are seen upon the „
wire, Polaris is very near the meridian.
A small interval of time (as 6 min. in
1908) will then be allowed to pass,
while Delta moves rapidly east and
Polaris slightly east to the actual me-
ridian. At that moment the cross wire
should be placed upon Polaris, and the
meridian firmly marked by stakes and
tack-heads.
This method is practicable only
when the star Delta is below the pole
during the night; when it passes the
meridian above the pole, it is too near
the zenith to be of service, in which
case the star Zeta (f), the last star but
one in the tail of the Great Bear, may
be used instead.
Delta (5) Cassiopeia; is on the me-
ridian below Polaris and the pole, at Cassio
midnight about April 10, and is, there-
fore, the proper star to use at that date and for some two or
three months before and after.
North Pole
peia
ON OBTAINING THE MERIDIAN 53
Six months later the star Zeta (fl, in the tail of the Great Bear,
will supply its place, and will be used in precisely the same manner.
The diagram, drawn to scale, exhibits the principal stars of
the constellations Cassiopeia and Great Bear, with Delta (5) Cas-
siopeiae, Zeta (f) Ursse Majoris (also called Mizar), and Polaris
on the meridian, represented by the straight Line; Polaris being
at lower culmination.
In the above process, the interval of waiting time may
be found for the proper year from the following data :
(1910 .
* For Zeta Urs. Maj. { 1920 .
(1930 .
1910 .
For Delta Cass.
!1930
6.5 min. ( annual
10.6 ' < increase
14.7 " ( .41 min.
7.1 min. ( annual
11.0 " < increase
14.9 " ( .39 min.
* Data furnished by Prof. Robt. W. Willson.
Instead of the transit the plumb line may be used for
this observation in much the manner described later on.
At certain times of year it is inconvenient to observe
Polaris at culmination, and for other reasons as well it is
more usual to observe the star at elongation. The Land
Office instructions follow, and the table for azimuths of
the star and for time of elongation which are required.
To ESTABLISH A MERIDIAN AT ELONGATION BY TELESCOPIC
INSTRUMENT
Set a stone, or drive a wooden peg, firmly in the ground, and
upon the top thereof make a small, distinct mark.
About thirty minutes before the time of the eastern or western
elongation of Polaris, obtained from the table, set up the transit
firmly, with its vertical axis exactly over the mark, and carefully
level the instrument.
Illuminate the cross wires by the light from a suitable lantern,
the rays being directed into the object end of the telescope by an
assistant; while great care will be taken, by perfect leveling, to
insure that the line of collimation describe a truly vertical plane.
Place the vertical wire upon the star, which, if it has not reached
its elongation, will move to the right for eastern, or to the left for
western elongation.
While the star moves toward its point of elongation, by means of
the tangent screw of the vernier plate it will be repeatedly covered
by the vertical wire, until a point is reached where it will appear to
remain on the wire for some time, then leave it in a direction con-
trary to its former motion ; thus indicating the tune of elongation.
Then while the star appears to thread the vertical wire, depress
54 A MANUAL FOR NORTHERN WOODSMEN
the telescope to a horizontal position; five chains north of the
place of observation set a stone or drive a firm peg, upon which
by a strongly illuminated pencil or other slender object, exactly
coincident with the vertical wire, mark a point and drive a tack
in the line of sight thus determined; then, to eliminate possible
errors of collimation or imperfect verticality of the motion of the
telescope, quickly revolve the vernier plate 180°, direct the glass
at Polaris and repeat the observation ; if it gives a different result
find and mark the middle point between the two results. This
middle point, with the point marked by the plumb bob of the
transit, will define the trace of the vertical plane through Polaris
at its eastern or western elongation, as the case may be.
By daylight lay off to the east or west, as the case may require,
the proper azimuth taken from the following table (page 56) ; the
instrument will then define the meridian. The needle may be
read then, giving the magnetic declination, east or west as the case
may be. Or the line may be permanently marked for reference
at another time or with another instrument.
To DETERMINE A MERIDIAN WITHOUT A TELESCOPE
Attach a plumb line to a support situated as far above the
ground as practicable, such as the limb of a tree, a piece of board
nailed or otherwise fastened to a telegraph pole, a house, barn,
or other building, affording a clear view north and south.
The plumb bob may consist of some weighty material, such as
a brick, a piece of iron or stone, weighing four to five pounds,
which will hold the plumb line vertical, fully as well as one of
finished metal.
Strongly illuminate the plumb line just below its support by a
lamp or candle, care being taken to obscure the source of light
from the view of the observer by a screen.
For a peep sight, cut a slot about one-sixteenth of an inch wide
in a thin piece of board, or nail two strips of tin, with straight
edges, to a square block of woqd, so arranged that they will stand
vertical when the block is placed flat on its base upon a smooth
horizontal rest, which will be placed at a convenient height south
of the plumb line and firmly secured in an east and west direction,
in such a position that, when viewed through the peep sight, Po-
laris will appear about a foot below the support of the plumb line.
The position may be practically determined by trial the night
preceding that set for the observation.
About thirty minutes before the time of elongation, as obtained
from the table, bring the peep sight into the same line of sight with
the plumb line and Polaris.
To reach elongation, the star will move off the plumb line to
the east for eastern elongation, or to the west for western elonga-
tion ; therefore by moving the peep sight in the proper direction,
east or west, as the case may be, keep the star on the plumb line
until it appears to remain stationary, thus indicating that it has
reached its point of elongation.
ON OBTAINING THE MERIDIAN 55
The peep sight will now be secured in place by a clamp or
weight with its exact position marked on the rest, and all further
operations will be deferred until the next morning.
By daylight, place a slender rod at a distance of two or three
hundred feet from the peep sight, and exactly in range with it and
the plumb line ; carefully measure this distance.
Take from the table on page 56 the azimuth of Polaris cor-
responding to the latitude of the station and year of observation ;
find the natural tangent of said -azimuth and multiply it by the
distance from the peep sight to the rod ; the product will express
the distance to be laid off from the rod exactly at right angles to
the direction already determined (to the west for eastern elonga-
tion or to the east for western elongation), to a point, which with
the peep sight, will define the direction of the meridian with suffi-
cient accuracy for the needs of local surveyors.
Example: Sept. 10, 1915, in latitude 45° N, longitude
71° W, it is desired to obtain the declination of the needle.
From the table giving times of elongation it is found that
Polaris is at eastern elongation on Sept. 1st at 53.2 minutes past
8 P.M.
Correction A is not required in this case.
Correction B, for the 9 days elapsed since Sept. 1st, is 35.3 rain.,
to be subtracted.
Correction C, for 71° longitude, is 16 min., to be subtracted.
Correction D, for 45° latitude, is 0.85 min., to be added.
Correction E is 0.2 min., to be added.
8 hrs. 53.2 min. — 35.3 min. — 16 min. + .85 min. + .2 min.
= 8 hrs. 3 min., time of elongation by the watch.
The star having been observed at the time indicated and brought
down to the horizon, its azimuth is ascertained from the table of
azimuths. For 1915 and latitude 45°, this value is 1° 37.4' and
there is no appreciable correction for apparent place. The merid-
ian then is that much to the west of the line determined. In this
case, with the instrument on the azimuth line the needle was
allowed to settle and a reading of N 17° 50' E obtained. 17° 50' —
1° 37.4' = 16° 12.6'. 16° 12.6' is therefore the magnetic declination
for the place and time, or 16° 15' as near as a needle can be
read.
In practice corrections D and E may usually be neglected.
Using the table for time of elongation with corrections A, B, and C
applied to it, the surveyor will ascertain when to be on hand for
the observation. Then, watching the star, when satisfied by its
motion that it has reached elongation he will bring his instrument
down without regard to time. In fact, Polaris traverses less than
4' of azimuth in the hour before and the hour after elongation.
56 A MANUAL FOR NORTHERN WOODSMEN
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ON OBTAINING THE MERIDIAN
57
The table on the preceding page was computed with
mean declination of Polaris for each year. A more ac-
curate result will be had by applying to the tabular values
the following correction, which depends on the difference
of the mean and the apparent place of the star. The
deduced azimuth will in general be correct within 0.3'.
For Middle of
Correction
For Middle of
Correction
January
February
March
April
May
June
— 0.5
— 0.4
=8:o3
tti
July
August
September
October
November
December
+ 0.2
+ 0.1
— 0.1
— 0.4
— 0.6
— 0.8
LOCAL CIVIL (NOT STANDARD) TIME OF THE ELONGATIONS
OF POLARIS IN THE YEAR 1915. (COMPUTED FOR LATI-
TUDE 40o NORTH AND LONGITUDE 90° OR 6h WEST
OF GREENWICH)
(From United States Coast and Geodetic Survey)
Date
Eastern Elongation
Western Elongation
1915
h.
m.
h.
m.
January 1
0
51.7 P. M.
0
46.0 P. M.
January 15
11
56.4 A. M.
11
46.8 P. M.
February 1
•» 10
49.2 A. M.
10
39.7 P. M.
February 15
March 1
8
54.0 A. M.
58.7 A. M.
9
8
44.4 P. M.
49.2 P. M.
March 15
8
3.5 A. M.
7
54.0 P. M.
April 1
6
56.6 A. M.
6
47.1 P. M. .
April 15
6
1.6 A. M.
5
52.0 P. M.
May 1
4
58.7 A. M.
4
49.2 P. M.
May 15
4
3.8 A. M.
3
54.2 P. M.
June 1
2
57.2 A. M.
2
47.6 P. M.
June 15
2
2.4 A. M.
1
52.8 P. M.
July 1
0
59.8 A. M.
0
50.2 P. M.
July 15
0
5.0 A. M.
11
55.4 A. M.
August 1
10
54.5 P. M.
10
48.8 A. M.
August 15
9
59.8 P. M.
9
54.1 A. M.
September 1
8
53.2 P. M.
8
47.5 A. M.
September 15
October 1
7
6
58.3 P. M.
55.5 P. M.
7
6
52.6 A. M.
49.8 A. M.
October 15
6
00.6 P. M.
5
54.9 A. M.
November 1
4
53.7 P. M.
4
48.0 A. M.
November 15
3
58.6 P. M.
3
52.9 A. M.
December 1
2
55.6 P. M.
2
49.9 A. M.
December 15
2
00.4 P. M.
1
54.7 A. M.
58
A MANUAL FOR NORTHERN WOODSMEN
A. To refer the above tabular quantities to years subse-
quent to 1915:
For year 1917
subtract
0.7 minute
1918
add
0.9 minute
1919
add
2.5 minutes
1920
4.0 minutes
0.1 minute
up to March 1
on and after March 1
1921
add
1.6 minutes
1922
add
3.1 minutes
1923
add
4.5 minutes
5.9 minutes
up to March 1
1924
1 add
2.0 minutes
on and after March 1
1925
add
3.3 minutes
1926
add
4.6 minutes
1927
add
5.9 minutes
1928
/add
add
7.2 minutes
3.3 minutes
up to March 1
on and after March 1
B. To refer to any calendar day other than the first and
fifteenth of each month, subtract the quantities below from
the tabular quantity for the preceding date.
Day of Month
Minutes
No. of Days Elapsed
2 or 16
3.9
1
3 or 17
7.8
2
4 or 18
11.8
3
5 or 19
15.7
4
6 or 20
19.6
5
7 or 21
23.5
6
8 or 22
27.4
7
9 or 23
31.4
8
10 or 24
35.3
9
11 or 25
39.2
10
12 or 26
43.1
11
13 or 27
47.0
12
14 or 28
51.0
13
29
54.9
14
30
58.8
15
31
62.7
16
For the tabular year, two eastern elongations occur on
January 14, and two western elongations on July 13.
C. To refer the table to standard time: Add to the tab-
ular quantities four minutes for every degree of longitude
the place is west of the standard meridian and subtract
when the place is east of the standard meridian.
D. To refer to any other than the tabular latitude between
the limits of 25° and 50° North: Add to the time of west
elongation 0.10 min. for every degree south of 40° and
ON OBTAINING THE MERIDIAN 59
subtract from the time of west elongation 0.16 min. for
every degree north of 40°. For eastern elongations sub-
tract 0.10 min. for every degree south of 40°, and add 0.16
min. for every degree north of 40°.
E. To refer to any other than the tabular longitude : Add
0.16 min.for each 15° east of the ninetieth meridian and sub-
tract 0.16 min. for each 15° west of the ninetieth meridian.
The deduced time of elongation will seldom be in error
more than 0.3 min.
For Evening Observation. Study of the tables will
show that at certain times of the year a choice of methods
is offered. Since, however, evening observation is usually
most convenient, the following directions have been ar-
ranged with that in view. The time limits for these
observations, it will be understood, vary somewhat with
the latitude.
On the tenth of January observe western elongation
at midnight and for each fifteen days thereafter earlier
by one hour. This may be done until late March.
From late March to early June, use lower culmination
with the help of Delta of Cassiopeia. On April 1st the
culmination occurs at 12.37 and after that for each fifteen
days earlier by one hour.
From early June to early October use eastern elonga-
tion. On June 15th it occurs at 2 A. M.
From early October to middle January use upper cul-
mination with Zeta of the Great Bear.
60 A MANUAL FOR NORTHERN WOODSMEN
SECTION VHI
THE UNITED STATES PUBIJC LAND SURVEYS
In the original States there is a great variety of system,
or lack of system, in the division of land for ownership.
Land which has ever been a part of the Public Domain of
the United States — and that embraces in general the
territory north of the Ohio River and from the Mississippi
River west to the Pacific coast — has been surveyed, with
small exceptions, under a common system, the so-called
" System of Rectangular Surveying." An account of this,
so far as it concerns the woodsman, follows.
Chapter III of the Public Land Laws contains the fol-
lowing sections:
SEC. 99. The public lands shall be divided by north and south
lines run according to the true meridian, and by others crossing
them at right angles, so as to form townships of six miles square,
unless where the line of an Indian reservation, or of tracts of land
heretofore sun-eyed or patented, or the course of navigable rivers,
may render this impracticable; and in that case this rule must
be departed from no further than such particular circumstances
require.
Second. The corners of the townships must be marked with
progressive numbers from the beginning ; each distance of a mile
between such corners must be also distinctly marked with marks
different from those of the corners.
Third. The township shall be subdivided into sections, con-
taining, as nearly as may be, six hundred and forty acres each,
by running through the same, each way, parallel lines at the end
of every two miles ; and by making a corner on each of such lines
at the end of every mile. The sections shall be numbered, re-
spectively, beginning with the number one in the northeast section,
and proceeding west and east alternately through the township
with progressive numbers till the thirty-six be completed.
Fourth. The deputy surveyors, respectively, shall cause to
be marked on a tree near each corner established in the manner
described, and within the section, the number of such section
and over it the number of the township within which such section
may be.
Fifth. Where the exterior lines of the townships which may
be subdivided into sections or half-sections exceed or do not ex-
tend six miles, the excess or deficiency shall be specially noted
UNITED STATES PUBLIC LAND SURVEYS 61
and added to or deducted from the western and northern ranges
of sections or half-sections in such townships, according as the
error may be in running the lines from east to west, or from north
to south ; the sections and half -sections bounded on the northern
and western lines of such townships shall be sold as containing
only the quantity expressed in the returns and plats, respectively,
and all others as containing the complete legal quantity.
Sixth. All lines shall be plainly marked upon trees, and meas-
ured with chains, containing two perches of sixteen and one-half
feet each, subdivided into twenty-five equal links ; and the chain
shall be adjusted to a standard to be kept for that purpose.
SEC. 100. The boundaries and contents of the several sections,
half-sections, and quarter-sections of the public lands shall be as-
certained in conformity with the following principles:
First. All the corners marked in the surveys returned by the
surveyor-general shall be established as the proper corners of
sections, or subdivisions of sections, which they were intended to
designate, and the corners of half and quarter-sections, not marked
on the surveys, shall be placed as nearly as possible equidistant
from two corners which stand on the same line.
Second. The boundary lines, actually run and marked in the
surveys returned by the surveyor-general, shall be established as
the proper boundary lines of the sections or subdivisions for which
they were intended, and the length of such lines as returned shall
be held and considered as the true length thereof. And the
boundary lines which have not been actually run and marked
shall be ascertained by running straight lines from the established
corners to the opposite corresponding corners; but in those por-
tions of the fractional townships, where no such opposite corre-
sponding corners have been or can be fixed, the boundary lines
shall be ascertained by running from the established corners due
north and south or east and west lines, as the case may be, to the
water-course, Indian boundary line, or other external boundary
of such fractional township.
Third. Each section or subdivision of section, the contents
whereof have been returned by the surveyor-general, shall be
held and considered as containing the exact quantity expressed
in such return; and the half -sections and quarter-sections, the
contents whereof shall not have been thus returned, shall be held
and considered as containing the one-half or the one-fourth part,
respectively, of the returned contents of the section of which they
may make part. (Act of Feb. 11, 1805, and R. S., 2396.)
SEC. 101. In every case of the division of a quarter-section
the line for the division thereof shall run north and south, and the
corners and contents of half-quarter-sections which may there-
after be sold shall be ascertained in the manner and on the prin-
ciples directed and prescribed by the section preceding.
62 A MANUAL FOR NORTHERN WOODSMEN
In elaboration of the law are the following rules laid
down by the Federal Land Office:
24. Existing law requires that in general the public lands of
the United States "shall be divided by north and south lines run
according to the true meridian, and by others crossing them at
right angles so as to form townships six miles square," and that
the corners of the townships thus surveyed "must be marked with
progressive numbers from the beginning."
Also, that the townships shall be subdivided into thirty-six sec-
tions, each of which shall contain 640 acres, as nearly as may be,
by a system of two sets of parallel lines, one governed by true
meridians and the other by parallels of latitude, the latter inter-
secting the former at right angles, at intervals of a mile.
25. In the execution of the public surveys under existing law,
it is apparent that the requirements that the lines of survey shall
conform to true meridians, and that the townships shall be six miles
square, taken together, involve a mathematical impossibility due
to the convergency of the meridians.
Therefore, to conform the meridional township lines to the
true meridians produces townships of a trapezoidal form which
do not contain the precise area of 23,040 acres required by law,
and which discrepancy increases with the increase in the con-
vergency of the meridians as the surveys attain the higher latitudes.
26. In view of these facts, and under the provisions of Sec-
tion 2 of the Act of May 18, 1796, that sections of a mile square
shall contain 640 acres, as nearly as may be, and also under those
of Section 3 of the Act of May 10, 1800, that "in all cases where the
exterior lines of the townships, thus to be subdivided into sections
and half-sections, shall exceed, or shall not extend six miles, the
excess or deficiency shall be specially noted, and added to or de-
ducted from the western or northern ranges of sections or half-
sections in such township, according as the error may be in run-
ning lines from east to west, or from south to north ; the sections
and half-sections bounded on the northern and western lines of
such townships shall be sold as containing only the quantity ex-
pressed in the returns and plats, respectively, and all others as
containing the complete legal quantity," the public lands of the
United States shall be surveyed under the methods of the system
of rectangular surveying, which harmonizes the incompatibilities
of the requirements of law and practice, as follows:
First. The establishment of a principal meridian conforming
to the true meridian, and, at right angles to it, a base line conform-
ing to a parallel of latitude.
Second. The establishment of standard parallels conforming
to parallels of latitude, initiated from the principal meridian at
intervals of 24 miles and extended east and west of the same.
Third. The establishment of guide meridians conforming to
true meridians, initiated upon the base line and successive standard
UNITED STATES PUBLIC LAND SURVEYS 63
parallels at intervals of twenty-four miles, resulting in tracts of land
twenty-four miles square, as nearly as may be, which shall be sub-
sequently divided into tracts of land six miles square by two sets
of lines, one conforming to true meridians, crossed by others con-
forming to parallels of latitude at intervals of six miles, containing
23,040 acres, as nearly as may be, and designated townships.
Such townships shall be subdivided into thirty-six tracts, called
sections, each of which shall contain 640 acres, as nearly as may
be, by two sets of parallel lines, one set parallel to a true meridian
and the other conforming to parallels of latitude, mutually inter-
secting at intervals of one mile and at right angles, as nearly as
may be.
27. Any series of contiguous townships or sections situated
north and south of each other constitutes a RANGE, while such a
series situated in an east and west direction constitutes a TIER.
28. By the terms of the original law and by general practice,
section lines were surveyed from south to north and from east to
west, in order to uniformly place excess or deficiency of measure-
ment on the north and west sides of the townships. But under
modern conditions many cases arise in which a departure from
this method is necessary. Where the west or the north boundary
is sufficiently correct as to course, to serve as a basis for rectangular
subdivision, and the opposite line is defective, the section lines
should be run by a reversed method.
For convenience the well-surveyed lines on which subdivi-
sions are to be based will be called governing boundaries of the
township.
29. The tiers of townships will be numbered, to the north or
south commencing with No. 1, at the base line; and the ranges
of the townships, to the east or west, beginning with No. 1, at the
principal meridian of the system.
30. The thirty-six sections into which a township is subdi-
vided are numbered, commencing with No. 1 at the north-
east angle of the township, and proceeding west to number six,
and thence proceeding east to number twelve, and so on, alter-
nately, to number thirty-six in the southeast angle. In all cases
of surveys of fractional townships, the sections will bear the same
numbers they would have if the township was full; and where
doubt arises as to which section numbers should be omitted, the
proper section numbers will be used on the side or sides which
are governing boundaries, leaving any deficiency to fall on the
opposite sides.
31. Standard parallels (formerly called correction lines) shall
be established at intervals of twenty-four miles, north and south of
the base line, and guide meridians at intervals of twenty-four miles,
east and west of the principal meridian ; thus confining the errors
resulting from convergence of meridians and inaccuracies in meas-
urement within comparatively small areas.
64
A MANUAL FOR NORTHERN WOODSMEN
In pursuit of this system, during the course of the pub-
lic land surveys twenty-four initial points have been
established, a principal meridian has been run due north
and south from each of these, and a base line east and
west. Each twenty-four miles north and south of the
initial point standard parallels or correction lines have
been started on which, as they were run east and west,
marks have been left each six miles for the starting of
township lines. These are run due north to the next
standard parallel; each fourth one being run first and
Standard
Parall
el
1
f
i
I
i
i
E
E
j
\
I
1
\
FIHST SUBDIVISION op LAND
Standard Parallel
DIVISION INTO TOWNSHIPS
most accurately as a guide meridian. On the north and
south lines township corners are fixed each six miles by
measurement, and each pair of corners is later connected.
A township corner is common to four townships except on a
standard parallel. There, owing to convergence of merid-
ians, the corners of the townships north are farther from the
principal meridian than those of the townships south ; farther
east or west, as the case may be. The ranges of townships
connected with any given initial point are numbered east
and west from the principal meridian, and the townships
themselves are numbered north and south from the base
line. Thus the sixth township north of a base line in the
fourth range east of a principal meridian is designated as
township 6 north, range 4 east. Each township contains
UNITED STATES PUBLIC LAND SURVEYS
65
thirty-six square miles or 23,040 acres, neglecting the nar-
rowing effect of the convergence of the meridians. These
relations are indicated clearly in the diagrams.
As the township lines are run, corner marks are left each
mile, and the township is divided into thirty-six sections by
beginning on the south side at each mile mark and running
north, marking each mile or section corner, also each half
mile or quarter-section corner. At the north end these
lines are made to close on the mile marks left in surveying
the north line of the township, with the exception of those
on a standard parallel. Here the section lines are run
straight out to the parallel, which thus serves as a "cor-
rection-line" for the sections as well as for the townships.
N
G
5
4
3
2
1
7
8
9
10
11*
12
18
17
16
.15
14
13
19
20
21
22
23
24
30
29
28
27
26
25
31
32
33
34
35
36
X. W. %
160 acres
N. E. M
100 acres
Yf T/
ofS.W.
80 acres
ofS.W.
N.W. J^
ofS.E.
54
40 acres
40 acres
S.E.Ji
ofS.E.
SECTIONS IN A TOWNSHIP
SUBDIVISION OF A SECTION
The east and west section lines are run between corre-
sponding corners on the north and south lines, always
marking the half-mile or quarter-section point. The
effect on area of convergence of meridians is localized in
the case of sections, in the first place by chaining the
latitudinal township lines always from the east end, thus
confining any deficiency of width to the westerly board
of sections; in the second place by running the north and
south lines not due north exactly, but with a westerly
bearing sufficient at one, two, three, four, and five miles
from the east line to keep them at equal distances apart
throughout their length. Short area is thus confined to
66 A MANUAL FOR NORTHERN WOODSMEN
the westerly board of sections in each township when
surveys are accurately made. For the same purpose,
reduction in the number of irregular units, quarter corners
for the north and west tiers of sections are placed exactly
forty chains from the interior corners, not at the middle
point of the section lines.
The Land Office instructions to surveyors contain
several articles on the marking of lines, of which those of
interest to the woodsman are quoted on page 24 of this
work. Instructions for establishing corners and erecting
monuments are also given, but are far too elaborate to be
here quoted in full. Corner monuments consist of an ob-
ject marking the corner itself and its accessories. They
are to be set up at the intersection of all the lines noted
in the instructions quoted above and at some other points
to be mentioned hereafter. Several approved forms of
corner monuments are described below. Any one may
be used for a township, a section, or a quarter-section
corner, the marks upon it indicating what the corner is.
1. Stone with pits and mound of earth.
2. Stone with mound of stone.
3. Stone with bearing trees.
4. Post with pits and mound of earth.
5. Post with bearing trees.
6. Mound of earth, with marked stone or charcoal de-
posited inside, and stake in pit.
7. Tree with pit and mound of stone.
8. Tree with bearing trees.
Posts of wood and stone and bearing trees have been
employed largely as corner monuments in timbered
country. The post is set not to exceed one foot out of the
ground. At a standard, closing, or quarter corner it is set
facing cardinal directions, diagonally at a corner common
to four townships or sections. Plain figures and initial
letters inscribed on the faces give the location, and this in
the case of section corners is also indicated by notches cut
in the edges or by grooves on faces. These notches, on
account of their durability, are of much service in identi-
UNITED STATES PUBLIC LAND SURVEYS 67
fication of section corners. They are placed on the south
and east angles of the posts, one for each mile to the town-
ship boundary in the given direction. Quarter corners are
not notched; township corners are cut six times on each
face or angle.
Equally serviceable are the bearing trees. These are
blazed rather close to the ground so that the stump can
be identified if the tree is cut down. The blazes face the
corner, and that on each tree at township or section corners
is plainly scribed with the township number and range and
that of the section in which it stands. Thus, T 10 S R
6 E S 24 B T (B T for bearing tree).
There are several exceptions to the system of rectan-
gular surveying and the regular scheme of monuments
resulting therefrom, which it is necessary for the woodsman
to understand.
1. Toimship and Section Corners on Standard Parallels.
It will be noted after careful reading of the above that
township or section corners are common to four townships
or sections, with the exception of those on the standard
parallels which are four townships apart. Here the corners
for the townships north of the parallel are not the same as
for those south, but are further from the principal me-
ridian. The former are called "standard corners" and are
marked S C in addition to other marks placed on them for
their identification. In a similar way the corners relating
to land subdivisions lying south of the parallel are marked
C C, "closing corner." This last term is also applied in
other connections, as when a rectangular survey closes on
the boundary of a state, a reservation, or a previous land
claim, while occasions for its application have often been
found in connection with errors or departures from instruc-
tions in the system of surveying.
2. Meander Lines and Corners.
Ownership of considerable streams or lakes, with the
exception of certain "riparian rights," is not conveyed
with a land title, the legal limit being high-water mark, or
the line at which continuous vegetation ends and the sandy
68 A MANUAL FOB NORTHERN WOODSMEN
or muddy shore begins. This line is surveyed in connec-
tion with a United States land survey, the process being
called " meandering."
At every point where a standard, township, or section
line intersects the bank of a navigable stream or other
meanderable body of water, corners are established at the
time of running these lines. These are called " meander
corners." They are always marked M C in addition to any
other marks left for their identification.
In the same way, when a line subdividing a section runs
into a considerable body of water, a " special meander
corner" is established and marked in the same way.
3. Witness Carriers and Witness Points.
A key to the location and meaning of these will be found
in the following sections from the " Instructions."
49. Under circumstances where the survey of a township or
section line is obstructed by an impassable obstacle, such as a
pond, swamp, or marsh (not meanderable), the line will be pro-
longed across such obstruction by making the necessary right-
angle offsets; or, if such proceeding be impracticable, a traverse
line will be run, or some proper trigonometrical operation em-
ployed to locate the line on the opposite side of the obstruction ;
and in case the line, either meridional or latitudinal, thus regained,
is recovered beyond the intervening obstacle, said line will be sur-
veyed back to the margin of the obstruction.
50. As a guide in alignment and measurement, at each point
where the line intersects the margin of an obstacle a witness point
will be established, except when such point is less than twenty
chains distant from the true point for a legal corner which falls in
the obstruction, in which case a witness corner will be established
at the intersection.
51. In a case where all the points of intersection with the ob-
stacle to measurement fall more than twenty chains from the proper
place for a legal corner in the obstruction, and a witness corner
can be placed on the offset line within twenty chains of the inac-
cessible corner point, such witness corner will be established.
97. The point for a corner falling on a railroad, street, or
wagon road, will \>e perpetuated by a marked stone (charred stake
or quart of charcoal), deposited twenty-four inches in the ground,
and witnessed by two witness corners, one of which will be estab-
lished on each limiting line of the highway.
In case the point for any regular corner falls at the intersection
of two or more streets or roads, it will be perpetuated by a marked
stone (charred stake or quart of charcoal), deposited twenty-four
inches in the ground, and witnessed by two witness corners estab-
UNITED STATES PUBLIC LAND SURVEYS 69
lished on opposite sides of the corner point, and at the mutual in-
tersections of the lines limiting the roads or streets, as the case
may be.
94. When the true point for any corner described in these
instructions falls where prevailing conditions would insure its
destruction by natural causes, a witness corner will be established
in a secure position, on a surveyed line if possible, and within
twenty chains of the corner point thus witnessed.
95. A witness corner will bear the same marks that would be
placed upon the corner for which it is a witness, and in addition,
will have the letters W C (for witness corner) conspicuously dis-
played above the regular markings on the NE. face when witness-
ing in township or section corner; such witness corners will be
established, in all other respects, like a regular corner, marking
bearing trees with the proper numbers for the sections in which
they stand.
W C will also be cut into the wood of each bearing tree above
the other markings.
98. Witness points will be perpetuated by corners similar to
those described for quarter-section corners, with the marking W P
(for witness point), in place of J, or J S, as the case may be.
If bearing trees are available as accessories to witness points,
each tree wUl be marked W P B T.
4. Fractional Sections, Lots, etc.
A section or quarter-section made of less than full size by
water is called "fractional," and in some cases is subdivided
according to special rules laid down by the Land Office.
The sections on the westerly board of a township, into
which, under the plan of survey, shrinkage of area due to
convergence of township lines toward the north is crowded,
are called fractional as well. Within these sections again,
the westerly quarters and forties will be fractional for the
same reason. The final subdivisions of irregular area —
the system is followed next the north as well as the west
line of the townships — are called "lots." In a regular
township there are four to each section, numbered from
1 to 4 for each, beginning with the east or north, with seven
lots for Section 6. In timbered country, however, they
are seldom run out on the ground.
While the above are usual features of the public land
surveys, numerous exceptions were made, as for instance
in case of a defective east or south boundary in a township,
70 A MANUAL FOR NORTHERN WOODSMEN
when subdivision was begun from the opposite side.
Somewhat different rules also were in force during the
very early surveys. Then hi addition irregularities due
to the errors of surveying, and these sometimes of an
extreme nature, are sometimes found.
PART II
FOREST MAPS
PART II. FOREST MAPS
SECTION I. . THE TRANSIT 73
1. Adjustments 73
2. Care of the Transit 77
3. Stadia Measurement 77
4. Uses of the Transit 80
5. Summary . . . • 87
SECTION II. THE LEVEL 87
1. Adjustments 88
2. Uses of the level 90
SECTION III. THE HAND LEVEL AND CLINOMETER . . 93
SECTION IV. COMPASS AND PACING 94
SECTION V. THE TRAVERSE BOARD 98
SECTION VI. THE ANEROID BAROMETER 103
SECTION VII. METHODS OF MAP MAKING 113
1. Introductory 113
2. Small Tracts 117
3. Large Tracts 121
A. With Land already subdivided 121
B. Based on Survey of Roads or Streams . . . 121
C. Subdivision and Survey combined 123
D. Western Topography. Use of the Clinometer 129
SECTION VIII. ADVANTAGES OF A MAP SYSTEM 133
PART II. FOREST MAPS
SECTION I
THE TRANSIT
THE transit in general engineering work is the most
useful and most frequently employed of surveying instru-
ments. It is commonly used to measure horizontal and
vertical angles, but, having a magnetic needle, it may be
used to take bearings, and, when provided with stadia
wires, to measure distances. It may also be used as a
levelling instrument. A cut of a transit is shown here-
with, also a sectional view through the axis of the same
instrument.
The essential parts of an engineer's transit are described
below. The telescope is attached by means of a hori-
zontal axis and standards to the upper of two circular
plates. The two plates move freely on one another, the
lower being graduated, while the upper has a vernier
which allows readings to be made with accuracy. A
compass circle is also attached to the upper plate. A
clamp fixes the upper to the lower plate, and a tangent
screw secures a slow adjusting movement between the
two. A similar arrangement is placed between the lower
plate and the head of the instrument.
The whole instrument is supported on a tripod ; levelling
screws serve with the aid of cross levels to fix the plates in
a horizontal position ; and a finely turned spindle and socket
arrangement guides the plates in their movement on one
another. By means of a plumb line attached to the lower
end of the spindle the instrument may be set with its axis
exactly over any desired point.
1. ADJUSTMENTS OF THE TRANSIT
The object of these adjustments is to cause (1) the
instrument to revolve in a horizontal plane; (2) the line
of sight to generate a vertical plane when the telescope is
73
74
A MANUAL FOB NORTHERN WOODSMEN
revolved on its axis; (3) the axis of the telescope bubble
to be parallel to the line of sight, thus enabling the instru-
ment to be used as a level ; (4) the vernier on the vertical
THE TRANSIT
circle to be so adjusted as to give the true altitude of the
line of sight. These results may be secured as follows:
a. To adjust the plate levels so that each is in a plane
THE TRANSIT
75
perpendicular to the vertical axis of the instrument. Set
up the transit and bring the bubbles to the center of their
respective tubes. Turn the plate 180° about its vertical
axis, and see if the bubbles remain in the center. If they
move from the center, turn the capstan-headed screws on
the bubble tube until the bubble moves half-way back to
the center, or as nearly so as this can be estimated. Each
bubble must be adjusted independently. The adjust-
ment should be tested again by relevelling and reversing
as before, and the process continued until the bubbles re-
main in the center when reversed. When both -levels are
adjusted, the bubbles should remain. in the center during
the entire revolution about the vertical axis.
CROSS-SECTION OF THE TRANSIT HEAD
b. To make the line of sight perpendicular to the hori-
zontal axis so that the telescope when revolved will
generate a plane. To do this choose open and nearly level
ground. Set up the transit carefully over a point A, sight
accurately at a point B at about the same level and 200 or
300 feet away, and clamp both plates. Revolve the tele-
scope and set C in line with the vertical cross-hair at about
the same distance and elevation. B, A, and C should then
be in a straight line. To test this, turn the instrument
76 A MANUAL FOR NORTHERN WOODSMEN
about the vertical axis until B is again sighted. Clamp the
plate, revolve the telescope, and observe if point C is in
line. If not, set a third point D in the new line. Then,
to adjust, the cross-hair ring must be moved until the
vertical hair appears to have moved to the point E, one-
fourth the distance from D toward C, since, in this case,
a double reversal has been made.
The cross-hair ring is moved by loosening one of the
screws which hold it in the telescope tube and tightening
the opposite screw. The process of reversal should be
repeated until no further adjustment is required. \Yhen
finally adjusted, the screws should hold the ring firmly but
without straining it.
c. To make the horizontal axis of the telescope per-
pendicular to the vertical axis of the instrument, so that
the telescope in its revolution will generate a vertical
plane. Set up the instrument and level it carefully. Sus-
pend a fine, smooth plumb line twenty or thirty feet long
some twenty feet away from the instrument with a weight
on the lower end hanging freely in a pail of water. Set the
line of sight carefully on the cord at its upper end. Clamp
both plates and bring the telescope down until it reads on
the lower end of the cord. If the line of sight does not cut
the cord, raise or lower the adjustable end of the horizon- •
tal axis until the line of sight does revolve in a vertical
plane. Constant attention must be given to the plate
bubbles to see that they do not indicate an inclined verti-
cal axis.
If more convenient two points in a vertical line may be
used, as points on a building. Set on the top point and turn
down to the bottom one, marking it carefully. Revolve
both plate and telescope 180° and set again on the bottom
point. Raise the telescope again and read on the top point.
The second pointing at the top point should correspond
with the first. If it does not, adjust as above for half the
difference.
d. To make the telescope bubble parallel to the line of
sight. This adjustment is performed in the same way as
for a level, as explained on pages 89 and 90.
e. To make the vernier of the vertical circle read zero
THE TRANSIT 77
when the line of sight is horizontal. Having made the
axis of the telescope bubble parallel to the line of sight,
bring the bubble into the center of the tube and adjust the
vernier of the vertical circle until it reads zero on the limb.
If the vernier is not adjustable, the reading in this position
is its index error, to be applied to all readings.
2. CARE OF THE TRANSIT
The transit should be protected from wet and dust as
much as possible, a waterproof bag to cover it being useful
for that purpose. The tripod legs should move freely, but
not too freely; there should be no lost motion about their
shoes or elsewhere. Dust or water should be removed from
the glasses by a camel's hair brush or the gentle use of a
clean handkerchief; grease may be removed by alcohol.
Care should be taken not to strain the parts of the instru-
ment by too great pressure on the screws when using or
adjusting it. Before the transit is picked up, the levelling
screws should be brought approximately to their mid po-
sition, the telescope should be turned vertically and lightly
clamped, and the clamp of the lower plate should be loos-
ened. Then, if the instrument strikes anything while being-
carried from point to point, some part will move easily and
severe shock will be avoided.
3. STADIA MEASUREMENT
Measurement of distance by stadia is secured by simply
sighting with a transit at a graduated rod held on any de-
sired point and noting the space on the rod included
between two special cross-hairs set in the focus of the in-
strument. This is a very rapid method of measurement,
being especially handy and effective over broken land; it
gives a degree of accuracy sufficient for very many pur-
poses ; it allows the computation of the difference in ele-
vation between two points. Thus for many purposes it is
the most effective method of survey, and it is coming
into general use.
The Instrument. A transit intended for stadia work is
78 A MANUAL FOR NORTHERN WOODSMEN
provided with two additional horizontal hairs, usually fas-
tened to the same diaphragm as the ordinary cross-hairs,
and placed at a known distance apart. The space be-
tween these two extra hairs is preferably fixed, but in
some transits the diaphragm is so arranged that it can be
adjusted. The instrument must also be provided with a
level on the telescope and a circle or arc for measuring
vertical angles, since the telescope is seldom level when
measurements are taken.
Stadia rods are usually 10 or 12 feet long. They are
plainly painted in such a design as to be read at long dis-
tances. Engineers generally use rods graduated to feet
and tenths, the hairs cutting off one foot on the rod at a
distance of 100 feet. Hundredths of a foot are generally
estimated. For use in connection with a land survey it may
be more convenient to graduate the rod or adjust the hairs
so that one unit will be cut off at a distance of 66 feet or
one chain.
Inclined Sights. The distance between instrument and
rod is measured directly if the sight is taken horizontally,
and a vertical angle between them of 5° or less does not so
affect the sight as to matter particularly in many kinds of
work. If, however, a sight of greater inclination is taken,
a reading is obtained that represents a greater distance
than the horizontal one between instrument and rod. If
for an inclined reading the rod is also inclined, so as to be
perpendicular to the line of sight, the reading represents
the inclined distance, and the horizontal distance is the
cosine of the angle of inclination multiplied by the inclined
distance. Similarly, the difference in elevation is the in-
clined distance multiplied by the sine of the angle.
It is usual, however, and better, to hold the rod plumb,
and here the computation of horizontal and vertical ele-
ments is not so simple. Tables, however, have been com-
puted which give these elements, horizontal distance and
difference of elevation, directly. A compact stadia table
will be found on page 211 of this work and an example
showing the method of its use is given on page 80.
What has been written above needs, however, one
qualification. Stadia wires to read truly at all distances
THE TRANSIT 79
must cut off the unit distance on the rod not at a distance
of 100 or of 66 feet, but at a greater distance equal to the
distance from the center of the instrument to the objective
lens + the distance from the cross-wires to the same lens
when focused on a distant object. This correction, (/ + c)
as it is called, is about 1 foot in common transits.
In testing the instrument on measured bases, therefore,
these should be measured out from the plumb line or
center of instrument to the required distance + the
constant above described, and for accurate determina-
tion of distance the constant should be added to the
distance observed. In working out inclined sights from
the table this constant may be added to the rod reading
before the reductions for horizontal distance and elevation
are made.
In the practice of woodsmen, however, work will generally
be accurate enough if this constant is neglected, all the
more so since this error tends to be compensated by that
arising from neglect of the small vertical angles noted above.
There are, indeed, a few transits so constructed that no
such constant correction as that above stated has to be
considered.
Accuracy. The accuracy of stadia measurement de-
pends largely on the state of the atmosphere. If that is
hazy, or unsteady from the effects of heat, long shots can-
not be taken and measurements on shorter distances
cannot be accurately obtained. There is furthermore the
possibility that the line of sight by the lower hair when
passing over very hot ground may be refracted more than
the other and thereby give too small a reading. Other-
wise than here and above stated the only sources of in-
accuracy are due to errors in rod readings which for small
errors are as apt to be + as — and so mainly balance one
another. Thus while on single shots stadia measurement
may be appreciably inaccurate, the relative error decreases
with the length of the line run.
In general it may be said that stadia measurement gives
satisfactory results for very many purposes, and that it has
great advantages in the way of rapidity and cheapness.
With good instruments and clear air it can be employed
80
A MANUAL FOR NORTHERN WOODSMEN
on distances from one quarter to one third of a mile, giving
results which are accurate to within a few feet.
Example and Reduction of Readings. 1' on rod cut off
at distance of 100'. In computation, correction made for
1' instrumental constant. True horizontal distance and
difference of elevation between points both worked out.
Height of instrument over station obtained at each setting
and center hair for vertical angle read at same height on
rod.
Observed
Computed
Bearing
Rod
Reading
Vert.
Angle
Distance
Diflf.
Elev.
Elev.
N. 5° E.
2.00'
+ 1° 30'
200.86'
+ 5.27'
5.27'
N. 5° E.
1.80'
+ 4° 10'
179.84'
+ 13.12'
18.39'
N. 5° E.
1.05'
+ 8°
103.94'
+ 14.61'
33.00'
N. 5° E.
1.50'
— 30'
150.98'
— 1.31'
31.69'
635.62'
31.69'
Computation. First shot, with v. a. of 1° 30', rod reading 2.00'.
Add .01' for instrument constant, making 2.01', for corrected rod
reading. From table the horizontal distance fof 1' rod reading is
found to be 99.93' the difference of elevation 2.62'. For 2.01' rod
reading the elements are 99.93 X 2.01 and 2.62 X 2.01 or 200.86'
and 5.27', as above.
Second shot, 1.80 + .01, = 1.81, corrected rod reading.
For v. a. 4° 10' and rod reading 1', horizontal distance 99.47
and diff. elev. 7.25 are found in the tables. 99.47 X 1.81 and
7.25 X 1.81 = 179.84 and 13.12.
Similarly for succeeding shots
4. USES OF THE TRANSIT
To Take the Bearing of a Line. Set up over the first
point, level the instrument, free the needle, and turn the
telescope toward the other point. Read the bearing in the
same way as with a compass.
When set up on the forward one of two points, exactly
the same bearing may be read as if the instrument were
THE TRANSIT 81
set up on the rear point, if the telescope is revolved before
the pointing is made and the bearing taken.
To Measure a Horizontal Angle. Set up the instru-
ment, center it by means of the plumb line over the vertex
of the angle required, set the zeros of the two plates to-
gether, clamp them, and turn the telescope toward one of
the points, making the final adjustment by means of the
lower tangent screw. Then loosen the upper clamp, turn
toward the other point, clamp again, and set finally by the
upper tangent screw. Read the angle turned by means of
the vernier. If the instrument has two verniers, both may
be read and the average taken.
Measurement by Repetition. A more accurate meas-
urement may be had by turning the angle several times, tak-
ing the final reading, and dividing it by the number of
times the angle has been turned. If the final reading is
about 360°, possible errors in the graduation of the instru-
ment will have no effect on the angle read, and if later the
telescope is inverted and the angle turned in the opposite
direction from the first turning, other sources of error will
have been eliminated. The exact program for an obser-
vation of this kind is as follows :
a. Telescope direct.1
1. Clamp plates on zeros, and set on left station. Clamp
below.
2. Unclamp above and set on right station.
3. Unclamp below and set on left station.
4. Unclamp above and set on right station.
Continue until the desired number of turnings have been
made, when the final reading may be taken.
b. Telescope inverted.
1. Clamp plates on zeros and set on right station.
Clamp below.
2. Unclamp above and set on left station.
3. Unclamp below and set on right station.
4. Unclamp above and set on left station.
Continue for the same number of turnings as before
1 That is, with the level tube underneath the telescope.
82 A MANUAL FOR NORTHERN WOODSMEN
and read the final angle. If the instrument has two ver-
niers both should be read. It is customary to record the
reading after turning the angle once, as a check on
the repeated reading. The true reading is the average of
the values obtained for the angle with telescope direct
and telescope inverted.
To Prolong a Straight Line. Set up the instrument over
the forward point and sight the telescope on. the rear one.
Set both clamps, revolve the telescope on its axis, and set a
new point as far ahead as convenient or desired.
More Accurately. With the telescope in its natural
position, turn on the rear point, clamp, revolve the tele-
scope as above, and set a stake and tack at the forward
pointing. Then, leaving the telescope inverted as it is,
swing the plates around half a circle and set on the rear
point again. Revolve the telescope, and again sight at
the forward point. If the two pointings ahead do not
coincide, set a tack half-way between the two and it will
be in the line desired.
To Measure a Vertical Angle. For this purpose the ver-
tical circle must be adjusted so as to read zero when the
telescope is level, or, if it is not adjustable, the error of its
reading must be obtained, as explained under adjustments
of the transit. Then the angle of elevation or depression
to any point may be measured by sighting the telescope
upon it and reading the vertical angle by means of the
vertical circle and its vernier.
To Survey a Piece of Ground with the Transit. Set
up on the initial point of the survey, turn to the second
point, read the bearing of the line, recording it for a check
on later angles, and measure the line. Set up over the
second point, set the two plates to read zero, and clamp
them together; then turn the telescope at a rod held ver-
tical and carefully centered over the first point. Set the
lower clamp and loosen the upper one, swing the tele-
scope with the upper plate around until the third point is
sighted, and read the angle so turned. Head the bearing
for a check, and measure the line. Proceed in this way
until all the angles have been turned and all the sides
measured. Interior angles should always be read, though
THE TRANSIT 83
they may be more than 180°. The magnetic bearings
may be used to figure out the angles as a check on
measurement; they also help to locate an error if one
exists, but a more accurate check is the sum of all the
angles which should equal twice as many right angles
less four as the figure has sides.
Computed bearings are worked out by applying the
angle measurements to the bearing of the first line. Com-
puted, not observed, bearings should be used for plotting
or for computing traverse. Notes may be kept as follows:
/Votes of -Survey of F/e/cf
Sfa.
Inf. Any /e
Oiserux/
ffear/ny
Computed
Bear/ry
D/sfance.
o
N8/°£
M8I°£
JJ8.63fh
1
aea" /9'
A/8'JS'W
/V8"/9'W
48 J3 "
a
af°32'
N7S45E
/V75°49'£
300.53"
3
85° /Z'
S9°30'E
S9°23'E
183.60 "
4
eras'
S79°/JW
S799W
813.96"
J
86°J6'
A/7"4S'W
A/7*47'W
134.85"
0
9l°/3'
M8/°£
48.19'
819.96'
SKETCH OP SURVEY
Instead of interior angles, deflection angles may be
read, a deflection angle being the angle which any course
makes with the prolongation of the one preceding. To
get this, after the instrument has been turned on the rear
point, revolve the telescope on its axis and turn to the point
ahead. The deflection must be recorded as right or left,
A MANUAL FOR NORTHERN WOODSMEN
along with the amount of the deflection. Notes may be
kept as follows:
Instr.
at
Deflection
Angle
Observed
Bearing
Computed
Bearing
Distance
0
N. 81° E.
K.WE.
518.63 ft.
1
89° l^L.
N. 8° 15' W.
N. 8° 19' W.
48.19 ft,
2
84° 8'R.
N. 75° 45' E.
N. 75° 49' E.
300.53 ft.
In any case, a sketch kept on the right-hand page of the
note book will be an aid to clearness. The whole survey,
indeed, may be recorded in that form.
A Survey or Traverse by Azimuths. Azimuth is the
angle which a line forms with the meridian, or with any
other line which is selected as a basis. It is similar to bear-
ing, but is measured in one direction, commonly from
south around through west, north, and east up to 360°, and
transits are commonly graduated so as to be read directly
in this way. The method of work is as follows :
Set up on the initial point of the survey, set the zeros of
the two plates together, clamp them, and turn until the
telescope points south, as shown by the needle. Clamp
below, loosen above, and point the telescope at the second
point of the survey, recording the angular reading, and the
bearing for a check upon it. Clamp above and loosen
below. Measure the line.
Set up over the second point, revolve the telescope, and
turn on the first point, making sure not to start the upper
clamp at any time during the process. Clamp below ; then
revolve the telescope into its natural position, loosen above,
and turn on the third point of the survey. The azimuth of
this line may now be read off the plate and bearing by the
needle for a check. Measure the second line. Proceed in
this way until the survey is completed. If the survey is a
closed one, when the transit is finally set up again at the
initial point, the azimuth of the first line should be the
same as it was at the beginning.
THE TRANSIT
Notes may be kept as follows:
85
Line
Azimuth
Bearing
Distance
A — B
162° 12' 30"
N. 17° 45' W.
6.40 ch.
B — C
223° 30'
N. 43° 30' E.
7.25 ch.
C — D
280° 25'
S. 79° 30' E.
4.92 ch.
D— E
5° 43' 30"
S. 5° 45' W.
6.10 ch.
Caution. In transit surveying, where angles are read,
each line is referred to the one that goes before, and in
consequence an error in reading one angle is perpetuated
throughout the survey. Further than that, some of the
errors arising from lack of adjustment of the instrument
are multiplying errors, increasing as the work proceeds,
and unless every precaution is taken they may, though
individually small, mount up to a very considerable size
in the course of a survey.
With compass surveying, on the other hand, though
bearings cannot be read with great exactness and single
angles are not so accurately determined as with the transit,
yet errors have not the same opportunity to accumulate
because each course in the survey is referred anew to the
meridian.
The man who is not in constant practice, therefore, will
be likely to find that he attains better results with the
needle than by turning angles, and in that case, unless the
telescope is wanted for stadia measurements, the compass
is the instrument to use. The matter of cost is, in woods
conditions, strongly on the side of the compass, for it is
usually expensive to cut away for the long, clear sights
requisite to the running of a reliable transit line.
Typical examples of stadia surveys such as the woods-
man may have occasion to perform are as follows:
Stadia Survey of a Pond as carried out on the ice.
The needle was relied on in this case, but it will readily be
understood that angles might be read instead of bearings
and the survey so rendered independent of the magnetic
needle. If the survey were to be made in summer, points
86
A MANUAL FOR NORTHERN WOODSMEN
and islands would have to be used for observing stations,
and it might be necessary to do a good deal of traversing
of the shore.
Base lines read on fore and
back sight for check
Shots to locate shore
Stadia Survey of Road. 1 foot on rod cut off at dis-
tance of one chain. Instrument set up at alternate stations
only, except where a check on local attraction of the needle
is desired. Vertical angles of less than 5° neglected as hav-
ing no material effect on horizontal distance.
Bear/^g
Oist
RemarAs
o-l
1-0
3-2.
3-4-
S-4-
S-6
7-6
7-8
3-8
9-JO
10-3
578°30£
Z.30
2..30
6./6
/JO
6.S2
S.30
6./O
e.&
3.SO
9. SO
ZAOch
tffi,rOH!£A
' t>< eaf/e.
-2'
6./0"
8./S'
3.60'
9.50"
Sfa. O 0/7 WsssA///7» offrocf /mf/e.
J~6. S c/ra/rrs •So. on //• as •S/roiv/r t>y
Surrey of 6>ot//fafary
These courses a/o/y Sotr/& stye
onfo shoulder com/ry fron N£
2.4S on this course t>n*>A crosses
Test of sreecf/e.
THE LEVEL 87
5. SUMMARY
The transit of late years has gained a considerable field
of use among working foresters for map making and other
purposes. The instrument has for woods work great
advantages over the plane table in that it is more portable,
is less liable to accident, and is not so easily driven off the
field by bad weather.
The uses for it, present and prospective, are as follows:
(1) It is the instrument for land surveys when great ac-
curacy is required or the needle is seriously disturbed.
When it is so employed the stadia wires in some cases
afford the most effective means of distance measurement.
(2) It may be used as a level in dam and road building
or for topographic purposes.
(3) Two men using transit and stadia can traverse roads,
streams, or lake shores very rapidly, using the needle and,
except for a check on local attraction, setting up the instru-
ment on alternate points only.
(4) Uses (2) and (3) may be combined, allowing a
traverse and a profile to be run at the same time by the
same party.
(5) A skeleton of accurately run lines, embracing both
horizontal and vertical angles, may be made the basis of
topographic surveys, and the method is in fact highly
serviceable in some kinds of country.
(6) With its various capacities again utilized, the
transit is sometimes employed to work out the detail
of small tracts requiring great accuracy.
SECTION II
THE LEVEL
The engineer's level consists of a telescopic line of sight
joined to a spirit level, the whole properly supported, and
revolving on a vertical axis. The outside parts of the frame
which support the telescope are called the wyes, and the
88 A MANUAL FOR NORTHERN WOODSMEN
corresponding bearings on the telescope tube, the pivot
rings. The telescope can be lifted out of the wyes by lift-
ing up the clips over the rings. The attached bubble
enables the line of sight in the telescope to be brought
into a horizontal position.
THE LEVEL
1. ADJUSTMENTS OF THE LEVEL
(a.) Make the line of sight coincide with the axis of
the pivot rings. Pull out the pins which hold the clips on
the telescope and turn the clips back so that the telescope
is free to turn in the wyes. Sight the intersection of the
cross-hairs at some well-defined point. Then rotate the
telescope 180° in the wyes, so that the bubble tube is above
the telescope. The intersection of the cross-hairs should
still be on the point. If not, move the horizontal cross-
hair half-way back to its first position by means of the
upper and lower adjusting screws of the cross-hair ring.
Then move the vertical cross-hair half-way back to its
first position by the other pair of screws. Repeat the test
until the adjustment is perfect.
(b.) Place the line of sight and the bubble in the same
vertical plane. Bring the bubble to the center of the tube.
Revolve the telescope a few degrees in the wyes and note
the action of the bubble. If it runs to one end, bring the
tube under the axis of the telescope by means of the lateral
THE LEVEL OV
adjusting screws. When the two axes are in the same
plane, the bubble will remain in the center while the
telescope is revolving.
(c.) Make the level tube parallel to the line of sight.
This may be done in two ways. The first or indirect
method is as follows :
Clamp the instrument over a pair of levelling screws ;
then bring the bubble to the center of the tube, lift the tele-
scope out of the wyes, turn it end for end, and set it down
in the wyes again. The eye end now is where the objective
was originally. This operation must be performed with
the greatest care, as the slightest jar of the instrument will
vitiate the result. If the bubble returns to the center of the
tube the axis of the tube is in the correct position. If it does
not return to the center, the end of the tube provided with
the vertical adjustment should be moved until the bubble
moves half-way back to the center. This test must be
repeated to make sure that the movement is due to defec-
tive adjustment and not to the jarring of the instrument.
For the second, the direct or peg adjustment, select the
points A and B, say 200 feet apart. The distance need not
be measured. Set up the level close to A so that when the
rod is held upon it the eyepiece of the telescope will swing
within about half an inch of its face. Bring the bubble to
the middle of the tube and looking through the telescope
wrong end to, put a pencil mark on the rod at the center
of the small field of view. Note the rod reading thus ob-
tained. Then turn the telescope toward B and take a rod
reading in the usual way, making sure that the bubble is
in the middle of the tube. The difference between these
two rod readings is the difference in elevation of the two
points + or — the error of adjustment. Next take the
level to B and repeat the above operation. The result here
gained is the difference in elevation — or + the error
of adjustment, and the mean of the two results is the differ-
ence of elevation between points A and B. Now, knowing
the difference between A and B and the height of the in-
strument above B, the rod reading at A which will bring
the target on the same level as the instrument may be com-
puted. With the horizontal cross-hair on the target, the
90 A MANUAL FOR NORTHERN WOODSMEN
adjustable end of the level tube is raised or lowered by
means of the adjusting screws until the bubble is in the
middle. The adjustment should then be correct, but it
will be well to test it.
EXAMPLE
Instrument at A
Rod reading on A = 4.062
Rod reading on B = 5.129
Diff. elev. of A and B = 1.067
Instrument at B
Rod reading on B = 5.076
Rod reading on A = 4.127
Diff. elev. of B and A = 0.949
Mean of the two results = 1.067 +0.949 = 1.008, true diff. in elev.
2
Instrument is now 5.076 above B.
Rod reading at A should be 5.076 — 1.008 = 4.068 to give a level
sight.
This method of adjustment may be used for the transit
with this difference — that instead of adjusting the level
tube to the line of sight, the level tube is first made hori-
zontal and then the line of sight is made parallel with it
by adjusting the cross-hair. The same is true of a dumpy-
level.
(d.) Make the axis of the level tube perpendicular to
the vertical axis of the instrument.
Bring the two clips down over the telescope and fasten
them. Level the instrument, bring the bubble precisely to
the middle of the tube over one set of levelling screws, and
then turn the telescope 180° about the vertical axis. If
the 'bubble moves from the center, bring it half-way back
by means of the adjusting screws at the foot of one of the
wye supports.
Since the bubble is brought to the center of the tube each
time a rod reading is taken, this last adjustment in no way
affects the accuracy of levelling work, but it is a con-
venience and a saving of time.
2. USE OF THE LEVEL
Levelling is employed to get the difference in elevation
between points. With the level set up and the rod held on
THE LEVEL
91
a point whose elevation is known or assumed, the reading
that is obtained is called a (+) or backsight. Similarly,
a reading on a point ahead or unknown is called a (— ) or
foresight. A point occupied by the rod in this way, but
not recorded or used further, is called a turning-point.
When two points have been connected by a series of read-
ings of this kind, the sum of the backsights minus the sum
of the foresights gives the difference in elevation. If the
backsights are greater, the second point is the higher of the
two. If the foresights are greater, it is the lower. A brief
set of notes is given and worked out illustrating this
matter. Work of this kind is called differential levelling.
B.S.
F.S.
Remarks
9.52'
10.12'
4.45'
3.27'
.B.S. onto B.M. of previous
survey.
8.56'
1.01'
7.40'
5.71'
3.65'
8.62'
F.S. to pond level required.
Pond is above B. M.
39.25'
23.06'
23.06'
16.19'
When levelling is employed to get the elevation of a
large number of points in a region, several or many fore-
sights may be taken from one position of the instrument.
It is customary then to note the height of instrument, and
the elevation of any point observed will be that height
less the foresight to the point.
A benchmark is a point whose elevation has been deter-
mined and which is marked and left for reference. It is
noted B. M. in level notes.
The following set of notes illustrates those commonly
kept in running profiles of a road or railway. The form
may be easily modified for any other class of work.
Summary. Levelling is comparatively simple work.
Even though a level is somewhat out of adjustment, accu-
A MANUAL FOR NORTHERN WOODSMEN
rate results may nevertheless be had by taking backward
and forward sights of equal length, and this check it is easy
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to secure by pacing. It is important that the rod should
be held plumb during the levelling operation. This position
is secured by careful attention on the part of the rodman
and by waving the rod slightly. The length of sight varies
with the instrument, the condition of the air, and the ac-
curacy desired. About 300 feet is stated to be in general
the best length on the score of accuracy, but speed will
often require that much longer shots be taken. In accu-
rate work, it should be remembered that error may be
introduced by the slightest causes, such as disturbance of
the tripod.
Levelling is employed by woodsmen in constructing
dams and ascertaining the area of flowage, in laying out
roads and railroads, and for the basis of topographic work.
COMBINED HAND LEVEL AND CLINOMETER 93
For these uses a light and cheap form of the level, some-
times called the architect's level, costing about half as
much as one adapted to railway work, is commonly
sufficient.
SECTION III
COMBINED HAND LEVEL AND CLINOMETER
A pocket instrument capable of a great variety of uses
is shown in the accompanying figure. The eye is placed
at a peep hole at the right end (a) of the main tube.
The cross-wire is over (6) in the figure, and beside it,
occupying half the orifice of the tube, is a mirror set at
an angle of 45°. Directly over the wire and mirror is a
spirit tube (c), shown inclined in the figure. It is fixed to
the milled wheel (d) which turns it, and the graduated
arm (e), which serves to set the bubble parallel to the
line of sight of the instrument, or to read the angle of
inclination between them. When the bubble is in the
center of the tube, the mirror below reflects it side by
side with the cross-wire back through the peep hole.
This instrument is largely used by northwestern lum-
bermen in laying out roads, locating dams, etc., and it
ought to be in the outfit of every woodsman. To use it
as a hand level the zeros of the graduated arm and the
scale must first be set together. The observer then sights
an object through the tube, which he brings to a level
by the bubble reflected in the mirror. He may then place
himself on a level with the object by sighting at it directly,
94 A MANUAL FOR NORTHERN WOODSMEN
or, if difference in elevation is required, a pole or level rod
may be used to measure the amount.
The instrument may be used to find the difference in
elevation between any two points without the use of a
level rod. To 'do this the observer begins at the lower
point, and, after levelling the instrument, sights in the
desired direction and notes the point on the ground ahead
intersected by the cross-wire. He then advances to that
point and repeats the operation, and so moves on up the
grade until the upper point is reached. As between every
two observations he has advanced to a height equal to the
distance from the ground to his eye, the height of the hill
will be the product of that distance by the number of
sights taken.
The instrument may also be used as a clinometer to
measure slope. To do this the observer sights along the
slope parallel to the ground, and then uses the hand wheel
to turn the level tube until the bubble shows it is level.
The measuring arm, turning with the wheel and the level,
sweeps the scale and indicates the slope in degrees, or in
per cents, according as the instrument is graduated.
In the same way, and with the aid of a table of tangents,
one may use the instrument to obtain the height of a tree
or a hill. This process is explained and illustrated on
page 166.
For an improved form and more complicated use of
the instrument, see pages 130-131.
SECTION IV
COMPASS AND PACING
The staff compass, with folding sights, cross levels, and
a needle from 2| to 4 inches long, is familiar to most
woodsmen. It is a very compact and practical instrument,
has long been employed for retracing lines, and of late
years, as forest lands have come to be handled more
systematically, has attained a great extent and variety of
uses. It has also been constructed in a variety of forms,
combined with other instruments in some cases. The form
COMPASS AND PACING 95
shown in illustration is the pattern of the U. S. Forest
Service. The base is flat so that the instrument may be
used to orient a plane table — it is square also and gradu-
ated on its edges with a protractor and two scales for draft-
ing purposes; declination can be set off by means of a
vernier; inside the box a pendulum is fitted and the staff
mountings permit of turning the instrument and holding
it edgewise while employed as a level or clinometer.
STAFF COMPASS
A main use for the staff compass in topographical and
timber work is for making foot traverses, a purpose for
which it is thoroughly adapted. The common pocket
compass with needle If to 2 inches long, indeed, may be
used for the same purpose, and when it .enables a man to
travel a mile with only 1° or 2° of angular swing, as it
will do if carefully used, it deserves to be called a surveying
instrument.
Pacing. The pace has been long used as a check on
short distances, but the real capacity of pacing as a method
of measurement has only recently been developed. It
is of special value to woodsmen who must travel their
country over in any case, and who by a little extra pains
taken in this direction can bring out much valuable infor-
96
A MANUAL FOR NORTHERN WOODSMEN
mation. As against chaining, pacing has the advantage
of cheapness, it can be done by one man alone, and its
accuracy is frequently quite sufficient.
The natural gait of the woodsman should be tested on
measured lines and in pacing for distance he should always
walk at his natural gait, not try to take a three-foot stride.
The slope of the ground, if it is considerable, affects the
length of step ; the step is shortened whether one goes up
or down hill.
This matter has been investigated accurately and the
results of one extensive test are given in the table below,
INFLUENCE OF SLOPE ON LENGTH OF PACE AS TESTED
Otf MOUNTAIN TRAILS
Slope
Length of step ascending
Length of step descending
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 "
when nothing seems to go right. Keeping the count also
is a source of frequent error. Woods travel is too uneven
COMPASS AND PACING 97
as a rule to allow a pedometer to be employed. Some
men register double paces. Others count up to a hundred
in the head and take down the hundreds on a "clicker,"
in a note book, or by breaking an elbow in a tough twig
carried in the teeth or hand.
Accuracy. With all its limitations, pacing is a very ser-
viceable means of measurement and a man who has duly
trained himself can get very good results. Johnson's
" Surveying " says, that when a man's gait has been stand-
ardized and on the work he walks at a constant rate, " dis-
tances can be determined by pedometer or by counting the
paces to within 2 per cent of the truth." That refers,
without doubt, to open land. In woods work too there
Section Lines
Compass Bearings
Pacing Traverses .
POND SURVEYED FROM SECTION LINES BY CROSS BEARINGS AND THE
COMPASS AND PACING METHOD
are many men who can be depended on for results as clbse
as that, but errors up to 5 per cent in a straight mile on
uneven land is for the writer the usual standard of work.
This is not serious. When the error is distributed over the
mile by plotting, the utmost probable error in the location
of any point is not over 25 yards.
Uses of the Method. (1) The staff compass is largely
used in retracing old lines. Pacing may well be employed
with it as a means of finding blind marks and corners, for
this purpose replacing the chain.
98 A MANUAL FOR NORTHERN WOODSMEN
(2) In timber estimating, the area of waste lands, heavy
bodies of timber, etc., can often be obtained quickly and
with a fair degree of accuracy by this method, and these
facts often furnish very great help in securing a close
estimate.
(3) The compass and pacing method is the cheapest for
mapping roads, streams, ponds, and other topographic
details in wooded country. For a real map, however,
this method of survey should not cover too long distances,
but should tie into more accurate work.
(4) Compass and pacing may be used to get a recon-
noissance map of a region of any size, using a road or any
other avenue of travel that passes through it. Not only
the line of travel may be mapped, but the hills and other
features of the country that can be seen. Cross bearings
with the compass will locate them in the horizontal posi-
tion, and the clinometer will serve to get their height.
Specimen notes illustrating this method of work com-
bined with the use of the aneroid barometer for determin-
ing height, and a diagram showing how it is made to
contribute to the production of a topographic map will
be found on pages 130-132.
SECTION V
THE TRAVERSE BOARD
The plane table in its simplest form is called a traverse
board, and consists of a square board without levels
mounted on a tripod. On this board a sheet of paper
is pinned, and the map is developed in the field. A
compass needle set into the edge of the board serves to
" orient " it, or, in other words, to fix one edge always in
the north and south position. A brass ruler with vertical
sights attached serves both to sight with and to draw lines
and scale off distances on the map. It is called an
alidade.
A simple use for the board is to traverse a road, a
stream, or the shore of a pond. Suppose, for instance, it is
desired to survey a stream on the ice in winter, and a point
THE TRAVERSE BOARD
99
on it is known by the crossing of a section line. The
instrument should be set up at the known point, with one
edge of the board set north and south as shown by the
needle. A point is then chosen on the sheet to represent
the one occupied on the ground, the edge of the ruler is
swung about it until the sights range- toward the second
point to be occupied, say the next turn of the stream, and
TRAVERSE BOARD
a line is drawn in its direction. The distance between the
two points is then chained or paced, and when this has
been scaled off a second point on the map is obtained.
The board must then be set up at the new point and
oriented as before, when, the ruler being swung about the
new point, a ray may be drawn from it to a third, and
so on. Little difficulty will be experienced by one who
understands compass surveying in working this instru-
ment. A point on the sheet always represents the point
occupied, and that is always the point to work from.
The map is carried to completion right in the field and
that, as regards both cost and accuracy, constitutes the
advantage of the method.
100 A MANUAL FOR NORTHERN WOODSMEN
Another method of working is by intersections. For
this, it is necessary to have two known points or a measured
base. The instrument is set up at one of the known
points, and, the alidade being pointed at the other, a line
Plane Table Map
ROUND LAKE
Washington Co.
Maine
C. A. Gary 1907
Area 343 Acres
. Scale of Feet
1500 2000 2500
is drawn and the known distance scaled off upon it.
Then, from that end of the base line representing the
point occupied, rays are drawn in the direction of other
well-defined objects on the shore which it will be desir-
able to locate. Flags may be used to define them, but
natural objects will often suffice. The instrument is then
THE TRAVERSE BOARD
101
taken to the other known point, and set up by the range
back to the first. Then swinging the ruler about the
second point located on the sheet, the surveyor draws
rays from this to the same objects as before. The in-
tersection of pairs of rays directed toward the same object
in the field fixes that point upon the map. This is done
directly and graphically, no computation or reduction
being required.
More complicated forms of the instrument, telescopic
alidades, the application of the vertical angle, etc., need
not be here discussed, as they are hardly likely to be em-
ployed by other than specialists. It seems likely, how-
ever, that among a large class of foresters and woodsmen
this simple form of the plane table will find general use.
The following survey of a small lake made with the
traverse board involves a somewhat . more complicated
use of the instrument than that described above. This
particular piece of work took the time of two men for two
days, but on the ice it could have been done more quickly.
The steps in making, the survey were as follows :
1. Base line A B measured, the longest straight line
that could be had on the shore and in wading depth of
water. Flags set up at its ends and at C, D, E, F, and G,
prominent points on the shore visible from both ends of
the base line.
2. Plane table set up at A as oriented by the needle.
Point a selected on the paper, line drawn from it in direc-
tion of B and a b measured to scale. Rays a c, a d, a e, a f,
a g drawn in direction of C, D, E, F, and G.
Board at A Board at B
3. Table set up at B, oriented by ranging b a at A and
checked by the needle. Rays drawn from b toward C and
102 A MANUAL FOR NORTHERN WOODSMEN
D. These where they intersect corresponding rays from
a fix points c and d. Rays also drawn toward E, F, and
G, but the angles made with the corresponding rays from a
are so small that these points are not given a good location.
4. Board taken to C and oriented by A and B. Check
ray drawn to d. Rays toward E, F, and G, intersecting
similar rays from a, fix e, /, and g.
Board at C
Board at D
5. Board taken to D and similar process performed for
a check. E, F, and G may also be checked with one
another.
6. Fix other points on the shore such as prominent
rocks or trees.
(a) By intersecting rays from any two of the primary
points in the same manner as these were fixed.
(6) By drawing a ray from one of the primary points as
c toward any object as X, setting up at X, using c x to
orient by, and then fixing a; by a ray brought back in the
range A a until it cuts c x.
Board at X
Board at Y
(c) By setting up the board on any desired point on the
shore as Y, oriented by the needle, and ranging back from
THE ANEROID BAROMETER
103
any two flags or fixed points, through the corresponding
points on paper, to an intersection which will fix the
point occupied.
7. Fill in the shore line as the other work progresses,
whatever at the time is nearest the instrument, by traverses,
sketching, etc.
SECTION VI
THE ANEROID BAROMETER
The aneroid barometer is a cheap and handy instrument
which, when carried from one point to another, will tell
approximately their difference in height. This it does by
measuring the pressure of the air, varying as that does
when one goes up or
down hill. .
The essential parts
of an aneroid bar-
ometer are out of
sight. The instru-
ment consists of a
vacuum box with one
very flexible and sen-
sitive side, which
works in and out
with varying pres-
sure of the air. This
slight movement is
multiplied, and con-
verted into the cir-
cular motion of the
pointing hand seen
on the face of the
instrument. At sea
level the hand points
to one part of the ANEROID BAROMETER
dial. As the instru-
ment is carried up a hill or mountain the hand, worked by
expansion of the box within, turns round to the left. The
104 A MANUAL FOR NORTHERN WOODSMEN
face is graduated to correspond with the height of column of
a mercurial barometer, 30, 29, 28, etc., inches, these even
inches being divided into fractional parts.
This change in pressure corresponds with definite change
in altitude. One inch on the scale means roughly 900 feet
in altitude; a half inch means 450 feet, and so on. As
a matter of fact, there is a foot scale on most aneroids
outside the inch scale, movable and graduated from zero
up to the capacity of the instrument. Thus, if one knows
how high he is above sea level, he may turn the foot scale
of his instrument until the registering hand points to that
height, and, going either up or down hill, read directly the
elevation of any station which he may occupy.
Just this process answers many purposes, but when best
results are sought for, the operation is not quite so simple.
First, there is the Correction fer the Temperature of the
Air. An inch difference in pressure at a tejnperature of
32°, for instance, converted into height, means one thing;
at 70° it means a good deal more. In order to get accu-
rate results, therefore, on considerable elevations, it is
necessary to read the inner or inch scale of the instrument,
take the temperature of the air at the two points, and
obtain the elevation from tables. Such tables will be
found on pages 111 and 112 and full directions for their
use accompany them.
Correction for Weather Change. The other liability to
error arises from the fact that the air pressure is frequently
changing with the weather. This does not hamper work
seriously in the western country where the weather and
pressure remain steady for long periods at a time, but diffi-
culty does arise from this source throughout the East.
With an approaching storm the air grows lighter, and the
reverse in clearing weather. This effect is best seen on a
stationary barometer, but it has a like effect on one that
is in motion. Thus, if an explorer starts at a lake of known
elevation and takes two hours in going to the top of a hill,
the air pressure meanwhile may have changed so as to
throw his height readings off materially.
There are three ways of obviating this, outside the evi-
dent one of working only in steady weather. One is to
THE ANEROID BAROMETER
105
return to the lake and take a second reading, using the
average of the two to compare with that observed at the
summit. A second, often available in cruising timber, is
to read on the same point two or more times during the
day and so ascertain the course of the barometer. The
third method of correction is by means of another instru-
ment which is left at the base station or some other
convenient point, and read by another person every hour
or half hour while the observer is in the field. Since in
ordinary weather the air changes are the same over large
areas, this arrangement tells what the field barometer
would have read on the base station at any hour during
the day. Better than this, however, is a self-recording
barometer, or barograph, which makes a continuous record
of pressure. The explorer compares his pocket instru-
AROGRAPH
ment with this as he starts out on his work, and again
when he comes in. If these comparisons are satisfactory,
he has the means of telling what his field instrument would
have read on the base station at any time while he was
gone, and so obtains the correct figure for comparison
with any given field observation. This arrangement en-
ables him to stay away from known elevations half a day
106 A MANUAL FOR NORTHERN WOODSMEN
or a day at a time and still make fairly satisfactory height
determinations.
This is all good in theory, but it must be said that in
practice it does not always work out to one's entire sat-
isfaction. The air, in the first place, is not the homoge-
neous fluid that it has been considered, but varies more or
less from point to point. Then aneroids are not sure in
their workings. Different instruments of the same make
and cost vary greatly in reliability, and the observer needs
to watch the best of them to see that they do not get out
of order or play some kind of a trick. Barographs, again,
are not thoroughly reliable. In particular, some of them
do not follow the changes in pressure as fast as the port-
able instrument. Nevertheless, trial has shown that by
the methods outlined sufficiently accurate results for many
purposes can be obtained. In general it may be said of
aneroid work that, while it cannot be counted on for re-
fined accuracy, there is a large field open to it of good,
useful work which no other instrument, on account of con-
siderations of cost, can do. It is particularly serviceable in
a timbered country where it is difficult to see from point to
point, having there the same sort of advantage that the
compass possesses in the same field.
Aneroids for ordinary work should be 2$ to 3 inches in
diameter, graduated to the equivalent of 20 feet, and have
as open a scale as may be. Such instruments cost from
$20 to $35. For the finer class of work it may be advisable
to employ a larger and more delicate instrument furnished
with a vernier. A barograph costs from $40 to $50. Ther-
mometers suitable for the work, in a nickel or rubber case
about the size of a lead pencil, can be had for $.50 to $1
each.
The following Working Rules have grown out of the
experience of the writer and others :
1. Each instrument should be tested not only under
the air pump but for general behavior in the field.
2. The best place to carry an aneroid while at woods
work is in a leather case hung on the belt. The case serves
to protect it trom damage, also from extreme heat and
rapid changes of tempera turfc.
THE ANEROID BAROMETER 107
3. Any considerable blow is likely to throw the instru-
ment out of order for the time being, if not permanently.
Two instruments carried are a considerable insurance.
4. The aneroid should always be held in the same posi-
tion when read, and be given a little time to adjust itself.
By gentle tapping on the face the observer should assure
himself that its various parts are all free and in working
order.
5. In starting out for work it is well to carry the instru-
ment a while, so as to get it into its regular field working
order, before reading on the base station.
6. One should check on points of known elevation as
often as possible, and, if there is a choice of readings to
refer to, he should depend on that which is nearer, time
and elevation both considered.
7. A general caution may be needed that the proper
use of the instrument is to obtain relative elevation of
points by means of readings on the two. One must not
expect by one reading to obtain his height above sea
level.
REDUCTION OF ANEROID READINGS BY USE OF THE
TABLES AND WITH CORRECTION FOR TEMPERATURE
AND WEATHER CHANGES
(See tables on pages 111 and 112)
PROBLEM I. — Given barometric readings on two stations
and temperature at each, to find the difference in elevation
of the two points.
Rule. — Enter the first column of Table I with the read-
ings of the barometer on the two stations, and take out the
corresponding numbers from column 2 (column 3 is for
help in interpolating). Take the difference between these
two figures. Call this result for the present a.
Add the two temperatures together (or if the tempera-
tures of the two stations do not differ materially, multiply
that of the region by two). With this enter Table II, that
for temperature correction, and find in dolumn 1 the near-
est number of degrees given. Take out of column 2 the
number corresponding, noting the + or — sign, and
108 A MANUAL FOR NORTHERN WOODSMEN
multiply a above by this percentage. Let us call this b.
If b has a plus sign, add it to a; if a minus sign, subtract
from a. The result will be the desired elevation.
Example. — The barometric reading on a lake of known
elevation is 29.500 inches, and the temperature there 72° F.
Shortly after, the reading on a hill not far away is found to
be 28.760 and the temperature 63°. How high is the
hilltop above the lake ?
From Table I we have
Barometric elevation of hill 1150 feet
Barometric elevation of lake 458 feet
Difference (a above) 692 feet
From Table II we have for t + t' = 135°, C = + .042.
6 therefore = 692 X .042, is = 29 feet. This must be
added to a, since the sign of the factor is +, and the
result (692 +29= 721) gives 721 feet as the required
answer.
A short cut to the same result, which is accurate enough
and which will save much labor in reducing a number of
readings referred to the same base station, is as follows:
Between 29.500 and 28.760 inches the difference of eleva-
tion corresponding to .1 inch pressure is 94 feet. This
is obtained instantly by inspection of column 3 of Table
I. Stated another way, the difference of elevation in feet
is 6 per cent less than the difference between barometric
readings expressed in thousandths of an inch. But the
temperature correction for the conditions is + 4 per cent,
leaving a net loss of 2 per cent on the difference in the
barometric readings.
Now 29.500- 28.760= .740, and 740- 2 per cent =
725. Answer, 725 feet.
PROBLEM II. — To correct for changes of pressure due
to the weather, as shown by regular readings on a station
barometer or the record of a barograph.
The barograph sheet reproduced herewith shows for
the working hours of that Friday a steady fall of pressure.
At 6.30 in the morning when the party left camp the
indicated pressure was 29.250 inches. When they got in
THE ANEROID BAROMETER
109
at 5 P. M. it was 29.160. That difference in pressure
corresponds to nearly 150 feet in elevation, and height
observations made during the day would be uncertain to
very wide limits if the change could not be allowed for.
THURSDA Y FRIDA Y
8 1,0 yT 2 4 6 8 10 XII 2468 10/jfT2 468 10 XII 2 4 6 8 1.0OT 2
7/7 ////////// / / //////////////
±±
\\\\\\\\
The possibility of correction rests in two suppositions:
(1) that at any moment of time the air pressure is constant
over a considerable horizontal area, and (2) that the field
barometer and the station barometer work together, and
that they both follow exactly and quickly the change of air
pressure. The latter point may be expressed in this way —
that the field barometer, if left at the base station, would
have followed the same course as did the instrument which
in fact was left there.
The field barometer may not read the same as the
barograph when they are brought together, but that
" index error," as it is called, does not matter if the differ-
ence between the two remains constant. In this case the
field barometer at camp in the morning read 29.350 and at
night 29.200, .1 inch higher than the barograph. One
may, therefore, when he gets to computing, draw on the
110 ' A MANUAL FOR NORTHERN WOODSMEN
barograph sheet a curve through these two new points
and parallel to the one made by the barograph pen.
From this curve he may take off the reading for any hour
in the day to compare with a field reading taken at the
same time. Such a supplementing curve is shown on the
sheet illustrated.
Example. — At 11 A. M. on the day in question at a
point two miles away from camp the field barometer
read 29.270. What was the elevation relative to the base
station ?
The field reading can not be compared with the morning
reading at camp because the barometric pressure is known
to have been changing. Neither can it be compared with
the night reading, for the same reason. The short curve
on the sheet, however, does tell what the field instrument
would presumably have read at camp at any hour in the
day. The curve at 11 A. M. is at 29.270, and the two points,
therefore, are of equal elevation.
In view of the low accuracy of aneroid work, different
users of the instrument have devised schemes for shorten-
ing or obviating the labor of computation. One that is
serviceable where temperature at different seasons shows
wide variation is as follows:
On the foot scale of most instruments 1000 feet at the
higher elevations will be found to occupy a smaller sector
on the scale than 1000 feet at low elevations — as 5000-
6000 as against 0-1000. This can be tested by comparing
against identical marks on the inner scale.
Now, being at a known or assumed elevation, set the
corresponding graduation against the movable hand and
observe where the thousand-foot marks above and below
cut the inner or inch scale; next, take the values so ob-
tained and compute difference of elevation accurately,
correcting for temperature. If the result obtained varies
seriously from 1000 feet, shift the foot scale by even
thousands until a portion is found so graduated that it
does correspond. With a constant correction of even
thousands, elevations may now be had directly. Correc-
tion is not thus made for weather changes, however.
THE ANEROID BAROMETER
111
TABLES FOR REDUCING READINGS OF THE ANEROID
BAROMETER1
I — Barometric Elevation
Reading
Inches
Elevation
Feet
Difference
for .01 inch
Feet
Reading
Inches
Elevation
Feet
Difference
for .01 inch
Feet
20.0
20.1
11047
10911
-13.6
23.4
23.5
6770
6654
—11.7
—11.6
20.2
20.3
10776
10642
—13.5
—13.4
23.6
23.7
6538
6423
-11.6
—11.5
20.4
10508
—13.4
23.8 •
6308
—11.5
20.5
10375
—13.3
23.9
6194
—11.4
20.6
20.7
10242
10110
—13.3
-13.2
24.0
24.1
6080
5967
—11.4
—11.3
20.8
20.9
9979
9848
—13.1
-13.1
24.2
24.3
5854
5741
—11.3
-11.3
21.0
9718
-13.0
24.4
5629
—11.2
21.1
9589
-12.9
24.5
5518
—11.1
21.2
9460
—12.9
24.6
5407
—11.1
21.3
9332
—12.8
24.7
5296
-11.1
21.4
9204
-12.8
24.8
5186
—11.0
21.5
21.6
9077
8951
—12.7
-12.6
24.9
25.0
5077
4968
—10.9
—10.9
21.7
8825
—12.6
25.1
4859
—10.9
21.8
8700
—12.5
25.2
4751
—10.8
21.9
8575
-12.5
25.3
4643
—10.8
22.0
8451
—12.4
25.4
4535
—10.7
22.1
22.2
8327
8204
—12.4
-12.3
25.5
25.6
4428
4321
—10.7
—10.6
22.3
8082
-12.2
25.7
4215
—10.6
22.4
7960
—12.2
25.8
4109
-10.5
22.5
22.6
7838
7717
—12.2
—12.1
25.9
26.0
4004
3899
—10.5
—10.5
22.7
22.8
7597
7477
—12.0
—12.0
26.1
26.2
3794
3690
—10.4
—10.4
22.9
23.0
23.1
7358
7239
7121
—11.9
—11.9
-11.8
26.3
26.4
26.5
3586
3483
3380
—10.3
—10.3
-10.3
23.2
23.3
7004
6887
—11.7
—11.7
26.6
26.7
3277
3175
—10.2
—10.2
t Taken from Johnson's "Surveying " and Report of U. S. Coast and
Geodetic Survey for 1881.
A MANtTAL FOR NORTHERN WOODSMEN
I — Barometer Elevation — continued.
Reading
Inches
Elevation
Feet
Difference
for .01 inch
Feet
Reading
Inches
Elevation
Feet
Difference
for .01 inch
Feet
26.8
3073
-10.1
28.7
1207
-9.5
26.9
2972
—10.1
28.8
1112
—9.4
27.0
2871
—10.1
28.9
1018
—9.4
27.1
2770
—10.0
29.0
924
—9.4
27.2
2670
—10.0
29.1
830
—9.4
27.3
2570
—10.0
29.2
736
—9.3
27.4
2470
-9.9
29.3
643
—9.3
27.5
2371
— 9.9
29.4
550
-9.2
27.6
2272
— 9.9
29.5
458
—9.2
27.7
2173
— 9.8
29.6
366
—9.2
27.8
2075
— 9.8
29.7
274
—9.2
27.9
1977
— 9.7
29.8
182
—9.1
28.0
1880
— 9.7
29.9
91
—9.1
28.1
1783
— 9.7
30.0
00
— 9.1
28.2
1686
— 9.7
30.1
-91
—9.0
28.3
1589
— 9.6
30.2
181
—9.0
28.4
1493
— 9.6
30.3
271
—9.0
28.5
1397
-9.5
30.4
361
—9.0
28.6
1302
— 9.5
30.5
—451
—9.0
II — Correction for Temperature in Degrees Fahrenheit
t + t'
C.
t+t'
C.
t+t'
C.
0°
—0.1025
60
—0.0380
120
+0.0262
53
-0.0970
65
—0.0326
125
+0.0315
10°
—0.0915
70
-0.0273
130
+0.0368
15°
— 0.0860
75
-0.0220
135
+ 0.0420
20°
— 0.0806
80
— 0.0166
140
+0.0472
25°
—0.0752
85
—0.0112
145
+ 0.0524
30°
— 0.0698
90
— 0.0058
150
+ 0.0575
35°
—0.0645
95
—0.0004
155
+0.0626
40°
— 0.0592
100
+ 0.0049
160
+ 0.0677
45°
— 0.0539
105
+0.0102
165
+ 0.0728
50°
—0.0486
110
+0.0156
170
+ 0.0779
55°
—0.0433
115
+0.0209
175
+ 0.0829
60°
-0.0380
120
+ 0.0262
180
+ 0.0879
METHODS OF MAP MAKING 113
SECTION VII
METHODS OF MAP MAKING
1 . INTRODUCTORY
There is a well defined call at the present time for good
maps of small forest areas — maps which show topo-
graphic features and record essential facts about timber
stand. With the consolidation of large forest properties
and their more careful and foresighted management, the
need is felt for good maps of these as well, and it is certain
that this demand will increase.
The maps of the past are of all grades of accuracy and
utility. A checkerboard of lot lines, with the waters
roughly laid down, and estimates of the stand of timber, is
the utmost that many lumber companies can command.
Some improve this by hatching to represent mountains and
divides, and by going more carefully into water lines and
areas.
Hatched Maps. The accompanying map represents part
of a township owned by a Maine lumber company, and is a
good example of a class of maps now having wide use. For
the purposes of the map and of administration, the township
was divided into sections, and as the lines were run, chain-
age was taken at the crossings of streams and main divides.
In addition, some cruising was done within the lots,
chiefly to ascertain the amount of timber. On this basis
the map was drawn. The course of streams is shown
approximately. Mountains and prominent ridges are
hatched in. Main existing roads may be put in roughly.
A map like this, with lines on the ground to correspond
with it, is of great service in the management of forest
property. Logging contracts can be let with clearly
defined boundaries; distance to haul is approximately
known ; in a rough way the nature of the ground is repre-
sented. It has, however, very evident limitations. Off
the section lines, it is all judgment or guesswork, and the
details of the country, such as have a very material effect
114 A MANUAL FOR NORTHERN WOODSMEN
on all operations, are not shown and cannot be shown with
that method of representation.
The cost of such a map is very slight over and above the
cost of the survey work in sectioning. That in the region
named commonly costs from $600 to $800 per township.
If a region is divided into sections or quarter-sections, a
good cruiser can produce a map like this as fast as he can
travel over the country.
Contour Maps. The actual shape of a country is best
represented by contour lines. A contour line is a line of
equal elevation, the line a man would follow if he traveled
round a country keeping at a constant height, or what
would be the shore line could a country be submerged to
a given level. The base level of a map representing a
country near the seashore would naturally be sea level.
The first contour on the map might follow the line of 100
METHODS OF MAP MAKING 115
feet elevation, the second run 100 feet above that, and so
on, one for each 100 feet. A little consideration will show
that the lines indicate not only direction of the slope of the
land, but also the rapidity of slope, for when contours are
close together the ground is steep, while on flat land they
are wide apart. Hill tops are circled by a succession of
contour lines. On lower land they often run in a very
sinuous course.
When one examines such a map and thinks of its con-
struction, the first idea is that a tremendous amount of
labor is involved. To follow out a succession of contour
lines with ordinary surveying methods would indeed be
an endless task. That is not the method of construction,
however. It is rather sketching, guided by the location,
in horizontal position and height, of a sufficient number of
points. If one knows how high the top of a hill is above its
base, that tells one at once how many contours, 100 feet
apart, come between the two, and a glance at the hill
perhaps will tell if it is of even slope. Similarly the location
of divides and ridge tops, and, on the other hand, of low
points, whether occupied by water or not, gives control
points which aid in representing the slope of the land.
The main problem of the topographer is how best to make
these locations — most accurately and at least cost.
General Considerations. The instruments and methods
available for the production of topographic maps have
been described on previous pages. In employing them, to
secure practical results, very much depends, of course, on
their effective use and proper combination. In this rela-
tion, some general principles of surveying work and the
conditions of woods work, as distinct from those of ordinary
surveying, require first to be stated.
1 . A hunger for accuracy is part of the make-up of every
good surveyor and map-maker. At the same time, he has
to remember that if such work costs more than it is
worth to the man who pays for it, it will not be done.
Accuracy to a certain degree is necessary; on the other
hand, there are limits of cost. A proper balance between
the two is required. The result may be called an "
map.
116 A MANUAL FOB NORTHERN WOODSMEN
2. In securing an efficient map, a main principle to hold
in mind is the relation between accurate and expensive
work and work of a lower degree of accuracy. If elevations
in a topographic survey were put in by level only, and
horizontal positions fixed by compass and chain, an
accurate result would be had, it is true, but it would be at
enormous cost. On the other hand, the use of barometer
and pacing alone might furnish a map so inaccurate as to
be of little account. The effort must be to construct a
skeleton of reliable points and lines, to which less accurate
and costly work may be tied — to put points within reach,
one might say, of the weaker method or instrument. Sur-
veyor's compass and chain, staff compass and pacing, and
sketching form such a series in the horizontal determination
of points. The level, the aneroid, and sketching are similarly
related in height work. Sketching is the final term in any
case, and much depends on it for both accuracy and
appearance. In a way, it is easy, but real excellence in
the art depends on a combination of eye, memory, and
artistic sense.
3. Throughout any ordinary work of this kind, it has to
be understood that much detail is too fine for representa-
tion or is really unessential, and on that account the
topographer should neglect it. Makers of accurate maps
neglect only what does not show on the scale of the map.
Woodsmen will generally find it necessary to adopt a
more liberal rule.
The conditions under which forest mapping is done have
an influence on methods in the following ways.
1. Timber growth itself presents an obstacle to clear
sighting. That favors the compass as against the transit
for boundary work, and in the same way, in topographic
mapping, triangulation and the vertical angle are put at
a disadvantage as agaiast methods which can be carried
on under the cover of the woods.
2. Forest topography should generally be tied to
property boundaries, rather than to topographic promi-
nences. Commonly, a survey of his boundaries is the first
and most important work to be done for an owner who
wants accurate knowledge about his land. It will, there-
METHODS OF MAP MAKING 117
fore, save time and money if the interior features can be
tied to them.
3. Topographic maps of forest property should be
especially clear in respect to road lines and other points of
importance in lumbering operations. The map-maker
should, therefore, understand these operations. It will,
also, save time and money if topography and timber can
be examined together, at the same time, and by the same
man.
With these principles in view, the following are methods
recommended for the production of forest maps. It is
well in discussion of the matter to divide the work into
two classes — that on small tracts, where close work is
required, and that on larger tracts, where different methods
must be employed and a lower standard of accuracy may
be allowed.
2. MAPPING SMALL TRACTS
A tract of eighty-nine acres, well timbered and of strong
relief, that was surveyed by the class of 1907 in the Harvard
School of Forestry will serve as illustration. The following
steps were taken in the process.
1. Boundaries surveyed by compass and chain ; marked
stakes left every twenty rods ; bounding lines and corners
remarked. Two days' work for three men, more if there is
special difficulty with the old boundaries.
2. Elevation of one convenient point ascertained or
assumed, and levels run over the roads crossing the tract,
leaving bench marks plainly marked every twenty rods or
so. Levels, also, run down to point x. (See page 119.)
One half day's work for two men.
3. Outlines of tract plotted to scale on paper; this
pinned on traverse board with meridian of survey parallel
to N and S edge of board ; roads run in with the chain and
position of bench marks taken. One half day's work for
three men.
4. Sheet on the board without the tripod taken into the
field, a scale serving for alidade; detail mapped in by
short foot traverses from the known points ; elevations got
partly by aneroid, partly by hand level. One day's work
118 A MANUAL FOR NORTHERN WOODSMEN
for one man. Any board to hold the sheet will do, a small
compass being used to orient it. By the time this work is
done, a practical man may, in addition, have learned
about all he wants to know regarding the timber.
Clark Lumber Go's.
"PARKER" LOT
Woodstock Mass.
Surveyed by
MO 400 300 800 100
5. Since the lot is to be operated from a portable mill set
near its northeast corner, go over the lot with the map in
hand and see that the topographic difficulties and oppor-
tunities are correctly represented.
METHODS OF MAP MAKING
119
Alternative Methods. 1. Compass and chain may be
used to survey the roads and the plotting done off the field.
This is most convenient in wet weather, but when a traverse
board is at hand and can be used, it will be found the
quickest method of survey and the least liable to error.
Diagram showing
Method of Survey
Lines surveyed & chained
Points marked for refprpnna t i | i
Levelled lines
Bench marks O O O
Traverses with barometer
or hand level
2. Transit and stadia might be substituted for both
level and traverse board in the survey of the roads, and,
where the woods are open enough, in mapping the detail
of the topography. This method involves much comput-
ing, is generally cumbersome, and except in the hands of a
skilled and practiced man is liable to give rise to error.
120 A MANUAL FOR NORTHERN WOODSMEN
3. After the boundaries are surveyed and the primary
point in elevation is fixed, a topographic survey and timber
estimate might be made together by means of the strip
system of survey described on page 188. For the topo-
graphic work, a barometer would be carried in the party
Same Tract
as Surveyed by
Strip System
and the elevation of needed points read and noted or
plotted down in connection with the chainage by the note-
keeper. If the air pressure was not steady, it would be
necessary for the barometer man once in a while to leave
the party and go back to the base for correction. The
combination of barometer and barograph gives rise, in a
METHODS OF MAP MAKING 121
method already not too accurate, to additional errors, and
should not be employed except when it is the only practi-
cable method.
This method of survey may suffice in favorable condi-
tions, and where the requirements are not of the strictest.
Work with the level, however, is quick and sure, and in
general it will be found advisable to use it freely.
The Map. In plotting tracts of this size, and up to a few
hundred acres in extent, scales of 400 feet or 20 rods to the
inch are found to go well with a 10-foot contour interval,
and to furnish a serviceable map. A larger scale and a
smaller contour interval would naturally go together.
3. MAPPING LARGE TRACTS
A. With Land already Subdivided. If the region to be
mapped comes under the public land surveys, or if there are
plain and reliable lines of other origin on the ground, a
skeleton of level lines with barometer work tied to them is
the treatment indicated. Generally the level work is best
carried along the waters or roads. Ponds and lakes form
the best sort of reference points, and frequently natural
water levels perform a large part of the work required.
Section lines may, however, furnish in some cases the best
routes available, while on very broken land it might be
necessary to resort to the vertical angle.
^How the barometer work shall be done depends on
circumstances. If the weather is perfectly steady, or the
level points are near enough together, elevations may be
read direct without a weather change correction. If,
however, the weather is shifting, and the cruiser must stay
away from known points many hours at a time, a station
barometer or barograph will have to be employed. In any
case, the topography can be mapped at the same time that
the timber is being examined.
B. Topography Based on Survey of Roads or Streams.
If the tract to be surveyed is an undivided township, or is in
any other form that is too large for accurate mapping, it may
be cut up by one means or another into smaller areas that
can be handled. The lines of easy subdivision naturally
122 A MANUAL FOR NORTHERN WOODSMEN
furnished by a large timber tract are its streams. On
these transit and stadia furnish the most efficient means
of survey. If roads are available, the same method may
be employed, or another may be substituted.
One Mile
Surveyed bounds with chainage marks .
Road surveyed by stadia, reference points
fixed by stadia and by level -
Strip surveys with barometer.
On the tract used in illustration, the road, rather than
the stream, was used for the subdivision. The different
steps in the process of survey were as follows :
1. Outside boundaries run with compass and chain.
Chainage marks for reference left every quarter mile.
2. Road across the tract surveyed by transit and stadia,
using the needle and setting up the instrument at alternate
stations. Points marked at short intervals. See notes on
page 86.
3. Level line run along road, giving elevation of points
established in the stadia traverse.
4. Strip surveys run between the road and the boundary
METHODS OF MAP MAKING 123
(see page 188), tying into the marks left. Elevations got
by aneroid, corrected by barograph. Numerous modifica-
tions of the rectangular system made as required.
Alternative Methods. 1. On roads the traverse board
with chain is undoubtedly the best instrument for making
a survey of fair accuracy. The compass and chain might
also be used. But when streams are utilized, unless on ice,
stadia measurement will be found to be best and quickest.
2. The level might be dispensed with, and the transit
used as a level on the same settings from which it is used
to get bearing and distance. This works best on a stream
with grade all one wray, and, in the case of a party by itself
in the backwoods, is probably the best means of getting
data of this kind. One additional man is then required
for maintenance.
3. Instead of the strip survey, using compass and chain,
compass and pacing may be employed with circular plots
for the timber. It may also be better or necessary to
discard both rectangular systems, and work out the topog-
raphy by means of. road lines, passes, etc., controlling
features in the lumbering development.
C. Subdivision and Topographic Survey Combined.
The following procedure has been carried out on a con-
siderable scale on undivided townships in New England.
The methods employed have been found to be cheap and
practical, and the maps resulting have stood the tests of
use and time.
1. Boundaries renewed and tract divided into sections
by compass and chain. Topographic notes taken ; chain-
age marks left every quarter mile. Two months' work for
a party of seven men.
2. Elevation of some point above sea level obtained, if
possible ; if not, datum plane assumed at or below lowest
point on the tract. Level lines run over roads and streams
to ponds, camps, and other accessible points, well distrib-
uted through the tract. Commonly a week's work for
two men.
3. Detail of topography and timber worked out together.
Mountain peaks located by cross bearings; streams and
roads by compass and pacing traverse; other features
124 A MANUAL FOR NORTHERN WOODSMEN
partly by traverse, partly by straight-line travel across the
sections. Elevations by barometer checked by the baro-
graph whenever it is necessary to remain away from known
points a considerable time. Timber estimated and topo-
graphic notes obtained at same time. Cruising, reduction
of notes, and map making about six weeks' work for the
explorer, who may need a companion or camp man.
Comments. 1. Division into mile squares may look
expensive, like going a long way round to secure topo-
graphic data. These lines, however, have value on other
accounts; have, in fact, proved their value over and over
again in timber land administration. As before stated,
they are useful in definitely bounding logging contracts,
they are perfectly understood by logging foremen, and
are of great service to them in their timber estimates
and the laying out of their roads. They are, in addition, of
great service in keeping track of subsequent cutting or
other developments on the land.
On the other hand, the mile square is not so large an
area but that it can be mapped accurately and its timber
estimated according to the methods here recommended.
2. The strip survey system might, of course, be used
instead of the one-man system employed. The advantages
of each will be understood from what comes before and
after.
3. It may be advisable in some cases to separate entirely
the topographic and timber work. In general, however,
the thoroughly equipped man will find that travel that
helps him in one direction helps also in the other.
The Maps. Maps of forest property should be on a
large scale to allow the preservation of notes about small
bunches of timber, etc. Four inches to the mile for tracts of
large size has proved serviceable. As to contours, a fifty-
foot interval will serve, in the rough land of New England,
to represent most features of the topography.
The results of such a survey are, for business purposes,
best embodied in two map sheets, one showing the waters,
relief, and other permanent features of the country, the
other exhibiting all the. facts concerning the timber.
This last should be on tracing linen, so that it may be laid
METHODS OF MAP MAKING 125
over the topographic sheet, and the two seen in relation.
Not only the amount of timber is thus exhibited, but the
steepness of the ground it stands on, and the distance it
must be hauled. It will appear, too, whether a valley
has been cut clean to a divide. On this timber sheet, cut-
tings and other operations of succeeding years may be
plotted. If it gets too complicated, it may be thrown away
and a new one substituted.
A sample map of this kind is reproduced on reduced
scale herewith. These maps may also be supplemented
by topographic models. Contour maps are "not read easily
by every person, as, for instance, by some lumbermen,
but a model of the land, as it lies out of doors, is imme-
diately grasped by all. With the aid of a blue print of
the map which may be cut up and used as a pattern a
model is cheaply built out of cardboard or veneer. With
such a model at hand, a contract may be let or plans
of work talked over in the office with the same clearness
as to major features as if men stood on the ground.
Following is a topographic map of a section of land as
derived from traverse of the boundaries, a road, and two
trips across it. After that come notes of the road traverse
and of one of the trips across it. For notes of survey of
south line see page 29. On the map observed elevations
are written in. ' Contours as seen are solid; contours in-
ferred are broken.
Principles of Cruising. A plan of cruising designed
to secure topographical and timber data every man will
think out for himself and a new one for each tract under-
taken. The following, however, are believed to be sound
principles for guidance in this class of work.
1. Main streams, roads, lakes, etc., should of course be
traversed, and they may be important enough to demand
some other method of survey than compass and pacing.
One should be very careful, too, about waste lands, burns,
and the boundaries of heavy bodies of timber.
2. It is generally advisable to explore the country one
section at a time, for in that way one comes out with the
clearest ideas upon it.
3. Cross country travel which locates brooks and ridge
126 A MANUAL FOR NORTHERN WOODSMEN
tops by intersection may suffice for topographical purposes,
while it gives a juster view of the timber than could other-
wise be gained. Locations, too, will be more accurate
along such a line than where a crooked route is followed.
4. Extreme points are in general the -ones to read on
for height, — that is to say, ridge tops, brook crossings, etc.
One may combine with this also a system of reading at
regular intervals. It will be enough to read the thermom-
eter half a dozen times during a day to get the course of
the temperature, unless extremely high points are occupied.
5. Relative heights are frequently of far more importance
for logging purposes, as, for instance, in connection with the
grade of roads, than is absolute elevation. It is often ad-
visable, therefore, to establish sub-centers of work and
determine elevations relatively around them rather than
refer readings always to a distant base station. On the
same principle, if a region is hard to get at with the level, it
may serve the purpose of the map to fix the height of some
central point in it by two or more aneroid readings, and
then work around that.
METHODS OF MAP MAKING
127
f
•St-arf/
7? ai~6
•jt//fi ///7e of 7bw/7S/7//), £S~/T3ds £ 0/7 rtre •S ///r&
ofSe
-fy'o/7 a
5 q/ife/? /'/? survey /7o/»s. £/evafa'o/7 37O ft
as 05
CQffa//,
ed frv/n /3O/7C/ /?ear6y dsfer/7?//?ec/ 6y /ere/.
Tfience //7^ecfib/? 2S
Searing
rbces
A/20°£
2OO
A/o/iy easy 6/o/oe r/g/rf; /ft good f/mber;
MS"£
3SO
f~o syya/np
WSO'E
7S
/o sma// brooA rurtfl/nq <5£. £/evaf-/bfi 94o'
MJJ£
2SO
ctf~ /OO ' //7/D /7/7?6es~ cryo//7
A/73°E
/SO
Up s/q/oe, /o pass be,fween /7///S
#65£
32S
r/ghf- & /etf- £/er. /o<$o '
V42E
/7S
on agenerti/ S/ope Easf- of a6oirf- /o%
M2S°£
4OO
' fo -f/af /and and
N20£
tes
£/e\saf/or? 3&O '
N
30O
f/7 f/af /and w/fh fft/cA spruce- growth
Ww
22S
to Norrh //'/7e -secfrb/? 2S- /-9O /-ods £asf
on // crsg/ye/7 6>y Survey /?0r&s.
£/er.880fr Greeted on 0.Af./ra/f an four fab-
COMPASS AND PACING TRAVERSE OF ROAD ACROSS SAME SECTION.
ELEVATIONS READ FROM FOOT SCALE OF BAROMETER
6. There is occasionally a locality especially critical
from the lumbering point of view, such, for instance, as a
pass which makes it possible to haul from one drainage to
another with a level road. The topographer ought to be
enough of a lumberman to recognize these points, and
when he does he will put special time and pains upon them.
7. Field observations may be recorded either in the form
of running notes, or mainly in the shape of sketches on a
plat of the ground. Probably a combination of the two
methods will be found most satisfactory. A note book
especially ruled for the purpose to the same scale as the final
128 A MANUAL FOR NORTHERN WOODSMEN
/"
Bar Camp. (Eter. 6y/eve/3o;') 6A.M. 29. JSO
TA. 60" Barvgrapf, 6A.M. £3. 2 JO Bar. <%%%$?,_
Canada road on /V. /irre section £S T/me 7JO 23.3 6O
•88/'
Steps
60 Wesf on -Section /i/?e
'90
i/7?i/e mart of5i/rrey. f~/af fyruce aroi/nd. 23. 36S
876
S/0
% mile mark. S/ope M£. then //. 29. 29S
935
SIS
Section cor/xv: Gevf/es/o/vA/.W. A// spruce
timber. Bar. 7.4O 2.9.30S
920
Ref-urn fo /OO steps £. of % m/7e /nar* and
go 5.7° W. /n Section. Starfaf 7.S0 A.M.
350
Genf/e S/ope MMW. S/?rvce growt/? 29.ZOS
/0/6
400
Top of A///. fa//s Sfeep/y £.wdW. £3.390
1220
470
Down strong grade S.W. 7/m heron hi// mixed
ffrrdsnorf. ffotfom roiyh 29.I7S
IO3S
/7S
Canada nay road on easy /and 2.9. /9J
so/s
37S
Down easily w /arge /n/jred^row/'n fo edge
of snrampy /and Z9.26O
350
280
Town s nip ///?e 6~O sfeps Easf of %. n?i/e mart
Bar ass (TA . 6S°J 29 aao
930
Bar Camp //A. M. (TA. 6S>J £9. 28O
Barograpfi //, E9./7S
STRAIGHT TRAVERSE ACROSS SECTION. ELEVATIONS BY BAROMETER
CORRECTED BY BAROGRAPH
map will be found a great saving of labor and an aid to
clearness.
8. The map is best worked up on the ground. The
added accuracy and certainty gained in this way more than
pay for the cost of carrying necessary equipment around.
The topography may be drawn in pencil on the final
manuscript sheet, and an outline sketch on any kind of
paper will serve to gather up the timber notes temporarily.
TIMBER SHEET
Explored I 900 Cutting since that date marked by section lining
28.9$.
T33H8
•
'ttch on an
PORTION OFTOWNSHIP 5 R IV OXFORD CO. MAINE
Topographical Sheet Datum Plane, Umbagog Lake
Contour Interval = 50 feet
METHODS OF MAP MAKING 129
D. Western Topography. Use of the Clinometer.
The above described methods grew up in the East among
varied conditions of topography and value. Brush that
interferes with sighting is widely prevalent, and another
determining factor is the general employment of horse
logging, a style of operation for which close regulation of
grades is not essential. Conditions in the West are fre-
quently different from the above, in respect to one or
more particulars.
The aneroid barometer has not on that account yielded
its place entirely. Particularly in Western Washington
and Oregon does it still hold the field, because of the dense
brush widely encountered, which makes almost impossible
the clear sighting necessary for the employment of any
other height-determining instrument. On the contrary,
the temptation is to rely on the aneroid for work that it
should not be called upon to do. Where, as is the case
here, railroads are employed for nearly all mam transpor-
tation, heights with a reliable basis are essential if a
map is to be widely serviceable. Frequently the ground
lies in such a way that the routes of future railroad de-
velopment are evident. Levels run along these routes,,
with aneroid work for the rest, is then the natural treat-
ment. Just this method has been employed in numerous
cases.
Such logical and adequate treatment is not always
possible, however, nor is it always permissible under the
restrictions of the work in hand. A variety of methods is
in fact employed, especially for the control work. As
for the detail, the fact remains that when points in eleva-
tion have been reliably determined at distances not more
than from one to two miles apart, good aneroids intelli-
gently used will give topography sufficiently accurate for
general purposes, while here as elsewhere their use saves
expense by permitting the topographic and estimating
work to be done together. Complaints of the results of
aneroid work frequently arise from unskilled use and from
employment of instruments of inferior character. The
quality of instruments obtainable at moderate cost has
within a very few years greatly improved. It is not to be
130 A MANUAL FOR NORTHERN WOODSMEN
denied, however, that rapid weather changes sometimes
make accurate work difficult.
Some interior mountain territory is characterized by
lightly forested ridges contrasting with great density of
timber and brush along the streams, while logging methods
are often such that accurate knowledge of grades on valley
lines is not essential. In circumstances such as these,
circuits of transit and stadia work carried over the ridges
have proved a satisfactory method of height control.
When areas concerned have never been covered by the land
surveys, angles have been turned and read in addition for
the purpose of control in the horizontal direction.
With control laid out in this way the early plans of
reconnaissance in such country involved, as the next step,
the crossing of valleys with strip surveys, the aneroid
being relied on for elevation. This plan of work, starting
from known points on the ridges and running long lines
independent of one another, crossing the brooks and valley
bottoms (where grade was most important) at a long
distance from known bases both horizontally and verti-
cally, made demands on the aneroid which it was not able
to meet successfully.
Height work along the stream lines was an evident
corrective, but a substitute scheme that at the time of
writing seems to be filling the requirement is the use of the
tape and clinometer.1 Both instruments have, however,
been subjected to modification. The clinometer has been
made more efficient in numerous ways; in particular the
arc has been enlarged and so graduated that instead of
degree or per cent of slope it gives difference of elevation in
feet for the given slope and a stated distance (66 feet or one
chain in present practice). The tape used for the purpose
is 2| chains long, two chains of it marked in links as usual,
while the extra length or "trailer" is so graduated that
the inclined distance along any slope which corresponds to
two chains horizontal may be set directly. By these
devices two short cuts are accomplished : first, difference in
1 For a fuller description of this method see "The Timberman,''
March, 1916, or "Engineering News," Vol. 75, No. 1, p. 24.
METHODS OF MAP MAKING 131
elevation is found directly from the slope observation;
second, with similar directness surface chainage is con-
verted into horizontal distance. These two things are the
essentials wanted. To facilitate the work, the graduations
on the trailer of the tape correspond with those on the arc
of the clinometer.
The method will be grasped from the accompanying
figure and the following explanation : If a party is ascend-
ing the slope indicated in the figure, the man ahead (who
serves not only as head chainman, but runs the compass,
takes notes, and sketches topography), as the tape comes
to its end, sights with his clinometer at the height of his
eye on the rear man (who may be the timber cruiser as
well as rear chainman). The reading obtained, in this
case 38, is the vertical rise per 66 feet horizontal on the
slope between the two men. That corresponds to a vertical
angle of 30°, but the fact, not being needed, is neglected.
The topographer now calls out "38" to the rear man, who
lets the tape run out to that mark, as a matter of fact 20.42
feet beyond the two-chain point. When the chain to this
mark has been drawn straight and taut and pins are set,
two chains is the horizontal distance between them. This
the topographer may now plot on his map. The height of
the new point (twice 38, or 76 feet above the first one) may
also be used as the basis of sketching.
132 A MANUAL FOR NORTHERN WOODSMEN
Two miles per day are readily covered by two men,
drawing topography carefully and estimating a good stand
of timber. Not only has cruising work been done by this
method, but control work as well, using more care and two
instruments. This last use of the method requires making
circuits several miles in length around either subdivisions of
tact*.
land or topographic areas. For cruising work the method
is carried at farthest two miles to a tie point. Errors in
direction and distance are seldom over \ chain per mile
and the average error in height work is 10 feet. In very
brushy country some tricks of the trade are introduced in
the interest of speed, as sighting to the flash of a mirror or
the metal note holder of the cruiser. In country of long
METHODS OF MAP MAKING 133
open slopes an alternative method is to take longer shots to
noted objects, chain up, and compute the elevation.
Above is practice developed; in the United States For-
est Service. The cost is given as 12 cents per acfe as a
total for topography and cruise. Some commercial work
is done on the same general plan, a five-chain tape being
used and correction for distance made from tables in the
field.
The accompanying map of mountainous land in Idaho
shows at the left the topography along two miles of section
line as developed by a survey for control purposes which
surrounded four sections. This control work naturally is
performed and checked in advance of the detail work.
To the right the topography of the greater part of the area
has been filled in, but a strip left blank indicates how it is
built up, from parallel lines 10 chains' apart crossing the
territory. This map is completed in the field, a board and
outline section sheets facilitating the purpose.
This method, though developed in special conditions in
the West, promises, with some of its modifications, to win
a considerable field of employment.
SECTION VIII
ADVANTAGES OF A MAP SYSTEM
Following are the advantages which a good set of maps
renders to a large business concern. To secure these a
good man will be required in the field to keep up lines,
map the cutting of successive years, and watch the con-
dition of the timber.
1. Great saving in the aggregate can be effected through
the detection of small losses, such as windfalls and insect
depredations, also by finding bodies of unhealthy timber,
and as far as possible having such material cut and hauled.
2. The location of all sorts of roads, whether railroads,
logging roads, or supply roads, is greatly facilitated.
Exploring is saved, and distances are accurately known.
3. Operations can be planned and largely controlled
from a center with all sources of information at hand.
134 A MANUAL FOR NORTHERN WOODSMEN
The timber resources are known; also their location, and
all related facts. The cut can be located for years ahead
to the best advantage, sotli to make driving and the haul-
ing of supplies, for instance, come cheapest and handiest.
4. A map system preserves information about the land.'
An old lumberman or cruiser has a lot of information in
his head that is lost to a business when he dies or steps out,
unless it is fixed in some permanent form.
5. A concern knows what it is possessed of, and has that
information in the form most easily taken in by all intelli-
gent men whom it may be desirable to inform ; for instance,
stockholders, and possible money lenders.
6. A good map system in a business may pay for itself at
the first change of management. A new manager coming
into a business is in the hands of his employees for years
until he can get first-hand knowledge of his country. With
the aid of a good map system working command of a big
property may be had in a year.
7. A reliable map system followed up for a term of
years through a series of pictures of the land furnishes a
record of its growth, and so enables a concern to grapple
with the question of future supplies.
PART III
LOG AND WQOD MEASUREMENT
PART HI. LOG AND WOOD MEASUREMENT
SECTION I. CUBIC CONTENTS
SECTION II. CORD WOOD RULE
SECTION III. NEW HAMPSHIRE RULE
SECTION IV. BOARD MEASURE
1. General
2. Scribner and Decimal Rules
3. Spaulding or Columbia River Rule
4. Doyle Rule
5. Maine Rule
6. New Brunswick Rule
7. Quebec Rule
8. Theory of Scale Rules and Clark's International
Log Rule
SECTION V. NEW YORK STANDARD RULE
SECTION VI. SCALING PRACTICE
SECTION VII. MILL TALLIES
SECTION VHI. CORD MEASURE
PART III. LOG AND WOOD MEASUREMENT
SECTION I
CUBIC CONTENTS
THE simplest way to measure the contents of a log is to
take its length and mid-diameter and ascertain the cubic
contents of a cylinder having those dimensions. Bark may
be taken in or left out. By the use of a caliper and tape,
a very close result may be had on logs that are not too
long, provided care is taken either by inspection or by cross
measurement to get a true mid-diameter. Trees cut nearly
full length are given as a rule too large a value when
measured in this way, — larger, that is to say, than their
actual cubic contents. The percentage of overrun for large
spruce cut off at 5 to 8 inches diameter in the top is about
6 per cent of their true volume.
When logs are placed in a pile the best that can be done
is to use a diameter which is an average between the diam-
eters of the ends, swell at the stump, if present, being
disregarded.
First among the tables for log measurement given in the
back of this work is a table of cylinders with contents
in cubic feet, standard measure. The lengths in feet are
given in the first vertical column, the diameters in inches
on the upper horizontal line, and the contents of any log is
read off opposite its length and beneath its diameter. If
the length is not given, add together such lengths as will
make it up. Thus a log 12 inches in diameter and 47 feet
long has the contents of a log 40 feet long + that of a log
7 feet long, or 31 + 5.5 cu. ft. = 36.5 cu. ft.
For practical purposes results near enough will be had
if fractions of inches more than \ inch are taken as of the
inch above, and fractions of \ inch and less are disregarded.
138 A MANUAL FOR NORTHERN WOODSMEN
For convenient use in scaling, these figures should be
stamped on the bar of a log caliper. They may be so ar-
ranged on a bar as to throw out a fair proportion for bark.
This system of log measurement is in actual use in but
one business concern, so far as known to the writer, yet it
is the simplest and most natural measurement for logs that
are to be converted into pulp, shingles, excelsior, etc. It
is not a difficult matter to arrange a factor or factors for
converting cubic measure into board measure.
SECTION II
CORD WOOD RULE
The figures given in the table on page 239, those for cord
measure, are not cubic feet of solid wood, but what have
been called " stacked cubic feet " ; — the space which wood
will occupy in a pile. 128 of these make a cord. Like the
preceding, these figures are ordinarily placed for conven-
ient use on the bar of a caliper rule.
These figures have been long and widely tested in prac-
tice, and when used as designed have given satisfaction.
Logs should not be measured in too long lengths, for whole
trees measured in this way may not hold out. Again,
small, crooked, and knotty timber will pile up rather more
cords than the rule gives. On a good quality of pulp wood
these figures yield just about the same return as the re-
sults of piling. For further details see Section VIII, on
cord measure.
SECTION III
THE NEW HAMPSHIRE RULE
The New Hampshire Log Rule is exactly the same as
the last in principle, only an artificial unit of measure has
been created. The " cubic foot " of New Hampshire log
measure is 1.4 times the cubic foot of standard measure,
and nearly twice the foot of the cord wood rule. The New
Hampshire law regarding the matter is as follows :
All round timber, the quantity of which is estimated by the
thousand, shall be measured according to the following rule: A
BOARD MEASURE 139
stick of timber sixteen inches in diameter and twelve inches in
length shall constitute one cubic foot, and the same ratio shall
apply to any other size and quantity. Each cubic foot shall con-
stitute ten feet of a thousand board feet.
This rule is extensively used in scaling spruce in Maine,
New Hampshire, and Vermont. A broad caliper bar is
stamped with the figures, and the stiff iron jaws attached
throw out f inch from the diameter for bark. The diam-
eter is taken in the middle of the log, and in ordinary
practice logs of any length are measured as one piece.
The values given by the rule run parallel to actual cubic
contents and the rule is therefore a fair one as applied to
pulp wood. It is not a satisfactory measure of the yield
of logs at the saw, small logs being for that purpose over-
valued and very large logs undervalued. As with cubic
measure, however, its values could be readily converted
into board measure by the use of different factors for logs
of different sizes.
It is now the uniform practice wherever the New Hamp-
shire rule is in use to take 115 feet by the rule for 1000
feet of lumber.
SECTION IV
BOARD MEASURE
1. General. A board foot is a piece of sawed lumber 12
inches square and one inch thick, or any piece, as 3 X 4
or 2 X 6, which if reduced to 1 inch thickness has 144
square inches of area. It is properly the unit of sawed
lumber, and there must always be more or less difficulty in
adjusting it to the measurement of logs.
There are a large number of rules in the country to-day
purporting to give the contents of logs of given dimensions
in feet, board measure. Among these rules there is wide
variation in the value given to logs of the same dimensions.
In the manner of their use, too, there is a good deal of
divergence, resulting sometimes in dispute and loss.
The figures of eight rules in extensive use in the United
States and Canada — the Scribner, the Doyle, the Deci-
mal, the Maine, the New Brunswick, the Quebec, the
140 A MANUAL FOR NORTHERN WOODSMEN
Spaulding, and the British Columbia — are printed in
this work (see pages 243-260). The International rule,
devised by Dr. Judson F. Clark, formerly forester of On-
tario, is also given (page 254). In regard to these rules
and their relation to log measurement and saw product
several general observations may be made.
(1.) On sound, smooth, soft-wood logs when manufac-
tured according to the best present practice, the figures of
all the commercial rules are conservative with the exception
of the Doyle rule on very large logs. This is especially
true with reference to small logs.
(2.) Board rules give to large logs a greater valuation in
proportion to cubic contents (actual amount of wood) than
to small ones. Thus the Scribner log rule to 8-inch logs
of small taper allows five feet per cubic foot of wood con-
tents; to 16-inch logs seven feet, to 30-inch logs eight feet.
This principle is a just one for logs that are in fact to be
sawn, because the waste in manufacturing in the case of
small logs is much greater, but on this account a board
rule is not a just measure for logs designed for pulp or
other such uses.
(3.) The rules are adapted to use on short logs with little
taper. When logs are long enough to be cut in two for
sawing, or to yield side boards for a part of their length,
to derive contents from length and top diameter is not a
fair thing. In such cases a second measure of diameter
should be taken, and this can be done accurately only with
a caliper. Allowance for " rise " or toper, whether for each
log by judgment or according to some rule agreed upon,
is more or less inaccurate and should be resorted to only
in case of necessity. It may be said as a general rule that
20-foot lengths are as long as it is safe to scale logs in.1
On the other hand, since strongly tapering logs in almost
every case are rougher than those of gentle taper, varying
taper in logs of reasonable length is largely neutralized
by quality.
(4.) There is wide variation in the details of scaling prac-
tice, and a trustworthy rule in consequence may, in the
hands of an unskilled or careless man, give very unsatis-
1 Except in the case of PaciBc Coast timber.
BOARD MEASURE
141
factory results. In some matters, especially culling for
defects, latitude must be allowed to the sealer. In general,
however, practice is weak in the direction of strict mechan-
ical accuracy. Reference is made to section VI following.
The method of construction, field of use, and relation to
saw product of the above named rules are as follows :
2. Scribner and Decimal Rules. The figures of the
original Scribner rule were obtained by drawing diagrams
of the end sections of logs 12 to 48 inches in diameter and
the boards which in the mill practice of the time could be
sawed out of them. It is a very old rule and in wide use.
As printed, extended down to 6 niches, it is the legal rule
in the state of Minnesota.
Omitting unit figures of the Scribner rule and taking the
nearest tens has given the Decimal rule, so called, legal in
Wisconsin and adopted by the United States Forest
Service.
3. Spaulding or Columbia River Rule. This rule was
derived by similar methods as the preceding, 1 inch being
allowed for saw kerf. It is in more extensive use on the
Pacific Coast than any other.
4. Doyle Rule. This rule was constructed by the fol-
lowing formula : — Deduct 4 inches from the diameter of
Diameter
No. Logs
Doyle
Scale
Product
Overrun
6-8 in.
28
289
903
213%
7-9 in.
54
831
2159
159%
8-12 in.
101
2603
5471
110%
10-17 in.
104
6324
9976
58%
18-20 in.
90
15440
20215
31%
21-24 in.
126
30929
37744
22%
25-33 in.
31
11866
13368
12%
the log for slab, square J of the remainder, and multiply
by the length of the log in feet. This is a very illogical
rule and gives results widely varying from saw product in
142 A MANUAL FOR NORTHERN WOODSMEN
logs jof different sizes, though in a run of logs the results
obtained may approximate a fair thing. Very small values
are given to small logs, too small by far for normal logs
economically manufactured, while beyond about 36 inches
in diameter values are given that are above the product of
the saw. It crosses the Scribner rule at 25 inches in
diameter, the Maine rule at 34. A test made by Dr. J. F.
Clark in 1905 in a Canadian band mill cutting sound,
straight pine into boards resulted as shown on page 141.
The Doyle rule is in more general use than any other in
the United States and Canada, and is the one printed in
recent editions of Scribner's " Lumber and Log Book."
This rule has been combined with the Scribner into the
Doyle-Scribner rule, the figures of the Doyle rule being
taken for small logs where the Doyle figures are lower,
and of the Scribner rule on the largest logs where these
figures are less. This Doyle-Scribner rule has been used
largely on hard woods.
5. Maine, also called Holland Rule. The figures of this
rule were derived from diagrams. That is to say, circles
6, 7, 8, etc. inches in diameter were plotted and within
these the boards that could be sawed, an inch thick with
J inch for saw kerf. Not only the boards derived from the
inscribed square were reckoned, but the side boards if
they were as much as 6 inches wide. No rounding off of
the figures was done, so they are a little irregular, but that
takes care of itself in a run of logs.
This rule is used largely in Maine and to some extent
elsewhere. It has been carefully tested at the saw, and
the conclusions are as follows : — Sound spruce and pine
logs 12 to 18 feet long, of best merchantable quality,
manufactured at a circular saw cutting J-inch kerf will
yield in the shape of inch boards just about the number of
feet of edged lumber that the rule gives. A band saw will
get more, and there will be a larger product if the logs are
put into plank or timber. More will also be got the longer
the logs run, up to the poinl where they are scaled in two
pieces.
How sawing practice affects the product at the saw was
clearly shown by a test made by the United States Forest
BOARD MEASURE
143
Service in Various spruce mills of Maine. Some results of
this test are given in tabular form. All logs were straight
and sound, and exact conditions were as follows:
Band Mill No. 1, |-inch saw kerf, lumber cut just 1 inch
thick. Mill run for economy and utmost product of long
lumber, giving product of about 40 M daily.
Band Mill No. 2, same saw kerf. Mill run for speed
rather than economy, product being 58 M a day.
Rotary Mill, ffr-inch saw kerf, lumber even inch thick.
Gang Saw, ^-inch kerf, lumber even inch thick, logs
sawed alive or through and through.
TABLE I. YIELD IN INCH BOARDS OF LOGS 16 FEET
LONG AS SAWED IN DIFFERENT MILLS
Top
Diam.
sa
11
1|
nd Mill No. 2
Sawed alive
!j
Gang
Scale by
Maine
Rute
r
I1"
c3~"
m
6 in.
30
26
20
18
24
20
7 in.
41
36
29
25
34
31
Sin.
53
47
39
35
43
44
9 in.
66
59
51
46
54
52
10 in.
81
73
64
59
67
68
11 in.
96
88
79
73
80
83
12 in.
112
106
95
89
94
105
13 in.
130
125
113
107
109
120
14 in.
149
. . .
133
127
126
140
15 in.
171
154
145
161
16 in.
196
178
165
179
144 A MANUAL FOR NORTHERN WOODSMEN
TABLE II. PRODUCT IN INCH BOARDS OF LOGS OF DIF-
FERENT LENGTHS AS SAWED IN BAND MILL NO. 1
Shows how in careful practice yield increases relative to
scale as the logs are longer.
Lengths in Feet
Top
Diam.
8
10
12
14
16
18
20
22
24
6 in.
13
17
22
26
30
34
39
44
50
Sin.
25
32
39
46
53
60
68
76
84
10 in.
39
49
59
70
81
91
101
113
124
12 in.
54
68
83
97
112
126
141
156
172
14 in.
73
92
111
130
149
170
ISO
211
232
16 in.
95
120
145
170
196
223
250
278
306
TABLE III. PRODUCT OF MILLS WHEN SAWING DIMEN-
SION STOCK, MOSTLY 2 AND 3 INCH PLANK
Overrun is the percentage by which the product ex-
ceeds the scale of the logs as given by the Maine log rule.
Band Mill No. 1
Rotary
Lengths
Average
Top
Diam.
Over-
run
Lengths
Average
Top '
Diam.
Over-
run
16 ft. and under
10 in.
24%
16 ft. and under
10 in.
o%
17-20 ft.
10 in.
23%
17-20 ft.
10i in.
6%
21-24 ft.
81 in.
37%
21-24 ft.
12 in.
H%
25-28 ft.
9j in.
15%
6. New Brunswick Rule. This is the legal rule for scal-
ing lumber cut on the crown lands of New Brunswick, and
is generally employed for log measurement in that province.
Its values are somewhat below those of the Maine rule.
When logs of a smaller top diameter than 11 inches are
to be scaled, it is done under the following rule : A 7-inch
BOARD MEASURE 145
log contains 2 ft. B. M. per foot of length, an 8-inch log
2j ft., a 9-inch log 3 ft., a 10-inch log 4 ft.
One notable thing about the New Brunswick rule is that
taper is allowed for in lengths over 24 feet.
7. Quebec Rule. This is the legal rule for measuring
logs in the province of Quebec. Values are close to the
Scribner Rule; in many cases they are identical. The
figures were derived by plotting.
8. Theory of Scale Rules and Clark's International
Log Rule. The theory of the measurement of saw logs
in board measure has been more carefully studied by
Dr. Judson F. Clark L than by anyone else, and a rule
called the International Log Rule was devised by him,
on the basis of this reasoning, which he also tested at
the saw. The main points in this study are as follows :
Taper of Logs. While logs exhibit a great variety of
taper, it has been found (1) that rough logs taper more
than clear, smooth logs, so that quality tends to neutralize
taper ; (2) that average taper does not differ greatly in dif-
ferent localities or with different species. This average
taper as a result of much measurement is found to be
safely 1 inch in 8 feet. This in modern economical mill
practice increases the yield of lumber in the form of side
boards, and the above stated allowance for taper is there-
fore introduced into the rule for all lengths over 8 feet.
Crook and Sweep. In this study due allowance was
made for irregularity of surface, and crook averaging l£
inches in 12 feet of length, found to be characteristic of
white pine logs on the Ottawa River, was counted normal.
Above the limit of 1^ inches in 12 feet, any given degree
of crook was found to affect the product of small logs more
than of large logs, and that in proportion to their diameters.
That is to say, a crook of 3 inches in 12 feet throws out
twice as great a percentage from a 10-inch log as from one
20 inches in diameter.
Shrinkage and Seasoning. Logs are commonly scaled
green, while sawed lumber must hold out on a survey made
when it is dry. In computing his rule Dr. Clark figured
that boards would be cut 1^ inch thick to allow for this.
1 See Forestry Quarterly, Vol. IV, No. 2.
146 A MANUAL FOR NORTHERN WOODSMEN
Saw Kerf. This loss in logs of different sizes is pro-
portional to the area of their cross-section, or tp the square
of the diameter. It varies in proportion to the thickness
of saw kerf as well. As embodying an average of good
present practice, J inch was allowed.
Loss in Edging Lumber. This includes not only that
portion of a log which is thrown away in the form of edg-
ings, but also the fractions of inches in the width of boards,
which in Dr. Clark's studies were uniformly thrown off.
It is counted to be in all logs proportional to the surface,
or, what amounts to the same thing, to the diameter.
Counting boards to be merchantable down to the size of
2 ft. B. M., Dr. Clark found that an allowance of .8 foot
board measure for each square foot of surface under the
bark, or, what amounts to much the same, a layer .8 inch
in thickness around the surface, would justly allow for
this waste.
Formula for the Rule. The above elements being put
into mathemetical form with D representing top diameter
inside bark, there is obtained for 4-foot sections the formula
(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 fa inch kerf add 1.3 per cent
For -fs inch kerf subtract .5 per cent.
For { inch kerf subtract 9.5 per cent.
For J5 inch kerf subtract 13.6 per cent.
For | inch kerf subtract 17.4 per cent.
For Js inch kerf subtract 20.8 per cent.
Should the ^-inch allowance for shrinkage not be made
in the mill practice in question, this may be allowed for
in a similar way. According to Dr. Clark's assumptions,
each board with its saw kerf means l-fo inch in thickness
taken out of the log.
If mill practice in other ways is not so economical as
the rule presupposes, that is to say, if logs are sawed
with more waste in slab and edging than has been assumed,
or if logs vary in taper and straightness from the standard,
that is considered by Dr. Clark to be proportional to the
THE NEW YORK STANDARD RULE 147
surface or diameter, and he recommends that it be allowed
for by making a comparison between the scale and mill
product, and then adjusting the zero mark on the scale
stick more than one inch from the inch mark on the stick
in accordance with the results of that comparison. Dr.
Clarke's rule will be found on page 254 in the same section
with the other board rules.
SECTION V
THE NEW YORK STANDARD RULE
In northern New York logs are cut as a rule 1 3 feet long,
and a log of that length and 19 inches in diameter at the
top, inside bark, is the common unit of log measure-
ment. It is called a " market "or " standard," and logs
of other dimensions are valued in proportion.
The " standard " is thus another artificial unit of log
measurement, more artificial, perhaps, than any other here
dealt with. Standard measure in logs of the same length
runs very close to cubic measure. Thus a log 19 inches in
diameter at the top and 13 feet long has 26 cubic feet in it;
four logs 9j inches in diameter and 13 feet long, also
making one standard, contain the same amount of wood
approximately, while a 38-inch log of the same length has
four standards and 104 cubic feet of contents. A log 26
feet long, however, has more than twice the wood contents
of a 13-foot log on account of taper. For that reason the
use of standard measure outside of a region where short
standard lengths are cut would be likely to make trouble.
Standard measure does not run parallel to board measure
or to the yield of logs of different sizes at the saw. The
standard log, — a log, that is to say, 19 inches in top diameter
and 13 feet long, — scales by the Scribner rule 195 feet, and,
in practice, five standards are often reckoned as the equiv-
alent of a thousand. Four 9^-inch logs, together making
one standard, scale but 144 feet by the rule, or seven stand-
ards to the thousand, and the actual ratio between stand-
ards and thousands is stated to run all the way from 4'
to 14.
148 A MANUAL FOR NORTHERN WOODSMEN
The ratio between cords and standards is nearly con-
stant in logs of all sizes if cut of equjil length. In the
Adirondack woods 2.92 standards are commonly reckoned
as one cord.
SECTION VI
SCALING PRACTICE
Logs are best scaled when they are being handled over,
as on a landing or mill brow, for then all parts can be seen
and got at. Measurement in the pile, especially for long
logs, is both difficult and unsatisfactory.
1. Length. A tape worked by two men is an accurate
measure of length. Short logs may be accurately measured
with a marked pole, and for long logs a carefully adjusted
wheel with brads in the ends of its spokes is cheap to use
and reasonably accurate. Measurement with a four-foot
stick has a very wide range of accuracy, according to
the way it is done.
pLiii
k^iOiaiu"
8"7£St*:
GERMAN NUMBERING HAMMER
Valuable timber cut into standard log lengths is com-
monly allowed two inches extra to permit trimming at
the saw, this amount being disregarded in the scale. If
logs are cut without measuring, in which case they are as
likely to be ten inches over foot lengths as two inches, the
extra inches are commonly thrown off just the same. That
practice, however, means in 16-foot logs a loss of 2£ per
cent on the scale or the timber. On 30-foot logs, it means
l£ per cent.
2. Diameter. The diameter measure for any board rule
is obtained at the small end of the log and inside the bark.
It is important in large and valuable timber that an aver-
age diameter be taken. In dealing with fractional inches,
SCALING PRACTICE 149
there is a variety of practice. Some sealers read uniformly
from the inch nearest the exact diameter ; some disregard
all fractional inches and take the next inch below; some
vary the practice according to length and taper of the
individual logs.
Probably, the most just practice to follow, as a general
rule, is to throw off all fractions of inches up to and in-
cluding one half inch, and to read fractions over one half
as of the inch above. This practice, in logs under 16
inches in diameter, gives results from 7 to 10 per cent
greater than if all fractions of inches are thrown out.
3. Culling for Defects. Defects in logs consist in irregu-
larity of form, in shakiness, and in decay. Knots are not
properly considered as defects, but as a factor in general
quality. All these matters vary with the species, with the
locality, and with the individual log. They are matters
which have to be dealt with locally and individually, and
little can be written that is likely to be of service and not
liable to do more harm than good.
The curved or sweeping form is a common defect in
logs. Sealers frequently have rules for allowing for it,
but these differ so widely that they cannot be transcribed
here. (See page 145 for the result of this defect in logs of
different sizes.)
Irregular crooks in logs cannot be classified. A man can
sight along a log and estimate what proportion of it can be
utilized «by the straight cuts of a saw, and this guided by
mill experience is the only way of dealing with the matter.
Seams caused by frost and wind form another class of
defect, more frequent in northern woods and in trees grown
on exposed places. Sometimes these are shoal and have
little or no effect on saw product. Sometimes they reach
nearly or quite to the heart of a log.
A fairly general practice on northern spruce cut for saw-
mill use is to discount 10 per cent for straight, deep seams,
and for twisting seams up to 33 per cent, or even to throw
out the whole log.
It is to be remarked that these defects have, when reck-
oned in percentage, a far greater effect on small logs than
on large ones. Thus a three-inch sweep in a 15-inch, 12-
150 A MANUAL FOR NORTHERN WOODSMEN
foot log takes but a small percentage out of its total yield
at the saw, while a 6-inch log with the same sweep is
practically useless for full length, edged lumber. Again,
strong taper may largely neutralize the effect of consider-
able irregularity in outside form. Lastly, in practical
scaling, a certain amount of irregularity in outside form
must be considered normal and be taken care of by the
conservatism of the log rule.
Shakiness in logs is far more frequent in some species
than in others. Thus hemlock is largely affected by it,
while there is very little of it in spruce. In large measure,
it should be considered as an element of quality, affecting
the grade of the product, not a defect affecting the scale of
the logs. When, however, a considerable section of a log
is rendered worthless, it should be thrown off in the scale.
How much to throw off is a matter of judgment and of mill
experience.
Decay may be complete, utterly destroying the value of
a whole log or a section, or it may be partial, allowing the
production of a low grade of lumber. Decay varies much
according to species and locality, and it occurs in various
forms. Of the northern soft-wood trees, fir is most liable
to unseen defects, — a log perfectly sound to all outside
appearance may " open out " very poor at the saw. To
a less extent white pine in some localities is affected in the
same way.
Generally, however, the ends of a log or some mark on
its surface, such as rotten knots, " punks," and flows of
pitch give indication to the practiced eye of defect beneath.
How much to allow is then a matter of judgment based
on mill experience.
The following table 1 has been made up, giving the loss
due to round center defects extending through or affecting
the full length of a log. For four- or five-inch defects, it
amounts to the same thing as throwing out a scantling
having the same side as the hole has diameter.
As stated at the start, careful mill training is the only
safe basis for the correct culling or discounting of logs.
Some sealers have that; some do not, and have to rely either
1 Graves' " Forest Mensuration."
MILL TALLIES
151
TABLE OF LOSS BY HOLES OR ROT NEAR THE CENTER
OF LOGS, GOOD FOR DEFECTS MORE THAN 4
INCHES FROM THE BARK
Diam.
of Hole
Length of Logs in Feet
10
12
14
16
18
20
Inches
Board Feet
2
3
4
5
6
8
9
10
5
9
14
20
27
36
45
56
67
6
11
17
24
33
43
54
67
81
7
13
1
38
50
63
78
93
8
15
23
32
44
57
72
89
107
9
16
25
36
49
65
81
100
120
10
18
28
40
55
72
90
112
133
on arbitrary rules or on guesswork. Proper discount may
vary greatly, too, with the mill practice and product. A
mill with a box factory attached, or sawing round-edged
stuff which is measured regardless of crooks, wastes little
or nothing on account of defective form. For a mill
which can market only three-inch deals at a profit, an
entirely different system of scaling is appropriate.
SECTION VII
MILL TALLIES
Thousands of unrecorded tests of scale rules have doubt-
less been made at the saw, using local and current scaling
and sawing methods. During the last few years a number
of such tests have been made under stated conditions so
carefully guarded that they may serve a general purpose.
Reference is made to the tests recorded on pages 143 and
144 of this work. The following also are reliable and of
interest to northern workers in timber.
The wide variation in the yield of logs as sawed under
different conditions is a matter of great importance in
several ways to the worker in timber, chiefly, perhaps, for
its bearing upon timber estimates. The relative compe-
152 A MANUAL FOR NORTHERN WOODSMEN
tence of sawyers is one cause of this, and that, according to
careful mill men, may readily amount to 10 per cent. Then
market demand affects the matter, some mills being so
situated that they can market only the larger sizes of lumber.
The type of saw employed and the methods of handling
on the carriage also have their effect.
TABLE I
Yield in inch boards, squared, of second growth white pine
logs. Based on 740 logs; study by Harvard Forest School.
Growth extra tall and smooth; large and small trees in
the stand, which was cut clean; logs with 2 in. crook or
over thrown out. Sawed by circular saw cutting }-inch
kerf. In scaling, fractions of inches up to .5 were thrown
off, fractions of .6 and over taken as if of inch above.
Boards merchantable down to 2 feet, surface measure;
some wane allowed.
Top
Yield B.M.
Diameter
12-foot Logs
14-foot Logs
5 inches
14
15
6 inches
20
23
7 inches
26
30
8 inches
34
39
9 inches
43
50
10 inches
53
61
11 inches
67
76
12 inches
81
90
13 inches
95
105
14 inches
110
122
15 inches
128
139
16 inches
147
160
17 inches
170
18 inches
202
A practice that in some localities of recent years has
greatly increased tjje merchantable product of logs is that
of sawing waney or round-edged boards. Portable mills in
southern New England sawing lumber for boxes or finish
follow this practice largely, and stationary mills in many
localities have a box or other saw to which they can turn
over the small and crooked logs for this most economical
MILL TALLIES
153
form of manufacture. When boards in this form are sur-
veyed they are measured at the average width, inside bark,
on the narrow side, without discount for crooks. -
This practice has brought about great economy in the
use of timber, and when done with thin saws, has secured
from logs a far greater product than current scale rules
give. Several of the tables given herewith are of special in-
terest in this connection. In all these tables top diameter
means diameter of the upper end of the log inside bark.
TABLE II
Yield in inch boards of second growth white pine logs,
saived with a circular saw cutting \-inch kerf. Greater part
of boards not edged, but measured for width at an average
width, inside bark, on narrow side, without discount for
crook.
Based on 1180 logs. From Massachusetts State Forester.
Length of Log — Feet
Inches
10
12
14
16
Vol.
Vol.
Vol.
Vol.
Bd. ft.
Bd. ft.
Bd. ft.
Bd. ft.
4
9
13
17
21
5
13
17
21
26
6
17
22
27
32
7
23
29
35
40
8
30
37
44
51
9
47
55
64
10
48
58
68
79
11
58
70
82
98
12
69
83
97
115
13
80
96
113
136
14
92
111
131
158
15
104
129
150
180
16
117
146
170
205
17
131
165
192
230
18
184
220
256
As the edged lumber was taken from the larger and
straighter logs and after those logs had been sided on the
carriage and turned down, the yield was probably as large
as if all boards had been left round-edged.
154 A MANUAL FOB NORTHERN WOODSMEN
TABLE III
Same logs but grouped according to mid diameter outside
bark.
Length of Log — Feet
Mid
Diam.
10
12
14
Inches
Contents — Board Feet
5
7
8
10
6
10
13
16
7
15
19
23
8
22
27
31
9
28
34
40
10
35
43
50
11
44
53
63
12
53
64
77
13
61
76
91
14
70
88
106
15
82
104
125
16
95
119
144
17
109
136
163
18
155
184
19
173
204
20
193
226
21
211
247
22
235
273
23
256
298
24
281
328
25
304
355
26
384
The figures of the above tables were closely confirmed,
except in the smallest sizes of logs, by similar figures ob-
tained by the U. S. Forest Service for the Forest Commis-
sion of New Hampshire. The saws in this latter test cut
J-inch kerf; 60 per cent of the product was round-edged
stuff, the balance being squared ; 70 per cent of the lumbei
was cut 1 inch thick, the balance 2^ and measured as 2
inches. In the sizes under 8 inches the Massachusetts
mills cut somewhat closer.
MILL TALLIES
155
TABLE IV
Comparison of Maine Log Rule and results of sawing
as shown in Tables I and II. IZ-foot logs.
Results of Sawing
Top Diameter
Inches
Maine Log
Rule
Edged Lumber
Table I
Round-edged
Lumber
Table II
4
13
5
i4
17
6
'is
20
22
7
23
26
29
8
33
34
37
9
39
43
47
10
51
53
58
11
62
67
70
12
78
81
83
13
90
95
96
14
107
110
111
15
121
128
129
16
134
147
146
17
154
170
165
18
174
202
184
TABLE V
Yield in %-inch boards of pine logs 4 feet long (+ 2 inches
for trimming).
Yield
Basis
Surface Measure
4 inches
4 feet
3 logs
5 inches
6 feet
48 logs
6 inches
9 feet
121 logs
7 inches
13 feet
109 logs
8 inches
9 inches
17 feet
22 feet
75 logs
84 logs
10 inches
28 feet
40 logs
11 inches
34 feet
36 logs
12 inches
41 feet
21 logs
13 inches
49 feet
11 logs
14 inches
57 feet
6 logs
15 inches
66 feet
4 logs
16 inches
75 feet
6 logs
156 A MANUAL TOR NORTHERN WOODSMEN
Log diameter taken at top end, inside bark. Saw kerf
£ inch. Boards not edged, but measured at an average
width on narrow side. From Massachusetts State Forester.
A cord of pine wood sawed and measured in {his fashion
yields about 1000 feet of box boards. Sawed one inch
thick, it is counted by Massachusetts box board men to
yield about 650 feet surface measure.
TABLE VI
Yield in round-edged boards of second growth hard
wood logs 12 feet long cut 1% inch thick with circular saw
cutting \-inch kerf. Based on 1831 logs.
Grouped according to top
diameter.
Grouped according to mid
diameter.
Top Diameter
Inside Bark
Yield, Surface .
Measure, of 12-
foot Logs
4 inches
8 feet
5 inches
11 feet
6 inches
16 feet
7 inches
22 feet
8 inches
30 feet
9 inches
39 feet
10 inches
51 feet
11 inches
65 feet
12 inches
82 feet
13 inches
100 feet
14 inches
120 feet
15 inches
141 feet
16 inches
165 feet
17 inches
192 feet
18 inches
222 feet
Mid Diameter
Outside Bark
Yield, Surface
Measure, of 12-
foot Logs
6 inches
11 feet
7 inches
15 feet
8 inches
21 feet
9 inches
29 feet
10 inches
37 feet
11 inches
49 feet
12 inches
61 feet
13 inches
75 feet
14 inches
91 feet
15 inches
107 feet
16 inches
126 feet
17 inches
143 feet
18 inches
165 feet
19 inches
187 feet
20 inches
210 feet
From New Hampshire Forestry Report for 1905-1906.
CORD MEASURE 157
SECTION VIII
CORD MEASURE
The exact legal definition of the term " cord " varies in
different localities. For the present purpose it is a pile of
wood 8 feet long and 4 feet high, with the top sticks ris-
ing somewhat above the line, the sticks themselves sawed
4 feet long or chopped so as to give an equivalent. Such
a pile occupies 128 cubic feet of space. A cord foot is £ of
a cord, or a pile 4 feet high, 4 feet wide, and 1 foot long.
The actual solid contents of the wood which a piled cord
contains depends on a number of factors. First is the care
used in piling, a matter which need only be mentioned
here. Other factors are the straightness and smoothness
of the wood, its size, assortment, and whether split or not.
In regard to the first of these factors, while it is per-
fectly evident that straight, smooth, well-trimmed wood
must pile closer than its opposite, no hard and fast rules
can be given. Taking round wood of given quality, the
following rules can be laid down :
1. Large wood piles closer than small wood.
2. The same wood put up in one pile with sizes mixed
occupies a little less space than if the larger and smaller
sizes are piled separately.
3. The effect of splitting varies much with the quality.
Smooth, straight-grained wood when split may be packed
into the same space that it occupied before. On the other
hand, small or crooked wood when split piles much more
loosely.
In regard to the actual solid contents of a piled cord,
the following rules will approximately hold.
1. Smooth, round wood 8 inches and up in diameter,
such, for instance, as the best pulp wood, has .8 of its
contents in solid wood or yields 102 cubic feet solid to
the cord. White birch of best quality will yield nearly
or quite the same.
2. Small pulp wood from 3 to 8 inches in diameter con-
tains about .7 of its stacked volume in solid wood, or 9Q
158 A MANUAL FOB NORTHERN WOODSMEN
cubic feet to the cord. Smooth hard wood yields about the
same.
3. Still smaller round wood, wood that is crooked and
knotty, and good split hard wood contains in solid wood
about .6 of the outside contents of the pile or 77 cubic feet
per cord.
4. Small, crooked wood cut from limbs may run down
as low as 27 solid cubic feet per cord.
5. 1 The longer a lot of wood is cut, the greater will be
the vacant space left in piling. Fair sized pulp wood, for
instance, which when cut 4 feet long will measure a cord,
if cut in 2-foot lengths will pile up in 2 to 3 per cent less
space. The same wood, on the other hand, if cut 8 feet
long and measured in the pile will measure nearly 6 per
cent more; if 12 feet long, about 12 per cent more.
Wood in thorough air-drying shrinks about 10 per cent
on the average, hard woods as a rule more than soft. If
wood checks and cracks freely, something like half the
total shrinkage is taken up in this form. Two inches extra
height in the pile are commonly allowed on green wood
in Massachusetts.
To Measure Wood in Cords. When the wood is 4 feet
long, measure the height and length of the pile in feet,
multiply together, and divide by 32. The result will be
contents in cords. If the wqod is more or less than 4 feet
long, multiply length, width, and height of the pile together,
and divide by 128. If wood is piled on sloping ground,
the length and height should be measured perpendicular
to one another.
For measurement of logs into cord measure, see page 138.
The French cord of the Province of Quebec is 8' 6" X 4'
X 4' 3", containing, therefore, 144 cubic feet, as against
128 for the cord current elsewhere.
1 See Zon on this subject in Forestry Quarterly, Vol. I, No. IV.
PART IV
TIMBER ESTIMATING
PART IV. TIMBER ESTIMATING
SECTION I. INTRODUCTION
SECTION II. INSTRUMENTAL HELPS
SECTION III. HEIGHT MEASUREMENT
SECTION IV. VOLUME TABLES AND TREE FORM
SECTION V. PRACTICE OF TIMBER ESTIMATING
A. Small and Valuable Tracts
B. Larger and Less Valuable Tracts ....
1. Type and Plot System
2. The Strip System
3. Line and Plot System
C. Summary
D. Pacific Coast Methods
161
162
165
167
173
174
186
187
188
192
195
196
PART IV. TIMBER ESTIMATING
SECTION I
INTRODUCTION
METHODS of estimating timber vary greatly in different
regions and with different men. They vary also with the
value of the timber involved and with the purpose for
which the work is done. In this last connection cost is
a guiding principle; in general, that method of doing a
piece of work is best which secures a result sufficiently
accurate for the purpose with the smallest expenditure
of time and money.
Lump Estimate by the eye has not gone out of use, and
in fact never will cease to be employed. The immediate
judgment that a good lumberman forms, simply by walk-
ing through a piece of timber, that it contains a hundred
thousand, a million, or ten million feet, is for many pur-
poses close enough to the mark.
Similarly an experienced man, in timber of a kind
with which he is familiar, forms an idea by direct impres-
sion of how much a piece of land will yield per acre. The
men who can do that are more numerous than those who
are able to judge the whole piece. The faculty is easier
to acquire, and in general the results are safer and more
reliable.
Such estimates as these are indispensable in actual
business. Frequently they enable a man to pass correctly
upon a proposition for purchase or sale. But while
their necessity and their reliability within limits may be
admitted, no illusions should be indulged in with regard
to them. For one woodsman who can actually give a
close and reliable estimate after these methods, there are
many who only think they can ; nothing is better known
in the timber business than widely variant and totally
erroneous estimates of standing timber. Further, a man
162 A MANUAL FOR NORTHERN WOODSMEN
who uses these methods is frequently very lame when he
gets into a country with which he is unfamiliar. Lastly,
when time consumed and training involved are considered,
estimates of this nature may not be the cheapest by any
means.
There is a general tendency among timber estimators,
commendable in the main on the ground of safety and
conservatism, to put their figures below the mark. As for
the general degree of accuracy obtained, there seems to
be no reason founded on experience this side of the At-
lantic to greatly change the verdict of experience in Europe '
that good and experienced men in timber with which they
are familiar are liable to errors up to 25 per cent.
It is true, moreover, that the weakness of these tra-
ditional methods is generally recognized. More careful
and elaborate methods are in fact practiced in many
sections of the country, and the area is fast extending in
which the treatment demanded by the situation is not
really an estimate but a survey.
SECTION II
INSTRUMENTAL HELPS
The helps that may be used in the survey of standing
timber are as follows:
1. FOR DIAMETER MEASUREMENT
Calipers for measuring the diameter of trees may be
constructed by the woodsman himself, or they can be
purchased of dealers. The best are made of light-colored
hard wood and have the inches plainly marked on both
flat sides of the bar. The jaws are detachable for con-
venience in transportation, and the sliding arm is so fitted
with adjustable metal bearings that it is truly square and
gives a correct diameter when pressed firmly against a
tree or log.
Substitutes for the caliper, useful in some circumstances,
are the Circumference Tape, a steel tape so graduated
that when a circumference is measured a diameter is read,
1 Schlich's "Manual of Forestry."
INSTRUMENTAL HELPS
163
and the Biltmore Stick. This last is in construction a
wooden bar of about the dimensions of an ordinary scale
rule; in use it is held horizontal, tangent to the tree being
measured, and at the natural (but a constant) distance
from the eye of the observer. Then, one end of the stick
being aligned with one side of the tree, where the line of
sight to the other side cuts the stick it is graduated for the
given diameter.1 Both instruments have proved service-
able on the Pacific Coast, where the timber is so large that
a caliper is cumbersome, and because of their portability
they have a field of use elsewhere. They are not, however,
as quickly manipulated as the caliper hi steady work on
timber of ordinary dimensions.
]
TREE CALIPER
2. COUNTER OR TALLYING MACHINE. TIMBER SCRIBE.
BARK BLAZER
These simple little instruments, the last of which can
be home-made if necessary, are very serviceable in forest
work, particularly in timber estimating.
3. THE DENDROMETER
The dendrometer is an instrument for measuring the
diameter of a tree at a considerable distance above the
ground. There are several forms of this instrument,
most of them costly and complicated, that are employed
in scientific investigation. With these the practical woods-
1 See Appendix on theory and accuracy of this instrument.
164 A MANUAL FOR NORTHERN WOODSMEN
man has no concern. Such a man when he wishes to
know the diameter of a standing tree at a point out of
reach will ordinarily either estimate it or cut the tree
down.
ARK BLAZER
Occasionally, however, timber
may be met with which is of suf-
ficient value for special purposes
to require measurement in this
way. In such a case the engineer's
(,^ -^-^ ^^ transit may be employed, and by
3 1 its aid it is not a difficult matter
* to determine either the height at
which any given diameter is at-
tained or the diameter at any given
height. A very simple little in-
strument for diameter measure-
ment has been devised, which is described by its inventor
as follows : *
TIMBER SCRIBE
" The Biltmore pachymeter is used in connection with
a target or piece of board graduated in inches, marked
1 Forestry Quarterly, Vol. IV, p. 8.
HEIGHT MEASUREMENT 165
black and white, which target is fixed horizontally at any
point desirable at the base of the tree.
" The instrument itself consists of a piece of metal about
18 inches long and l£ inches wide, containing a longi-
tudinal slot about J inch wide and 17 inches long. The
edges of this slot must be strictly parallel. Its actual
width is entirely irrelevant from the mathematical stand-
point.
" It might be stated that any stick or pole, even a walking-
cane, having parallel edges, will answer the purpose of
establishing and measuring upper diameters. The Bilt-
more pachymeter is merely a device convenient to handle.
" The observer holds the pachymeter pendulum fashion
by the hand of the outstretched arm in a position parallel
to the tree trunk, and moves the instrument backward
or forward until the edges of the slot cut off even with the
desired diameter shown on the target. Then, the eye
following upward along the trunk and sighting through
the slot, that point on the tree bole is readily obtained
where the bole cuts off with the edges of the slot. The
position of this point above ground can be ascertained
easily with the help of any hypsometer."
SECTION III
HEIGHT MEASUREMENT
There are many methods of measuring the height of
trees. As serviceable as any are the following:
1. Windfalls are often of great assistance in ascertain-
ing the height of timber.
2. A pole 15 or 20 feet in length may be set up along-
side the tree to be estimated and then, standing some dis-
tance away, the cruiser may run his eye up the tree and
judge how many times the length of the pole will be con-
tained in it. A pencil held erect at arm's length in range
of the pole and then run up the tree will help the eye in
making the judgment.
3. A cane or staff may be used on the principle of similar
triangles. Hold the staff firmly in the hand with the arm
straight and horizontal. Swing the end of the staff down
166 A MANUAL FOR NORTHERN WOODSMEN
by the face and adjust the hold till the end of the staff
just comes by the eye. The distance from the e"ye to the
staff and from the hand up to the end of the staff are now
equal. Go off from the tree to be measured, holding the
staff erect, until you can sight by the fist to the base of the
tree and by the top of the staff to the top of the tree. Pace
or measure to the tree and this will give its height.
4. The Abney clinometer, shown on page 93 of this
work, may be used for height measurement in much the
same manner. Set the level tube at an angle of 45° with
the line of sight and go off from the tree on a level with
FAUSTMANN'S HEIGHT MEASURE
its base until, sighting at the top of the tree, you see by
the bubble that the tube is level. The distance from the
observer to the tree is then equal to the tree's height.
5. A second method employing the same instrument
is as follows : Stand at a point where both the top and the
base of the tree can be seen and at some convenient dis-
tance from it, as 100 feet. Sight to the top of the tree and
observe the angle of inclination, and again to the base of
the tree, observing that angle also. Go into the table of
tangents with the angles in turn, find the decimals corre-
sponding, and multiply by the length of base. The sum
of the two figures is the total height of the tree.
VOLUME TABLES AND TREE FORM 167
Example : Standing 80 feet from a tree, the angle to the top is
found to be 31 ° and that to the base 8} °, of depression. From the
tables the tangent of 31 ° is found to be .6009 ; multiplying this by
80 gives 48 feet for the height of the tree above the level of the eye.
Again the tangent of 8J° is found from the tables to be .1495 and
this multiplied by 80 gives 12 feet. 48 + 12 = 60 feet, the total
height of the tree.
6. Faustmann's height measure works in much the
same manner, but gives the desired height directly without
the use of tables. This instrument may be had of dealers
at a cost of from $6.50 up. It is compact, not complicated,
and will be found of great service in estimating.
SECTION IV
VOLUME TABLES AND TREE FORM
A competent woodsman can tell from the looks of a
tree somewhere near what it will scale, saw out, or yield
in cord wood according to the practice with which he is
familiar, and this without any measurements. Or a
caliper may be used instead of the eye for diameter, and
some kind of determination made of the height of the
tree or the length and size of the logs into which it may
be cut. The point of such judgment and measurements
as a rule is their wider application. The single tree so
examined is taken as the type of many, and the stand of
an acre or of a considerable territory is thus estimated.
In this process the assumption is made that trees of the
same dimensions are approximately similar in shape,
while for the individual tree the fundamental factors de-
termining contents are recognized as height and diameter.
These two factors in any kind of timber work cannot
possibly be disregarded. Whatever the scaling or mill
practice of a locality may be, and into whatever form a
tree's trunk is dissected before manufacture, the height of
the tree and its diameter at some point near the base are
the chief factors determining contents. These factors,
consciously or unconsciously, are in the mind of every
estimator.
Scientific study of tree form began by making the same
assumption and selecting the same factors. While it
168 A MANUAL FOR NORTHERN WOODSMEN
was known that single trees depart widely from the
type, it was assumed that for trees having the same di-
ameter and height an average volume could be ascer-
tained which would hold approximately throughout the
distribution of the species. Proceeding on this assump-
tion, tables were worked out for the different tree species
and these when applied in actual business proved close to
the fact and vastly improved the work of timber valuation
in Germany a hundred years ago.
European measurements of logs and standing timber do
not recognize anything corresponding to the board foot,
but everything is reckoned in solid contents. The same
rule holds in the scientific study of tree form in all coun-
tries where it has been pursued, the unit in the United
States being the cubic foot. For all such studies, too, the
total height of the tree as a well-defined factor capable
of ready measurement has usually been employed rather
than any size limit set part way up, and a diameter breast
high, or 4^ feet above the ground, has been settled upon
as the basis of all diameter comparisons. The area of a
cross-section of a tree at this point is called the basal area,
and the same term is applied to a number of trees or to a
stand of timber. In the study of tree form, the term form
factor has proved to be a useful one. The form factor of a
tree is the percentage which the volume of any tree (usu-
ally reckoned in cubic feet, outside the bark) makes of
the volume of a cylinder having the same height and the
tree's breast diameter. Illustration: A tree 15 inches in
breast diameter and 75 feet high may, after caliper meas-
urement every 4 feet along it, prove to have 38.6 cubic feet
in it. A cylinder of these dimensions contains 92 cubic
feet. The form factor, therefore, is .42.
For many years past the study of tree form has been
ardently pursued, and many interesting facts and laws
have been ascertained. In large measure these results
have been brought to bear on the actual business of Euro-
pean countries where timber is grown as a crop under
uniform conditions. In this country, where the forests
are natural and as a rule irregular, it will be many years
before the same can be true. The following, however,
VOLUME TABLES AND TREE FORM 169
may for one reason or another be of interest to the worker
in timber:
(a) Near the ground a section taken lengthwise of a
tree is concave outward, due to the swell of the roots.
Above that, to a point somewhere near the lower limbs of
a forest-grown tree, the stem has almost a true taper.
From the lower limbs up, the form is roughly conical, with
a sharper taper than below, the taper usually increasing
toward the top.
(6) Of two trees having the same breast diameter, the
shorter will usually have the larger form factor. This
results from the relation just mentioned. Of two trees
having the same height, the stouter, more openly grown
tree will usually have a little larger form factor than the
other.
(c) Of two trees having the same dimensions, the older
one, as a rule, has the larger form factor. The effect of
other conditions of growth can seldom be clearly traced.
(d) Different soft wood species do not differ from one
another so greatly but that a volume table made for one
may for some purposes be used for others.
A large form factor in all these cases simply means
that the given tree more nearly approaches the form of a
cylinder, or, in other words, that it has a large amount of
wood for its height and diameter. That carries with it
more scale, more sawed lumber, or more cord wood.
A table giving the contents of trees of stated dimensions
is called a Volume Table. For scientific purposes solid
content is given, standard measure, but a table may be
worked out in cords, board feet, or any other unit required.
The tables employed by European foresters at the present
day are worked out commonly on the basis not only of
height and diameter but of age classes or of some other
determining factor, and they have proved to give the con-
tents of standing timber very accurately.
Tables of this kind have also been frequently devised
for estimating in this country. Usually these are local,
worked out in the timber of the region in question accord-
ing to local scaling methods; often also allowing the cull
which is found to characterize the region. Such volume
170 A MANUAL FOR NORTHERN WOODSMEN
tables have frequently been based on diameter alone. In
other cases — and this is essential unless a region is very
uniform in its timber growth — height has been taken
into consideration as well.
Thus many western and southern cruisers have made up
tables giving the contents of trees of each inch in diameter
and yielding 2, 3, 4, etc., logs as these would be cut in
local practice. Again, an old Adirondack manager made
up a table showing the number of spruce required per
cord of pulp wood for trees 7, 8, 9, etc., inches in di-
ameter, and short, medium, or tall, as the case for his
region might be. Local volume tables, thoroughly based
and used correctly, are the most reliable kind.
General Volume Tables for business purposes are of
two varieties, the trees being classified either by total
height or by length of merchantable timber. The assump-
tion on which the first is based, that trees which have the
same diameter and total height do not, when taken in
numbers, vary in form throughout the region of their
distribution, may, with a caution on the matter of age,1
be considered safe for most purposes. It is true, however,
that some Pacific Coast timbers, with a very variable
thickness of bark and the root swelling of large trees run-
ning above a man's height oftentimes, have to be handled
with special caution.
The other variety of tables classifies trees in height by
the number of standard log lengths they will yield or the
height at which their boles attain a specified diameter.
Under this plan the point to be observed is brought nearer
the estimator. It is not, however, as sharply defined a
point as in the other case, while, as explained on pages
277-278, special opportunities for error arise through vari-
ability in lumbering practice.
Another matter that has to be reckoned with in the
valuation of standing timber, and which becomes in some
species and regions a consideration of great importance, is
defectiveness in quality. This no general volume table can
allow for. It has to be worked out for each locality accord-
ing to the judgment or experience of the estimator.
1 See pages 169, 262, and 275.
VOLUME TABLES AND TREE FORM 171
Thirdly, a general volume table given in units of mer-
chantable material assumes certain standards of lumber-
ing practice. In one region, or on a property carefully
handled, stumps may be sawed close to the ground, tops
taken up to a small diameter, and every economy em-
ployed in cutting to advantage the material between;
while in another region, or on another property, a large
percentage of the wood of every tree cut down may be
left to rot on the ground. Similarly in the mill there is
great variety of practice, — location, equipment, market re-
quirement, and men's capacity all having their effect here,
as was explained and illustrated in earlier pages of this
work. Then the question may not be at all of saw practice,
but of the results of scaling, and here, as every lumberman
knows, there is the widest diversity. The scale rules in
actual use differ from one another in the values they give
to the same log, in some cases by a ridiculous amount,
while the practices that have grown up in their application
are in some cases entirely artificial. Details need not be
entered into here — a word to the wise is sufficient — but
an example will bring the fact home. The Maine log rule,
for instance, is believed by many to be the best commercial
rule on the market, agreeing closely with the results of
good saw practice; yet a Penobscot mill man once testi-
fied before a legislative committee that buying 26 million
feet of logs by market scale for a season's stock, he sawed
30 million feet of long lumber out of it and slabbed heavily
for a pulp mill besides.
Of the volume tables included in this work it may be
said that their basis is clearly stated, including the num-
ber of trees involved, the standards of cutting and mill or
scaling practice assumed, and the responsibility for the
observations. They can, therefore, to a large extent be
changed over to suit practice of another type. The tables
original with this work, those for spruce and white pine,
are based on figures taken from a large number of trees.
These came from a wide range of country, and the compu-
tations show that no clear difference of form was intro-
duced by the element of locality. Each tree was computed
separately for its volume in the units desired (cubic feet,
172 A MANUAL FOR NORTHERN WOODSMEN
board feet, or cords); the results have been averaged,
evened by curves, and then the board-foot tables have
been discounted by a small percentage to allow for normal
defects of form and quality. Cutting practice that is
economical, but not extreme, has been supposed through-
out, the idea being to get, as nearly as possible, a conserva-
tive figure for good and economical practice.
In applying all these tables, considerable defects must be
allowed for in the form of a discount. It is further to be
clearly understood that they apply to timber as it runs
and may be considerably off as applied to single trees.
In volume tables for hard woods merchantable length
is in most cases preferable to total height as a factor
because these trees characteristically spread out at the
top, at once rendering total height hard to measure and
destroying utility for lumber. Such tables also, because
of greater irregularity of form and greater liability to
defect in hard woods, are in general less trustworthy than
soft wood tables. Several "graded volume tables,"
classifying the yield of trees by lumber grades, are in
existence, but their utility apart from the local conditions
in which they were constructed does not seem clear.
The way in which these volume tables may be tested
and made to conform to the practices of any given locality
is illustrated as follows:
A spruce property is to be explored on which cutting and
scaling methods are as follows : — Timber runs up to about
20 inches in diameter and 75 feet in height ; trees are cut
down to the size of 12 inches on the stump or 11 breast high.
Logs cut for saw lumber, one log from a tree, cut off where
it will scale best. Logs are therefore seldom over 40 feet
long and run from that down to 28 or 30. Scaling done
with Maine log rule. If a log is 26 feet long or under, it is
scaled as one log with the top diameter inside bark ; if 27
to 30 feet, as two logs of equal length giving the butt log
an inch larger diameter than the top ; from 31 to 35 feet in
the same way but allowing 2 inches "rise," and 3 inches on
log lengths of 36 to 40 feet. In addition a level discount
of 10 per cent is made on all logs to cover defects.
A half day's time spent following the logging crew and
PRACTICE OF TIMBER ESTIMATING
173
examining trees as they are felled results as follows: —
20 normal trees 17 to 20 inches in breast diameter when
scaled by the above methods give 4730 feet B. M., while
trees of the same dimensions are given in the volume table
on page 238 5720 feet. The actual scale, therefore, is 17
per cent less than the tabular values.
24 trees 14 to 16 inches in diameter which by the table
should yield 4080 feet scale up 3480, or 15 per cent less.
30 trees 11 to 13 inches in diameter that by the table
should yield 4380 feet, actually scale 3500, or 20 per cent
less.
The figures of the volume table may now be reduced by
these percentages in those heights and sizes where on the
given job the figures are required. The working table
will then be as follows:
Breast
Feet in Height
Inches
50
55
60
65
70
75
11
12
1
56
68
64
80
72
88
%
92
108
13
72
80
92
100
112
125
14
85
100
110
125
140
155
15
100
115
130
145
160
175
16
130
143
155
175
ISO
17
142
158
175
ISO
210
18
155
175
195
210
230
19
175
195
215
240
265
20
195
220
245
270
295
SECTION V
PRACTICE OF TIMBER ESTIMATING
The methods that should be employed in a survey of
standing timber depend on a great variety of facts of which
the main ones are these: the size of the tract to be ex-
amined, the method and fineness of its subdivision, the
variety in its stand of timber, the value of the timber, and
the experience and qualifications of the estimator. These
methods are best discussed in two divisions, — first,
methods for small tracts with valuable timber as a rule;
and second, those for large tracts where more extensive
processes must be employed.
174 A MANUAL FOR NORTHERN WOODSMEN
A. SMALL TRACTS
1. In the case of very valuable timber it may pay the
owner or purchaser to examine each tree individually,
ascertain its contents carefully, and study it for defects.
The net contents of each tree as so ascertained will then
be put down separately in the notes, and in case several
parties are interested, each tree may be stamped with a
number to correspond with one in the notes. At any rate,
blazing each tree examined is a good means to make sure
that all are taken and to prevent measuring any twice.
Such procedure as this is appropriate to very large and
valuable pine or to valuable but over-mature hard woods,
which are especially liable to be defective. Volume tables
might help in such cases, but they cannot be fully trusted ;
a scale rule at hand would be to many men of quite as
much assistance. For instruments, a caliper would come
in play along with an instrument to measure heights
accurately, while use might be found for some form of
the dendrometer. But the best part of the equipment of
the estimator in such cases is local experience in cutting
and sawing the same class of timber.
2. When timber in good stand and of considerable
value is involved, it may be advisable to caliper each of
the trees and measure a sufficient number to obtain the
range of heights. After the stand is measured, sample
trees of different sizes may be estimated after careful
examination, or such trees may be felled and measured.
Better than either of these methods, however, is a volume
table giving the yield of trees of the given kind and dimen-
sions. Volume tables, however, cannot be depended on
to allow justly for defects. That is a matter for the judg-
ment of the estimator.
The above method works well in woods of approximately
even type. When, however, the stand has a great variety
of form and quality, the difficulty in making a true valua-
tion is greater. In that case it may be practicable to cut
it up into nearly homogeneous parts.
The following example taken from practice will illus-
trate the methods of working in a simple case.
PRACTICE OF TIMBER ESTIMATING
175
Estimate of about 7 acres of land, covered nearly throughout
with white pine standing fairly evenly, but not as a rule very dense.
Concluded after inspection that no such differences of type or
Field Observations
Computed Volumes
Breast
Diam.
No.
Trees
Observed Heights
Deduced
Height
Scale
Each
Total
Scale
8"
85
51-47-50-54-59
50'
50'
4250'
9
70
50-47-52-48-56-57
55
70
4900
10
70
69-55
60
95
6650
11
75
56-56-66-67-68
65
130
9750
12
78
72-75-69-80-69-63
69
162
12636
13
69
57-65-71-75-73
73
203
14007
14
66
77-75
76
245
16170
15
81
74-78-80-79-83
78
290
23490
16
71
74-80-85
80
335
23785
17
63
77-77-86-81
80
370
23310
18
63
77-83-86
80
405
25515
19
52
80-77
80
445
23140
20
47
75-82
80
485
21855
21
32
79-83-81
80
525
17800
22
12
76
80
570
6840
23
11
79-82-83
80
620
6820
24
6
77-86-77-82
80
665
3990
25
8
87
80
715
5720
26
3
80
770
2310
Total 252938
Plot of Observed Heights and
Deduced Height Curve
1
'
. •
0
did
?-
^
ss?
£:0
£
y
A fin
/
7> rr
/
B M
/
40
9 10 11 12 ia 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Diameter Breast High — Inches
form existed as to call for differentiation of treatment. Instru-
ments employed, caliper and Faustmann's hypsometer. Steps of
the survey as follows:
a. Merchantable trees (those 8 inches and over in diameter
breast high) calipered and scored in inch diameter classes.
176 A MANUAL FOR NORTHERN WOODSMEN
b. Some 60 heights measured with the hypsometer. These
might have been averaged for each diameter class, but a better
plan is to plot all the heights on cross-section paper and draw a
curve through them as in the accompanying sketch. From this curve
the average height of the 8-inch trees is read off as 50 feet, of the
9-inch trees as 55 feet, and so on. The larger trees of the grove,
those 16 inches and over in diameter, averaged 80 feet in height.
c. From the proper volume table the contents of a single tree of
each size class is now taken and multiplied by the number of trees
in the class. For the tract in question Table No. 4 gives the
figures wanted, the product of the trees in boards, both round-edged
and square-edged lumber. In this table the contents of a tree 8
inches m breast diameter and 50 feet high is given as 50 feet B. M. ;
that of a tree 9 inches x 55 feet, 70 feet, and so on. No discount
appearing necessary for defects, by addition of the contents of the
size classes the total stand of the lot is obtained. This comes to
253 M feet, of which in the practice of the locality 20 per cent may
be sawed into good plank, 30 per cent into edged boards, and the
balance of 50 per cent, the smaller trees and rougher logs, put into
round-edged box-board lumber. The recorded figures, the plot
and height curve, and a table showing the way the figures are put
together, are given on the preceding page.
The estimate after this fashion of 250 M feet of timber
of this size is a light day's work for two men. Three men
form an economical crew for big jobs.
3. In the valuable timber lands of the Lake States and
South it is customary to estimate each forty acres by
itself, and the methods of estimation frequently cover
the whole stand. Pacing is largely used as a measure of
distance, and the cruiser is generally equipped with some
kind of volume table giving as often as not the board
contents of trees of different diameters yielding 2, 3, 4, or
5 16- ft. logs. Usually two men work together. In that case
the helper may run a compass line across one end of the
" forty," ten rods or so from its boundary, leaving marks
enough so that on the return trip it can be followed.
Through the strip so cut off the cruiser circulates, keep-
ing watch of his other bound and scoring down, as he
passes, the merchantable trees according to species and
in appropriate classes. As a rule very little measurement
of height or diameter has been done in the past. The two
men keep abreast of one another. When one strip has
been covered another is taken in the same way. After
the whole " forty " has been covered addition of the
PRACTICE OF TIMBER ESTIMATING
177
figures obtained gives its timber stand. In well-timbered
land two to four " forties " a day can usually be covered
by these methods.
In recording the results of such an estimate the size
and quality of the timber are of course noted as well as
its amount, and general notes on the growth, topography,
and lumbering conditions of the land are also recorded.
Following are sample notes of such an exploration:
Twp. 29 N. R. 7 W. S. E. i of S. E. i of Sec. 8.
White Pine, 7 logs average to M. ; 30% uppers 835,000
Norway Pine, 8 logs to M. 110,000
Hemlock, 11 logs to M. 175,000
Basswood, 7 logs to M. 15,000
Maple, 14 logs to M. 65,000
Total 1,200,000
Land slopes to North. Clay soil; very stony. Two ravines
running N. W. and S. E. through the " forty." Tamarack swamp
of about five acres in N. W. corner.
Another method of timber cruising carried out by one
man alone is described as follows in the "Woodsman's
Handbook " :
A "forty" is 80 rods square. The cruiser who uses the method
now to be described has found by trial that 500 of his natural
paces are required to go 80
rods. He begins at the cor-
ner of a " forty," say at the
southeast corner, and steps
off 125 paces on the south
line, and so covers one-
quarter of the side. He then
stops and, facing north,
counts the trees of the
"forty," first to an estimated
distance of 125 paces on the
right hand, and then to an
estimated distance of 125
paces on the left hand, and
m each case to a distance
of 100 paces in front of him, thus including the area represented
in the diagram as Plot I. He then steps north 100 paces, and
in the same way counts the trees in Plot II, and repeats the opera-
tion successively for Plots III, IV, and V. He has then a complete
count of the trees on the eastern half of the " forty." He then
walks west 250 paces along the north line of the " forty." Facing
south, he now counts all the trees on Plots VI, VH, Mil, TK,
and X in the same way as before, and thus completes counting
the trees on the entire " forty. "
Plot
VI
Plot
V
Plot
VII
Plot
TV
Plot
VIII
Plot
III
Plot
IX
Plot
II
Plot
X
Plot
I
178 A MANUAL FOR NORTHERN WOODSMEN
There is, of course, great variety in the details of the
work as practiced by different men, and a plan that is
really inadequate may be effective nevertheless because
of the ability of the cruiser. Such a method as the fore-
going cannot be called a survey. It is an estimate purely,
depending on the training of the cruiser and subject to the
errors which change in his condition and his surroundings
introduce. Nor does the fact that all the area is supposed
to be covered give assurance on the matter of accuracy.
It may indeed set up a standard too difficult to be actually
carried out, so becoming a source of additional error.
4. The following, from an old Michigan cruiser whose
work has been largely in hard woods, serves to introduce
the principle of covering a percentage of the tract to be
estimated, a principle more fully illustrated in connection
with large tracts on later pages.
I have been a surveyor, engineer, "land-looker" since boyhood,
and the system that I use is based upon the information that I
have been able to pick up along that line during that period.
The work has carried me to the forests of nearly every state that
counts forest products among its most important assets.
The usual object of an estimate is to fix a value that can be
used as a medium of exchange, although I have recently been
called upon to estimate many tracts just before the commence-
ment of logging operations in order to ascertain what the probable
product would be.
The report of the cruiser is required to show the log scale of a
given tract, also the amount of tan bark, cord wood, telephone
poles, railroad ties, etc., — in fact the entire forest product that is
of value. This must be not only of standing timber, but of down
timber that has a value as well.
His report must also show the topography of the tract, and the
channels through which the product must be passed in the course
of its transportation from the land, whether by railroad, water, or
logging road.
This work must be based upon some system that will eliminate
so far as is possible all guesswork. There are many systems of
cruising now in use, each of which has its advocates. I do not
know of any other cruiser who is using the same system that I use,
perhaps for the reason that I have made it up from my own work.
In my work I use a tree caliper. I have a book printed especially
for the tally of the trees as I call them off to my assistant. I have
also a form of report blank made to fit the rest of the scheme.
You will note that I number each forty-acre parcel in an undi-
vided section on the same plan that sections are numbered in a
PRACTICE OF TIMBER ESTIMATING
179
township, except of course that there are only 16 lots in this case.
Hereafter the term " lot " applies to a forty-acre tract.
Arriving at the tract to be examined, I usually first go entirely
around the area so as to discover if there are any high ridges, and
if so to determine their course ; also to see whether or not the tract
is all timbered, and to locate any vacant areas on its outer edges.
While making this circuit we mark points at each 125 paces on the
boundary. If the land is uniformly level, it is immaterial at which
point on the boundary line the work is commenced. If the tract
is very rolling, the strips taken must be
at as nearly right angles as is possible.
'R3.W..
____________ Go..Cheboygan. ___ Sta.te.Mich
Suppose we are at the southeast corner of the section and that we
have an entire section of fairly level land to examine. My pacer
and compassman (I have but one assistant) steps off 125 paces,
say in a westerly direction, along the south line of lot 16, starting
from the southeast corner of the section. This brings us to a
point 20 rods west of this corner and a line drawn directly north
from this point should be parallel with the east line of the lot, also
parallel with the center line, if one were in existence, and 20 rods
distant from each of them. We proceed north from this point. At
50 paces the assistant halts, gets his tally-book and hard pencil into
action, and jots down each tree as I call them off to him. He
heads the vertical columns with the varieties of timber common to
the tract and tallies each kind under the proper heading.
180
A MANUAL FOR NORTHERN WOODSMEN
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As soon as the assistant reports that he is ready I take the
nearest tree and put the calipers upon it at a point where it would
be cut in ordinary logging operations. I then walk around the tree
and " size it up " generally to find any defect that may exist, also
to judge how many 16-ft. logs would be cut from this particular
tree. Suppose it is a maple and that it calipers 22 inches, and that
it will yield a 48-ft. stem or three 16-ft. logs. I call to my pacer
" Maple, 22 — 3," and he tallies in the maple column opposite the
22 — 3 of the figures in the left-hand margin of the page. In this
way we get a record of every tree in a strip 4 rods wide, 2 rods each
side of our compass line. My caliper blade is graduated to 57
inches from the stationary arm, just $th of two rods, and if there is
any question as to a tree's being in the strip it is very quickly set-
tled by taking seven lengths of the caliper blade as I walk toward
the tree from the compass line.
Having taken the trees to a point a little in advance of my as-
sistant, he proceeds on for 50 paces more and the calipering process
is repeated. If the undergrowth is of sufficient density to prevent
our seeing any large pine, bit of cedar swamp, or anything else
that we should see, we make frequent explorations from the end
of each 100 steps, my assistant going in one direction at the same
time that I go in the opposite. No trees are measured in these
side explorations unless we find something that is not common to
the entire tract. Having returned to our line we proceed north,
halting at each 50 steps -to take the timber, also to note any ridges,
logging roads, streams, springs, or other points that should appear
in the report. When we have arrived at 500 paces my assistant
changes his tally to lot 9 and we proceed north in the same way,
changing at 1000 paces to lot 8 and at 1500 to lot 1. At 2000
paces, if the section is "full" we should be at the north line of the
section, at a point 20 rods west of the northeast corner. As it
rarely occurs that our compass line has been so accurate as to
bring MS out at exactly this point, we find the mark made during
PRACTICE OF TIMBER ESTIMATING 181
our circuit of the section and pace from it westerly along the north
line of the section for 250 paces, 40 rods. This brings us to a point
from which a line drawn south will be parallel with the center line
of lots 1, 8, 9, and 16, and with the west line of these lots and 20
rods distant from them. We proceed south on this line, taking the
timber in the same manner as we took it in going north in the east
half of the same lots. Arriving at the south side of the section we
again go west 250 steps and then north through the easterly half of
lots 15, 10, 7, and 2, and so on until the section is completed. A
single "forty" or "eighty" or any sized tract is handled in the
same way. This gives a caliper measure of every tree on 4 acres
of each lot or on ^th of its area. Should a closer estimate be nec-
essary the strips are taken every 10 rods instead of 20 rods, which
gives Jth of each lot. If there are places in the tract from which
owing to any cause the timber has been removed, the area must
be shown on the report and proper deductions made from the esti-
mate. If these vacant areas are crossed by the strips, care must be
taken that they are not crossed lengthwise, as that would lessen
the estimate too much; on the other hand, if they are crossed
properly no deduction need be made from the tally.
When the calipering of the trees on the tract is completed
the contents of the trees tallied are taken from the volume table, the
scales footed, and the several footings multiplied by 10 or 5 accord-
ing to the number of the strips taken.
My volume table is of my own making. During the last twenty
years I have been called upon very frequently to measure trespass
until measures have been taken of thousands of trees of each
diameter. This work has been done in every section of the State
in which hard wood has been cut during that period, and has been
added to at every opportunity that has offered. The stumps were
calipered by taking the measure both outside and inside the bark ;
the length of the stem was taken, together with the diameter of
the top, inside the bark. On this basis the log scale was made ac-
cording to the Doyle rule. The scale of trees of the same diameter
and even of the same stump diameter and length vary considerably
on account of the different tapers toward the tops, making it nec-
essary to get a large number of trees from which to work up a table.
The average of the total scale of all the trees of a certain diameter
has been taken as the amount of scale to be allowed for all trees of
a certain stump diameter and height.
The results of the work as I have stated have been very satis-
factory. Many of the tracts have been cut the same season that
we made the estimate, and the log scale is usually from 10 per cent
to 20 per cent above my estimate. I should not care to get much
nearer than this. It would not be safe, as some firms cut the
timber much more closely than others, depending upon the article
to be made from the timber, the disposal of the waste product for
fuel, and so on.
No accurate estimate can be made without the use of the cali-
per. It entirely eliminates all favoritism on account of ownership
182 A MANUAL FOR NORTHERN WOODSMEN
or employer, and it makes possible a close acquaintance with the
trees which shows up the defects. No cruiser sees the timber alike
every day. His judgment varies as the man himself varies each
day. The caliper eliminates this trouble, as it always measures the
trees just as they are.
Care should be taken to get the smallest diameter at the base ;
many trees, especially on slopes, are flat and measure several inches
more one way than another. Trees that show much defect are an
unknown quantity and should be thrown out entirely.
Two active men will get over a half-section in a day, and do it
well if the timber is not too small and the undergrowth is not too
dense.
Sometimes I am called upon to give a rough estimate of a tract
in a hurry. I handle this in the same way that I have shown above,
except that I do not use the calipers, but guess at the diameters as
well as at the length. In this manner one can get over the ground
as fast as the assistant can tally the trees, and we usually estimate
about 12 lots per day under this system. Of course the results are
not so accurate as when the caliper is used.
The above is illuminating in many directions, suggestive
of varying conditions and requirements, and varying
methods of treatment in response. Further under this
subdivision there will be included only a reference to the
"horseshoe" plan of cruising employed by many Lake
States and Southern cruisers. Diagrams of a northeast
quarter- section and of a forty illustrate the plan of travel,
so designed as to reach into all parts of the subdivision
concerned. Along this route the cruiser commonly covers
by detail estimate a strip 50 paces wide, which gives a
large percentage of the whole area.
5. The field of ocular estimate is to be found especially
PRACTICE OF TIMBER ESTIMATING 183
in small bodies of timber and in tracts of small dimensions.
This is because a man can really see and grasp them.
Such estimates are particularly useful for timber of small
value or in very bunchy and irregular woods, which it is
hard to survey. In such circumstances the judgment of a
good woodsman is sometimes the best valuation that is
practicable.
The ability to estimate timber after this fashion is gained
by practice, and is based on personal experience and ca-
pacity ; consequently each man goes about it in a way of his
own. To know the area of the tract in question is generally
of great assistance, and most men will be continually study-
ing the matter of average stand per acre. As a prelimi-
nary step in arriving at this it is generally desirable to settle
maximum and minimum stand as well.
For the contents of single trees a woodsman may rely
on a mere glance, or he may figure carefully. A northern
Maine lumberman, for instance, looking at a fair-sized
spruce might estimate that it will cut a log 10 inches in
diameter at the top and 30 feet long, and such a log he
might know will measure 180 feet in local scaling prac-
tice. Again, in regions where logs are cut short, and
several are taken from a good-sized tree, men frequently
jot down the estimated contents of the several logs and
add up the figures to get the tree's total contents. Using
such methods to get at the size of the trees, lumbermen
then go on, in one way or another, to get the contents of
bodies of timber or stand per acre.
Frequently, however, the impression gained is a direct
one, of quantity on a whole tract or of constituent bunches.
A man cannot tell just how such figures come into his
mind, but they do arise there, dependent somehow on his
experience, perhaps in laying out roads or chopping timber.
Such training is effective, and when the judgment arising
as a result of it has been actually tested and found suffi-
ciently close and reliable for any given purpose, it would be
folly not to use it. But every one knows that such judg-
ments are fallible, as in the nature of the case they could
not fail to be. Differences in size and height may escape
a man if the stands traversed look generally alike; the
atmosphere and the lav of the land both have an effect on
184 A MANUAL FOR NORTHERN WOODSMfiN
the appearance of timber; a man's condition also varies
from day to day, affecting his judgment in this matter, as
in every other.
The above is the faculty of the old lumberman. On
the other hand, the forester who has studied the rate of
growth and the yield of timber has, in area, soil quality,
and density of stocking, factors which he can profitably
use to help him in his estimate of quantity. A fully stocked
acre of white pine on good soil in Massachusetts, for in-
stance, will yield at forty to sixty years of age a thousand
feet of lumber for each year it has been growing, — a
standard which a man may use to check the judgment
through a considerable range of conditions.
Ocular estimate has been spoken of as especially ap-
propriate to small tracts of land, but as a matter of fact
the methods and principles here stated are still employed
to a large extent in the valuation of the largest tracts as
well, and even for the purposes of sale and purchase.
This is perhaps not as it should be, but it has at least
partial justification in the fact that as business goes the
amount of timber on a tract is not the only element in
value; often it is not the largest, even, for in addition
availability, safety, the suitability of a tract to given pur-
poses, and the financial situation of the parties concerned
must all be considered. Sometimes a tract by reason of
its relation to a given investment or manufacturing enter-
prise really must be had, almost regardless of its timber
resources ; while, on the other hand, though rich in timber,
another tract may be dear at a small price. Accurate es-
timates of the quantity of timber, therefore, may be a
secondary matter.
When large tracts are estimated by the eye, it is com-
monly done on the basis of so much to the acre, either
from the looks of the stand or by comparison with some
similar tract already cut. Subdivisions, if they exist, might
be estimated separately, and the estimated area of waste
lands would then be thrown out of account. Some old
lumbermen might also estimate by valleys, judging quan-
tity from the density of the timber and the length of the
roads necessary to operate it.
6. Recount of the work done on a tract of 89 acres
PRACTICE OF TIMBER ESTIMATING 185
in Massachusetts, having considerable value and a varied
stand of timber, will illustrate the different methods of
timber estimation and the way of going to work in a par-
ticular case. This tract was mapped topographically. The
methods employed for that purpose are described in Part
II and a complete map of the tract is given on page 114.
The steps contributing to the timber estimate are as follows :
a. Boundaries run out to get area; chainage marks left
at frequent intervals.
b. Some 65 M feet of heavy and valuable pine timber cal-
ipered tree by tree; numerous heights measured; con-
tents ascertained from volume table.
c. Three bodies of thick young pine circled by staff
compass and pacing to get area. Average stand of each
bunch ascertained by laying out quarter-acre sample plots
representing 10 to 20 per cent of the area. Trees on these
plots calipered; heights measured or estimated; contents
taken from volume tables.
d. Ten acres of hard-wood swamp in north end esti-
mated for cord wood by similar but quicker methods.
e. Balance of 60 acres of ground is covered with scatter-
ing pine and hemlock, chestnut fit either for box boards
or railway ties, poplar, red oak, and other hard woods.
Northerly 37 acres considerably better than the other 23.
Ran strip surveys across the two parts representing 10 per
cent of the area, running the strips across the ridges
and the belts of timber. Calipered the trees into classes
of pine, hemlock, chestnut, poplar, hard woods fit to saw,
and cord wood; estimated saw contents from tables, such
as were at hand, adjusted to the locality and practice,
with due reference to heights; estimated cord wood from
tables, experience, and judgment.
The field work involved in steps b, c, d, and e represented
one day's work for four men. Result was the following :
ESTIMATE OF CLARK BROS'. PARKER LOT, WOODSTOCK,
MASS.
White Pine (including 50 M good plank) 660 M
Hemlock 35 "
Chestnut 156 "
Poplar 63 "
Red oak, etc. 67 "
Total saw timber 981 "
Also hard-wood fire wood, 600 cords.
186 A MANUAL FOR NORTHERN WOODSMEN
These methods are those of an estimator not in frequent
dealings with timber of this class. The owner of the lot,
a man of long experience and in constant practice, would
have chained or paced out the pine areas, and estimated
their stand per acre from experience. The scattering soft
wood and the heavy bunch of pine he would have esti-
mated in a lump sum. The main elements of value being
then dealt with, he would probably rely on his judgment
for the rest after looking carefully through it. With a
helper, he would take as much time as was actually con-
sumed, or more. This man, one of the most successful
operators in Massachusetts, says that using these methods
he can estimate pine lots within 5 to 10 per cent as a rule,
but occasionally makes a blunder of 30 to 50 per cent.
Other successful men in the same region, a region where
stumpage values are high and competition for merchant-
able lots very sharp, show great variety in their methods.
One man calipers all the timber on a lot he expects to pur-
chase, assuring himself about stand and value in that way,
and in addition securing data which tell him what he can
best put the trees into. Others use no instruments but,
relying on experience and taking plenty of time to look
around, make a lump estimate. That there is great dif-
ference in cost among all these methods is not certain. It
is sure, however, that for most men that method is best
which has in it less guess work than measuring. But the
facts recounted illustrate the principle that there may be
several good methods of doing a given piece of work, and
that the choice may turn on the training and habits of the
estimator.
B. ESTIMATION OF LARGER TRACTS
When land areas, as is frequently the case in the United
States, are of large size, and particularly if the stand upon
them is small and the value low, only a percentage of the
area can be covered by a timber survey, and the problem
is to make that percentage as representative of the whole
as possible. Amidst the great variety of methods em-
ployed, three main types of work may be distinguished.
PRACTICE OF TIMBER ESTIMATING 187
1. TYPE AND PLOT SYSTEM
According to this method the land to be passed on is
divided up into types of known area and approximately
like stand, without, however, necessarily leaving marks on
the ground. Through these subdivisions of his area the
cruiser travels, studying the size, height, density, and con-
dition of his timber, and forming as he goes an estimation
of the average stand. This estimate he checks by a number
of sample plots, run out with the tape, and examined with
care. The plots are usually laid out either in square
or circular form, though the strip system is perfectly
applicable.
Very satisfactory results have been arrived at by this
method where a considerable area in sample plots has
been surveyed or where the estimator is a man of judg-
ment and experience. But choosing a few sample plots to
represent a tract is recognized as a very delicate matter.
Beginners generally select too good a piece, and the man
who is really competent to do it can usually make a close
guess at the whole thing. As with all other methods of
estimating, area should be known from surveys, and. that
in not too large units.
A good example of the application of this
system comes from a national forest super-
visor who had to estimate for a timber sale
a tract of some 1200 acres. It lay in the
form shown, with a ridge running down
the middle of it, which naturally formed
the first line of subdivision. The tract was
therefore surveyed with compass and chain and a dividing
line run along the ridge top.
Then on each side of the ridge three distinct types of
timber stand were recognized. The heaviest timber, red
fir of good size, was in the middle; the north end was
lighter, with a mixture of lodgepole pine; the south end
had been damaged and rendered very thin by fire. These
blocks were therefore blazed out and roughly surveyed?
Thus the land was divided into six compartments of ap-
proximately even stand and of known area.
188 A MANUAL FOR NORTHERN WOODSMEN
Then with a party of three men the supervisor ran 4-rod
strip surveys l through each compartment, covering in each
from 10 to 15 per cent of the area. Having no volume
tables, he scored down instead the logs judged to be in the
trees passed, in 16-ft lengths and by inch-diameter classes.
In the office the contents of these logs were ascertained
from the scale rule, multiplied by the number of each size,
and added together. If then 10 per cent of a compartment
had been covered, multiplying by 10 gave the stand of
the compartment, which was the result desired.
With trustworthy volume tables and calipers better re-
sults could probably be had. but those here obtained were
satisfactory. General good judgment is essential in carry-
ing out such a survey, but, that given, a man can do it
who has not had long woods and mill training. In fact,
in the same forest one or two green but intelligent men are
said 'to have been quickly trained so that their figures
could be relied on within 10 or 15 per cent.
2. THE STRIP SYSTEM
The strip system of estimating has been used rather
widely in woods work, not infrequently in connection with
.land subdivision. . As a survey party is running through
the woods, it is sometimes made the duty of the chainmen
to count the merchantable trees for a stated distance on
each side of the line run, the contents of the trees being
determined oftenest by an estimate of the number neces-
sary to make up a thousand feet. The same system in
effect is sometimes used by the cruiser who counts the
trees passed within a certain distance as he travels across
a lot, or the work may be done more elaborately, and the
caliper and hypsometer introduced to any extent thought
advisable.
The methods of a Michigan cruiser who employs this
system were described on page 178. Following are
methods pursued on tracts of considerable size by a
number of progressive concerns at the South dealing with
pine and a variety of hard wood timbers.
The strip lines are usually % mile apart; they may be
1 See next article.
PRACTICE OF TIMBER ESTIMATING
189
carefully run and marked in advance by a survey party,
or a compassman going along with the timber estimator
may run and pace them. Topography may be mapped;
notes are taken of swamp boundaries and other changes
in the character of ground or timber.
The strip estimated is either one or two chains wide,
split by the line of travel; thus either 5 or 10 per cent of
the gross area is covered. The estimating party proper
consists of three men, two to caliper the timber breast
high, and one of good training who is responsible for the
work as a whole and who does the recording and estimat-
ing. His note book has separate space for each species
and under each a line for diameters by inch classes. Each
tree on the strip is scored down as calipered, or it may be
the number of 16-foot log lengths.
In such a vast region there is bound to be much varia-
tion in utilization, scaling, and mill practice so that when
volume tables are employed they are usually of local
origin to correspond. Since, however, the country is of
very gentle topography, height and taper within the same
species are unusually even. Two inches taper for each
-16-foot log above the butt log has been found to be widely
characteristic of pine timber, and three inches of hard
wood timber. Some tables then have been made up on
the basis of these regular tapers.
Small Diameter
of Butt Log
Inside Bark
Number of 16-foot logs
1
2
3
*
5
6
Contents in Feet Board Measure
15
16
17
18
160
180
200
230
280
320
360
410
360
420
480
550
410
480
560
650
440
520
610
710
540
640
750
Accompanying is an extract from a volume table J con-
structed on this plan, giving figures that, when manufac-
1 From "Southern Timber Tables" by Howard R. Krinbill,
Newbern, N. C. Copyrighted.
190 A MANUAL FOR NORTHERN WOODSMEN
ture of highest present economy is practiced, approximate
mill output. A peculiar feature will be noted in this
table — that the base diameter employed is not diameter
breast high, but diameter inside bark at the top of the
first log length. A reduction from calipered diameters is
required therefore, for bark thickness and for taper.
This reduction is made either tree by tree in the field by
estimate or in the office by classes on the basis of meas-
ures taken in logging operations. Timber quality is a
matter of importance. It is seldom or never dealt with
in the field other than by way of general comparison and
experience.
The strip system was also largely employed in the
early years of the United States Forest Service, with the
object of ascertaining not merely the merchantable tim-
ber on the tracts examined but also the number and
kind of young trees growing there as a basis for re-
commendations as to treatment. The method and cost of
strip survey work as carried out by the Service men are
indicated in the following extract from the " Woodsman's
Handbook":
Sample acres are laid off in the form of strips, 10 surveyor's
chains long and 1 chain wide, and the diameters of all trees to be
included in the estimate are measured at breast height with
calipers. At least three men are required to do effective work
under this method. One man carries a note book, or tally sheet,
and notes the species and their diameters as they are called out
by the men who take the measurements. The tallyman carries
the forward end of the chain, the other end of which is carried
by one of the men taking the measurements. The chain is first
stretched on the ground and the trees are calipered within an
estimated distance of 33 feet (one half chain) on each side of the
chain. When all trees adjacent to the chain have been calipered
the whole crew moves on the length of another chain in the direc-
tion chosen (by the tallyman). The chain is again stretched on
the ground and the trees are calipered on each side of it as before.
This same operation is repeated until the trees have been measured
on a strip 10 chains long. Notes are then made of the general
character of the forest and the land, according to the requirements
of the investigation. If heights are desired they may be taken
by a separate crew, or as the calipering crew encounter from time
to time trees whose heights are desired, they may stop long enough
to take such measurements.
In an average virgin forest a crew of three men will caliper the
trees on from 20 to 40 acres in one day if only trees of merchant-
PRACTICE OF TIMBER ESTIMATING
191
able size are included, or from 15 to 25 acres if the small trees also
are calipered. Small trees are measured principally in studying
the question of future growth.
FORM OF NOTES
Local ity.. T. 5. R 18,.. W..E..L.S.f Maine.
Tjpe-Hardu-ood. Slope..... I)ate-Sept..l7^.1901
Sheet No. A. 41
D.B.H
Spruce
Dead
Fir
White
Birch
Beech
Hard
Maple
Pine
Popl.
2 in.
Hn
H
3 «
la :.
4 «
0.
•
6 "
M.
6 "
K. .
7 "
11
M'
8 "
K.
9 "
.
R:.
RT.
10 «
11 "
On large tracts satisfactory estimates can be made by the
measurement of about 1 out of every 30 acres. In very extensive
forest tracts the Bureau of Forestry usually measures not more
than one or two out of every hundred acres.
This method is clearly adapted to securing knowledge
of the make-up of a forest, and of its stand of merchant-
able timber if good volume tables are at hand to go with
it. In the latter connection perhaps the greatest difficulty
that arises is in applying the proper heights to the different
diameters. This is slight if the tract is of small size and
uniform character, but considerable on large tracts with
uneven topography and varying stand. In addition con-
stant care is required to make sure that the strip is kept
of right width, in other words that all trees less than 2
rods from the line run are included and none at a greater
distance. Careful men do indeed quickly get trained to
192 A MANUAL FOR NORTHERN WOODSMEN
this so that their eyes are true, but with the best of men
an occasional swing-off of the chain is necessary. Defects
in timber also remain to be allowed for.
As applied to large tracts the strip system may either
be employed within types the boundaries of which have
been ascertained, as was explained in the last article, or
it may be laid out in long lines across country and itself
be used to define those boundaries and to get the topog-
raphy. A number of townships in Maine have been
surveyed in the following manner:
a. Township lines re-run and re-blazed ; chainage marks
left every half mile.
b. A center line run through the township, this also
being chained and marks left each half mile. '
c. From a main camp on the center line, 4-man parties
ran strip surveys from a mark on the center line out to
the boundary, checked on the mark there, set over a half-
mile, and ran back. This was 2 days' work, and the
party consequently carried outfit required to stay out one
night, the main camp meanwhile being moved along the
center line. Note was kept of the ridges and streams
crossed, also of the lay of the land, of the bounds of cut-
tings, and of marked types of timber. Elevations on such
a survey may be got by barometer, and a topographic
map made up as a result.
3. LINE AND PLOT SYSTEM
A third system employed with some variations in different
parts of the country, most largely perhaps among spruce
men in the East, combines features from both the fore-
going. Under this system the cruiser while at work
travels in straight lines through the country to be ex-
plored, using his eyes as well as may be while actually
traveling, but stopping at regular intervals to count and
estimate the trees on an area about him. The area usually
chosen is a quarter acre, which has a radius of 59 feet,
or, for most men, of 23 paces. For a check on this dis-
tance a tape line should always be carried in the pocket,
and every morning, as well as occasionally through the
day, the eye should be checked by actual measurements.
PRACTICE OF TIMBER ESTIMATING 193
Carefully training in this way, a man will find himself
able to guess within 2 feet of the 59.
The timber may be estimated according to any method
deemed most satisfactory. It may be calipered by an
assistant and the factor of height gone into to any extent
thought best, but most men in the spruce region do that
only as a check, while in common practice, after count-
ing the trees of any species or class, they estimate their
contents on the basis of so many to the cord or to the
thousand. Occasional calipering and height measurement
as a check on the eye* are highly desirable, and volume
tables also are a help in most cases. But some species of
trees (as cedar and beech in many localities) are so im-
perfect and defective that volume tables, if they were in
existence, could not be depended upon. Such timber
has to be estimated out of hand, and lumbering expe-
rience, together with the figures of the scale rule carried
either in a man's head or in his pocket, will prove the best
equipment for it.
One advantage of this method is its cheapness — one
man may do the work alone. Further, all doubtful points
are settled on the ground, face to face with the timber — -
there is no discounting or computing afterwards more
than to add up the results. Then the small size of the
area and the nearness of the observer to the trees under
consideration enable him, if he has proper experience and
judgment, to set contents very close. Lastly it will be
seen that the systematic travel followed gives, in a simple
country, material for mapping its timber types, also its
topography, as was explained in Part 2 of this volume.
Following are specimen notes of a line of estimate run
directly across a section with quarter-acre counts taken
150 paces apart. The timber is scored in the following
classes : (a) spruce above cutting limit of 14 inchej
stump diameter in board feet; (6) smaller spruce down
to 6 inches breast diameter in cords; (c) fir in cords;
(d) cedar in feet B. M. ; (e) pine; (/) good hard- wood
logs. Number and contents of trees both given.
This method of timber cruising may be employed on
land areas of any size, and has been largely employed on
areas of a mile square, or " sections."
194 A MANUAL FOR NORTHERN WOODSMEN
To travel the boundaries of a square mile and twice
across it, taking quarter acres each 20 rods as determined
by pacing, gives about 2^ per cent of the area actually
covered by the estimate, and that percentage can be
relied upon to give, in land which has any regularity of
type, a close approximation to the truth. To do that
and what goes with it, section after section through a
township, is just about a fair day's work.
^~
SflLqgs
Sp.Pa/p
Fjr
Cedar
PJne
HardtYoort
4-400
3 -.3
16- Is
& -300
9-1200
28-4
8-/80O
2.
8-1
Soft no
QC/S on f/af
3-400
7-1
f-100
/and, S/o
r?y buf~
3-SOO
7-1
34-4
Smooth
/ogg/ng.
fO-2000
7-JB
24-3
4-100
dbunctan
f rejorocfucf"-
9 -/3OO
a —
9-J.3
/on of fi
7 wMyruce
8-/OOO
7-1
IZ-li
2-300
& occasio,
Kr/p/fK 'tf
//- ISOO
23-2^
8-1
O/Xf?mg~
s-iooo
37-3
S-80O
/3-2
£Uf
£as1-6l
roofs //?
2-300
3 -700
6-£
4-.3
mixed
fifVIYft?
J--900
"SSfjod
S.4C.
4.7C
/J3'
J33'
The last two methods described as usually employed
are alike in this, that in the endeavor to get at a fair sample
of the country they depend mainly, on mechanical arrange-
ments rather than choice. This as a general rule is a
safe thing to do. There will always be enough things left
to exercise the best judgment of the estimator. On the
other hand, neither this nor any other system should be
followed blindly. If part of the tract is especially valua-
ble, especial pains should be taken with it. As a rule it
will be found safe to ascertain the area of such tracts and
PRACTICE OF TIMBER ESTIMATING 195
estimate them separately, while on the other hand the
area of bogs, burnt lands, barren mountain tops, etc.,
should be ascertained and thrown out of account.
C. SUMMARY
The above described ate well tried methods of timber
estimating and survey, but what has been written affords
hardly more than suggestions as to how any particular
job may best be done. Each method has its merits which
may strongly recommend it for some particular circum-
stances. Very much too depends on the training and
qualifications of the man doing the work. Every man
long in the business commonly has a line of work in which
he becomes proficient, developing methods best suited
to himself to which in ordinary cases he will adhere. In
conclusion, the following guiding principles may be laid
down:
1. Estimates by lump sum are not usually reliable or
at the present day sufficient.
2. Estimates of so much to the acre are much easier
to make and more likely to be close to the fact.
3. In any kind of timber estimate or survey, the area
of the land ought to be known, and that in units not too
large. Within limits the smaller they are the better, all
the more so if each unit contains but one timber type.
4. Every time a measurement is substituted for a guess
or judgment, the more reliable will be the result. On the
other hand, experience and good judgment never cease
to be required in the business.
5. No estimate is worth much, practically speaking,
which fails to take height into account as well as diameter.
6. Quality in some circumstances is quite as material to
an adequate timber survey as quantity. Its determination
is fully as difficult.
7. "The more defective the trees are, the more pref-
erable is the cruiser's judgment and long local experience
in the mill and in the woods to mere measuring." 1 The
same is true where great differences in value are dependent
upon quality or grade.
1 Schenck's "Forest Mensuration."
196
A MANUAL FOR NORTHERN WOODSMEN
8. Very bunchy timber can be estimated only in bunches
or tree by tree. No general system of lines or plots can
be trusted to give safe results.
ft. In the emergencies which arise in actual business,
a little rough and ready land surveying is often the most
vital part of a reliable timber estimate. One or two lines
run with compass and chain will frequently check areas
of waste land or of different stand in effective fashion.
Transit and stadia work on streams or roads often
affords very material help. There is continual call for
the sort of results that can best be obtained by means of
compass and pacing.
D. PACIFIC COAST METHODS
Much Pacific Coast timber is 200 feet and over in height
and of diameter to correspond, while the stand sometimes
passes 20 million feet per quarter section. It is evident,
therefore, that because of the values involved intensive
methods of cruising are appropriate, .while peculiarities
of method are suggested by the very size and height of
the timber. Of the region as a whole the portion west of
the Cascade Mountains in Washington and Oregon, pro-
ducing Douglas fir, "Oregon pine" as it was called form-
erly, is most active and characteristic, and the following
refers to that region unless specified otherwise.
SUCCESSIVE LOGS IN A FIR '
Top
Diam.
Scale
Total
1st 32-foot log
31
1420
33
2nd 32-foot log
3rd 32-foot log
4th 32-foot log
28
25
20
1160
920
560
27
21
14
5th 32-foot log
14
230
5
Total
4290
100
Adjustment of methods to the conditions is illustrated
particularly by the volume tables employed, for those
at present in most extensive and responsible use are.;
PRACTICE OF TIMBER ESTIMATING 197
constructed on principles that have very seldom been
employed elsewhere. After basal diameter, taper per
32-foot 1 log is the next factor allowed for, total height of
the tree is disregarded, and number of logs is the third
factor in the tabulation. This has reason behind it as
well as experience. In timber of such dimensions total
height is not readily estimated; the lower logs of the tree
are very much the largest and far the best in quality;
a log more or less in the top, comparatively small in size,
full of large knots and liable to be broken up in felling, is
of small account in the estimate anyway.
In connection with these tables, basal diameter also is
handled in a peculiar manner. In some tree species thick-
ness of bark is very variable, while the root swelling of
large trees frequently reaches to the height of a man and
higher. Diameter therefore is taken as nearly as may be
where the tree takes on its regular form, considerably
above breast height as a rule; deduction is made for any
swelling not thus allowed for, and double the thickness
of bark as actually found is then subtracted. By this
means, the wood alone is dealt with, and basal diameter
is aligned with the general shape of the tree.
In view of the facts above mentioned it is clear further
how windfalls furnish the best obtainable assistance to
the cruiser's judgment in respect to height and taper,
also that the diameter tape and Biltmore stick possess
advantages over the caliper. Then two additional prob-
lems arising out of the size of the trees confront the cruiser :
first, breakage in felling is a much more important factor
than elsewhere, and its amount varies widely with the
ground conditions; second, the defect arising from decay
and other sources, very hard to judge, to detect even, in
timber of this height, has to be handled with extreme
care — careful looking, the examination of windfalls,
experience, perhaps the outturn of adjacent timber serv-
ing as a guide to it.
The "forty" is the ordinary unit of area for cruising
and a timber report, and it is gridironed with straight
line travel. Pacing serves ordinary purposes as a dis-
1 Tables based on 16-foot logs are also in existence.
198 A MANUAL FOR NORTHERN WOODSMEN
tance measure; a vernier compass is usually employed
for the sake of more accurate line running. Twenty to
fifty per cent of the gross area is commonly covered by
actual estimate, one hundred per cent in some cases.
The unit party for the work consists of two men, compass-
man and cruiser, of whom one handles distance, area,
and topography, while the other is responsible for the
timber. Details of practice vary much, as elsewhere, in
accordance with the purpose of a cruise, conditions
found, and the training of different estimators. Follow-
ing is a description of a method as near standard as any,
widely employed in work of high responsibility.
a. Section lines are usually freshened up and re-
chained, and a center line may be run through each sec-
tion. The main purpose of this work is to set stakes for
the guidance of the cruising party. It is so laid out that
the actual cruise or estimating lines will run as nearly
as may be across the features of the topography.
b. The cruising party, starting at one corner of the
section to be examined, proceeds to the nearest stake,
2J^ chains from it, whence the compassman, with the
declination set off in his staff compass, travels parallel
to the side line of the section, keeping account of his
pacing, taking aneroid readings at changes of the ground,
and sketching topography. Behind him follows the cruiser,
who for a width of 5 rods on each side, estimates the timber.
500 steps, 4 tallies, make a quarter mile, the width of a
40. At that point the scoring of timber begins anew, for
the new forty being entered. So the work proceeds until
the opposite section line is met (or at half that distance
if the section is subdivided), when the pacing is checked
up, the compass work tested on the stake and declination
reset if necessary. Offset is then made to the second
stake, lYi chains from the corner, from which point a
parallel line is run in the opposite direction. Four such
lines are run across each tier of forties. With 1C such
lines the cruise of the section is completed.
c. The detail of the estimating work is as follows: —
First, in nearby timber being cut, or in ordinary circum-
stances by examination of windfalls, the cruiser trues up
PRACTICE OF TIMBER ESTIMATING
199
his judgment on the contents of the trees. In this con-
nection his volume table is of assistance since study of
the height and taper of the down timber shows to what
portion of his tables its form relates it. Two and three
inches per 32 foot log are light tapers, not infrequent in
hemlock and young fir, but four and five are usual in
mature fir timber. This examination also tells something
as to log quality and the amount of defect. Along with
it the cruiser makes sure by numerous tests that his eye
is true on basal diameter. With these points settled his
preliminary work is done and, with an eye out for factors
that influence breakage and particularly for "conks"
and other signs of unsoundness, he will proceed confi-
dently. The figures he sets down on his tablet represent
his judgment of the merchantable contents of trees as he
passes them, species, individual form, defect, and breakage
all being allowed for. The conscientious man, however,
applies frequent check by further examination of wind-
falls and occasional measurement of strip width and of
basal diameters.
SAMPLE OF CRUISER'S FIELD NOTES
(Usually made on celluloid sheets)
Dead
Poles
Fir
Cedar
D & D
Down
Fir
Hem.
Cedar
2-6 M
2
1-.7
.8
1-1.5
1-5 M
1
1
111
1-2.5
1.5
1-.4
2-2.5
6-30
2-7.5
1-3.
1-.3
1-1.
Average 45' long
9' diam. at middle
d. Checks from outside are a feature of the work as
carried out on a large scale commercially. The different
cruisers in a large party may be set to check one another
as a corrective and for uniformity; a head cruiser period-
ically checks each man to catch up any slackness, correct
any wrong tendencies, and give advice or directions.
Two miles of line per day are the standard product
for this method of cruising, giving eight working days to
£00 A MANUAL FOR NORTHERN WOODSMEN
the section, which involves a cost of about 25 cents per
acre outside of the checking, overhead and office work.
Ordinary variations are : —
a. Double running each forty instead of running four
times through it as above, a method widely practiced as
costing less and considered sufficiently accurate in many
circumstances. The cruise lines in this case are started
5, 15, 25, etc. chains from the section corner to divide
the area equally. Sometimes, also, the strip is widened.
6. For preliminary work, one strip only may be run
per quarter mile, and after a certain amount of that with
its results in training, even this may be discontinued and
a man rely on general observation.
c. A 100 per cent cruise is carried out in some cases.
In this case a second compassman may advantageously
be employed and the cruiser work between lines run and
marked by the two men, the "exact width of the strip
being then of no consequence. Sometimes, also, a second
estimator is employed to take care of certain classes of the
timber.
d. Some men, instead of estimating the timber on
strips, estimate circular areas so spaced along the compass
line that they touch one another. For this practice it is
claimed that a man can do better estimating work stand-
ing quietly at a center than while travelling, with his
mind more or less distracted about footing, etc. In
earlier times indeed a circular plot system was general,
- while another usual procedure was to count the trees on
these circles or on strips to the length of one tally, and
derive their contents from that of the average tree as
estimated. Few follow this last practice at present,
however.
In conclusion on this branch of the subject, the follow-
ing, by a man of long experience and acknowledged com-
petence in this line of work, is introduced for the light it
throws on the broad aspects of the matter.
We work in general by the strip system but under a less hard-
and-fast rule than formerly. More is left to the judgment of our
cruisers as to the number of runs through a subdivision neces-
sary to secure correct results. Thus, if we find one forty that
PRACTICE OF TIMBER ESTIMATING 201
is densely timbered with a small uniform growth, we find that
we secure better results by taking narrower strips, the equivalent
of one sixteenth of a forty instead of one eighth. Where trees
stand so thickly on the ground it is almost an impossibility for
men to keep an accurate count on a wide strip as they can on
one of hah* the width, and we find that the basis of much of the
error that occurs in our work is due to inaccurate tree counting.
If the timber is large and particularly accurate results are de-
sired, we now run 12 times through each forty and frequently work
between blazed lines. That is, instead of running through the
middle of the strip, the compassman sets over one-half its width
and spots the trees on the opposite side from the cruiser to give
the cruiser a line to work to on the return strip. This works very
satisfactorily where the brush is not too dense.
Again, under certain conditions where we have a uniform
stand of large timber, we run 4 times, taking strips equivalent
to one-twelfth of a forty. This plan, we believe, gives better results
than two strips each covering }/g of the whole.
These notes give some idea of how we attempt to carry on our
work, but in the last analysis this cruising business resolves itself
into one of personal capacity and attention upon the part of the
cruiser rather than the method employed. A careful, conscien-
tious and hard-working woodsman whom we can depend upon
to go over the ground is more valuable than a more expert cruiser
who takes much for granted. There was a. time when I hoped
to develop timber cruising to a point from which we could look
upon our estimates as being absolutely reliable, but so long as
there are influences that will work upon the minds of men, there
will be variation and error. A man may do excellent work to-
day and be totally unfit to be in the woods to-morrow, all for
reasons which none of us can explain. A man must have confi-
dence or he will be of little value. On the other hand I think I
may safely say that the greatest element of uncertainty and error
in men's work is their proneness to feel that familiarity has de-
veloped infallibility. The man who never develops absolute
confidence in his eye and judgment and who checks himself up
frequently, seldom goes far wrong.
There is, too, another side to this whole matter, one often
neglected, but of great importance, and that we consider in our
work as best we can. That is the standard of utilization of the
timber. As a matter of fact there is surprising difference in the
way timber is cut, though I could not define this as a percentage.
A concern milling its own timber cuts closer than one selling its
logs; and there is variation with the market itself. Then occa-
202 A MANUAL FOR NORTHERN WOODSMEN
sionally a tract is cut with such carelessness that the yield is
very materially cut down. We have to meet the wishes of our
customers if clearly expressed, but we protect ourselves by an
explicit statement of the kind of utilization which our estimates
imply, and by an exact showing of the basis on which the work
was done.
Timber Quality. While the above applies specifically
to the Douglas fir country, much the same methods are
employed in the Interior and California, with resort to
others of less intensiveness, similar to those in use else-
where, when stands are lighter or less valuable. The pre-
ceding, however, is inadequate in one field of importance,
in that quality of timber has been given scant emphasis.
This throughout the region is no less important a factor
in value than quantity. In fact, in very much territory
timber has no commercial value unless its products are
suitable for other than ordinary building purposes.
In the case of Douglas fir and timbers associated with
it west of the Cascades this matter is simplified by the
fact that log grades instead of lumber grades are made
the usual basis of quality rating, the log grading rules in
force in the market thus furnishing the standard to which
the field man works. Since, however, both dimension
and lumber quality enter into these, their application is
not simple.
The grading rules for Douglas fir logs in force on Puget
Sound follow; those of the other log markets are very
similar. Spruce is commonly graded like fir. With cedar,
because of the variety of products into which the wood
may be manufactured, grading varies from time to time
and locally. Hemlock logs and those of the species
rarely met are sometimes classed in two log grades, those
above 16* in diameter and surface clear, and all others.
No. 1 (also called Flooring) logs shall be logs in the
lengths of 16 to 32 feet and 30 inches in diameter inside
the bark at the small end and logs 34 to 40 feet, 28 inches
in diameter inside the bark at the small end, which in the
judgment of the sealer contain at least 50 per cent of the
scaled contents in lumber in the grades of No. 2 Clear
and better.
PRACTICE OF TIMBER ESTIMATING 203
No. 2 (or Merchantable) logs shall be not less than 16
feet long and which, having defects which prevent their
grading No. 1, in the judgment of the sealer, will be
suitable for the manufacture of lumber principally in
the grades of Merchantable and better. (Merchantable
lumber must be free from knots or other defects in size
or numbers such as to weaken the piece.)
No. 3 (also called No. 2} logs shall be not less than 16
feet long which, having defects that prevent their being
graded higher, are, in the judgment of the sealer, suitable
for the manufacture of Common lumber.
Cull logs shall be any logs which in the judgment of
the sealer will not cut 33^ per cent of sound timber.
An essential to reliable timber grading is experience, a
background of knowledge of the out-turn of similar tim-
ber. In the next place, close examination of the stand
is required as to the number and size of limbs and knots
and for indications of these, or of other defects, that
may lie beneath the surface. Age is a help here (these
stands are commonly even-aged over considerable areas).
Many cruisers go no farther than this and set percentage
figures for log grades as the result of a broad judgment.
When further detail is thought desirable, the volume
tables before mentioned are of assistance, giving as some
of them do for a tree of given diameter, taper, and mer-
chantable length the percentage each successive 32-foot
log bears to total contents. One standard volume table
contains the following directions : —
"Determine the percentages of the different grades as
contained in a given percentage of the trees on each 40
acres by selecting, for instance, an average tree on each
tally and carefully determining the percentage of the
different grades of logs contained in these sample trees
and apply ing the average to all trees on the forty."
To illustrate, in the notes on page 199, 11 trees, 46 M
feet, are scored down in the column of living fir, giving an
average volume of 4200. 4 inches taper and 4 logs may fit
this timber; if so, a tree yielding 4330 feet (see extract from
taper table) gives a close approximation. Of such a tree
a 32' butt log constitutes 37 per cent, the second log 28
204 A MANUAL FOR NORTHERN WOODSMEN
per cent, and the third 21 per cent, while top diameters
are approximately 33, 29 and 25 inches respectively.
One of these logs is large enough for No. 1 ; it may or may
not be clear enough. Second and third logs are of suffi-
cient size, and likely to be of a quality, to put them in
the second grade.
Methods in this branch of the work, however, vary
greatly. A few, in the endeavor to reduce the field of
judgment, have gone into much detail and devised forms
of notes which record trees by sizes and log grades in each
tree as its contents is estimated. Of the percentage of
successive logs, it may be said that the above relations
are fairly typical — that is to say in normal fir timber
large enough so that log grades are of importance, about
35 per cent of the total contents of trees is contained in
the butt log if cut 32 feet long, the second log will add
25 to 30 per cent more, and about 20 per cent will be
in the third log. Breakage and defect may throw out
these relations, and they are different in extremely tall
or short timber.
ti
3 Logs or 96 Feet
4 Logs or 128 Feet
Butt
Diam.
.a
.S
a
Logs
8
Logs
Inches
n
£
,S'
Contents
n
.
Contents
•n
H
1
B. M
6
-
3
S
B. M
~~
t-
£
Q
SN
^
S
S
l~
l-
l<
3
4
28
25
4230
3714
10
13
33
33
27
24
25
21
5128
4330
33
37
27
2s
22
'?!
18
14
5
22
3234
10
33
21
17
3610
4?,
2D
I'l
10
37
fi
19
2790
10
3;>
is
13
2979
17
30
17
00
7
16
2386
1.1
3"
11
S
13
2029
60
31
lid
9
10
1729
00
2s
00
NOTE. Half logs are given in the original tables.
Since a large share of the timber of the fir region is
realized on by its owners in the form not of lumber but
of logs, the inducement is small to go further than the log
in quality work in that region. It is otherwise, however,
in the regions characterized by pine, where there are no
PRACTICE OF TIMBER ESTIMATING 205
log markets and timber enters the commercial field in
the shape of lumber with its great range in quality and
value. Here the Forest Service, endeavoring in its own
business to get away from the judgment of the individual
applied in too broad a way, has started a line of inquiry
that should in time prove serviceable to business. Log
grades in this case again are made the basis to which the
field man works, but mill and yard studies, carrying the
product of those logs through the process of manufacture
to point of sale, afford a means of going further, to an
estimate of lumber quality and value. Definitions of the
log grades that have been formed for yellow pine follow,
and brief notes on the yield of those grades may be serv-
iceable to some, although, with a small field covered, it
has beeti found already that logs graded by the same man
under the same rules vary considerably by locality in
their yield of high grade lumber.
Yellow Pine Log Grades of the U. S. Forest Service.
Clear logs shall be 22 inches or over in diameter inside
the bark at the small end and not less than 10 feet long.
They shall be reasonably straight-grained, practically
surface clear, and of a character which in the judgment
of the sealer are capable of cutting not less than 25 per
cent of their scaled contents into lumber of the grades of
C Select and better.
Shop logs shall be 18 inches or over in diameter inside
the bark at the small end, not less than 8 feet long, and
which in the judgment of the sealer are capable of cut-
ting not less than 30 per cent of their scaled contents
into lumber of the grades of No. 2 Shop and better.
Rough logs shall be 6 inches or over in diameter inside
the bark at the small end and not less than 8 feet long,
having defects which in the judgment of the sealer pre-
vent their classification into either of the two above
grades.
Logs cut from rather large and high class timber at
different points of interior Oregon, graded according to
the above rules, have yielded as follows:
Clear logs 60-65 per cent No. 2 Shop and better, about
half of it of grades B and C Select.
206 A MANUAL FOR NORTHERN WOODSMEN
Shop logs 40-45 per cent No. 2 Shop and better, a fifth
to a fourth B and C.
Rough logs have yielded about 15 per cent No. 2 Shop
and better.
For the Novice. From the foregoing it will be inferred
that the best timber cruising in the Pacific region is a
highly expert business, requiring in addition to accuracy
and alertness, thorough personal training and judgment
in high degree. There are always learners in the field,
however, and occasionally inexpert men are so situated
that with whatever equipment they can command they
must do their best to size up the quantity and value of
timber. To such, a caution in respect to the loss of ap-
parent volume that breakage, shake and decay may
cause and the very large part that location, and especially
quality, play in the value of timber is an essential service.
Then it is true and worthy of regard that in these cir-
cumstances simple methods may actually give the best
results.
A man may learn much in a logging operation where
timber similar to that he is concerned with can be ex-
amined after it is felled and bucked into logs. He can
see how much is broken up, whether the timber is rotten
or sound, and from the cross cuts and surface indications
of the logs examined at close range get an idea of the prev-
alence of knots, shakes and other blemishes. Then he
can scale up the logs from a number of trees, ascertain-
ing the total length utilized and the quantity of mer-
chantable timber derived from each tree. This ' he will
attach to its length and base diameter and endeavor to
link up with trees of similar dimensions standing.
Such work as this will enable a man to understand a
volume table, and he may even get enough measures to
make one for himself iir some size groups, with which he
may check published volume tables. Or old devices and
short 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 best
result that can come from such work (it can be gained
only with time and experience, and some men never will
acquire it) is the capacity to make a close estimate of the
contents of a tree standing.
Contents of the average tree in a piece of timber, ob-
tained by methods of this kind, may be made a starting
point for the next step in the process. A man may count
all the trees standing on a small piece of ground, using
safeguards that he will readily think up to get all the
trees in and not to count any a second time. If the terri-
tory is too large for that, sample acres in any number
can be run out in fair average ground and the trees counted
up on them.1 A square acre is 209 feet on a side, about
80 paces. A circular acre is 236 feet in diameter. Or,
some form of the strip method may be used as described
on the preceding pages. The area of ground without tim-
ber should be thrown out; single trees or bunches that are
of exceptional size and quality should be treated separately.
Material loss from breakage enters when about 100 feet
in merchantable length is passed, and runs up to nearly or
quite 50 per cent on very broken land with heavy timber.
The above, compared with really adequate, profes-
sional cruising, is only an expedient; still, carried out by
a clear-headed man, it might really be worth more than
what passes oftentimes as something more ambitious.
Such a man, too, can sometimes find out what he wants
to know, or manage to protect his own interests in matters
of this kind, without resort to timber cruising. Some
men also have judgment on the contents of a body of
timber as a whole who are unfamiliar with a systematic
timber estimate, and would be slow and uncertain in the
execution of it.
32 feet long; multiply by the number of 32-foot logs less one-
half log.
Or, to base diameter add one-half of base diameter and divide
by 2; multiply by .8, square and divide by 12. The result is the
number of feet in the stick per foot of its length. 3 to 5 per
cent may sometimes be added for contents above the point
stated.
1 For a caution on this head, see page 187.
PART V
TABLES
SECTION I. TABLES RELATING TO PARTS I AND II . . 210
SECTION II. TABLES RELATING TO PARTS III AND IV . 235
SECTION III. MISCELLANEOUS TABLES AND INFORMATION 293
SECTION I
TABLES RELATING TO PARTS I AND H
1. STADIA REDUCTIONS 211
2. SOLUTION OF TRIANGLES 212
3. TRAVERSE TABLES 214
4. LOGARITHMS OF NUMBERS 220
5. LOGARITHMIC SINES, COSINES, TANGENTS, AND CO-
TANGENTS . . 222
6. SUPPLEMENTARY TABLES OF SMALL ANGLES .... 228
7. NATURAL SINES AND COSINES 230
8. NATURAL TANGENTS AND COTANGENTS 232
9. SPECIMEN LETTERING . . 234
TABLES RELATING TO PARTS I AND II 211.
STADIA REDUCTIONS
Horizontal Distance
1 ' i
I
0'
10'
20'
30'
40'
50'
0'
10'
20'
30'
40'
50'
0° 100.0
100.0
100.0
100.0
100.0
1000
M*
92.4
92.3
92.1 91.9
91.8
91.6
1° 100.0
2° 99.9
100.0
99.8
99.9
99.8
99.9) 99.9
99.8 99.8
99.9
99.8
17°
18°
91.5
90.4
91.391.1191.0
90.390.189.9
90.890.6
89.8 89.6
3°
4°
99.7
99.5
99.7
99.5
99.7
99.4
99.6
99.4
99.6
99.3
99.6
99.3
19°
20 J
89.4
88.3
89.2!89.0 88.9 88.7
88.1,87.987.7187.5
88.5
87.3
5°
99.2
99.2
99.1
99.1
99.0
99.0
21°
87.2
87.0186.8
86.686.4
86.2
6-
98.9
98.9
98.8
98.7
98.6
98.6
22 ;
86.0
85.8:85.6
85.4J85.2
84.9
7;
98.5
98.4
98.4
98.3
98.2
98.1
23°
84.7
84.5i84.3
84.1 83.9
83.7
8°
98.1
98.0
97.9
97.8
97.7
97.6
24°
83.5
83.2
83.0
82.8
82.6
82.4
V
97.5
97.5
97.4
97.3
97.2
97.1
25;'
82.1
81.9181.7
81.5
81.2
81.0
10-
97.0
96.9
96.8
96.7
96.6
96.5
2(i'-
80.8
80.6180.3
MM
79.9
79.6
11°
96.4
96.3
96.1
96.0
95.9
95.8
27°
79.-1
79.2
78.'.)
78.7
78.4
78.2
12
95.7
95.6
95.4
95.3
95.2
95.1
28'
7.x. o
77.7
77.5
77.2
77.0
76.7
13-
94.9
94.8
94.7
94.5
94.4
94.3
29"
7 (',..-,
7(1.2
76.0
75.7
75.5
75.2
94.2
94.0
93.9
93.7
93.6
93.4
:50C
75.0
74.7
74.5
74.2
74.0
73.7
15°
93.3
93.2
93.0
92.9
92.7
92.6
Difference of Elevation
Proportional Parts
0'
10'
20'
30'
4W
50'
1'
2'
V
4'
5'
6'
7'
8'
9'
0°
0.00
0.29
0.58
0.87
1.16
1.45
03
.06
.09
.12
.14
.17
.20
.23
.26
1°
1.74
2.04
2.33
2.62
2.91
3.20
.03
.06
.()!>
.12
.14
.18
.20
.2:;
.26
2°
3.49
3.78
4.07
4.36
4.65
4.94
.03 .06
.09
.12
.14
.17
.20
.23
.26
3°
5.23
5.52
5.80
6.09
6.38
6.67
;.03 .06
.09
.12
.14
.17
.20
.23
.26
4°
6.96
7.25
7.5:',
7.82
8.11
8.40
1.03 i. 06 1.09
.12
.14
.17
.20
.23
.26
5°
8.68
8.971 9.25
9.54
9.83 10.11
'.03:.06 .08
.11
.14
.17
.20
.23
.25
6°
10.40
10.68 10.96ill.25
11.53 11.81
.03 .06
.08
.11
.14
.17
.20
.23
.25
7°
12.10
12.38
12.66 12.94
13.22 13.50
.03 .06
.08
.11
.14
.17
.20
.22
:ir>
8°
9°
13.78
15.45
14.06
15.73
14.34 14.62
16.0016.28
14.90 15.17
16.55 16.83
.03 .06
.03 .06
.08
.08
.11
.11
.14
.14
.17
.17
.1!)
.1!)
.22
.22
.25
.25
10°
17.10
17.37
17.65 17.92
18.19.18.46
.03 1. 05 :. 08
.11
.14
.16
.19
.22
.24
11°
18.73
19.00
19.27 19.54
19.80 20.07
.031.05 .08
.11
.13
.16
.19
.21
.24
12°
13°
20.:M
21.'.)2
20.80 20.87 21.13
22.18 22.44 22.70
21.39
22.96
21.66
23.22
.03
03
.05
.05
.08
.08
.11
.10
.13
. 1 3
.16
.16
.18
.18
.21
.21
.24
.23
14°
2:;. 17
23.73 23.99 24.24
24.49
24.75
03
05
.08
.10
.13
.15
.18
.20
.23
15°
16°
25.00
26.50
25.25 25.50 25.75
26.7426.9927.23
26.00
26.25
27.72
i03
.02
.05
.05
.07
.07
.10
.10
.13
.12
.15
.15
.17
.17
.20
.20
.23
.22
17°
18°
27.96
2'.).:;,7
37.54
36.57 36.77
37.7437.93
36.96
38.11
.02.04
.02 .04
.06 .08 L 10
.06 .08 .09
.12
.11
.14
.13
.16
.15
.18
.17
25°
38.30 38.49
38.6738.86
39.04
39.22
.02 .04
.06 .07
.09
.11
.13
.15
.17
26°
39.40 139.58
39.7639.93
10.11
40.28
.02 .04
.05 .07
.09
.11
.12
.14
.16
27°
28°
29°
30°
40.45
41.45
42.40
43.30
40.62
41.61
42.56
43.45
40.79
41.77
42.71
43.59
40.96 41.12
41.93 42.09
42.8643.01
43.73 43.87
41.29
42.25
43.16
44.01
.02
02
.02
.01
.03
.0:;
.03
.03
.05
.05
.05
.04
.07
.06
01 i
.06
.08
.08
.08
.07
.10
.10
.09
.09
.12
.11
.11
.10
.13
.13
.12
.11
.15
.14
.14
.13
212 A MANUAL FOR NORTHERN WOODSMEN
SOLUTION OF TRIANGLES
The figure may refresh to good pur-
pose the memory of the field worker.
In it are graphically represented the
functions (sine, cosine, secant, and
tangent) of the angle BAC. The
cosine, cosecant,
/\ and cotangent of
triangle A B C are as follows :
BAC are respect-
ively the sine,
secant, and tangent of CAD, the
complement of BAC.
Represented as ratios, the functions
of the angle A in the right-angled
Tangent^ -
By these formulas, and the use of the tables of sines and
tangents, all the parts of any right-angled triangle may be
obtained if two sides, or an acute angle and a side, are
given.
All the parts and the area of an
oblique triangle may be obtained if
any three parts including one side
are given. Let A, B, C represent
the angles, and a, b, c the opposite
sides, of any oblique triangle ; then A ,
the solutions are as given on the
next page.
TABLES RELATING TO PARTS I AND II 213
Given
Sought
A, B, a
A, a, b
A,B,C,a
C,a, b
a, b, c
C, 6, c
B, C, c
Area
i(A+B)
*(A-B)
A
B
c
Area
A
B, C
Area
C = 180° - (A + B)
b a -in B
sin A
a -in C
sin A
b sin A
a
C = 180° - (A + B)
a sin C
sin A
a2 sin B sin C
2 sin A
i (X + B) = 90° - i C
ta n 4 f 4 R^ - t*n 4- />4 4- J^
4 = -J (4 + B) + i (4 - B)
0 - i (4 +;B)>- i (4 - £)
C -fa 1 MCOS^(^+B)
6) cos i (X - B)
fa Msin*(^45)
fc)Sini(^-B)
Area = % ab sin C
Let s = \ (a + b + c)
Then Sin \ i \/(8 ~b}(s~ C)
be
K i i \/s (s - a)
oc
ln 1 i A/(> -V(*~ C)
. (» - a)
Similar formulas
V* (« — a) '(* — b) (s — c)
214
TRAVERSE TABLE
j Dist. 5
[ Lat. DepT
!5.0000 0.0218
1 9(53
2181
1)931
9920
9726 5226 84 0
9703 5443
9679 5660
9653 5877
9627 j 0013 83 0
MOO
9672
6526
4.9543 0.6743
9278 8467
9240 8682
4.9202lo.8897
91631 9112
9123 9326
9081 9540
;nioj
9089
9039 9755
8996: 9968
89521.0182
89071 0396
8862 0609
8815| 0822
4.87C7 1.1035
8719 1248 77 0
8669 1460
8618 1672
8567, 1884
8515i 2096
8462! 23<'8
84' 7 2519
8*52 2730
8296J 2941
Dep7|~Lat.
~~Dtat5~~
45
30
15
87 0
45
45
45
30
15
0
45
30
• 15
75 0
Course
TRAVERSE TABLE
215
Pep. Lat. j Pep. Lat. Dep.| Lat. Pep. Lat.
Dist. 6 I Dist. 7 Diet. 8 Dist. 9
216
TRAVERSE TABLE
2.8944 0.7S91 3.8591
8909J 8017J 854;
8874 8143
0.9140 3.809C 1.2195 4.7621
45 0.9222 0.3S67
23 0 9205 3907
15 > 9188 3947
30 | 9171! 3987
45 9153! 4027
24 0 9135 4007
15' 9118 4107
30 9100 4147
45 90811 4187
25 0| 90631 422C
15 0.9045 0.426C
4305
45' 9007
Pep. Lat. j _Dep. Lat. i Pep. Lat. J)ep. ILat. ! Pep. Lat. I
I Dist. 1 I ~Dist2 II IMst. 3 ~~Digt'4~l' Dist. 5 '•
TRAVERSE TABLE
217
Course
i Dist. 6
Dist. 7
Dist. 8
Dist. 9
Dist. 10
| Lat. i Dep.
Lat. i Dep.
Lat.
Dep.
Lat.
Pep-
Lat. Dep.
15 15 5.7887 1.5782
6.7335 1 8412
7.7183
2.1042
8.C831
2.3673
9.64792.C303
74 45
30
7818
6034
7454
8707
7090
1379
6727
4051
G363
(,724
30
45
7747
6286
7372
9001
6996
1715
6621
4430
6246
7144
15
16 0
7676
6538
7288
9295
6901
2051
6514
4807
6126
7564
74 0
15
7603
6790
7203
9588
6804
2386
6404
5185
6005
7983
45
30
7529
7041
7117
9881
6706
2721
6294
5561
5882
8402
30
45
7454
7292
7030
2.0174
6606
3056
6181
5938
5757
882C
15
17 0
7378
7542
6941
0466
6504
3390
6067
6313
5630
9237
73 0
15
! 7301
7792
6851
0758!
6402
3723
5952
6689
5502
9654
45
30
7223
8040
6760
1049
6297
4056
5835
7064
5372
3.0071
30
45
5.7144
1.8292
6.6668
2.1341
7.6192
2.4389
8.5716
2.7438
9.5240
3.0486
15
18 0
7063
8541
6574
1631
6085
4721
5595
7812
5106
0902
72 0
15
6982
8790
6479
1921
5976
5053
5473
8185
4970
1316
45
30
6899
9038
6383
2211
5866
5384
5349
8557
4832
1730
30
45
6816
93SG
6285
2501
5754
5715
5224
8930
4693
2144
15
19 0
6731
9534
6186
2790
5641
6045
5097
93C1
4552
2557
71 0
15
6645
9781
6086
3078
5527
6375
4968
1672
4409
2969
45
30
6658 1 2.0028
5986
3366
5411
6705
4838
3.0043
42C4
3381
30
45
6471 0275
5882
3654
5294
7033
4706
C413
4118
3792
15
20 0
6382 0521
5778
3941
5176
7362
4562
0782
3969
4202
70 0
15
5.6291 20767
65673
2.4228
7.5055
2.7689
8.4437
3.1151
9.3819
3.4612
45
30
6200
1012
5565
4515
4934
8017
4300
1519
37 C7
5021
30
45
6108
1257
5459
4800
4811
8343
4162
1886
3514
5429
15
21 0
6dl5
1502
5351
5086
4686
8669
4022
2253
3358
5837
69 0
15
5920
1746
5241
6371
4561
8995
3881
2619
3201
6244
45
30
1990
5129
5655
4433
089
3738
2985
3042
6650
30
45
5720
2233
5017
6939
4305
9645
3593
3350
2881
7056
15
22 0
5631
2476
4903
6222
4176
9909
3447
3715
271 i-
7461
68 0
15
5532
2719
47881 6505
4043
3.0292
3299
4078
2554
7865
45
30
5433
2961
4672 i 6788
3910
0615
3149
4442
2388
8268
30
45
5.5332
2.3203
6.45542.7070
7.3776
3.0937
8.2998
3.4804
9.2220
3.8671
15
23 0
5230
3414
4435 7351
3640
1258
2845
6166
2050
S073
67 0
15
5127
3685
4315J 7632
3503
1580
2691
5527
1879| 9474
45
30
5(124
3925
«ltf« 7912
3365
1900
2535
5887
1706 9875
30
45
4919
4165
4072 8192
3225
2220
2375
6247
1531 4.0275
15
24 0
4813
4404
3948 8472
3084
2539
2219
6006
1355
0674
66 0
15
4706
4643
3823; 8750
2941
2858
2059
0965
1176
1072
45
30
4598
4882
3697 i 9029
2797
3175
1897
7322
0996
1469
30
45
4489
5120
3570 1 9306
2651
3493
1733
7U79
0814
1866
15
25 0
4378
5357
3442! 9583
2505
3809
1568 8036
0631
226265 0
15
5.4267
2.5594
6.3312 2 9800
7.2356
3.4125
8.1401 3.8391
9.0446
4.2657
45
30
4155
5831
3181 3.0136
2207
4441
1233 8746
H259
3051
30
45
26 0
4042
3928
6067
6302
3049 0411
2916| 0686
2056
1904
4756
5070
1063
0891
9100 0070
9453 8.9879
3445 15
383764 0
15
3812
6537
2781 0960
1750
5383
0719
9806
9687
4229
45
30
3696
6772
2645 1234
1595
5696
0644
4.0158'
9493
4620
30
45
3579
7006
2509 1507
1438
6008
0368
0509
9298
5010
15
27 0
3460
7239
2370 1779
1281
6319
0191
0859 '
9101
5399
63 0
15
3341
7472
2231! 2051
1121
6630
0012
1209:
8902
5787
45
30
3221
7705
2091 1 2322 !
0961
6940
7.9831
15571
8701
6175
30
45
5.3099
2.7937
6.1949 3.25931 7.0799
3.7249
7.9649
4.1905
88499
4.6561
15
28 0
2977
8168
18(6 2863
0636
7558
9465
2252
8295
6947
62 0
15
2853
8399
1662 3132
6471
7866
9280
2599
8089
7^32
45
30
2729
8630
15171 3401
0305
8173
9094
2944
7882
7716
30
45
2604
8859
1371 1 3669
0138
8479
8905
3289
7673
8(99
15
29 0
2477
9089
1223 3937 6.9970
8785
8716
3683
7462
8481
61 0
15
2350
9317
1075 4203
9800
9090
8525
3976!
7250
8862
45
30
2221
9545
0925 4470
9628
9394
8332
4318!
7036
9242
30
45
2092
9773
0774 4735
945i ;
9697
8148
4659 1
6820 ! 9622
15
30 0
1962 3.0000
0622 1 50CO 9282
4.0000
7942
5000
66035.0000
50 0
Dep. 1 Lat.
Dep. Lat. j Dep.
TatT
^pTTatT
Dep. Lat.
Dist. 6
Dist. 7 i| Dist. 8
Dist. 9
Dist. 10
Course
218
TRAVERSE TABLE
TRAVERSE TABLE
Course
30 15 5.1830 3.0226
0462
0(178
0902
1120
1350
1573
1795
2017
45
31 0
15
30
45
32 0
15
'30
0744
0603
45 5.0462 3.2458
3? 0 0320
15 0177
30| 0033
45^4.9888
34 0 9742
15| 9595
9448
45
0 9149
3G 0
15
30
45
37 0
15
0
15
30
45
39 0
15
30
46
40 0
30
45
41 0
15
30
45
42 0
15
30
43 0
15
30
45
44 0
15
30
45
45 0
7018
77m
1.7441 3.C733
7281
79i e
6131
85G7
15 4.5794 3.8767
5624
r,4r,4
45 4.4059 4.0728
6110
4037
4763
4589 4 0148
9628
9363
!t'n!
9037
5.88733.7868
8707
6024
5312
5532
6.5331 4.6172
6456
21109
2391
2172
I'.o.i
1730
1.-.07
5.M03 4.7516
1195 7740
0986 7963
0776! 8185
0565^ 8406
0354 i 8626
0141 8845
4.9928; fc 9064
9713 •' 9281
9477| 9497
7547
7.".04
70. ;o
Pep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. : Pep. Lat.
Lat. Dep
.-.4 SO
5266
5050
Dist. 10
Lat. I DeB
9340
9674
4832 5.0001
4613 0327
c,it;3
5941
5717
5491
5264
.-oar,
4so5
4.773
901811 3867 1
439!
41
3! US
3724
7.3498 5.1943
2263
3042
258(
2347
2113
1877
I04C
1401
0436
0190
6.9943
9695
944lj
9191
8944
0662
0077
1300
1022
321 *
353,4
3147
2!K.I4
21 1 u
1015
8.1664 5.7715
1412
1157 8425
0902 8779
0644 913:
0386 9482
0125
1129 15
150459 0
15
0
45
30
15
446457 0
45
30
15
56 0
45
30
15
'35855 0
45
.98646.018253 0
45
30
15
156652 0
1909
2251
15
821 ;i
7988
77 ir
743;
7102
5751'
5471
2537
•_'•_•: it;
1934
2'J3L
1946
5276
560649 0
45
30
15
691348 0
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
05(39
0607
0645
0682
0719
0755
12
0792
0828
0864
0899
0934
OJ69
1004
1038
1072
1106
13
1139
1173
1206
1239
1271
1303
1335
1367
1399
1430
14
1461
1492
1523
1553
1584
1614
1644
1673
1703
1732
15
1761
1790
1818
1847
1875
1903
1931
1959
1987
2014
16
2041
2068
2095
2122
2148
2175
2201
2227
2253
2279
17
2304
2330
2355
2380
2405
2430
2455
2 ISO
2504
2529
18
2553
2577
2601
2625
2648
2672
2695
2718
2742
2765
19
2788
2810
2833
2856
2878
2900
2923
2945
2967
2989
20
3010
3032
3054
3075
3096
3118
3139
3160
3181
3201
21
3222
3243
3263
3284
3304
3324
3345
3365
3385
3404
22
3424
3444
3464
3483
3502
3522
3541
3560
3579
3598
23
3617
3636
3655
3674
3692
3711
3729
3747
3766
3784
24
3802
3820
3838
3856
3874
3892
3909
3927
3945
3962
25
3979
3997
4014
4031
4048
4065
4082
4099
4116
4133
26
4150
4166
4183
4200
4216
4232
4249
4265
4281
4298
27
4314
4330
4346
4362
4378
4393
4409
4425
4440
4456
28
4472
4487
4502
4518
4533
4548
4564
4579
4594
4609
29
4624
4639
4654
4669
4683
4698
4713
4728
4742
4757
30
4771
4786
4800
4814
4829
4843
4857
4871
4886
4900
31
4914
4928
4942
4955
4969
4983
4997
5011
5024
5038
32
5051
5065
5079
5092
5105
5119
5132
5145
5159
5172
33
5185
5198
5211
5224
5237
5250
5263
5276
5289
5302
34
5315
5328
5340
5353
5366
5378
5391
5403
5416
5428
35
5441
5453
5465
5478
5490
5502
5514
5527
5539
5551
36
5563
5575
5587
5599
5611
5623
5635.
5647
5058
5670
37
5382
5694
5705
5717
5729
5740
5752
5763
5775
5786
38
5798
5809
5821
5832
5843
5855
5866
5877
5S8S
5899
39
5911
5922
5933
5944
5955
5966
5977
5988
5999
6010
40
6021
6031
6042
6053
6064
6075
6085
6096
6107
6117
41
6128
6138
6149
6160
6170
6180
6191
6201
6212
6222
42
6232
6243
6253
6263
6274
6284
6294
6304
6314
6325
43
6335
6345
6355
6365
6375
0385
6395
6405
6415
6425
44
6435
6444
6454
6464
6474
6484
6493
6503
6513
6522
45
6532
6542
6551
6561
6571
6580
6590
6599
6609
6618
46
6628
6637
6646
6656
6065
0075
6684 6693
6702
6712
47
6721
6730
6739
6749
6758
0767
6776 ; 6785
6794
6803
48
6812
6821
6830
6839
6848
6857
6866
6875
6884
6893
49
6902
6911
6920
6928
6937
6946
6955
6964
6972
6981
50
6990
6998
7007
7016
7024
7033
7042
7050
7059
7067
51
7076
7084
7093
7101
7110
7118
7126
7135
7143
7152
62
7160
7168
7177
7185
7193
7202
7210
7218
7226
7235
53
7243
7251
7259
7267
7275
7284
7292
7300
7308
7316
54
7324
7332
7340
7348
7356
7364
7372
7380
7388
7396
No.
0
1
2
3
4
5
6
7
8
9
TABLES RELATING TO PARTS I AND II
221
LOGARITHMS OF NUMBERS
7404
7482
7669
7634
7993
8062
8129
8196
8261
8325
8388
8451
8692
76 8751
76 8808
77 8865
78 8921
79
81
897
9085
9138
9191
9243
9294
9345
9395
9445
9494
9542
9590
9638
9685
9731
9777
9823
9868
9912
9956
8704
8762
8820
8S76
8932
8987
9042
9096
9149
9201
9253
9304
9355
9405
9455
9504
9552
9600
9647
9694
9741
9877
9921
7803
7875
7945
8280
834 1
8407
8531
8591
st',51
8768
ss-_>5
9047
9101
9309
9460
9557
8156
8222
M'S 7
8351
8414
8637
8597
8657
8774
9063
9106
9315
9465
9562
9750
8663
9004
9165
9320
9754
7752
8299
9325
9523
9619
9759
7459
7973
8041
8109
8848
9015
9175
9528
7619
7094
7767
8182
8248
8500
8739
8854
9074
9128
9533
9675
9814
7474
7551
7627
7701
7774
7846
7917
7987
8055
8122
8254
8319
8445
8567
8627
8686
8745
8802
8859
8915
8971
9025
9079
9133
9186
9238
9289
7340
9390
9440
9586
9633
9727
9773
9952
9996
A MANUAL FOR NORTHERN WOODSMEN
LOGARITHMIC SINES, COSINES,
Angle
Sin.
D.I'
Cos.
D.I'
Tan.
D.I'
Cot.
0° 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
7.4637
.7648
.9409
8.0658
.1627
301.1
176.1
124.9
96.9
792
2.5363
.2352
.0591
1.9342
.8373
89° 50'
89° 40'
89° 30'
89° 20'
89° 10'
1° 0'
8.2419
66 9
9.9999
• o
8.2419
67 0
1.7581
89° 0'
1° 10'
1° 20'
1° 30'
1° 40'
1° 50'
.3088
.3668
.4179
.4637
.5050
58.0
51.1
45.8
41.3
37 8
.9999
.9999
.9999
.9998
.9998
.0
.0
.1
.0
1
.3089
.3669
.4181
.4638
.5053
58.0
51.2
45.7
41.5
.6911
.6331
.5819
.5362
.4947
88° 50'
88° 40'
88° 30'
88° 20'
88° 10'
2° 0'
8.5428
9.9997
o
8.5431
1.4569
88° 0'
2° 10'
2° 20'
2° 30'
2° 40'
2° 50'
.5776
.6097
.6397
.6677
.6940
32.1
30.0
28.0
26.3
.9997
.9996
.9996
.9995
.9995
.1
.0
.1
.0
.5779
.6101
.6401
.6682
.6945
32.2
30.0
28.1
26.3
.4221
.3899
.3599
.3318
.3055
87° 50'
87° 40'
87° 30'
87° 20'
87° 10'
3° 0'
8.7188
23 5
9.9994
1
8.7194
23 5
1.2806
87° 0'
3° 10'
3° 20'
3° 30'
3° 40'
3° 50'
.7423
.7645
.7857
.8059
.8251
22.2
21.2
20.2
19.2
.9993
.9993
.9992
.9991
.9990
.0
.7429
.7652
.7865
.8067
.8261
22.3
21.3
20.2
19.4
.2571
.2348
.2135
.1933
.1739
86° 50'
86° 40'
86° 30'
86° 20'
86° 10'
4° 0'
8.8436
17 7
9.9989
8.8446
17 8
1.1554
86° 0'
4° 10'
4° 20'
4° 30'
4° 40'
4° 50'
.8613
.8783
.8946
.9104
.9256
17.0
16.3
15.8
15.2
.9989
.9988
.9987
.9986
.9985
.8624
.8795
;8960
.9118
.9272
17.1
16.5
15.8
15.4
14 8
.1376
.1205
.1040
.0882
.0728
85° 50'
85° 40'
85° 30'
85° 20'
85° 10'
5° 0'
8.9403
14 2
9.9983
8.9420
1.0580
85° 0'
5° 10'
5° 20'
5° 30'
5° 40'
5° 50'
.9545
.9682
.9816
.9945
9.0070
13.7
13.4
12.9
12.5
.9982
.9981
.9980
.9979
.9977
.9563
.9701
.9836
.9966
9.0093
13.8
13.5
13.0
12.7
.0437
.0299
.0164
.0034
0.9907
84° 50'
84° 40'
84° 30'
84° 20'
84° 10'
«° 0'
9.0192
11 9
9.9976
9.02 10
12 0
0.9784
84° 0'
6° 10'
6° 20'
6° 30'
6° 40'
6° 50'
.0311
.0426
.0539
.0648
.0755
11.5
11.3
10.9
10.7
10 4
.9975
.9973
.9972
.9971
.9969
.0336
.0453
.0567
.0678
.0786
11.7
11.4
11.1
10.8
.9664
.9547
.9433
.9322
.9214
83° 50'
83° 40'
83° 30'
83° 20'
83° 10'
7° 0'
9.0859
10 2
9.9968
9.0891
0.9109
83° 0'
7° 10'
7° 20'
7° 30'
.0961
.1060
.1157
9.9
9.7
.9966
.9964
.9963
.2
.1
.0<)'.!5
.1096
.1194
10.1
9.8
.9005
.8904
.8806
82° 50'
82° 40'
82° 30'
Cos.
D.I'
Sin.
D.I'
Cot.
D.r
Tan.
Angle
TABLES RELATING TO PARTS I AND II
223
TANGENTS, AND COTANGENTS
Angle
Sin.
D.I'
Cos.
D. r
Tan.
D.I'
Cot.
7° 30'
7° 40'
7° 50'
8° 0'
8° 10'
8° 20'
8° 30'
8° 40'
8° 50'
9° 0'
9° 10'
9° 20'
9° 30'
9° 40'
9° 50'
10° 0'
10° 10'
10° 20'
10° 30'
10° 40'
10° 50'
11° 0'
11° 10'
11° 20'
11° 30'
11° 40'
11° 50'
12° 0'
12° 10'
12° 20'
12° 30'
12° 40'
12° 50'
13° 0'
13° 10'
13° 20'
13° 30'
13° 40'
13° 50'
14° 0'
14° 10'
14° 20'
14° 30'
14° 40'
14° 50'
16° 0'
9.1157
.1252
.1345
9.5
9.3
9.1
8.9
8.7
8.5
8.4
8.2
8.0
7.9
7.8
7.6
7.5
7.3
7.3
7.1
7.0
6.8
6.8
6.6
6.6
6.4
6.4
6.3
6.1
6.1
6.0
5.9
5.8
5.7
5.7
5.6
5.5
5.4
5.4
5.3
5.2
5.2
5.1
5.0
5.0
4.9
4.9
' 4.8
4.7
9.9963
.9961
.9959
.2
.2
.1
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
.3
.2
.2
.3
.2
.3
.2
.3
.2
.3
.2
.3
.3
.2
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.4
.3
.3
.4
9.1194
.1291
.1385
9.7
9.4
9.3
9.1
8.9
8.7
8.6
8.4
8.2
8.1
8.0
7.8
7.7
7.6
7.4
7.3
7.3
7.1
7.0
6.9
6.8
6.6
6.7
6.5
6.4
6.3
6.3
6.1
6.1
6.1
5.9
5.9
5.8
5.7
5.7
5.6
5.5
5.5
5.4
5.3
5.3
5.3
5.1
5.2
5.1
0.8806
.8709
.8615
82° 30'
82° 20'
82° 10'
82° 0'
81° 50'
81° 40'
81° 30'
81° 20'
81° 10'
81° 0'
80° 50'
80° 40'
80° 30'
80° 20'
80° 10'
80° 0'
79° 50'
79° 40'
79° 30'
79° 20'
79° 10'
79° 0'
78° 50'
78° 40'
78° 30'
78° 20'
78° 10'
78° 0'
77° 50'
77° 40'
77° 30'
77° 20'
77° 10'
77° 0'
76° 50'
76° 40'
76° 30'
76° 20'
76° 10'
76° 0'
75° 50'
75° 40'
75° 30'
75° 20'
75° 10'
75° 0'
9.1436
9.9958
9.1478
0.8522
.1525
.1612
.1697
.1781
.1863
.9956
.9954
.9952
.9950
.9948
,1569
.1658
.1745
.1831
.1915
.8431
.8342
.8255
.8169
.8085
9.1943
9.9946
9.1997
0.8003
.2022
.2100
.2176
.2251
.2324
.9944
.9942
.9940
.9938
.9936
.2078
.2158
.2236
.2313
.2389
.7922
.7842
.7764
.7687
.7611
9.2397
9.9934
9.2463
0.7537
.2468
.2538
.2606
.2674
.2740
.9931
.9929
.9927
.9924
.9922
.2536
.2609
.2680
.2750
.2819
.7464
.7391
.7320
.7250
.7181
9.2806
9.9919
9.2887
0.7113
.287Q
.2934
.2997
.3058
.3119
.9917
.9914
.9912
.9909
.9907
9.9604
.2953
.3020
.3085
.3149
.3212
.7047
.6980
.6915
.6851
.6788
9.3179
9.3275
0.6725
.3238
.3296
.3353
.3410
.3466
.9901
.9899
.9896
.9893
.9890
.3336
.3397
.3458
.3517
.3576
.6664
.6603
.6542
.6483
.6424
9.3521
9.9887
9.3634
0.6366
.3575
.3629
.3682
.3734
.3786
.9884
.9881
!9875
.9872
.3691
.3748
.3804
.3859
.3914
.6309
.6252
.6196
.6141
.6086
9.3837
9.9869
9.3968
0.6032
.3887
.3937
.3986
.4035
.4083
.9866
.9863
.9859
.9856
.9853
.4021
.4074
.4127
.4178
.4230
.5979
.5926
.5873
.5822
.5770
9.4130
9.9849
9.4281
0.5719
Cos.
D.I'
Sin.
D.I'
Cot.
D.I'
Tan.
Angle
224 A MANUAL FOR NORTHERN WOODSMEN
LOGARITHMIC SINES, COSINES,
Angle
Sin.
D.I'
Cos.
D.I'
Tan.
D.I'
5.0
5.0
4.9
4.9
4.8
4.8
4.7
4.7
4.7
4.6
4.6
4.5
4.5
4.5
4.4
4.4
4.4
4.3
4.3
4.2
4.2
4.2
4.2
4.1
4.1
4.0
4.0
4.0
4.0
4.0
3.9
3.9
3.8
3.9
3.8
3.8
3.7
3.8
3.7
3.7
3.7
3.6
3.6
3^
3.6
Cot.
15° 0'
15° 10'
15° 20'
15° 30'
15° 40'
15° 50'
16° 0'
16° 10'
16° 20'
16° 30'
16° 40'
16° 50'
17° 0'
17° 10'
17° 20'
17° 30'
17° 40'
17° 50'
18° 0'
18° 10'
18° 20'
18° 30'
18° 40'
18° 50'
19° 0'
19° 10'
19° 20'
19° 30'
19° 40'
19° 50'
20° 0'
20° 10'
20° 20'
20° 30'
20° 40'
20° 50'
21° 0'
21° 10'
21° 20'
21° 30'
21° 40'
21° 50'
22° 0'
22° 10'
22° 20'
22° 30'
9.4130
4.7
4.6
4.6
4.5
4.5
4.4
4.4
4.4
4.2
4.3
4.2
4.1
4.1
4.1
4.0
4.0
4.0
3.9
3.9
3.8
3.8
3.7
3.8
3.6
3.7
3.6
3.6
3.5
3.6
3.5
3.4
3.4
3.4
3.4
3.3
3.3
3.3
3.3
3.2
3.2
3.1
3.2
3.1
3.1
3.0
9.9849
.3
.3
.4
.3
.4
.4
.3
.4
.4
.3
.4
.4
.4
.4
.4
.4
.4
.4
.4
.4
.4
.5
.4
.4
.5
.4
.5
.4
.5
.4
.5
.4
.5
.5
.5
.4
.5
.5
.5
.5
5
.5
.5
.6
.5
9.4281
0.5719
75° O7
74° 50'
74° 40'
74° 30'
74° 20'
74° 10'
74° 0'
73° 50'
73° 40'
73° 30'
73° 20'
73° 10'
73° 0'
72° 50'
72° 40'
72° 30'
72° 20'
72° 10'
72° 0'
7 50'
7 40'
7 30'
7 20'
7 10'
71° 0'
70° 50'
70° 40'
70° 30'
70° 20'
70° 10'
70° 0'
69° 50'
69° 40'
69° 30'
69° 20'
69° 10'
69° 0'
68° 50'
68° 40'
68° 30'
68° 20'
68° 10'
68° 0'
67° 50'
67° 40'
67° 30'
.4177
.4223
.4269
.4314
.4359
.9846
.9843
.9839
.9836
.9832
.4331
.4381
.4430
.4479
.4527
.5669
.5619
.5570
.5521
.5473
9.4403
9.9828
9.4575
0.5425 '
.4447
.4491
.4533
.4576
.4618
.9825
.9821
.9817
.9814
.9810
.4622
.4669
.4716
.4762
.4808
.5378
.5331
.5284
.5238
.5192
9.4659
9.9806
9.4853
0.5147
.4700
.4741
.4781
.4821
.4861
.9802
.9798
.9794
.9790
.9786
.4898
.4943
.4987
.5031
.5075
.5102
.5057
.5013
.4969
.4925
9.4900
9.9782
9.5118
0.4882
.4939
.4977
.5015
.5052
.5090
.9778
.9774
.9770
.9765
.9761
.5161
.5203
.5245
.5287
.5329
.4839
.4797
.4755
.4713
.4671
9.5126
9.9757
9.5370
0.4630
.5163
.5199
.5235
.5270
.5303
.9752
.9748
.9743
.9739
.9734
.5411
.5451
.5491
.5531
.5571
.4589
.4549
.4509
.4469
.4429
9.5341
9.9730
9.5611
0.4389
.4350
.4311
.4273
.4234
.4196
.5375
.540.)
.5143
.5477
.5510
.9725
.9721
.9716
.9711
.9706
.5650
.5689
.5727
.5766
.5804
9.5543
9.9702
9.5842
0.4158
.5576
.5509
.5541
.5673
.5704
.9697
.9692
.9687
.9682
.9677
.5879
.5917
.5954
.5991
.6028
.4121
.4083
.4046
.4009
.3972
9.5736
9.9672
9.6064
0.3936
.5767
.5798
.5828
.9667
.9661
.9656
.6100
.6136
.6172
.3900
.3864
.3828
Cos.
D.I'
Sin.
D.I'
Got.
D.I'
Tan.
Angle
TABLES RELATING TO PARTS i AND n
TANGENTS, AND COTANGENTS
Angle
Sin.
D.I'
Cos.
D.r
Tan.
D.r
Cot.
22° 30'
22° 40'
22° 50'
9.5828
.5859
.5889
3.1
3.0
9.9656
.9651
.9646
.5
.5
9.6172
.6208
.6243
3.6
3.5
0.3828
.3792
.3757
67° 30'
67° 20'
67° 10'
23° 0'
9.5919
9.9640
9.6279
0.3721
67° 0'
23° 10'
23° 20'
23° 30'
23° 40'
23° 50'
.5948
.5978
.6007
.6036
.6065
3.0
2.9
2.9
2.9
2 8
.9635
.9629
.9624
.9618
.9613
.6
.5
.6
.5
6
.6314
.6348
.6383
.6417
.6452
3.4
3.5
3.4
3.5
3 4
.3686
.3652
.3617
.3583
.3548
66° 50'
66° 40'
66° 30'
66° 20'
66° 10'
24° 0'
9.6093
2 8
9.9607
5
9.6486
3 4
0.3514
66° 0'
24° 10'
24° 20'
24° 30'
24° 40'
24° 50'
.6121
.6149
.6177
.6205
.6232
2.8
2.8
2.8
2.7
2 7
.9602
.9596
.9590
.9584
.9579
.6
.6
.6
.5
g
.6520
.6553
.6587
.6620
.6654
3.3
3.4
3.3
3.4
3 3
.3480
.3447
.3413
.3380
.3346
65° 50'
65° 40'
65° 30'
65° 20'
65° 10'
25° 0'
9.6259
2 7
9.9573
g
9.6687
3 3
0.3313
65° 0'
25° 10'
25° 20'
25° 30'
25° 40'
25° 50'
.62SG
.6313
.6340
.6366
.6392
2.7
2.7
2.6
2.6
2 6
.9567
.9561
.9555
.9549
.9543
.6
.6
.6
.6
3
.6720
.6752
.6785
.6817
.6850
3.2
3.3
3.2
3.3
3 2
.3280
.3248
.3215
.3183
.3150
64° 50'
64° 40'
64° 30'
64° 20'
64° 10'
26° 0'
9.6418
2 6
9.9537
9.6882
3 2
0.3118
64° 0'
26° 10'
26° 20'
26° 30'
20° 40'
26° 50'
.6444
.6470
.6495
.6521
.6546
2.6
2.5
2.6
2.5
2 4
.9530
.9524
.9518
.9512
.9505
.6
.6
.6
.7
g
.6914
.6946
.6977
.7009
.7040
3.2
3 1
3.2
3.1
3 2
.3086
.3054
.3023
.2991
.2960
63 50'
63° 40'
63° 30'
63° 20'
63° 10'
27° 0'
9.6570
25
9.9499
7
9.7072
3 1
0.2928
63° 0'
27° 10'
27° 20'
27° 30'
27° 40'
27° 50'
.6595
.6620
.6644
.6668
.6692
2.5
2.4
2.4
2.4
2 4
.9492
.9486
.9479
.9473
.9466
.6
.7
.6
.7
7
.7103
.7134
.7165
.7196
.7226
3.1
3.1
3.1
3.0
3 1
.2897
.2866
.2835
.2804
.2774
62° 50'
62° 40'
62° 30'
62° 20'
62° 10'
28° 0'
9.6716
2 4
9.9459
5
9.7257
3 0
0.2743
62° 0'
28° 10'
28° 20'
28° 30'
28° 40'
28° 50'
.6740
.6763
.6787
.6810
.6833
2!4
2.3
2.3
2 3
.9453
.9446
.9439
.9432
.9425
'.7
.7
.7
7
.7287
.7317
.7348
.7378
.7408
3.0
3.1
3.0
3.0
3 0
.2713
.2683
.2652
.2622
.2592
61° 50'
61° 40'
61° 30'
61° 20'
61° 10'
29° 0'
9.6856
2 2
9 .9418
9.7438
2 9
0.2562
61° 0'
29° 10'
29° 20'
29° 30'
29° 40'
29° 50'
.6878
.6901
.6923
.6946
.6968
2.3
2.2
2.3
2.2
2 2
.9411
.9404
.9397
.9390
.9383
.7
'.7
.7467
.7497
.7526
.7556
.7585
3.0
2.9
3.0
2.9
.2533
.2503
.2474
.2444
.2415
60° 50'
60° 40'
60° 30'
60° 20'
60° 10'
30° 0'
9.6990
9.9375
9.7614
0.2386
60° 0'
Cos.
D.r
Sin.
D.I'
Cot.
D.r
Tan.
Angle
226 A MANUAL FOR NORTHERN WOODSMEN
LOGARITHMIC SINES, COSINES,
Angle
Sin.
D.I'
Cos.
D.I'
Tan.
D.I'
Cot.
30° 0'
9.6990
9.9375
9.7614
3 0
0.2386
60° 0'
30° 10'
30° 20'
30° 30'
30° 40'
30° 50'
.7012
.7033
.7055
.7076
.7097
2.1
2.2
2.1
2.1
2 1
.9368
.9361
.9353
.9346
.9338
.7
.8
.7
.8
7
.7644
.7673
.7701
.7730
.7759
2.9
23
2.9
2.9
2 9
.2356
.2327
.2299
.2270
.2241
59° 50'
59° 40'
59° 30'
59° 20'
59° 10'
31° 0'
9.7118
9.9331
9.7788
2 8
0.2212
59° 0'
31° 10'
31° 20'
31° 30'
31° 40'
31° 50'
.7139
.7160
.7181
.7201
.7222
2.1
2.1
2.0
2.1
20
.9323
.9315
.9308
.9300
.9292
.8
.7
.8
.8
g
.7816
.7845
.7873
.7902
.7930
2.9
2.8
2.9
2.8
2 8
.2184
.2155
.2127
.2098
.2070
58° 50'
58° 40'
58° 30'
58° 20'
58° 10'
32° 0'
9.7242
2 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
8
.7986
.8014
.8042
.8070
.8097
2.8
2.8
2.8
2.7
28
.2014
.1986
.1958
.1930
.1€03
57° 50'
57° 40'
57° 30'
57° 20'
57° 10'
33° 0'
9.7361
1 9
9.9236
g
9.8125
28
0.1875
57° 0'
33° 10'
33° 20'
33° 30'
33° 40'
33° 50'
.7380
.7400
.7419
.7438
.7457
2.0
1.9
1.9
1.9
1 9
.9228
.9219
.9211
.9203
.9194
.9
.8
.8
.9
g
.8153
.8180
.8208
.8235
.8263
2.7
2.8
2.7
2.8
2 7
.1847
.1820
.1792
.1765
.1737
56° 50'
56° 40'
56° 30'
56° 20'
56° 10'
34° 0'
9.7476
1 8
9.9186
9
9.8290
2 7
0.1710
56° 0'
34° 10'
34° 20'
34° 30'
34° 40'
34° 50'
.7494
.7513
.7531
.7550
.7568
1.9
1.8
1.9
1.8
1 8
.9177
.9169
.9160
.9151
.9142
.8
.9
.9
.9
g
.8317
.8344
.8371
.8398
.8425
2.7
2.7
2.7
2 7
.1683
.1656
.1629
.1602
.1575
55° 50'
55° 40'
55° 30'
55° 20'
55° 10'
35° 0'
9.7586
1 8
9.9134
g
9.8452
2 7
0.1548
55° 0'
35° 10'
35° 20'
35° 30'
35° 40'
35° 50'
.7604
.7622
.7640
.7657
.7675
1.8
1.8
1.7
1.8
1 7
.9125
.9116
.9107
.9098
.9089
.9
.9
.9
.9
g
.8479
.8506
.8533
.8559
.8586
2.7
2.7
2.6
2.7
2 7
.1521
.1494
.1467
.1441
.1414
54° 50'
54° 40'
54° 30'
54° 20'
54° 10'
36° 0'
9.7692
1 8
9.9080
1 0
9.8613
2 Q
0.1387
54°' 0'
36° 10'
36° 20'
36° 30'
36° 40'
36° 50'
.7710
.7727
.7744
.7761
.7778
1.7
1.7
1.7
1.7
1 7
.9070
.9061
.9052
.9042
.9033
.9
.9
1.0
.9
1 0
.8639
.8666
.8692
.8718
.8745
2.7
2.6
2.6
2.7
2 6
.1361
.1334
.1308
.1282
.1255
53° 50'
53° 40'
53° 30'
53° 20'
53° 10'
37° 0'
9.7795
1 6
it.'. ()•->:{
9
9.8771
26
0.1229
53° 0'
37° 10'
37° 20'
37° 30'
.7811
.7828
.7844
1.7
1.6
.8014
.9004
.8995
1.0
.9
.8797
.8824
.8850
2.7
2.6
.1203
.1176
.1150
52° 50'
52° 40'
52° 30'
Cos.
D.I'
Sin.
D.I'
Cot.
D.I'
Tan.
Angle
TABLES RELATING TO PARTS I AND II
227
TANGENTS, AND COTANGENTS
Angle
Sin.
D.I'
Cos
D.I'
Tan.
D.I'
Cot.
37° 30'
37° 40'
37° 50'
9.7844
.7861
.7877
1.7
1.6
1 6
9.8995
.8985
.8975
1.0
1.0
1 0
9.8850
.8876
.8902
2.6
2.6
2 6
0.1150-
.1124
.1098
52° 30'
52° 20'
52° 10'
38° 0'
9.7893
1 7
9.8965
1 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
.8955
.8945
.8935
.8925
.8915
1.0
1.0
1.0
1.0
1 0
.8954
.8980
..9006
.8032
.S058
2.6
2.6
2.6
2.6
2 6
.1046
.1020
.0994
.0968
.0942
51° 50
51° 40'
51° 30'
51° 20'
51° 10'
39° 0'
9.7989
1 5
9.8905
9.9084
2 6
0.0916
51° 0'
39° 10'
39° 20'
39° 30'
39° 40'
39° 50'
.8004
.8020
.8035
.8050
.8066
1.6
1.5
1.5
1.6
1 5
.8895
.8884
.8874
.8864
.8853
1.1
1.0
1.0
1.1
.9110
.9135
.9161
.9187
.9212
2.5
2.6
2.6
2.5
2 6
.0860
.0865
.0839
.0813
0788
50° 50'
50° 40'
50° 30'
50° 20'
50° 10'
40° 0'
9.8081
1 5
9.8843
9.9238
2 6
0.0762
50° 0'
40° 10'
40° 20'
40° 30'
40° 40'
40° 50'
.8096
.8111
.8125
.8140
.8155
1.5
1.4
1.5
1.5
.8832
.8821
.8810
.8800
.8789
1.1
1.1
1.0
1.1
.9264
.9289
.9315
.9341
.9366
2.5
2.6
2.6
2.5
2 6
.0736
.0711
.0685
.0659
.0634
49° 50'
49° 40'
49° 30'
49° 20'
49° 10'
41° 0'
9.8169
9.8778
P.9392
2 5
0.0608
49° 0'
41° 10'
41° 20'
41° 30'
41° 40'
41° 50'
.8184
.8198
.8213
.8227
.8241
1.4
1.5
1.4
1.4
1 4
.8767
,8756
.8745
.8733
.8722
1.1
1.1
1.2
1.1
.9417
.9443
.9468
.9494
.9519
2.6
2.5
2.6
2.5
2 5
.0583
.0557
.0532
.0506
.0481
48° 50'
48° 40'
48° 30'
48° 20'
48° 10'
42° 0'
9.8255
1 4
9.8711
9.9544
2 6
0.0456'
48° 0'
42° 10'
42° 20'
42° 30'
42° 40'
42° 50'
.8269
.8283
.8297
.8311
.8324
1.4
1.4
1.4
1.3
1 4
.8699
.8688
.8676
.8665
.8653
1.1
1.2
1.1
1.2
.9570
.9585
.9621
.9646
.9671
2.5
2.6
2.5
2.5
2 6
.0430
.0405
.0379
.0354
.0329
47° 50'
47° 40'
47° 30'
47° 20'
47° 10'
43° 0'
9.8338
1 3
9.8641
9.9697
2 5
0.0303
47° 0'
43° 10'
43° 20'
43° 30'
43° 40'
43° 50'
.8351
.8365
.8378
.8391
.8405
1.4
1.3
1.3
1.4
1 3
.8629
.8618
.8606
.8594
.8582
1.1
1.2
1.2
1.2
.9722
.9747
.9772
.9798
.9823
2.5
2.5
2.6
2.5
25
.0278
.0253
.0228
.0202
.0177
46° 50'
46° 40'
46° 30'
46° 20'
46° 10'
44° 0'
9.8418
9.8569
9.9848
2 6
0.0152
46° 0'
44° 10'
44° 20'
44° 30'
44° 40'
44° 50'
.8431
.8444
.8457
.8469
.8482
1.3
1.3
1.2
1.3
.8557
.8545
.8532
.8520
.8507
1.2
1.3
1.2
1.3
.9874
.9899
.9924
.9949
.9975
2.5
2.5
2.5
2.6
.0126
.0101
.0076
.0051
.0025
45° 50'
45° 40'
45° 30'
45° 20'
45° 10'
45° 0'
9.8495
9.8495
0.0000
0.0000
45° 0'
Cos.
D.I'
Sin.
D.1-
Cot.
D.I'
Tan.
Angle
228 A MANUAL FOR NORTHERN WOODSMEN
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TABLES RELATING TO PARTS i AND n
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OS OS 05 03 OS OS OS 05 OS
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OS OS OS. OS O OS OS CS OS
x' x x x x x x x
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MWCCMCO •* Tf •* TP ^ ^ ^ •« Tf •* 10 US 10 U5 m U5 10 10 S 10 5
A MANUAL FOB NORTHERN WOODSMEN
NATURAL SINES AND COSINES
A.
Sin.
Cos.
A.
Sin.
Cos.
A.
Sin.
Cos.
0°
.000000
1.0000 90°
30'
.1305
.9914
30'
15°
.2588
.9659
75°
10'
20'
.002909
.005818
1.0000 50'
1.0000 40'
40'
50'
.1334
.1363
.9911
.9907
20'
10'
10'
20'
.2616
.2114 I
.9652
.9644
50'
40'
30'
.008727
1.0000 30'
8"
.139?
.9903
82"
30'
30'
40'
.011635
.9999 j 20'
10'
40' .2700
(tt)"S
20'
50'
.014544
.9999 ' 10'
20'
.1449
9894
40'
50'
.2728
.9621
10'
1°
.017452
.9998 i 89°
30'
.1478
.9890
30'
16°
.2756
.9613
74°
10'
20'
.02036
.02327
.9998 50'
.9997 , 40'
40'
50'
.1507
.1536
.9886
.9881
20'
10'
10'
20'
.2784
.2X12
.9605
/.i.V.iii
50'
40'
30'
.02618
.9997 30'
9"
.1564
.9877
81"
30'
.2840
30'
40'
50'
.02908
.03199
.9996 20'
.9995 10'
10'
20'
.1593
.1622
.9872
50'
40'
40'
50'
.2868
.2896
.'.'.T-ii
.9572
20'
10'
2°
.03490
.9994 88°
30'
.1650
.9863
30'
17"
.2924
.9563
73°
10'
.03781
.9993 50'
40'
.1679
.!iX5X
20'
10'
.2952
.9555
50'
20'
.04071
.9992 40'
,9xt>. >
20'
."979
.9546
40'
30'
.04362
.9990 I 30'
10°
.1736
.9848
80"
30'
.3007
.9537
30'
40'
50'
.04653
.04943
.9989 | 20'
.9988 10'
107
20'
.1765
.1794
.9843
9838
50'
40'
40'
50'
.3035 .9528
.3062 .9520
20'
10'
3°
.05234
.9986 ; 87°
30'
.1822
30'
18°
.3090
.9511
72°
10'
.05524
.9985 50'
40'
.1851
.9X2,
20'
10'
.3118
.9502
50'
20'
.05814
.9983 i 40'
50'
.9822
10'
20'
.3145
9-192
40'
30'
.06105
.9981 j 30'
11"
.1908
.9816
79"
30'
.3173
.9483
30'
40'
50'
.06395
.06685
.9980
.9978
20'
10'
10'
20'
.1937
1965
.9811
9SU5
50'
40'
40'
50'
.3201
.3228
.9474
.9465
20'
10'
4°
.06976
.9976
86°
30'
.1994
.9799
30'
19°
.3256
.9455
71°
10'
20'
.07266
.07556
.9974
.9971
50'
40'
40'
50'
.2051
.9787
20'
10'
10'
20'
.3283
.3311
.9446
.9436
50'
40'
30'
.07846
.9969
30'
12"
.2079
.97X1
78"
30'
.3338
.9426
30'
40'
50'
.08136
.08423
.9967
.9964
20'
10'
10'
20'
.2108
.2136
.9775
.9769
50'
40'
40'
50'
.3365
.3393
.9417
.9407
20'
10'
5°
.08716
.9962
85°
30'
2164
.9763
30'
20°
.3420
.9397
70"
10'
20'
.09005
.092J5
.9959
.9957
50'
40'
40'
50'
2193
2221
.9757
.9750
20'
10'
10'
20'
.3448
.3475
.9387
!i>377
50'
40'
30'
.09585
.9954
30'
13°
2250
.9744
77°
30'
.3502
30'
40'
50'
.09874
.10164
.9951
.9948
20'
10'
10'
2278
2306
.9737
.9730
50'
40'
40'
50'
3529
3557
.9356
.9346
20'
10'
6
.10153
.9945
84°
30'
2334
.9724
30'
21"
8584
9336
69"
10'
20'
.10742
.11031
.9942
.9939
50'
40'
40'
50'
2363
2391
.9717
9710
20'
10'
10'
20'
3611
3638
9325
9315
50'
40'
30'
.11320
.9936
30'
14°
2419
9703
76"
30'
36f>5
9304 ! 30'
40'
.11609
.9932
20'
50'
40'
3692
9293
20'
50'
.11898
.9929
10'
20'
2476
40'
50'
3719
9283
10'
r
.12187
.9925
83°
30'
2504
imVi
30'
22"
3746
9272
68U
10'
20'
.12476
.12764
.9922
.9918
50'
40'
40'
50'
2532
2560
9674
9667
20'
10'
10'
20'
3773
3KOO
9261
9250
50'
40'
30'
.13053
.9914
30'
15°
2588
9659
75"
30'
3827
9239
30'
Cos.
Sin.
A.
Cos.
Sin.
A.
Cos.
Sin.
A.
1
TABLES RELATING TO PARTS I AND II 231
NATURAL SINES AND COSINES — continued
A.
30'
40'
50'
23°
10'
20'
30'
40'
50'
24°
10'
20'
30'
40'
50'
25°
10'
20'
30'
40'
50'
26°
10'
20'
30'
40'
50'
27°
10'
20'
30'
40'
50'
28°
10'
20'
30'
40'
50'
29°
10'
20'
30'
40'
50'
30°
Sin.
Cos.
A.
Sin.
.5000
Cos.
A.
30'
40'
50'
38°
10'
20'
30'
40'
50'
39°
10'
20'
30'
40'
50'
40°
10'
20'
30'
40'
50'
41°
10'
20'
30'
40'
50'
42°
10'
20'
30'
40'
50'
43°
10'
20'
30'
40'
50'
44°
10'
20'
30'
40'
50'
45°
Sin.
.6088
.6111
.6134
Cos.
.7934
.7916
.7898
.3827
.3854
.3881
.9239
.9228
.9216
30'
20'
10'
67°
50'
40'
30'
20'
10'
66°
50'
40'
30'
20'
10'
65°
50'
40'
30'
20'
10'
64°
50'
40'
30'
20'
10'
63°
50'
40'
30'
20'
10'
62°
50'
40'
30'
20'
10'
61°
50'
40'
30'
20'
10'
60°
30°
10'
20'
30'
40'
50'
31°
10'
20'
30'
40'
50'
32°
10'
20'
30'
40'
50'
33°
10'
20'
30'
40'
50'
34°
10'
20'
30'
40'
50'
35°
10'
20'
30'
40'
50'
38°
10'
20'
30'
40'
50'
37°
10'
20'
30'
.8660
60°
50'
40'
30'
20'
10'
59°
50'
40'
30'
20'
10'
58°
50'
40'
30'
20'
10'
57°
50'
40'
30'
20'
10'
56°
50'
40'
30'
20'
10'
55°
50'
40'
30'
20'
10'
54°
50'
40'
30'
20'
10'
53°
50'
40'
30'
30'
20'
10'
62°
50'
40'
30'
20'
10'
51°
50'
40'
30'
20'
10'
5tt°
50'
40'
30'
20'
10'
49°
50'
40'
30'
20'
10'
48°
50'
40'
30'
20'
10'
47°
50'
40'
30'
20'
10'
46°
50'
40'
30'
20'
10'
46°
.5025
.5050
.5075
.5100
.5125
.8646
.8631
.8616
.8601
.8587
.3607
.9205
.6157
.7880
.7862
.7844
.7826
.7808
.7790
.3934
.3961
.3987
.4014
.4041
.9194
.9182
.9171
.9159
.9147
.6180
.6202
.6225
.6248
.6271
.5150
.8572
.5175
.5200
.5225
.5250
.5275
.8557
.8542
.8526
.8511
.8496
.4067
.4094
.4120
.4147
.4173
.4200
.9135
.9124
.9112
.9100
.9088
.9075
.6293
.7771
.7753
.7735
.7716
.7698
.7679
.6316
.6338
.6361
.6383
.6406
.5299
.5324
.5348
.5373
.5398
.5422
.8480
.8465
.8450
.8434
.8418
.8403
.4226
.9063
.6428
.7660
.4253
.4279
.4305
.4331
.4358
.9051
.9038
.9026
.9013
.9001
.6450
.6472
.6494
.6517
.6539
.6561
.6583
.6604
.6626
.6648
.6670
.7642
.7623
.7604
.5446
.8387
.5471
.5495
.5519
.5544
.5568
.8371
.8355
.8339
.8323
.8307
.7585
.7566
.4384
.4410
.4436
.4462
.4488
.4514
.4540
.4566
.4592
.4617
.4643
.4669
.4695
.8988
.8975
.8962
.8949
.8936
.8923
.8910
.8897
.8884
.8870
.8857
.8843
.8829
.7547
.7528
.7509
.7490
.7470
.7451
.5592
.8290
.5616
.5640
.5664
.5688
.5712
.8274
.8258
.8241
.8225
.8208
.6691
.7431
.6713
.6734
.6756
.6777
.6799
.7412
.7392
.7373
.7353
.7333
.5736
.8192
.8175
.8158
.8141
.8124
.8107
.5760
.5783
.5807
.5831
.5854
.6820
.7314
.4720
.4746
.4772
.4797
.4823
.8816
.8802
.8788
.8774
.8760
.6841
.6862
.6884
.6905
.6926
.7294
.7274
.7254
.7234
.7214
.5878
.5901
.5925
.5948
.5972
.5995
.8060
.8073
.8056
.8039
.8021
.8004
.4848 1 .8746
.6947
.6967
.6988
.7009
.7030
.7050
.7071
.7193
.4874
.4899
.4924
.4950
.4975
, .8732
.8718
.8704
.8689
.8675
.7173
.7153
.7133
.6018
.7986
.6041
.6065
.6088
Cos.
.7969
.7951
.7934
.7112
.7092
.5000
.8660
Sin.
.7071
Cos.
A.
Sin. A.
Cos.
Sin.
A.
A MANUAL FOR NORTHERN WOODSMEN
NATURAL TANGENTS AND COTANGENTS
A.
Tan.
Cot.
90°
50'
40'
30'
20'
10'
89°
50'
40'
30'
20'
10'
88°
50'
40'
30'
20'
10'
87°
50'
40'
30'
20'
10'
86°
50'
40'
30'
20'
10'
86°
50'
40'
30'
20'
10'
84°
50'
40'
30'
20'
10'
83°
50'
40'
30'
A.
Tan.
.1317
.1346
.IMTti
Cot.
A.
Tan.
Cot.
75°
50'
40'
30'
20'
10'
74°
50'
40'
30'
20'
10'
73°
50'
40'
30'
20'
10'
72°
50'
40'
30'
20'
10'
71°
50'
40'
30'
20'
10'
70°
50'
40'
30'
20'
10'
69°
50'
40'
30'
20'
10'
68°
50'
40'
30'
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
30'
40'
50'
8°
10'
21)'
30'
40'
00'
9D
10'
20'
30'
•10'
50'
10°
10'
20'
:;o'
10'
50'
II3
10'
20'
30'
40'
50'
123
10'
20'
30'
•10'
50'
13'
10'
20'
:;<)'
40'
50'
14
10'
20'
:;o'
10'
50'
15°
7.5958
7.I2S7
7.2687
30'
20'
10'
82°
50'
40'
30'
20'
10'
81°
50'
40'
30'
20'
10'
80°
50'
40'
30'
20'
10'
79°
50'
40'
30'
20'
10'
78°
50'
40'
30'
20'
10'
77°
50'
40'
30'
20'
10'
76°
50'
.40'
30'
20'
10'
75°
15°
10'
20'
30'
40'
50'
16°
10'
20'
30'
40'
50'
17°
10'
20'
30'
40'
50'
18°
10'
20'
30'
40'
50'
19°
10'
20'
30'
40'
50'
20°
10'
20'
30'
40'
50'
21°
10'
20'
30'
40'
50'
22°
10'
20'
30'
.2679
3.7321
.002909
.005818
.008727
.011636
.014515
343.7737
171.8854
114.5887
85.9398
68.7501
.2711
.2742
.277:-!
.2M)5
.283J
.2867
.2899
.2931
.2962
.2994
.:;o2i
3.6891
3.6470
3.6059
5.5650
5.5261
5.4874
3.4495
3.4124
;.:;75'.i
!.:i102
;.::0o2
.1405
7.1154
.1435
.1465
.1495
.1524
.1554
6.9682
1) S2'i!
6.6912
6.5606
6.4348
.017455
57.2900
.02036
.02328
.02619
.02910
.03201
49.1039
42.9641
38.1885
34.3678
31.2416
.1584
.1614
.1644
6.3138
6.1970
6.0S44
.03492
28.6363
.1673
.1703
.1733
5.'.)7f)S
5.8708
5.7694
.3057
,5.2709
.03783
.04075
.04366
.04658
.04949
26.4316
24.5418
22.9038
21.4701
20.205")
.3089
.3121
.3153
.3185
.3217
.3249
3.2371
i.20ii
5.171(1
;.i:;<>7
3.1084
.1763
5.6713
.1793
.1823
.1853
.1883
.1914
5.5704
5. is 15
5.396£
5.:iO'.i:
5.2257
05241
19.0811
3.0777
05533
05824
06116
06408
06700
18.0750
17.1693
16.3499
15.6048
14.9244
.3281
.3314
.3346
.:r,7s
.3411
3.0475
3.0178
2>.)SS7
2.'. K100
2.9319
.1944
.1974
.2004
.20:; 5
.20(15
.2095
5.1446
5.0658
4.9894
4.9152
-l..vi:;<
4.7729
06993
14.3007
.3443
2.-J012
07285
07578
07870
08163
08456
13.7267
13.1969
12.7052
12.2505
11.8262
.3476
.3508
.3541
2.S770
2.8502
2.s2:;'.i
o 7<)X()
2:7725
.2126
4.7046
.2156
.2186
.2217
.2247
.227*
4.6382
!. 57:ic
4.5107
I.11H1
4.3897
.36,4
.3607
.3640
08749
11.4301
2.7475
09042
09335
09629
09923
10216
11.0594
10.7119
10.3854
10.0780
9.7882
.3673
.3706
:!7:',!i
.3772
.3805
2.722S
2.6985
2. (17 1(1
2.(1511
2.(>27!l
.2309
4.3315
.2339
.2370
.2401
21M2
.2462
.2493
2524
2555
25SI1
2(117
2(1 IS
2679
Cot.
4.2747
4.2193
4.1653
4.1126
4.0611
10510
9.5144
3839
2.6051
10805
11099
11394
11688
11983
9.2553
9.0038
8.7769
8.5555
8.3450
3872
3
3!»305
4.0108
3.9617
5.<>i:;ii
;.si;r,7
;.s2()s
1.77(10
2 5:;st;
2.5172
2 I'.ind
12278
8.1443
4040
-1071
41 OS
4142
2.4751
12574
12869
13165
7.9530
7.7704
7.5958
2.4545
2.4:; 12
2.4142
3.7321
Cot.
Tan.
A.
Tan.
A.
Cot.
Tan.
A.
TABLES RELATING TO PARTS I AND II
NATURAL TANGENTS AND COTANGENTS
A.
Tan.
Cot.
A.
Tan.
Cot.
A.
Tan.
Cot.
30'
4142
2.4142
30'
30°
5774
1.7321
60°
30'
7673
1.3032
30'
40'
50'
4176
4210
2.3945
2.3750
20'
10'
10'
20'
5812
5851
1.7205
1.7090
50'
40'
40'
50'
7720
7766
1.2E54
1.2876
20'
10'
23°
4245
2.3559
67°
30'
5890
1.6977
30'
38°
7813
1.271S9
62°
10'
20'
30'
4279
4314
4348
2.3369
2.3183
2.2998
50'
40'
30'
40'
50'
31°
5930
5969
6009
1 .6864
1.6753
1.6643
20'
10'
59°
10'
20'
30'
.7860
.7907
.7954
1.2723
1.2647
1.2572
50'
40'
SO'
40'
50'
4383
4417
2.2817
2.2637
20'
10'
10'
20'
6048
6088
1.6534
1 6426
50'
40'
40'
50'
.8002
.8050
1.2497
1.2423
20'
10'
24°
4452
2.2460
66°
30'
6129
1.6319
30'
39°
.8098
1.2349
51°
10'
20'
4487
4522
2.2286
22113
50'
40'
50'
6168
6208
1.6212
1.6107
10'
10'
20'
.8146
.8195
1.2276
1.2203
50'
40'
30'
4557
2.1943
30'
32°
6249
1.6003
58"
30'
.8243
1.2131
30'
40'
50'
4592
4628
2.1775
2.160J
20'
10'
10'
90'
6289
6330
1.5SOO
1.5798
50'
40'
40'
50'
.8292
.8342
1.2059
1.1988
20'
10'
25°
4663
2.1445
65°
30'
6371
1.5697
30'
40°
.8391
1.1918
50°
10'
20'
4699
4734
2.1283
2.1123
50'
40'
40'
50'
6412
6453
1.5597
1.5497
10'
10'
?0'
.8441
.8491
1.1847
1.1778
50'
40'
30'
4770
2.0965
30'
33U
6494
1.5399
57U
30'
.8541
1.1708
30'
40'
50'
4808
4841
2.0809
2.0655
20'
10'
10'
20'
6536
6577
1 .5301
1 5204
50'
40'
40'
50'
.8591
.8642
1.1640
1.1571
20'
10'
26°
4877
2.0503
64°
30'
6619
1.5108
30'
41°
.8683
1.1504
49°
10'
20'
4913
4950
2.0353
20204
50'
40'
40'
50'
6661
6703
1.5013
1.4919
20'
10'
10'
90'
.8744
.8796
1.1436
1.1369
50'
40'
30'
40'
50'
4986
.5022
5059
2.0057
1.9912
1.9768
30'
20'
10'
34°
10'
?,0'
6745
^787
.6830
1.4826
Y.4733
1.4641
56°
50'
40'
30'
40'
50'
.8847
.8899
.8952
1.1303
1.1237
1.1171
30'
20'
10'
27°
.50J5
1.9626
63°
30'
.6873
1.4550
30'
42°
.6004
1.1106
48°
10'
W
.5132
.5169
1.9486
1.9347
50'
40'
40'
50'
.6916
.6959
1.4460
1.4370
20'
10'
10'
20'
.6057
.9110
1.1041
1.0977
50'
40'
30'
.5206
1.9210
30'
35U
.7002
1.4281
55°
30'
.9163
1.0913
30'
40'
50'
.5243
.5280
1.9074
1.8940
20'
10'
10'
20'
.7046
7089
1.4193
1 4106
50'
40'
40'
50'
.9217
.9271
1.0786
10'
28°
.5317
1.8807
62°
30'
.7133
1.4019
30'
43°
.9325
1.0724
47°
10'
20'
.5354
.5392
1.8676
1.8546
50'
40f
40'
50'
.7177
1.3934
1.3848
20'
10'
10'
20'
.9380
.9435
1.0661
1.0599
50'
40'
30'
.5430
1.8418
30'
36a
.7265
1.3764
54°
30'
.9460
1.0538
30'
40'
50'
.5467
.5505
1.8291
1.8165
20'
10'
10'
20'
.7310
7355
1.3680
1 3597
50'
40'
40'
50'
.9545
.9601
1.0416
10'
29°
.5543
1.8040
61°
30'
.7400
1.3514
30'
44°
.9657
1.0355
46°
10'
20'
.5581
.5519
1.7917
1.7796
50'
40'
40'
50'
.7445
.7490
1.3432
1.3351
20'
10'
10'
20'
.9713
.9770
1 .0295
1.0235
50'
40'
30'
.5858
1.7675
30'
37°
.7536
1.3270
53°
30'
.9827
1.0176
30'
40'
50'
.5896
.5735
1.7553
1.7437
20'
10'
10'
20'
.7581
7627
1.31CO
1 3111
50'
40'
40'
50'
.9884
.9942
1.0117
1.0058
10'
30°
.5774
1.7321
60°
30'
.7673
1.3032
30'
45°
1.0000
1.0000
45°
Cot.
Tan.
A.
Cot.
Tan.
A.
Cot.
Tan.
A.
234 A MANUAL FOR NORTHERN WOODSMEN
SECTION II
TABLES RELATING TO PARTS III AND IV
1. VOLUMES OF CYLINDERS (Locs) IN CUBIC FEET . . 236
2. AREAS OF CIRCLES OR BASAL AREAS 238
3. CORD WOOD RULE . 239
4. NEW HAMPSHIRE RULE 240
5. NEW YORK STANDARD RULE 242
6. SCRIBNER LOG RULE, LEGAL IN MINNESOTA . . . 243
7. DECIMAL RULE OF THE U. S. FOREST SERVICE . . . 244
8. DOYLE RULE 246
9. MAINE LOG RULE 248
10. QUEBEC RULE 250
11. NEW BRUNSWICK RULE " 253
12. CLARK'S INTERNATIONAL RULE 254
13. SPAULDING RULE OF COLUMBIA RIVER 255
14. BRITISH COLUMBIA RULE 258
15. VOLUME TABLES
A. Eastern
1. White Pine by the Scribner Rule 261
2, 3. Red (Norway) Pine by the Scribner Rule . . 262
4. White Pine as sawed in Massachusetts ... 263
5. White Pine in Cords 264
6. Spruce in Cubic Feet 264
7. Spruce in Feet, Board Measure 265
8. Spruce in Cords 266
9. Hemlock by the Scribner Rule 267
10. Hemlock as sawed in New Hampshire . . . 268
11. White (paper) Birch in Cords 268
12. Red Oak as sawed in New Hampshire .... 269
. 13. Peeled Poplar in Cords 270
14. Second Growth Hard Woods in Cords .... 270
- 15 . Form Height Factors for Southern Hard Woods 27 1
16,17. Northern Hard Woods in Board Measure . 272,273
18. Longleaf Pine in Board Measure 274
19. Loblolly Pine by the Scribner Rule .... 275
B. Western; Notes on Western Volume Tables .... 276
20. Western White Pine in Board Feet 281
21. Western Yellow Pine in Board Feet 282
22. Western Yellow Pine (16-foot log lengths) . . 283
23. Lodgepole Pine in Feet, Board Measure, and
in Railroad Ties 284
24. Western Larch in Board Measure 285
25. Engelmann Spruce in Board Measure .... 286
26. Douglas Fir of the Coast 287
27. Douglas Fir of the Interior 288
28. Washington Hemlock in Board Measure . . . 289
29. Washington Red Cedar in Board Measure . . 290
30. California Sugar Pine in Board Measure ... 292
-. C-|iOX?J>C
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3 288S88S3SS8SS2
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a r- «q "O •* co -H q os oq
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^H ^ ^' i-H (N N (N CO CO CO •*•*•*'•*•*•*' 10 l
0 1-< i-H rt r-i (N lO i-i X •<*
iO ~3 O 00 CO CO i-t
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CM CS CO CO •* •* lO
oooooooooc
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22S2S8!
oo t^ oo oo oo
omo
i-H Ol 00 C
S3SS§3e
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244 A MANUAL FOR NORTHERN WOODSMEN
Is
|!
DOST^OCOC^h-COOltOC
JOJCO^^iOtfJCOCOr^C
W t^. N t^. I-H O ^-< i
^TfiOiOOOI^I
CO t~ 00 O -H -t^-C
w lllll^llsl^is
00 O IN •* to 00 C
246 A MANUAL FOR NORTHERN WOODSMEN
^Suaq |
3 *5
as
;ciO'-(Wro^>ocDr--cccio
TABLES RELATING TO PARTS in AND iv 247
1 IN CO t^ r*- CO C5 Oi O
<— *OlNOiO
i-H I t» i-H CO •— ( CD O *Q O »O 0i ^J* O5 CO 00 CO 00 C I-H
CO I •* *O iO CD CD t^ l> GO X X Oi CS O O »-< i— ' W (N CO CO ^
S-^OCSt-lO^OOOOt
5N«D»wr^rtlOCB4
55
-,6
37
60
72
74
76
78
SO
102
105
10S
111
114
132
136
139
143
147
150
154
158
162
,.,
ISO
185
190
195
200
225
231
237
244
250
270
277
285
292
300
•;oo
308
317
325
333
360
370
580
390
400
420
432
443
455
467
480
493
507
520
533
555
1
601
617
630
647
665
682
700
TABLES RELATING To PARTS in AND iv
PROVINCE OF QUEBEC
Table of Contents of Saw Logs, Boom and Dimension Timber in
Feet Board Measure
DIAMETER IN INCHES
21
22
23
24
25
26
27
28
29
30
31
32 |
192
217
240
262
283
317
333
362
392
421
450
ft.
47510
211
238
264
289
312
348
367
399
431
463
495
52211
230
260
2S8
315
340
380
400
435
470
505
540
57012
249
282
312
341
368
412
433
471
509
547
585
617 13
268
303
336
367
397
443
467
507
548
589
630
665 14
287
325
360
394
425
475
500
544
587
631
675
71215
307
347
384
420
453
507
533
580
627
673
720
76016
326
368
408
446
482
538
567
616
666
715
765
80717
345
390
432
472
510
570
600
652
705
757
810
855 18
364
412
456
499
538
602
633
689
744
800
855
90219
383
433
480
525
567
633
667
725
783
842
900
95020
402
455
504
551
595
665
700
761
822
884
945
99721
422
477
528
577
623
697
733
797
862
926
990
1045 22
441
498
552
604
652
728
767
834
901
968
1035
1092 23
460
520
576
630
680
760
800
870
940
1010
1080
114024
479
542
600
656
708
792
833
906
979
1052
1125
118725
498
563
624
682
737
823
867
942
1018
1094
1170
1235 26
517
585
648
709
765
855
900
979
1057
1136
1215
1282 27
537
607
672
735
793
887
933
1015
1097
1178
1260
1330 28
556
628
696
761
822
918
967
1051
1136
1220
1305
1377 29
575
650
720
787
850
950
1000
1087
1175
1262
1350
1425 30
j594
672
744
814
878
982
1033
1124
1214
1305
1395
1472 31
613
693
768
840
907
1013
1067
1160
1253
1347
1440
1520 32
632
715
792
866
935
1045
1100
1196
1292
1389
1485
1567 33
652
737
816
892
963
1077
1133
1232
1332
1431
1530
161534
671
758
840
919
992
1108
1167
1269
1371
1473
1575
166235
690
780
864
945
1020
1140
1200
1305
1410
1515
1620
171036
709
802
888
971
1048
1172
1233
1341
1449
1557
1665
1757 37
728
823
912
997
1077
1203
1267
1377
1488
1599
1710
1805 38
747
845
936
1024
1105
1235
1300
1414
1527
1641
1755
1852 39
767
867
960
1050
1133
1267
1333
1450
1567
1683
1800
1900 40
A MANUAL FOR NORTHERN WOODSMEN
PROVINCE OF QUEBEC
Table of Contents of Saw Logs, Boom and Dimension Timber in
Feet Board Measure
DIAMETER iv INCHES
1 33
34
35
36
37
38
39
40
41
42
43
ft.
10 525
542
567
592
617
655
692
733
758
792
833
11 577
596
623
651
678
715
761
807
834
871
917
12 630
650
680
710
740
780
830
880
910
950
1000
13 682
704
737
769
802
845
899
953
986
1029
1083
14 735
758
793
828
863
910
968
1027
1062 1108
1177
15 787
812
850
887
925
975
1037
1100 1137
1187
1250
16 840
867
907
947
987
1040
1107
1173
1213
1267
1333
17 892
921
963
1006
1048
1105
1176
1247
1289
1346
1417
18 945
975
1020
1065
1110
1170
1245
1320
1365
1 425 i 1500
19 997
1029
1077
1124
1172
1235
1314
1393
1441 1504J1583
20 1050
1083
1133
1183
1233
1300
1383
1467
1517
1583 1667
21 1102
1137
1190
1242
1295
1365
1452
1540
1592
1662 1750
22 1155
1192
1247
1302
1357
1430
1522
1613
1668
1742 1833
23 1207
1246
1303
1361
1418
1495
1591
1687
1744
1821 1917
24 1260
1300
1360
1420
1480
1550
1660
1760
1820
1900 2000
25 1312
1354
1417
1479
1542
1625
1728
1833
1896
1979
2083
26 1365
1408
1473
1538
1603
1690
1796
1907
1972
2058
2167
27 1417
1462
1530
1597
1665
1755
1867
1980
2047
2137
2250
28 1470
1517
1587
1657
1727
1820
1937
2053
2123
2217
2333
29 1522
1571
1643
1716
1788.
1885
2006
2127
2199
2296
2417
30 1575
1625
1700
1775
1850
1950
2075
2200
2275
2375
2500
31 1627
1679
1757
1834
1912
2015
2144
2273
2351
2454
2583
32 1680
1733
1813
1893
1973
2080
2213
2347
2427
2533
2667
33 1732
1787
1870
1952
2035
2145
2282
2420
2502
2612
2750
34 1785
1842
1927
2012
2097
2210
2352
2493
2578
2692
2X33
35 1837
1896
1983
2071
2158
2275
2421
2567
2654
2771
2917
36 1890
1950
2040
2130
2220
2340
2490
2640
2730
2850
3000
37 1942
2004
2097
2189
2282
2405
2559
2713
2806 2929
3083
38 1995
2058
2153
2248
2343
2470
2628
2787
2882 i 3008
3167
39 2047
2112
2210
2307
2405
2535
2697
2860
2957 3087
3250
40 2100
2167
2267
2367
2467
2600
2767
2933:3033 3167
3333
TABLES RELATING TO PARTS III AND IV 253
NEW BRUNSWICK LOG RULE
p
Diameter at Top in Inches
11
12
13
14 15.
16
17
18
19
20
21
22
23
24
12
60
72
84
98
112
28
149
172
196
225
247
272
297
324
14
70
84
98
114
131
49
174
200
228
262
288
317
336
380
16
80
96
112
130
150
170
198
229
261
300
327
362
376
432
18
90
10S
126
147
168
192
223
258
294
337
370
408
445
486
20
100
120
140
163
187
213
248
286
326
375
411
453
495
540
21
105
126
147
171
196
223
261
301
343
393
432
476
519
569
22
110
132
154
179
205
234
275
315
359
412
453
498
544
594
24
120
144
168
196'224
256
298
344
392
450
494
544
594
648
26
142
168
196226
259
298
346
396
453
509
560
614
660
730
28
30
154
164
182
194
212 245
226 ' 261
280
299
523
344
374
398
428
457
490
523
550
588
605
644
653
698
716
756
788
840
32
176
208
242280320
568
427
490
561
627
689
738
808
898
34
36
186
198
220
234
256
273
297336
315360
590
415
452
481
519
552
594
631
664
707
732
778
784
853
877
931
952
1011
38
208
246
287
331
379
436
506
580
663
745
829
898
981
1065
40
220
260
303
350
400
461
534
612
701
786
864
948
1035
1123
42
231
273
318
367
419
484
562
644
736
825
908
995
1088
1181
44
242
286
333
384
43<
509
590
674
771
865
951
1042
1138
1235
46
252
298
347
401
458
531
613
703
804
903
992
1088
1188
1289
48
50
264
280
312 364
336392
420 480
450515
554
596
642
690
736
788
842
903
944
1003
1038
1104
1138
1208
1242
1308
1348
1430
UNDERSIZED LOGS
A log measuring 7 inches at the top contains twice as many superficial
feet as its own length.
A log measuring 8 inches, 2£ times its length.
A log measuring 9 inches, 3 times its length.
A log measuring 10 inches, 4 times its length.
254 A MANUAL FOR NORTHERN WOODSMEN
CLARK'S INTERNATIONAL LOG RULE
1
Length — Feet
Q
8
9
10
11
12
13
14
15
16
17
18
19
20
Ins.
Volume
— Board Feet
6
10
10
10
15
15
15
20
20
20
25
25
30
30
7
15
15
15
20
20
25
25
30
30
35
35
40
45
8
20
20
25
25
30
35
35
40
45
45
50
55
60
9
25
30
30
35
40
45
50
50
55
60
65
70
75
10
30
35
40
45
50
55
60
65
70
75
85
90
95
11
40
45
50
55
65
70
75
80
90
95
105
110
115
12
50
55
65
70
75
85
90
100
105
115
125
130
140
13
60
65
75
85
90
100
110
120
130
140
145
155
165
14
70
80
90
100
110
120
130
140
150
160
175 186
196
15
80
90
105
115
125
140
150
160
175
185
200 215
225
16
95
105
120
130
145
160
170
185
200
215
230, 245 260
17
105
120
135
150
165
180
195
210
225
245
260 275 296
18
120
135
155
170
185
205
220
240
255
275
295 310 330
19
135
155
175
190
210
230
250
270
290
310
330 350 370
20
150
170
195
215
235
255
300
320
345
365
390
410
21
170
190
215
235
260
285
305
330
355
380
405
430
455
22
185
210
235
260
285
315
340
365
390
420
445
475
500
23
205
230
260
285
315
345
370
400
430
460
490
520
550
24
225
255
285
315
345
375
405
440
470
500
535
565
600
25
245
275
310
345
375
410
445
475
510
545
580
615
650
26
265
300
335
370
405
445
480
520
555
595
630
670
705
27
290
325
365
405
440
480
520
560
600
640
680
725
765
28
310
350
395
435
475
520
560
605
645
690
735
780
825
29
335
380
425
470
510
560
605
650
695
740
790
835 885
30
360
405
455
500
550
600
645
695
745
795
845
895 950
31
385
435
485
540
590
640
695
745
800
850
905 960 1015
32
33
410
440
465
495
520
555
575
610
630
670
685
730
740
790
795
850
850 910 965 1025 1080
9051 970103010901150
34
470
530
590
650
715
775
840
900
965
1030 1095 1160 1225
1
495
525
560
595
625 1 690
665 735
755
800
825
875
890
945
965 1025 1095
1015 1085 1160
1160 1230 1300
1230 1305 1375
37
560
630
705
775
850
925
1000
1075
1150
1225
1300 1380 1455
38
39
590
020
665
705
745
785
820
865
895 975 1055'! 135 1210
945 1030 1110 1195 1280
1295
1365
1375 1455 1535
1450 1535 1620
40
655
740
825
910
995
1085
1170
1260
1345
1 435 ! 1525 1615 1705
41
42
690
725
780
820
870 960 1050 1140 1230
915 1010 1100 1200 1295
1325 1415 1510 1605 1700 1795
1390 1490-1585 1685 1785 1885
43
760
860
960
1060
1155
1260
1360
1460
1500
1665 1770 1870 1975
44
45
800
835
900 1005 1110 1215 1320 1425
945 1055 1160 1270 1380 1490
1530 1 635 i 1745 1855 1960 2070
1600 1715 1825 1940 2050 2165
46
875
990
1100
1215
1330
1445
1560
1675
1790
1910 2030 2145 2265
47
915
1035
1150
1270
1 390
1510
1630
1750
1870
1995;2120 2240 2365
48
955
1080
12051325 1450 1575
1700
1830
1955
2085
2210
2340
2470
TABLES RELATING TO PARTS III AND IV 255
SPAULDING LOG RULE OF COLUMBIA RIVER
BI DIAMETER IN INCHES
" 10
11
12
13
14
15 16
17
18
19 1 SO
21
22
ft.
12 38
47
58
71
86
103
121
141
162
184
207
231
256
14 44
55
67
82
100
120
141
164
IS'.)
214
241
269
298
16 50
63
77
94
114
137
161
188
210
245
276
308
341
18 57
70
87
106
129
154
181
211
243
276
310
346
384
20 63
78
96
118
143
171
201
235
270
306
345
385
426
22 69
86
106
130
157
188
221
258
297
337
379
423
469
24 76
94
116
142
172
208
242
282
324
368
414
462
512
26 82
101
125
153
186
22:i
262
305
351
398
448
500
554
28 88
109
134
164
200
240
282
328
378
428
482
538
596
30 94
117
144
176
214
257
302
352
405
459
517
577
639
32 101
125
154
188
228
274
322
376
432
490
552
616
682
34 107
132
164
200
243
2ni
342
399
459
521
586
654
725
36 113
140
174
212
258
308
362
422
486
552
620
692
768
38 120
148
183
224
272
325
382
446
513
582
655
731
810
40 126
156
192
236
286
342
402
470
540
612
690
770
852
42 132
164
202
248
300
359
422
493
567
643
724
808
895
44 138
172
212
260
314
376
442
516
5!H
674
758
846
938
46 145
179
222
272
329
KM
463
540
621
705
793
885
981
48 151
187
232
284
344
412
484
564
648
736
828
924
1024
50 157
195
241
295
358
429
504
587
675
766
862
962
1066
23
24
25
26
27 28
29
30
31
32
33
34
L2 282
309
337
36€
39(
> 427
459
492
526
561
597
634
14 329
360
393
427
462
! 498
535
574
613
654
696
739
16 376
412
449
48S
52J
569
612
656
701
748
796
845
18 423
463
505
54S
59-i
640
688
738
789
841
895
951
20 470
515
561
610
66C
711
765
820
876
935
995
1056
22 517
566
617
671
72€
782
841
902
964
1028
1094
1162
24 564
618
674
732
792
854
918
984
1052
1122
1194
1268
26 611
669
730
793
85S
925
994
1066
1139
1215
1293
1373
28 658
720
786
854
924
996
1070
1148
1226
1308
1392
1478
30 705
772
842
915
99C
1067
1147
1230
1314
1402
1492
1584
32 752
824
898
976
105f
1138
1224
1312
1402
1496
1592
1690
34 799
875
954
1037
1122
1209
1300
1394
1490
1589
1691
1796
36 846
926
1010
1098
118
1280
1376
1476
1578
1682
1790
1902
38 893
978
1066
115S
125-
1351
1453
1558
1665
1776
1890
2007
40 940
1030
1122
122C
132(
) 1422
1530
1640
1752
1870
1990
2112
42 987
1081
1178
1281
138f
> 1493
1606
1722
1840
1963
2089
2218
44 1034
1132
1234
1342
1452
! 1564
1682
1804
1928
2056
2188
2324
46 1081
1184
1291
140S
1515
i 1636
1759
1886
2016
2150
2288
2430
48 1128
1236
1348
1464
158-
1708
1836
1968
2104
2244
2388
2536
60 1175
1287
1404
152£
165(
) 1779
1912
2050
2191
2337
2487
2641
256
A MANUAL FOR NORTHERN WOODSMEN
SPAULDING LOG RULE — continued
x DIAMETER IN INCHES
o
" 35
36
07
38
39
46
Ol
ft.
12 673
713
755
798
843
889
936
984
1033
1086
1134
1186
14 785
831
880
931
983
1037
1092
1148
1205
1267
1323
1383
16 897
950
1006
1064
1124
1185
1248
1312
1377
1448
1512
1581
18 1009
1069
1132
1197
1264
1333
1404
1476
1549
1629
1701
1779
20 1121
1188
1258
1330
1405
1481
1560
1640
1721
1810
1890
1976
22 1233
1307
1384
1463
1545
1629
1716
1804
1893
1991
2079
2174
24 1346
1426
1510
1596
1686
1778
1872
1968
2066
2172
2268
2372
26 1458
1544
1635
1729
1826
1926
2028
2132
2238
2353
2457
2569
28 1570
1662
1760
1862
1966
2074
2184
2296
2410
2534
2646
2766
30 1682
1781
1886
1995
2107
2222
2340
2460
2582
2715
2835
2964
32 1794
1900
2012
2128
2248
2370
2496
2624
2754
2896
3024
3162
34 1906
2019
2138
2261
2osx
2518
2652
2788
2926
3077
3213
3360
36 2018
2138
2264
2394
2..2s
2666
2808
2952
3098
3258
3402
3558
38 2130
2257
2390
2527
L'. ;.;•.!
2814
2964
3116
3270
3439
3591
3755
40 2242
2376
2516
2660
2810
2962
3120
3280
3442
3620
3780
3952
42 2354
2495
2642
2793
2950
3110
3276
3444
3614
3801
3969
4150
44 2466
2614
2768
2926
3090
3258
3432
3608
3786
3982
4158
4348
46 2579
2733
2894
3059
3231
3407
3588
3772
3959
4163
4347
4546
48 2692
2852
3020
3192
3372
3556
3744
3936
4132
4344
4536
4744
50 2804
2970
3145
3325
3512
3704
3900
4100
4304
4525
4725
4941
47
48
49
50
51
52
63
"
66
56
57
58
L2 1239
1293
1348
1404
1461
15.19
1578
1638
1700
1763
1827
1893
14 1445
1508
1572
1638
1704
1772
1841
1911
1983
2056
2131
2208
16 1652
1724
1797
1872
1948
2025
2104
2184
2266
2350
2436
2524
18 1858
1939
2022
2106
2191
2278
2367
2457
2 .-,,-)(]
2644
2740
2839
20 2065
2155
2246
2340
2435
2531
2630
2730
2833
2938
3045
3155
22 2271
2370
2470
2574
2678
2784
2893
3003
3116
3232
3349
3470
24 2478
2586
2696
2808
2922
3038
3156
3276
3400
3526
3654
3786
26 26S4
2801
2920
3042
3165
3291
3419
3549
3683
3819
3958
4101
28 2890
3016
3144
3276
3408
3544
3682
3>22
3966
4112
4262
4416
30 3097
3232
3369
3510
3652
3797
3945
4095
4249
4406
4567
4732
32 3304
3448
3594
3744
3896
4050
4208
4368
4532
4700
4872
5048
34 3510
3663
3819
3978
4139
4303
4471
4641
4816
4994
5176
5363
36 3716
3878
4044
4212
4:is2
4556
4734
4914
5100
.-,2s-,
5480
5678
38 3923
4094
4268
4446
4626
ISO!)
4997
5187
5383
r,.-,s2
5785
5994
40 4130
4310
4492
4680
4870
5062
5260
5460
5666
5876
6090
6310
42 4336
4525
4716
4914
5113
5315
5523
5733
5949
6170
6394
6625
44 4542
4740
4940
5148
5356
5568
5786
6006
6232
6464
r,r,os
6940
46 4749
4956
5166
5382
5600
5822
6049
6279
6516
ti7f).x
7003
7256
48 4956
5172
5392
5U16
5844
6076
6312
6552
tisoo
7052
7304
7572
60 5162
5387
5616
5850
6087
6329
6575
(1S25
7083
7345
7612
7887
TABLES RELATING TO PARTS III AND IV 257
SPAULDING LOG RULE — continued
K DIAMETER IN INCHES
J »
60
61
62
63
64
65
66
67
68
69
70
ft.
12 1960
2028
2098
2169
2241
2315
2390
2467
2545
2625
2706
2789
14 2286
2366
2447
2530
2614
2700
2789
2878
2969
3062
3157
3253
16 2613
2704
2797
2V;,1>
2!NS
3086
3186
3289
3393
3500
3608
3718
18 2940
3042
3147
3253
3361
3472
3585
3700
3817
3937
4059
4183
20 3266
3380
3496
3615
3735
3858
3983
4111
4241
4375
4510
4648
22 3592
3718
3846
3976
4108
4244
4381
4522
4665
4812
4961
5113
24 3920
4056
4196
4338
4482
4630
4780
4934
5090
5250
5412
5578
26 4246
4394
4545
4699
4855
5015
5179
5345
5514
5687
5863
6042
28 4572
4732
4894
5060
5228
5400
5578
5756
5938
6124
6314
6506
30 4899
5070
5244
5422
5602
5786
5975
6167
6362
6562
6765
6971
32 5226
5408
5594
5784
5976
6172
6372
6578
6786
7000
7216
7436
34 5553
5746
5944
6145
6349
6558
6771
6989
7210
7437
7667
7901
36 5880
6084
6294
6506
6722
6944
7170
7400
7634
7874
8118
8366
38 6206
6422
6643
6868
7096
7330
7568
7811
8058
8312
8569
8831
40 6532
6760
6992
7230
7470
7716
7966
8222
8482
8750
9020
9296
42 6858
7098
7342
7591
7843
8102
8364
8633
8906
9187
9471
9761
44 7184
7436
7692
7952
8216
8488
8762
9044
9330
9624
9922
46 7512
7774
8042
8314
8590
8874
9161
9456
9755
48 7840
8112
8392
8676
8964
9260
9560
50 8166
8450
8741
9057
9337
9645
9959
258 A MANUAL FOR NORTHERN WOODSMEN
BRITISH COLUMBIA LOG SCALE
Established by the government, and derived from the
following rule: — Deduct \y% inches from the mean diam-
eter of the log at the small end ; square the result and mul-
tiply by .7854; deduct %; divide by 12; multiply by the
length of the log in feet.
Logs more than 40 and not over 50 feet long to be scaled
as two logs of equal length, the butt log taken as 1 inch
larger than the top. Logs over 50 and not over 60 feet
long to be treated similarly, but with 2 inches rise allowed
to the butt log; and so on, 1 inch of rise being added for
each 10 feet or part thereof over 40 feet.
n DIAMETER IN INCHES
5 10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
ft.
1 3
4
5
6
7
9
10
11
ft
15
16
18
20
22
24
26
10 34
43
53
63
74
87
100
114
130
146
163
181
200
220
241
263
12 41
52
63
76
89
104
120
137
155
175
195
217
210
264
289
315
14 48
60
73
88
104
121
140
100
isl
204
22S
253
2x0
30S
337
368
16 55
69
84
101
119
139
160
1x3
207
23:-;
201
200
320
352
386
421
18 62
77
94
113
134
150
ISO
2.10
233
202
203
320
360
300
134
473
20 69
80
105
126
149
173
20!)
229
259
292
326
302
400
440
4s2
526
22 76
94
115
138
104
191
220
252
2S5
321
358
398
440
484
530
578
24 83
103
151
17s
2ox
240
274
311
{50
301
131
ISO
52 S
57S
631
26 89
112
130
161
193
220
21')
207
337
',79
124
471
572
020
683
28 96
120
147
176
20x
213
280
320
303
108
150
507
500
010
075
736
30 103
129
157
189
223
200
300
343
889
137
189
513
000
600
723
789
32 110
137
168
201
238
278
320
360
415
466
521
579
640
704
771
841
34 117
140
17S
214
253
295
340
3X0
441
190
55 i
015
Ox()
748
xl9
894
36 124
155
189
227
20x
3 1 2
300
412
100
-,25
5SO
•,52
720
702
S07
946
38 131
103
199
239
2 S3
330
3X0
435
492
554
019
Oxx
700
S36
no
999
40 138
172
210
252
297
317
400
4.57
518
5S3
052
724
800
SSO
904
1051
TABLES RELATING TO PARTS III AND IV 259
BRITISH COLUMBIA LOG SCALE — continued
W DIAMETER IN INCHES
6
f,
27
28
29
30
31
32
33
34
35
36
37
ft.
1 29
31
33
36
39
41
44
47
50
53
57
60
10 286
309
334
360
387
414
443
472
503
534
567
600
12 343
371
401
432
464
497
531
567
603
641
680
720
14 400
433
468
504
541
580
620
661
704
748
793
840
16 457
495
535
576
619
663
708
756
804
855
906
960
18 514
557
602
648
G96
746
797
850
905
961
1020
1080
20 571
619
668
720
773
828
886
945
1005
1068
1133
1200
22 629
681
.735
791
850
911
974
1039
1106
1175
1246
1320
24 686
743
802
864
928
994
1063
1133
1207
1282
1360
1440
26 743
805
869
936
1005
1077
1151
1228
1307
1389
1473
1560
28 800
867
936
1008
1082
1160
1240
1322
1408
1496
1586
1679
30 857
928
1003
1080
1160
1243
1328
1417
1508
1602
1700
1799
32 914
990
1070
1152
1237
1325
1417
1511
1609
1709
1813
1919
34 971
1052
1136
1224
1314
1408
1505
1606
1709
1816
1926
2039
36 1028
1114
1203
1296
1392
1491
1594
1700
1810
1923
2039
2159
38 1086
1176
1270
1368
1469
1574
1682
1795
1910
2030
2153
2279
40 1143
1238
1337
1440
1546
1657
1771
1889
2011
2137
2266
2399
38
39
40
41
42
43
44
45
46
47
48
49
ft.
1 63
67
71
74
78
82
86
90
94
99
103
107
10 634
669
705
743
781
820
860
901
943
985
1029
1074
12 761
803
847
891
937
984
1032
1081
1131
1182
1235
1289
14 888
937
988
1040
1093
1148
1204
1261
1320
1379
1441
1503
16 1015
1071
1129
1188
1249
1312
1376
1441
1508
1577
1647
1718
18 1141
1205
1270
1337
1405
1475
1547
1621
1697
1774
1852
1933
20 1268
1339
1411
1485
1561
1639
1719
1801
1885
1971
2058
2148
22 1395
1472
1552
1634
1717
1803
1891
1981
2074
2168
2264
2362
24 1522
1606
1693
1782
1874
1967
2063
2161
2262
2365
2470
2577
26 1649
1740
1834
1931
2030
2131
2235
2342
2451
2562
2676
2792
28 1775
1874
1975
2079
2186
2295
2407
2522
2639
2759
2882
3007
30 1902
2008
2116
2228
2342
2459
2579
2702
2828
2956
3087
3222
32 2029
2142
2258
2376
2498
2623
2751
2882
3016
3153
3293
3436
34 2156
2276
2399
2525
2654
2787
2923
3062
3205
3350
3499
3651
36 2283
2410
2540
2673
2810
2951
3095
3242
3393
3547
3705
3866
38 2410
2543
2681
2822
2967
3115
3267
3422
3582
3744
3911
4081
40 2536
2677
2822
2970
3123
3279
3439
3602
3770
3941
4117
4295
260
A MANUAL FOR NORTHERN WOODSMEN
BRITISH COLUMBIA LOG SCALE — continued
a DIAMETER IN INCHES
i
B
3 50
51
52
53
54
55
66
67
58
59
60
61
ft.
1 112
117
121
126
131
136
141
147
152
157
163
168
10 1120
1166
1214
1262
1312
1362
1414
1466
1519
1574
1629
1685
12 1343
1399
1457
1515
1574
1635
1696
1759
1823
1888
1955
2022
14 1567
1633
1699
1767
1837
1907
1979
2052
2127
2203
2280
2359
16 1791
1866
1942
2020
2099
2180
2262
2346
2431
2518
2606
2696
18 2015
2099
2185
2272
2361
2452
2545
2639
2735
2832
2932
3033
20 2239
2332
2428
2525
2624
2725
2827
2932
3039
3147
3258
3370
22 2463
2566
2670
2777
2886
2997
3110
3225
3343
3462
3583
3707
24 2687
2799
2913
3030
3148
3269
3393
3519
3646
3777
3909
4044
26 2911
3032
3156
3282
3411
3542
3676
3812
3950
4091
4235
4381
28 3135
3265
3399
3535
3673
3814
3958
4105
4254
4400
4561
4718
30 3359
3499
3641
3787
3936
4087
4241
4398
4558
4721
4886
5055
32 35S3
3732
3884
4039
4198
4359
4524
4691
4862
5036
5212
5392
34 3807
3965
4127
4292
4460
4632
4807
4985
5166
5350
5538
5729
36 4030
4198
4370
4544
4723
4904
5089
527S
5470
5665
5864
6066
38 4254
4432
4612
4797
4985
5177
5372
5571
5774
5980
6190
6403
40 4478
4665
4855
5049
5247
5449
5655
5864
6077
6294
6515
6740
62
63
64
65
66
67
68
69
70
71
72
73
ft.
1 174
180
186
192
198
204
210
217
223
230
237
243
10 1742
1800
1859
1919
1980
2042
2105
2169
2233
2299
2366
2433
12 2091
2160
2231
2303
2376
2450
2526
2602
2689
2759
2839
2920
14 2439
2520
2603
26S7
2772
2859
2947
3036
3127
3219
3312
3407
16 2787
2880
2975
3071
3168
3267
3368
3470
3573
3678
3785
3893
18 3136
3240
3347
3454
3564
3676
3789
3903
4020
4138
42r,S
4380
20 3484
3600
3718
3838
3960
4084
4210
4337
4467
4598
4731
4867
22 3833
3960
4090
4222
4356
4492
4631
4771
4913
5058
5204
5353
24 4181
4320
4462
4606
4752
4901
5051
5205
5360
5518
5677
5840
26 4529
4680
4834
4990
5148
5309
5472
5638
5807
5977
6151
6327
28 4878
5040
5206
5374
5444
5717
5893
6072
6253
6437
6621
6813
30 5226
5401
5578
5757
5950
6126
6314
6506
6700
6897
7097
7300
32 5575
5761
5949
6141
6336
6534
6735
6939
7146
7357
7570
7787
34 5923 6121
6321
6525
6732
6943
7156
7373
7593
7816
8043
8273
36 62721 6481
6693
6909
7128
7351
7577
7807
8040
8276
8516
S760
38 6620 6841
7065
7293
7524
7759
7998
8240
S48C
sr:ic,
8989
9247
40 6968 7201
7437
7677
7920
8168
8419
8674
8933
9196
9462
9734
TABLES RELATING TO PARTS III AND IV 261
VOLUME TABLE No. 1. WHITE PINE BY THE SCRIBNER
RULE
Breast
Diam.
Inches
Total Height of Tree — Feet
60
60
75
90
100
120
140
160
70
70
85
100
115
135
160
185
210
240
270
80
90
100
110
120
130
140
150
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
80
100
115
135
155
180
210
240
270
310
350
390
440
490
540
95
115
135
155
180
200
240
270
310
350
390
430
480
540
600
660
720
§:
iso
210
230
270
310
350
390
440
480
540
600
660
720
790
850
920
990
'270
310
350
390
440
490
540
600
660
730
800
870
940
1020
1100
1180
1270
1360
1450
1550
1650
1750
;;;;
440
460
550
600
670
740
810
890
970
1040
1130
1210
1300
1400
1500
1600
1700
1800
1900
'680
750
830
910
990
1070
1150
1240
1330
1420
1520
1630
1750
1870
1980
2100
940
1020
1100
1190
1280
1370
1470
1580
1690
1800
1920
2040
2170
2300
1320
1420
1530
1640
1750
1860
1980
2100
2220
2360
2500
Based on 3000 trees cut in New York, the Lake States,
and Canada, cut as a rule into 16-foot logs. These scaled
with due allowance for crook and breakage, but not for
decay. Original.
262 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 2. RED PINE, IN BOARD FEET, BY THE
MINNESOTA SCRIBNER RULE
(Trees under 130 Years Old)
Diameter
S
Total Height in Feet
Inches
60
70
80
90
100
7
17
24
8
29
38
'SO
-
9
44
63
81
'94
10
61
72
88
104
119
11
80
92
110
130
148
12
100
114
136
159
180
13
120
138
160
189
214
14
140
164
189
222
250
15
190
220
257
292
16
252
296
340
17
334
394
18
372
450
VOLUME TABLE No. 3. RED PINE, IN BOARD FEET, BY THE
MINNESOTA SCRIBNER RULE
(Trees over 200 Years Old)
Diameter
Breast
Total Height in Feet
High
Inches
70
80
90
100
10
85
105
11
102
126
147
12
122
150
177
13
144
176
210
14
168
208
246
15
193
240
284
16
220
275
323
383
17
250
311
370
435
18
282
349
417
490
19
317
390
468
551
20
355
433
523
616
21
396
480
582
685 .
22
530
646
755
23
584
715
830
24
790
905
25
867
986
26
951
1075
27
'.'.'. 1041 1166
TABLES RELATING TO PARTS III AND IV 263
The preceding tables from Minnesota timber cut into
16-foot logs and scaled straight and sound. By H. H.
Chapman.
VOLUME TABLE No 4. WHITE PINE IN FEET — BOARD
MEASURE
(From State Forester of Massachusetts)
Diameter
Breast
Total Height of Tree — Feet
High
Inches
30
40
50
60
70
80
90
100
5
10
6
15
20
30
7
20
30
40
50
65
8
25
35
50
65
85
9
30
45
60
80
105
iis
'( '
10
40
55
75
95
125
145
11
65
90
115
145
170
200
230
12
75
105
135
165
200
230
260
13
85
120
155
190
235
260
295
14
100
140
175
215
265
300
335
15
115
160
200
245
300
340
375
16
180
230
275
335
380
420
17
260
310
370
425
470
18
295
350
410
475
530
19
335
390
455
530
600
20
380
435
505
580
660
21
480
550
635
720
22
520
595
680
780
23
565
640
730
835
24
600
690
780
890
25
645
740
830
940
26
'
885
995
Gives yield of trees from £ foot stump to 4 inches in
the top as sawed into round or waney-edged, or both round
and square-edged, lumber. In the smallest sizes of trees
appreciably more may be obtained by cutting to a smaller
size in the top.
£64
A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 5. WHITE PINE IN CORDS
(From State Forester of Massachusetts)
Diameter
Breast
High
Total Height of Tree — Feet
Inches
30
40
50
60
70
80
90
5
.03
6
.03
.04
.05
;
7
.04
.05
.07
.09
8
.05
.07
.09
.11
.13
9
.07
.09
.11
.13
.16
10
.11
.13
.16
.19
.22
11
.13
.16
.19
.23
.26
.30
12
.15
.19
.22
.27
.31
.35
13
.17
.22
.26
.31
.36
.40
14
.25
.30
.34
.41
.45
15
.28
.34
.40
.46
.51
Includes volume of tree above ^ foot from ground and
up to 4 inches diameter in the top.
VOLUME TABLE No. 6. SPRUCE IN CUBIC FEET
Breast
Diam-
eter
Total Height of Tree — Feet
Inches
40
45
50
55
60
65
70
75
80
CO
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
4.9
6.3
7.8
9.8
12.0
5.3
6.9
8.6
10.8
13.5
16.0
18.5
22.
5.8
7.6
9.5
12.0
150
18.0
21.
24.
28.
31.
6.5
8.5
10.6
13.4
16.5
19.7
23.
27.
30.
34.
38.
43.
47.
52.
56.
'9.6
12.0
15.0
18.2
22.
25.
29.
33.
37.
41.
46.
50.
55.
60.
14
17
20
23
27
31
36
40
44
49
54
59
65
72
79
87
96
'21
25
29
34
38
43
47
52
58
64
70
77
84
92
100
'27
32
36
41
46
51
56
62
69
76
82
88
95
104
'34
39
44
49
55
61
67
74
81
87
93
100
108
'63
70
77
85
93
98
105
114
123
'-'
TABLES RELATING TO PARTS III AND IV 265
Table No. 6 gives volume of tree from ground to tip
exclusive of branches. Includes bark, which is about 12^
per cent of the total volume. Based on 2500 trees cut in
Maine, New Hampshire, and New York, calipered each 4
feet, computed separately, and averaged. Original.
This table may without great modification be applied to
other soft wood species, regard being had to the remarks on
tree form on pages 167 — 173 of this volume. Balsam fir,
however, is believed to be pretty uniformly somewhat
slimmer than spruce, having, as would appear from the
results of a study on fir made by Mr. Zon of the United
States Forest Service, 8 per cent less volume for the same
breast diameter and height.
VOLUME TABLE No. 7. SPRUCE IN FEET, BOARD
MEASURE
Breast
Diam-
Total Height of Tree — Feet
eter
Inches
40
45
50
55
60
65
70
75
80
90
7
20
20
20
25
25
8
20
25
30
35
40
45
g
30
35
40
45
50
55
10
40
45
50
60
65
70
80
11
55
65
70
80
90
105
iis
12
65
75
85
100
110
120
135
i-50
13
75
CO
100
115
125
140
155
170
14
105
120
135
150
165
180
195
15
120
135
155
170
ISO
205
220
16
155
170
185
205
225
250
sis
17
170
190
210
230
250
275
350
18
185
210
235
255
280
310
390
19
205
235
260
290
320
350
430
20
235
265
295
325
355
385
470
21
300
330
360
390
425
510
22
330
360
395
430
465
550
23
360
400
435
470
510
600
24
400
440
480
515
555
650
Based on 2500 trees scaled in 16-foot log lengths up to
6 inches in diameter by the Maine rule and discounted
from 5 to 10 per cent. Purports to give the yield in edged
lumber of average spruce trees in economical woods and
mill practice,
•266
A MANUAL FOR NORTHERN WOODSMEN
VOLtTME TABLE No. 8. SPRUCE IN CORDS
Breast
Diameter
Total Height of Tree — Feet
Inches
40
45
50
55
60
65
70
75
80
6
.04
.05
.05
.06
7
.06
.06
.07
.08
.09
8
.07
.08
.09
.10
.12
.13
9
Of>
.10
.12
.13
.14
.16
10
.11
.12
.14
.16
.17
.19
.20
.22
11
.15
.17
.19
.20
.22
.24
.26
.28
12
.18
.20
.22
.24
.26
.28
.30
.32
13
.21
.23
.25
.27
.30
.32
.34
.37
14
.26
.29
.31
.34
.36
.39
.42
15
.32
.35
.38
.40
.43
.47
16
.36
.39
.42
.45
.48
.52
17
.40
.43
.46
.50
.54
.59
18
.45
.48
.50
.55
.59
.64
19
.49
.52
.56
.60
.65
.70
20
.52
.57
.62
.66
.72
.77
Table No. 8 derived from Table No. 6 by deducting
a fair allowance for waste in stump, also volume of top above
4 inches diameter, and dividing by 96, usual number of cubic
feet, solid wood, in a piled cord. The values in this table
are very closely confirmed by a table for second growth
spruce based on 711 trees that was made up in 1903 by
Mr. T. S. Woolsey of the United States Forest Service.
This table may be used for balsam fir, but in general with
some deduction. For the amount of this deduction see
the preceding page.
TABLES RELATING TO PARTS III AND IV 267
YIELD OF HEMLOCK BARK
Where the tanbark industry is large and well organized,
2240 Ibs. of dried bark constitute one cord. One thou-
sand feet of hemlock timber, log scale, yields £ cord
usually, up to a cord in some cases. Small, thrifty hem-
lock, if closely utilized at the saw, as in parts of New
England, yields about £ cord per M.
VOLUME TABLE No. 9. HEMLOCK, BY THE SCRIBNER RULE
(From Bulletin No. 152, U. S. Dept. Agriculture, by E. H. Frothingham)
Diam-
eter
Total Height of Tree — Feet
Diam-
eter
breast-
high
30
40
50
60
70
80
90
100
'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
8
17
120
150
180
210
220
240
8
18
140
180
210
240
260
280
8
19
160
200
240
280
300
320
9
20
180
230
280
310
340
360
9
21
200
260
310
350
380
410
9
22
220
290
350
390
430
470
10
23
330
380
440
480
520
10
24
360
420
490
540
580
10
25
390
460
530
600
650
10
26
430
510
580
660
720
11
27
470
550
640
720
790
11
28
500
590
690
780
870
11
29
540
640
750
850
940
11
30
570
680
800
920
1030
12
Based on 534 trees cut in the Lake States and scaled
from a 2-foot stump to diameter given in 16.3 foot log
lengths. Crook, breakage, and defect not allowed for.
A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 10. HEMLOCK IN BOARD FEET
(From Report N. H. Forest Commission for 1906-7)
Diameter
Breast
Total Height of Tree — Feet
High
Inches
30
40
50
60
70
6
5
7
10
'26
'SO
'42
8
17
28
39
50
9
26
36
49
60
10
36
46
59
71
"86
11
47
58
72
86
103
12
60
72
86
103
123
13
88
104
124
148
14
107
125
147
173
15
126
148
172
204
16
148
171
200
240
17
197
233
281
Based on 317 second growth trees grown in New Hamp-
shire, cut with good economy (4^ to 6^ inches in the top)
and sawed into edged boards and scantling. Figures
derived from actual tally of the sawed lumber.
VOLUME TABLE No. 11. PAPER BIRCH IN CORDS
(Adapted from Report of N. H. Forest Commission for 1906-7)
Diameter
Breast
High
Used Length of Tree — Feet
Inches
10
20
30
40
50
6
.02
.04
.05
.07
.08
7
.03
.05
.07
.08
.10
8
.04
.07
.09
.11
.13
9
.05
.08
.11
.13
.16
10
.05
.10
.13
.16
.19
11
.07
.12
.16
.19
.22
12
.08
.14
.19
.22
.26
13
.17
.22
.26
.30
14
.19
.25
.30
.34
15
.22
.29
.34
.38
Based on 427 trees cut to be sawed. Volumes given are
of used portion of tree only. Original figures by Forest
Service men in cubic feet converted into cords at the ratio
of 96 cubic feet solid per cord.
TABLES RELATING TO PARTS III AND IV 269
VOLUME TABLE No. 12. RED OAK IN BOARD FEET
(From Report of N. H. Forest Commission for 1906-7)
Diameter
Breast
Used Length of Tree — Feet
High
Inches
10
20
30
40
50
5
7
6
9
15
7
14
22
'29
'34
8
18
30
39
43
9
25
40
48
58
10
31
50
60
73
'99
11
37
63
74
90
118
12
44
78
89
110
143
13
54
93
107
132
174
14
65
109
126
160
208
15
124
149
190
243
16
143
173
225
288
17
163
201
262
330
18
181
232
308
19
202
265
356
20
••
223
300
405
Based on about 700 trees tallied through saw mills by
members of United States Forest Service. Trees from 50
to 80 years of age, cut off at from 5 to 9 inches at the top.
Lumber sawed round or waney-edged; 85 per cent of
the product 1^-inch boards surveyed as 1 inch; balance l£-
inch plank.
Table may be used for other second growth hard wood
species when similarly cut and manufactured.
270 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 13. PEELED POPLAR IN CORDS
(Adapted from Report of N. H. Forest Commission for 190&-7)
Diameter
Breast
High
Total Height of Tree — Feet
Inches
50
60
70
80
5
.02
.02
6
.03
.04
.05
7
.05
.06
.07
.08
8
.06
.08
.10
.12
9
.08
.11
.13
.15
10
.13
.16
.18
11
.20
.24
12
.25
13
.30
Based on 289 trees cut for pulp wood. All diameter
measures except diameter breast high taken on the wood
surface after peeling off the bark. Original figures in
cubic feet, converted into cords at the ratio of 90 cubic
feet solid wood per cord.
TABLE 14. SECOND GROWTH HARD WOODS IN CORDS
Diam.
Breast
High
Inches
Total Height of Tree — Feet
30
35
40
45
50
55
00
85
Number Trees per Cord
3-5
5-7
7-9
61
47
38
24
33
20
31
17
12
is
i4
10
'9
From study by Harvard Forest School on oak thinnings.
Wood used up to 2 inches in diameter. 80 cubic feet
solid wood per cord.
The study showed that when the bolts from the trees
3 to 5 inches in breast diameter were piled by themselves,
there were 250 bolts and 67 cubic feet in a cord; wood
from the 5- to 7-inch trees piled together gave 173 bolts
and 79 J cubic feet; from the 7- to 9-inch trees, 133 bolts
and 91 cubic feet.
TABLES RELATING TO PARTS III AND IV 271
FORM HEIGHT FACTORS FOR SECOND GROWTH
HARD WOODS IN CORDS
(Utilized to 1 inch in diameter; 80 cubic feet solid wood per cord.) Sec-
tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of
Wood
Diameter
Breast High
Basal
Area
Total Height in Feet
40
50
60
Inches
Sq. Ft.
Form Height Factors
6
7
8
9
10
11
12
.196
.267
,349
.442
.545
.660
.785
.26
.26
.27
.31
.31
.32
.33
.35
.37
.39
.36
.37
.38
.38
.40
.43
.45
SAME FOR CHESTNUT EXTRACT WOOD
(Smaller trees used to 5 inches; 90 cubic feet solid wood per cord.) Sec-
tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of
Wood
Total Height of Tree in Feet
Diameter
Breast
High
40
50
60
70
80
'90
.100
110
Inches
Form Height Factors
6
.20
.23
.28
9
.18
.21
.25
.30
12
.18
.21
.23
.27
.31
15
.17
.20
.22
.26
.29
.34
.38
18
.19
.22
.25
.28
.32
.36
21
.19
.21
.24
.27
.31
.34
24
.18
.21
.24
.27
.30
.33
27
.18
.21
.24
.27
.30
.32
.34
30
.20
.23
.26
.29
.31
.33
36
.22
.25
.28
.31
.33
45
.26
.28
.30
.32
If the cord is 4' X 5' X 8', deduct Vfc from above figures.
Above tables from "Biltmore Timber Tables," by
Howard Krinbill, copyrighted.
272 A MANUAL FOR NORTHERN WOODSMEN
To use, caliper or estimate the breast diameter of the
tree or stand and get the total height. Then multiply
the basal area in square feet (see table on page 238) by
the proper factor in the table above. The product gives
the result in cords. Considerable stands of timber
should be divided into diameter groups.
Example 1. A 10-inch tree is 50 feet high. How much
cordwood is hi it? .545 (basal area) X .35 (form height
factor) = .19 cord; or 1 -=-.19 = 5j, number of such
trees required for a cord if closely utilized.
Example 2. A bunch of chestnut averaging 80 feet
tall and running 13 to 17 inches in diameter, to be cut
into extract wood, proves after calipering to have a total
basal area of 95 square feet. 95 X .29 (form height
factor in second table above) = 27.55, number of cords
in the stand.
VOLUME TABLE No. 16. HARD WOODS, IN BOARD
FEET, BY THE SCRIBNER RULE
(From R. A. Brotherton, Negaunee, Mich.)
Stump
Diameter
Number of Sixteen-Foot Logs
Inches
1
2
3
4
10
30
50
90
12
55
95
130
14
80
140
180
16
110
180
250
18
140
250
340
390
20
190
320
440
540
22
240
400
550
650
24
300
470
640
750
26
360
560
740
900
28
420
680
900
1100
30
500
820
1100
1350
Stumps average about 3 'feet high. One and two log
trees may either be short trees, or those that above a
certain height are faulty or defective.
Elm in the sizes above 18 inches yields about 10 per
cent more than the above figures.
TABLES RELATING TO PARTS III AND IV 273
VOLUME TABLE No. 17. NORTHERN HARD WOODS (BIRCH,
BEECH AND MAPLE) BY THE SCRIBNER RULE
(Adapted from Bulletin No. 285, U. S. Forest Service,
by E. H. Frothingham)
Diameter
Number of 16-foot Logs
Diameter
inside
high
1
H
2
21
3
3i
4
bark of
top
Inches
Volume — Board Feet
Inches
9
20
30
45
6
10
20
35
50
70
6
11
25
40
60
80
100
6
12
25
50
70
95
120
140
7
13
30
55
80
110
140
170
7
14
30
65
95
130
160
190
230
7
15
70
110
140
180
220
260
8
16
80
120
160
210
250
290
8
17
140
190
240
280
320
9
18
160
210
270
320
380
9
19
240
300
360
430
10
20
270
340
410
490
10
21
300
380
460
550
11
22
340
430
520
620
12
23
380
480
580
690
12
24
420
530
640
770
13
Based on 800 trees cut in the Lake States scaled from
taper measures in logs 16.3 feet long from a stump 1 foot
high to top diameters found in actual logging: figures
evened by curves. As no allowance was made for crook
and defect, considerable discount is necessary in most
timber.
NOTE. Comparison between the values in this table and the preceding
shows striking differences, and the text indicates how these arose, from dif-
ferences in tree form and soundness, lumbering practice, and methods of re-
cording and computing. The cruiser is under obligation before he applies
either in practice t9 understand these points, and he will do well to check
the table he uses with local practice and on local timber. That done, how-
ever, the tables will apply throughout the distribution of the species.
274 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 18. LONGLEAF PINE. IN BOARD FEET,
BY THE SCRIBNER RULE
Diam-
Total Height of Trees — Feet
Diam-
eter
eter
breast-
inside
high
40
50
60
70
80
90
100
110
120
bark
of top
Inches
Volume
Inches
7
5
10
15
6
8
10
20
25
6
9
20
30
40
50
6
10
25
40
55
70
6
11
35
50
70
90
110
6
12
65
90
115
135
6
13
80
110
135
165
195
6
14
95
130
160
200
230
7
15
115
150
190
2,30
270
310
7
16
175
220
260
310
350
7
17
200
250
295
350
400
450
7
18
225
280
330
390
450
500
8
19
250
310
370
440
500
560
620
8
20
350
420
490
560
630
700
8
21
390
470
550
620
700
780
8
22
440
520
610
690
780
860
9
23
490
580
670
770
860
950
9
24
640
740
850
950
1050
10
25
710
820
930
1040
1140
10
26
780
890
1010
1130
1240
11
27
840
960
1090
1220
1340
11
28
1050
1180
1310
1440
12
29
1140
1280
1410
1550
12
30
1230
1380
1520
1670
13
31
1480
1630
1780
13
32
1580
1740
1900
14
33
1690
I860
2030
15
34
1980
2160
16
35
2110
2200
17
36
2230
2340
18
Based on 614 trees cut in Alabama scaled as a rule in
16-foot logs. Height of stump equal diameter breast-
high. By Franklin B. Reed of the U. S. Forest Service.
Shortleaf pine, as shown by other work of the Service,
follows Longleaf closely.
TABLES RELATING TO PARTS III AND IV 275
VOLUME TABLE No. 19. LOBLOLLY PINE. BY THE
SCRIBNER RULE
(Ashe in Bulletin No. 24, N. C. Geological and Economic Survey)
Diam-
Total Height of Tree — Feet
Diam-
eter
breast-
eter
inside
high
40
50
60
70
80
90
100
110
120
130
140
bark
at top
Inches
Contents — Board Feet
Inches
8
5
13
21
27
5
9
12
22
32
42
52
6
10
18
30
42
55
65
6
11
25
40
54
68
81
93
6
12
32
50
66
83
99
110
130
140
150
7
13
40
60
81
100
120
140
160
170
180
7
14
70
97
120
150
180
200
220
240
8
15
110
140
170
210
230
260
290
8
16
120
160
200
240
270
300
330
8
17
190
230
270
310
350
380
8
18
220
270
310
360
400
440
9
19
300
360 410
460
500
53Q
0
20
410 i 470
520
570
610
9
21
460
530
590
640
690
10
22
510
600
660
720
780
10
23
570
660
740
810
870
10
24
620
730
820
900
960
1020 11
25
810
910
990
1060
11301 11
26
890
990
1090
1170
1240: 11
27
970
1090
1190 1280
1350 12
28
1060 1180
1290!1390
1470; 12
29
1150 1280
1400 1500
1590 13
30
1240 1380
1510
1620
1710; 13
31
.... 1500
1630
1750
1860 13
32
1610
1750
1880
1980 14
33
1720
1870
2010
2130 14
34
1840
2000
2140
2250 15
35
2130
2270
2380 15
36
2270
2400
2510 15
Based on measurement of about 3000 trees scaled in
16.3 foot log lengths (with some shorter logs to avoid waste)
from a stump 1 or 1.5 foot high to top diameters stated.
Allowance made for normal but not excessive crook, and
not for defect or breakage. With the same outside dimen-
sions younger trees yield slightly less than old ones : 40 to
45 year old trees yield about 10% less than above figures.
276 A MANUAL FOR NORTHERN WOODSMEN
NOTES ON WESTERN VOLUME TABLES
The tables which follow are representative and the
most reliable in existence; all are in use in work of impor-
tance. No one, however, either East or West, should
harbor the idea that such tables will work his salvation.
Few will require caution as to the difference between
log scale and saw product. It is well understood that de-
fect has to be specially allowed for. The big part break-
age plays in the yield of Coast timber was emphasized in
earlier pages.
The fact that trees may have been scaled for a volume
table by a scale rule different from the one by which
timber in question is actually to be scaled will be con-
sidered of consequence only if the two rules vary enough
to signify among the inevitable errors of estimating. If
that is the case a comparison should be worked out, not
a difficult undertaking. Then varying practice in appli-
cation of the scale rule itself might make noticeable
difference. The general conclusion is that, before trust-
ing any volume table on responsible work, the cruiser
had better test it to see how it fits his timber and practice.
Further, it is indispensable, when such tables are relied
on, that the exact nature of the table itself should be un-
derstood and field practice governed accordingly. Three
different kinds of tables are, in fact, represented.
In No. 23, for lodgepole pine, total height of the tree
is used as the basis of height classification. Some men
will find it strange to work hi that dimension; it is habitual
with others, however. The general reliability of tables
of this kind was discussed on pages 170 and 171, and it
is necessary here to add only a suggestion on the head of
timber utilization. When the table in question was made
up, the logs were scaled to a diameter of 6 inches at the
top. If actual utilization in a given locality falls short
of that, a very few measurements on down trees will
enable a man to make proper deduction. If, for instance,
actual utilization of lodgepole pine should fall one log
length lower than the standard, a 6-inch 16-foot log,
TABLES RELATING TO PARTS III AND IV 277
scaling 18 feet by the Scribner rule, may be deducted
from the tabular values. It is not a large percentage of
sizable timber. If logs are cut and scaled in longer lengths
than 16 feet, adjustment may be made on somewhat the
same plan, as explained on pages 172 and 173. This
last adjustment may be made in any kind of table.
In most of the western tables total height is neglected
and the trees are classified by number of merchantable
log lengths. That follows the usual practice in western
cruising, practice connected apparently with the great
height of the timber. There are, however, two types of
tables in this class — those in which the timber is scaled
up to a single fixed diameter and those in which the top
diameter varies with actual utilization. Nos. 28 and 22,
tables for Washington hemlock and for yellow pine of
the Southwest, illustrate these two types.
The chances of error in connection with tables of the
type of No. 22 (leaving out of account now individual
variation of form) may be illustrated as follows: A
tree 31 inches in breast diameter with five 16-foot logs is
given a volume of 1410 feet and the figure is based (see
table 21) on utilization to a 13-inch top limit. If very
close utilization should secure another log length above
that, the fact would not greatly concern an estimator
because it would be so small in volume proportionally.
Even if one less log were taken out than the table con-
templates, it would amount to but 97 feet, 7 per cent of
the tabular volume. What is of more importance, how-
ever, is that the height at which the .tree reaches 13
inches diameter be estimated correctly. Should this
height be set a log length too low and the tree scored down
as of four logs instead of five, the value derived from the
table would be 1230 feet instead of 1410, 13 per cent too
little. An error of equal amount results if the tree is
scored a log too long.
Tables of the type of No. 28, scaling the logs up to a
small diameter uniform in all sizes of timber, present an
appearance of greater accuracy, but as a matter of fact
much larger errors than the above may arise from care-
278 A MANUAL FOR NORTHERN WOODSMEN
less use of such tables. A chief reason is that men tend
strongly to tally timber as yielding the log lengths to
which they are accustomed in practice, which in the case
of large trees departs widely from the theoretical utiliza-
tion. Thus, a 36-inch 5-log hemlock is given in table 28
as having 3430 feet of timber. In logging, however,
somewhere about 128 feet in log lengths would be got out
of it. If, then, a cruiser tallied it as a 4-log tree, his table
would give him 2530 feet, over 26 per cent less than the
true volume. That might indeed in a given case just about
make due breakage and defect allowance, but such a re-
sult accidentally arrived at is no justification of the practice.
The user of these tables, then, of whatever description,
must realize their exact nature and govern his field work
accordingly. Judgment also must supplement their use,
Diameter Breast High
Diameter at Top
Contents by
of Log
Decimal
Tree No.
Outside
Bark
Inside
Bark
(32 Feet)
Rule
Inches
Inches
1
2
3
4
5
Feet
1
27
23
19
16
13
10
1,110
2
38
32
26
23
20
15
2,590
3
53
45
36
32
27
21
5,030
4
84
74
62
57
51
46
36
19,570
5
23
18
15
11
850
6
23
20
18
16
is
12
1,750
7
26
24
20
17
14
8
1,290
8
39
36
31
28
24
17
2,760
9
46
43
36
31
26
19
io
4,870
10
51
48
41
37
32
24
12
7,040
11
48
43
39
34
25
11
7,690
12
48
40
37
32
21
11
6,760
13
30
27
25
21
12
2,790
14
30
25
23
19
12
2,310
15
74
63
60
46
41
17,090
16
.73
54
48
45
40
13,280
and some men, having arrived at direct, first-hand grasp
of timber quantity, find tables of use only incidentally.
On pages 196 to 197 volume tables produced by scal-
ing logs decreasing by a regular taper, as if trees were
conical in form, were referred to as in wide use in Oregon
TABLES RELATING TO PARTS III AND IV 279
and Washington. In the application of these to standing
timber somewhat the same difficulties are met as above,
while others arise due to the fact that only a very unusual
tree throughout its merchantable length has a true taper.
Normal and also unusual relations in northwestern trees
are illustrated above. The inference is easy that tables
of the kind mentioned are best left to the use of experts.
The first four of the above sets of figures, for Douglas
fir, represent normal form. The body of the tree is seen
to have less taper than either the butt log or the top; the
larger the tree's diameter the faster the taper normally,
and that shows in the butt log particularly. On this last
fact rests the practice of cruisers of taking base diameter
pretty high usually and frequently discounting the diam-
eter ascertained by measure. Their effort really is to
line the basal diameter with that at the top of the first
log and those above it.
Trees No. 5 and 6 are representative of quick and slow
taper, or what amounts to the same thing, of short and
tall timber. On the same base diameter one tree has
twice the contents of the other. No. 6 is a tree of very
unusual taper, however.
Other northwestern species, with the exception of
cedar, have form in general similar to fir, but a much
thinner bark, as Nos. 7 to 10, for hemlock and noble fir,
illustrate. Very heavy taper high up in the trees is also
shown here. The bearing of this last fact on the appli-
cability of a straight-taper volume table is illustrated
below from tree No. 10 in the series. (See also discussion on
pages 196 and 197.) The error in one case is 3 per cent, the
other 15 per cent. This last error is seen to be incurred
by inclusion in the reckoning of a log that contains only
2 per cent of the volume of the tree, and that likely to be
broken up in felling. The practice of commercial cruisers
in neglecting the contents of trees above a diameter equal
about half the base diameter is thus rationalized.
Contents of 4 lower logs, actual taper 6880 feet
Contents of 4 lower logs, regular taper 6660 feet
Contents of 5 logs, actual taper 7040 feet
Contents of 5 logs, regular taper 5960 feet
Contents of fifth log 160 feet
280 A MANUAL FOR NORTHERN WOODSMEN
The remaining figures illustrate variation of form and
irregularity. Nos. 11 and 12, having the same diameter
breast high and also at the top of the logs used, are yet
13 per cent apart in contents, while the second pair of
matched trees differ by 19 per cent, of the average value
in each cas*e. The taper of the body of these trees is
regular, however; the variation is in the butt and top
log sections, the former being far more significant. Trees
Nos. 15 and 16 show some real irregularity, though noth-
ing extreme. Much wider departures from type than
any of these could in fact be chosen.
In conclusion, a contrast will be drawn between present
commercial methods and the use of volume tables. In
the construction of these it is customary to throw out
swell butt and other abnormality of form, and, that
done, the tables derive strength from the law of averages.
Single trees may depart from the type and a certain
amount of variation goes with age, but the table, based
on a large number of trees and applied to large numbers,
if that is done in the same way the measures behind the table
were taken, gives results that are trustworthy within
reasonable limits. Present-day commercial estimates may
be equally correct, but that depends on a different thing
— on the ability of the cruiser to size up each tree as
seen, on the basis of his training of every description.
TABLES RELATING TO PARTS III AND IV 281
VOLUME TABLE No. 20. WESTERN WHITE PINE, IN
BOARD FEET. BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service)
Diam-
eter
Number of Sixteen-Foot Logs
breast-
Basis
high
2
3
4
5
6
7
8
9
10
Inches
Volume — Board Feet
Trees
8
40
60
85
105
7
9
45
70
95
120
40
10
55
85
110
140
165
65
11
65
95
125
160
190
76
12
75
110
145
180
215
245
104
13
125
165
200
240
280
76
14
145
190
230
270
320
360
107
15
165
215
260
310
360
400
86
16
185
235
290
340
400
450
80
17
255
320
380
450
510
570
104
18
275
350
420
500
570
640
111
19
295
380
460
550
630
720
117
20
320
410
500
600
690
790
880
115
21
430
540
650
760
870
980
103
22
460
580
710
830
960
1080
94
23
480
620
760
910
1050
1190
83
24
510
660
820
980
1140
1300
81
25
710
890
1060
1240
1410
69
26
760
950
1140
1330
1520
64
27
810
1010
1220
1430
1630
65
28
1080
1300
1530
1750
40
29
1150
1390
1630
1870
23
30
1220
1470
1730
1990
28
31
1550
1830
2110
14
32
1630
1930
2230
9
33
1710
2030
2360
14
34
2140
2490
6
35
2250
2630
6
36
2360
2770
4
1791
From timber grown in northern Idaho.
Trees scaled to a top diameter inside bark of 6 to 8
inches. Height of stump — 2 to 3 feet. All trees scaled
as though sound. Loss by breakage was 4 per cent.
Loss due to invisible rot was 5 per cent.
282 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 21. WESTERN YELLOW PINE IN
BOARD FEET, BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service)
Diam-
eter
breast-
high
Inches
Height of Tree-Feet
Diam-
eter of
^d*-
bark
Inches
Basis
Trees
40
50
60
70
80
90
100
110
120
12
50
60
70
80
8.3
13
60
80
90
100
8.5
23
14
70
90
110
120
146
150
8.7
48
15
90
110
130
150
170
180
166
8.9
91
16
110
130
160
180
200
220
230
240
9.2
117
17
130
160
180
210
230
260
280
290
310
9.4
142
18
160
180
210
240
270
300
320
350
370
9.6
136
19
180
210
250
280
310
350
380
410
430
9.9
135
20
210
250
'280
320
360
400
440
470
500
10.1
104
21
240
280
320
370
410
460
500
540
580
10.4
127
22
280
310
360
410
470
520
570
620
670
10.G
135
23
350
410
470
520
590
640
700
760
10.9
103
24
390
450
520
590
660
720
780
850
11.1
105
25
430
500
580
650
730
800
880
950
11.3
85
26
470
550
630
720
800
890
980
1070
11.6
93
27
610
690
790
880
980
1080
1190
11.9
83
28
660
760
860
960
1080
1190
1310
12.1
63
29
820
930
1040
1170
1300
1440
12.4
51
30
880
1000
1130
1270
1420
1570
12.7
42
31
940
1070
1220
1380
1550
1720
12.9
21
32
1010
1150
1310
1490
1680
1870
13.2
28
33
1230
1410
1610
1820
2020
13.5
22
34
1310
1510
1740
1960
2180
13.9
22
35
1390
1620
1870
2110
2330
14.3
17
36
1470
1720
1990
2260
2500
14.7
13
37
1810
2120
2410
2660
15.2
6
38
1900
2250
2550
2820
15.8
4
39
2390
2690
2980
16.4
5
40
2530
2840
3150
17.0
1
1822
Measurements by T. S. Woolsey, Jr., in Arizona.
Trees scaled to 8-inch top inside bark — straight and
sound. Allow 3 to 15 per cent for defects. The so-called
" black jack " variety requires a further reduction of
about 12 per cent, having a smaller volume than the older
" yellow pine."
TABLES RELATING TO PARTS III AND IV
VOLUME TABLE No. 22. WESTERN YELLOW PINE, BY
THE SCRIBNER RULE
Same trees classified by 16-foot log lengths
Diam-
Number of 16-foot Logs
eter
breast-
high
1
2 3
*
5
6
Basis
Inches
Volume — Board Feet
Trees
13
50
80
22
14
60
100
140
190
47
15
70
120
160
210
93
16
80
140
180
240
119
17
100
160
210
270
142
18
120
190
240
310
380
140
19
140
220
270
350
430
138
20
160
250
310
400
490
108
21
290
360
450
550
128
22
330
410
500
610
136
23
380
460
560
680
101
24
420
520
630
760
108
25
470
580
700
840
86
26
530
640
780
920
ioeo
95
27
580
710
860
1010
1150
85
28
630
790
950
1100
1250
€5
29
870
1040
1200
1360
54
30
960
1130
1300
1470
43
31
1050
1230
1410
1590
25
32
1140
1340
1530
1710-
28
33
1240
1460
1660
1830
21
34
1340
1580
1780
1960
21
35
1710
1910
2090
14
36
1830
2040
2220
12
37
1950
2160
2340
5
38
2060
2280
2450
3
39
2160
2400
2560
3
40
2260
2520
"2670
2
1844 .
The values in this table are materially higher than
those of other Forest Service tables for the same species
made in California and Oregon.
284 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 23. LODGEPOLE PINE, IN BOARD
FEET, BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service) .
Diam-
eter
Total Height of Tree — Feet
Basis
high
Inches
50
60
70 .
80
90
100
Trees
10
50
65
75
90
105
125
495
11
60
75
90
105
125
155
478
12
75
90
105
125
150
185
296
13
90
105
125
145
180
215
146
14
105
125
145
170
215
250
120
15
140
170
200
250
285
113
16
160
195
230
285
315
60
17
225
260
315
350
44
18
250
290
350
385
25
19
275
320
380
420
17
20
300
345
415
460
14
Figures by Tower and Redington from trees cut in
Gallatin County, Montana. Trees scaled in logs 10 to
16 feet long up to 6 inches in top.
YIELD OF LODGEPOLE PINE IN RAILROAD TIES
(From Study by Students of University of Washington)
Diam-
eter
breast-
high
Inches
Average Number Obtained per Tree
Hewn Ties
Sawed Ties
Tall
over 80'
Medium
60-80'
Short
under Qff
Tall
over 80'
Medium
60-80'
Short
under 60'
10
11
12
13
14
15
16
17
18
19
20
1.7
3.0
4.0
4.9
5.5
6.0
6.4
6.7
6.9
7.1
7.2
1.5
2.7
3.5
4.0
4.4
4.7
5.0
5.0
5.0
1.1
1.8
2.2
2.5
2.7
2.9
0.9'
1.9
3.0
3.9
4.6
5.1
5.5
5.9
6.1
6.3
0.8
1.7
2.6
3.3
3.8
4.2
4.2
4.2
0.7
1.2
1.8
2.2
2.5
Results from 267 trees cut in eastern Oregon : Hewn ties
from timber not less than 8^ inches in diameter, made
7 inches thick; sawed ties, 6 by 8 inches; both kinds, 8 feet
long. Average height of 10-inch trees, 68 feet; of 15-inch
trees, 85 feet; of 20-inch trees, 93 feet.
TABLES RELATING TO PARTS III AND IV 285
VOLUME TABLE No. 24. WESTERN LARCH, IN BOARD FEET.
BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service)
Diam-
eter
breast-
high
Inchea
Number of 16-Foot Logs
Diam-
eter
of top
inside
bark
Inches
Basis
Trees
3
4
5
6
7
8
11
95
140
3
12
105
155
7.3
15
13
120
165
220
7.4
31
14
135
185
240
7.5
93
15
155
205
270
7.6
114
16
175
230
295
380
7.7
119
17
195
260
325
415
7.8
128
18
220
285
365
455
7.9
100
19
240
315
400
490
8.0
93
20
265
345
435
535
645
8.1
127
21
380
475
585
705
8.1
86
22
415
520
635
775
8.1
89
23
450
560
695
840
ioos
8.2
80
24
485
605
745
905
1085
8.2
79
25
525
655
805
975
1180
8.2
52
26
565
700
865
1055
1275
8.2
32
27
605
755
930
1130
1375
8.3
32
28
650
805
995
1210
1470
8.3
35
29
855
1060
1295
1565
8.4
17
30
910
1130
1385
1670
8.5
21
31
1205
1465
1770
8.7
12
32
1280
1560
1875
8.8
10
33
1360
1650
1975
9.0
4
34
1440
1745
2085
9.2
8
35
1525
1845
2190
9.4
1
36
1600
1945
2295
9.6
5
37
1685
2040
2395
9.8
3
38
1770
2145
2505
10.0
2
39
1850
2240
2610
10.2
40
1930
2340
2715
10.4
1391
Above table by L. Margolin from timber cut in Flat-
head County, Montana. Trees scaled without allowance
for breakage and defect, which in this timber amounted
to 5 per cent. In addition 5 per cent or more should be
allowed for " butts " left if logs are driven.
286 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 25. ENGELMANN SPRUCE, IN BOARD
FEET, BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service)
Diam-
Diam-
eter
breast-
high
Height of Tree — Feet
eter
of top
inside
bark
Basia
Inches
40
50
60
70
80
90
100
110
120
Inches
Trees
8
15
20
30
6.2
8
9
15
25
35
50
70
6.3
19
10
20
30
45
60
80
6.4
19
11
25
40
55
70
90
iio
6.5
35
12
30
50
65
85
110
135
6.6
45
13
40
60
80
100
130
160
6.7
44
14
50
70
95
120
150
185
220
6.8
51
15
60
80
110
140
170
210
250
6.9
37
16
70
95
125
160
190
240
280
340
7.0
61
17
110
140
180
220
270
320
380
7.1
57
18
125
160
200
250
300
360
430
7.1
55
19
180
225
280
330
400
470
7.2
45
20
205
250
310
360
440
520
600
7.2
43
21
230
280
340
400
480
560
650
7.3
41
22
250
310
370
440
520
610
700
7.4
29
23
340
400
480
560
660
760
7.4
21
24
370
430
520
600
710
820
7.5
21
25
470
560
650
760
880
7.5
10
26
500
600
700
820
950
7.6
11
652
From trees cut in Colorado and Utah measured by
H. D. Foster. Stump height l|-3 feet.
TABLES RELATING TO PARTS III AND IV 287
VOLUME TABLE No. 26. DOUGLAS FIR OF THE COAST
BY THE SCRIBNER DECIMAL RULE
(U. S. Forest Service)
Diameter
Number of Thirty-two-Foot Logs
at Stump
Outside
Average
Bark
H
2
21
3
31
4
4*
5
6j
6
61
7
Inches
Volume — Board Feet in Tens
18
40
28
34
41
50
58
20
50
32
39
47
56
65
22
62
44
53
66
78
92
24
77
49
60
75
88
102
26
91
55
68
84
'.IS
112
122
28
105
01
76
95
110
124
130
30
125
GO
84
106
124
141
157
32
145
92
115
138
162
182
34
169
100
1 2.->
149
176
203
36
195
120
138
164
192
'227
247
38
228
183
212
253
278
40
270
228
280
313
42
312
246
306
342
385
437
44
365
208
332
374
120
462
46
425
280
358
403
454
494
48
480
388
133
187
534
592
50
535
420
468
528
581
644
52
588
450
502
566
598
680
730
54
' 645
480
530
595
654
722
774
56
705
630
697
771
830
58
765
008
744
821
60
830
711
790
872
942
62
900
760
838
926
1009
64
972
80,8
886
985
1082
66
1048
S04
953
1066
1171
68
1133
1030
1147
1261
.70
1226
1118
1225
1345
72
1310
1198
1312
1420
74
1413
1285
1390
1486
76
1515
1364
1465
1556
Based on 1394 trees measured in logging operations in
Lane County, Oregon. Diameters, taken outside bark,
on the stump, which was ordinarily about 4 feet high, are
closely comparable with the diameter at breast height.
Trees scaled without deduction for defect or breakage, to
a point 10 inches in diameter at the top, unless unmer-
chantable to this point. The majority of the logs were
24 feet long, though the length varied from 16 to 36 feet.
288 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 27. DOUGLAS FIR OF THE INTERIOR
IN BOARD FEET, BY THE SCRIBNER RULE
(From Bulletin No. 36, U. S. Forest Service)
Diam-
Diam-
eter
breast-
high
Total Height of Tree — Feet
eter
of top
inside
bark
Basis
Inches
60
70
80
90
100
110
Inches
Trees
8
20
30
6.2
1
9
30
40
60
6.3
7
10
40
60
70
6.5
4
11
60
70
90
iio
6.6
23
12
70
90
110
130
6.7
53
13
90
110
130
160
190
6.8
57
14
100
130
150
180
220
6.9
51
15
120
150
170
210
250
7.0
55
16
140
170
200
240
290
7.2
59
17
150
190
230
270
320
7.3
51
18
170
220
250
300
360
400
7.4
64
19
190
240
280
330
400
450
7.5
57
20
210
270
320
370
440
500
7.6
55
21
230
300
350
410
480
550
7.8
57
22
250
330
380
450
530
600
7.9
50
23
360
420
490
580
650
8.0
45
24
390
450
540
630
710
8.2
40 |
25
420
490
580
690
770
8.3
26
450
530
630
750
830
8.5
31
27
480
580
680
810
900
8.6
22
28
520
620
730
870
970
8.8
12
29
670
790
940
1040
8.9
9
From timber cut in Wyoming and Idaho measured by
Messr. Redington and Peters.
TABLES RELATING TO PARTS III AND IV
VOLUME TABLE No. 28. WASHINGTON HEMLOCK BY THE
SCRIBNER DECIMAL RULE
(By E. J. Hanzlik of U. S. Forest Service)
Diameter
Number of Thirty-two-Foot Logs
Breast:
High
Average
Outside
U
2
21
3
3J
4
4J
5
5J
Bark
Inches
Volume — Board Feet in Tens
12
14
16
21
13
20
17
23
28
32
14
26
18
26
31
37
'44
15
32
19
29
35
42
49
16
39
21
32
39
47
55
17
46
23
35
43
52
61
18
53
26
47
58
68
78
19
62
42
52
64
76
87
20
70
46
57
71
84
96
21
80
50
62
77
91
104
22
90
54
67
84
100
112
iio
23
100
57
73
90
108
122
148
24
111
80
96
116
130
156
25
122
86
104
124
139
165
26
134
92
112
133
148
174
27
146
100
120
141
158
184
28
158
106
128
149
167
193
226
29
170
113
139
158
177
204
237
30
183
121
147
168
186
214
248
31
197
156
177
197
226
260
32
212
165
186
208
238
274
33
228
173
195
219
250
34
245
181
204
229
263
305
353
35
264
190
213
242
278
323
376
36
284
222
253
293
343
404
37
304
231
266
310
366
436
38
326
240
280
330
393
477
39
346
250
294
351
424
519
40
368
259
308
378
460
561
Based on 1440 trees, in both pure and mixed stands,
measured at logging operations at various points in west-
ern Washington. A stump height equal breast diameter
allowed. Trees scaled in 16-foot log lengths (with trim-
ming allowance) to a diameter inside bark of 8 inches.
No deduction for defect or breakage.
Actual utilization a little over 80 per cent of above
figures.
The true firs are formed very nearly like hemlock.
290 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLES No. 29. WASHINGTON RED CEDAR
BY THE SCRIBNER DECIMAL RULE
TALL TIMBER
Diameter
Breast
High
First 32' Log
Second 32' Log
If
fl
3
"3 £3
11
'— o
Outside
Bark
Top
Diam
Scale
%&
Top
.Diam
Scale
%of
Total
r
|S
Feet
16
11
140
70
7
*60
30
200
18
12
160
70
8
70
30
230
20
13
190
61
10
120
39
310
22
14
230
62
11
140
38
370
24
16
320
67
12
160
33
480
26
17
370
59
13
190
30
ii(J)
630
28
18
430
55
14
230
30
10
780
30
19
480
53
15
280
31
11
900
32
21
610
56
16
320
29
12
1090
34
22
670
51
17
370
28
13
ii(i)
1300
36
23
750
50
18
430
28
14
12(i)
1490
38
24
810
48
19
480
28
15
10
1690
40
25
920
47
20
560
29
16
11
1940
42
27
1100
49
21
610
27
17
11
2220
44
28
1160
46
23
750
29
18
12
2500
46
29
1220
44
24
810
29
19
13
2700
48
30
1310
42
25
920
30
20
14
3000
50
31
1420
42
26
1000
30
21
15
3300
The above and following table are based on field
measurements of about 1200 sound and normal trees
grown in fully stocked mixed stands in the Puget Sound
region, at elevations from 200 to 1000 feet, by A. G. Jack-
son of the U. S. Forest Service. Scaled from taper meas-
urements in 32-foot logs to diameters stated. Data
arranged to promote timber grading.
Cedar scaled in short lengths, if at the same time it is
sound, of good form, and fully utilized, will yield more
than these values. On the other hand the tree is so
largely subject to swell butt, rot and breakage, that tables
must be used with great caution and often discarded
altogether.
TABLES RELATING TO PARTS III AND IV 291
SHORTER TIMBER
Diam-
eter
First 32' Log
Second 32' Log
St
!<
ll
High
Outside
Bark
Top
Diam.
Scale
% of
Total
Top
Diam.
Scale
% of
Total
"S-5
3Q
H
¥
H£
Feet
16
10
120
70
6
50
30
170
18
11
140
70
7
60
30
200
20
12
160
70
8
70
30
230
22
13
190
68
9
90
32
280
24
14
210
69
10
120
31
330
26
15
280
67
11
140
33
420
28
17
370
70
12
160
30
530
30
18
430
63
13
190
28
10(i)
680
32
19
480
61
14
230
29
12(1)
790
34
20
560
58
15
280
32
10
960
36
22
670
57
17
370
31
11
1180
23
750
55
18
430
33
12
1340
40
24
810
55
19
480
32
13
1480
42
25
920
50
20
560
31
15
11(4)
1830
44
27
1100
52
21
610
29
16
12(1)
2110
46
28
1160
48
23
750
31
17
11
2420
48
29
1220
47
24
810
31
18
12
2620
50
30
1310
45
25
920
32
19
13
2900
The trees in this table are really of good length. Meas-
urements on short mountain timber are not available.
Cedar Shingle Bolts. Very defective trees, the break-
age of logging operations, and sometimes the whole
usable contents of trees above about 20 inches in breast
diameter are largely utilized in this form. The bolts are
cut 52 inches long and the larger pieces split; they are
then piled and measured in the cord 8X4 feet. In
present practice from 18 to 25 bolts make a cord which
careful measurement has shown to contain of solid wood
about 70 per cent of its outside contents. A cord is
equivalent to from 500 to 700 feet log scale, less in the
smaller sizes of timber.
292 A MANUAL FOR NORTHERN WOODSMEN
VOLUME TABLE No. 30. SUGAR PINE IN CALIFORNIA
BY THE SCRIBNER DECIMAL RULE
(U. S. Forest Service)
Number of Sixteen-Foot Logs
MJ4
-£a
Diameter
e £
Breast-
high
2
3
4
5
6
7
8
9
10
11
12
c ,52 fc"1
si*
11
Inches
Volume — Board Feet in Tens
Inches
12
9
15
22
8
14
10
17
24
8
'i
16
10
lf)
27
39
g
2
18
13
20
30
43
9
7
20
17
25
37
50
65
79
9
28
22
31
43
57
74
89
9
23
24
40
53
67
83
100
i22
g
35
26
50
64
78
96
113
136
9
35
28
63
78
92
110
128
152
10
44
30
80
94
108
125
144
170
189
10
53
32
113
127
145
163
192
218
10
50
34
135
149
166
187
217
247
10
38
36
100
173
191
213
246
279
310
11
36
38
IS"!
200
220
245
278
313
346
11
40
40
210
I.'-")
253
280
313
349
386
11
41
42
240
261
_'ss
319
354
390
427
463
11
43
44
271
295
;«,-,
359
398
435
473
515
12
39
46
aiw
3:50
365
401
445
482
523
567
12
31
48
337
366
105
446
493
532
575
623
12
43
50
401
446
493
544
586
630
681
749
12
41
52
438
iyi
544
598
642
686
740
818
12
56
54
472
532
597
653
698
742
801
885
13
36
56
575
652
711
756
800
862
953
13
25
58
619
709
769
814
860
923
1022
13
25
60
660
764
829
872
921
987
1090
14
28
62
704
820
886
930
983
1051
1159
14
25
64
66
876
933
943
1000
990
1053
1046
1109
1116
1181
1227
1297
14
14
27
11
68
989
1058
1115
1173
1250
1366
15
9
70
1048
1117
1177
1239
1319
1434
15
17
73
1176
1240
1305
1388
1502
15
6
74
1235
1303
1370
1456
1570
16
2
76
1296
1368
1435
1523
1639
16
6
78
1358
1431
1500
1590
1707
16
4
80
1420
1497
1565
1659
1778
16
3
910
Average stump heights 1.3 to 3.1 feet.
Logs scaled in commercial lengths as cut.
SECTION III
MISCELLANEOUS TABLES AND INFORMATION
1. RULES FOR AREA AND VOLUME OF DIFFERENT
FIGURES 294
2. WEIGHT OF MATERIALS 296
3. HANDY EQUIVALENTS 297
4. NUMBER OF PLANTS PER ACRE WITH DIFFERENT
SPACING 297
5. COMPOUND INTEREST TABLE 298
6. TIME IN WHICH A SUM WILL DOUBLE 298
7. TABLE OF WAGES AT GIVEN RATES PER MONTH . . 299
8. THE BILTMORE STICK 301
RULES FOR AREA AND VOLUME OF DIFFERENT
FIGURES
Area of Square. Multiply the length of side by itself,
or, as is said, " square " it.
Area of Rectangle. Multiply the base by the altitude.
FIGURE A
Area of Parallelogram. (Figure A.) Multiply base a b
by altitude b c, not by b d. If b d and the angle at d are
known, b c may be found by the formula
be = bd X sine of angle at d.
Area of Triangle. (Figure B.) Multiply base a b by
altitude c d and divide by 2.
Area of Triangle with 3 Sides Given. (Figure B.) Add
the 3 sides together and divide the sum by 2. From this
half sum take each side in succession. Multiply the half
sum and the remainders all together and take the square
root. The formula is
V|»(i*-a)(i»-6)(J*— c)
Circle. Circumference equals diameter X 3.1416.
Area of Circle. (Figure C.) Square the diameter,
multiply by 3.1416, and divide by 4.
MISCELLANEOUS TABLES AND INFORMATION 295
Right-Angled Triangle. The
square of the hypothenuse of a
right-angled triangle equals the
sum of the squares on the other
two sides, or, in the figure,
AB* + AC2 = BC2,
01 O + N = M.
By means of this rule, when any
two sides of a right-angled triangle
are given, the third can be
found.
Volume of Cylinder. (Figure E.)
of the base by the altitude.
Volume of Cone. (Figure F.) Multiply the area of the
base by one-third of the height.
0
^Ss,//
A
B
N
FIGURE D
.) Multiply the area
FIGURE E
FIGURE F
Volume of Prism whether Eight or Oblique. (Figure
G.) Multiply area of base by the vertical height.
Volume of Pyramid. (Figure H.) Multiply base by
one-third of the height.
To Measure the Contents of a Box or Solid with Sides
at Right Angles to One Another. Multiply length by
breadth by height. If the dimensions are in feet the result
will be the contents in cubic feet.
296 A MANUAL FOR NORTHERN WOODSMEN
WEIGHT OF MATERIALS
A cubic foot of water weighs 62i Ibs.
A cubic foot of cast iron weighs about 450 Ibs.
A cubic foot of wrought iron or steel weighs about .... 480 Ibs.
Woods when thoroughly seasoned weigh per cubic foot
about as follows. Absolute drying in a kiln will lessen
these figures about 10 per cent. Green wood is from 50
to 80 per cent heavier.
White pine, white spruce, balsam fir, aspen 27 Ibs.
Red spruce, hemlock, poplar 30 Ibs.
Pitch pine, Norway pine, black spruce, white maple .... 31-35 Ibs.
White birch, red maple, tamarack, white ash, yellow birch,
red oak 40-45 Ibs.
Beech, sugar maple about 48 Ibs.
White oak, black birch about 52 Ibs.
A cord of green spruce pulp wood weighs about 4500 Ibs. ;
fir and white pine a little more. A cord of dry spruce pulp
wood weighs 3000 to 3500 Ibs. Pine, fir, and poplar are
somewhat lighter if in exactly the same moisture condition.
Green hard wood by the cord varies greatly in weight.
A cord of white birch spool- wood weighs 6000 to 7000 Ibs. ;
sugar maple and yellow birch are 10 per cent heavier; soft
maple, ash, basswood, and poplar are somewhat lighter
than white birch. For green split cord wood 4000 to 6000
Ibs. are the usual limits of weight. Medium dry birch,
beech, and maple, split, 66 per cent solid in the pile, weighs
about 3000 Ibs. to the cord.
A thousand feet of old growth spruce logs, Andros-
coggin scale, weighs about 6000 Ibs., and this is probably
the lower limit for green soft-wood lumber, while southern
yellow pine at 8000 to 10,000 Ibs. is the limit in the other
direction. Between these limits there is wide variation by
reason of scale and quality.
Seasoning decreases the weight of timber by 30 to 50
per cent as a rule, and at the same time increases its
strength by 50 to 100 per cent.
MISCELLANEOUS TABLES AND INFORMATION 297
HANDY EQUIVALENTS
There are 160 square rods in an acre.
A square acre is 208.71 feet on a side.
118 feet is approximately the radius of a circular acre,
83 feet of a half acre, and 59 feet of a quarter acre.
There are 5280 feet in a mile.
A meter contains 39.37 inches ; a kilometer is .62 mile.
A liter contains 61 cubic inches, — nearly the contents
of a quart.
A hectare contains 2.47 acres.
A gram weighs 15.432 grains, Troy weight.
A kilogram or kilo contains 2.2 Ibs avoirdupois.
There are 231 cubic inches in a U. S. liquid gallon.
There are 2150.42 cubic inches in a U. S. struck bushel.
A horsepower is the work done in lifting 33,000 pounds
1 foot in 1 minute. A flow of 528 cubic feet of water per
minute with 1 foot fall generates one horsepower.
A miner's inch is the flow of water through an orifice
1 inch square under a head (in some States) of 6 inches.
In California 50 miner's inches equal 1 cubic foot per
second, equal 1.9835 acre feet per day, nearly an inch an
hour. In some States 40 miner's inches equal this flow.
NO. OF PLANTS PER ACRE WITH
DIFFERENT SPACING
Spacing
No.
3 X 3 ft.
4840
4X4
2720
5X5
1740
6X6
1210
7X7
890
8X8
680
9X9
538
10 X 10
436
298 A MANUAL FOR NORTHERN WOODSMEN
COMPOUND INTEREST TABLE
Amount of $1 principal after any number of years and at
given rates percent
Yrs.
2%
24%
3% 34% | 4% 1 4i%
5%
5i%
6%
1
1.020
1.025
1.030 1.035 1.040 1.045
1.050
1.055
1.060
2
1.040
1.051
1.061 1.071 1.082 1.092
.103
1.113
1.124
3
1.061
1.077
1.093 1.103 .125 .141
.158
1.174
1.191
4
.082
1.104
1.126 1.148 .170 .193
.216
1.239
1.262
5
.104
1.131
1.159 , 1.188 .217 .246
.276
1.307
1.338
6
.126
1.160
1.194 ! 1.229 .265 1.302
.340
1.379
1.419
7
.149
1.189
1.230 1.272 .316 1.361
.407
1.455
1.504
8
.172
1.218
1.267 1.317 .369 1.422
.478
1.535
1.594
9
.195
1.249
1.305 1.363 .423 1.486
.551
1.619
1.660
10
1.219
1.280
1.344 1.411 .480 1.553
.629
1.708
1.791
11
1.243
1.312
1.384 1.460 .540 1.623
710
1.802
1.898
12
1.268
1.345
1.426 1 1.511 .601 1.696
.796
1.901
2.012
13
1.294
1.379
1.469 i 1.564 .665 4.772
.886
2.006
2.133
14
1.320
1.413
1.513 ! 1.619 .732 1.852
1.980
2.116
2.261
15
1.346
1.448
1.55S 1.675 .801 1.935
2.079
2.233
2.397
16
1.373
1.485
1.605 1.734 .873 2.022
2.183
2.355
2.540
17
1.400
1.522
1.653 1.795 .948 2.113
2.292
2. 485
2.693
18
1.428
1.560
1.702 1.853 2.026 2.209
2.407
2.622
2.854
19
1.457
1.599
1.754 ! 1.923 2.107 2.308
2.527
2.766
3.026
20
1.486
1.639
1.806 1.990 2.191 12.412
2.653
2.918
3.207
25
1.641
1.854
2.094 2.363 2.666 3.005
3.386
3.813
4.292
30
1.811
2.098
2.427 2.807 3.243 3.745
4.322
4.984
5.744
35
2.000
2.373
2.814 3.334 3.946 4.667
5.516
6.514
7.686
40
2.208
2.685
3.262 3.959 4.801 5.816
7.040
8.513
10.286
45
2.438
3.038
3.782 ! 4.702 5.841 J7.248
8.985
11.127
13.765
8
2.692
3.437
4.384 j 5.585 7.107 19.033
11.467
14.542
18.420
TIME IN WHICH A SUM WILL DOUBLE
Rate
Per cent
Simple Interest
Compound Interest
2
50 years
35 years
24
40 years
28 years 1 month
3
33 years 4 months
23 years 54 months
t
28 years 7 months
25 years
22 years 2} months
20 years
20 years 24 months
17 years 8 months
15 years 9 months
14 years 2* months
9
18 years 7 months
16 years 8 months
12 years 114 months
11 years 11} months
Note in above tables that a sum at compound interest doubles when rate
of interest X number of years equals (very nearly) 71. With this remem-
bered many problems in compound interest can be solved mentally.
MISCELLANEOUS TABLES AND INFORMATION 299
TABLE OF WAGES, AT GIVEN RATES PER MONTH
OF TWENTY-SIX DAYS
1
D
$15
$16
$17
$18
$19 $20
$21
1
0.58
0.62
0.66 0.69
0.73 0.77
0.81"
2
1.15
1.23
1.31
1.38
1.46 ! 1.54
1.62
3
1.73
1.85
1.96
2.08
2.19
2.31
2.42
4
2.31
2.46
2.62
2.77
2.92
3.08
3.23
5
2.88
3.08
3.27
3.46
3.65
3.85
4.04
6
3.46
3.69
3.92
4.15
4.38
4.62
4.85
7
4.04
4.31
4.58
4.85
5.12
5.38
5.65
8
4.62
4.92
5.23
5.54
5.85
6.16
6.46
9
5.19
5.54
5.88
6.23
6.58
6.92
7.27
10
5.77
6.15
6.54
6.92
7.31
7.69
8.08
11
6.35
6.77
7.19
7.62
8.04
8.46
8.88
12
6.92
7.38
7.85
8.31
8.77
9.23
9.69
13
7.50
8.00
8.50
9.00
9.50
10.00
10.50
14
8.08
8.62
9.15
9.69
10.23
10.77
11.31
15
8.65
9.23
9.81
10.38
10.96
11.54
12.12
16
9.23
9.85
10.46
11.08
11.69
12.31
12.92
17
9.81
10.46
11.12
11.77
12.42
13.08
13.73
18
10.38
11.08
11.77
12.46
13.15
13.85
14.54
19
10.96
11.69
12.42
13.15
13.88
14.62
15.35
20
11.54
12.31
13.08
13.85
14.62
15.38
16.15
21
12.12
12.92
13.73
14.54
15.35
16.16
16.96
22
12.69
13.54
14.38
15.23
16.08
16.92
17.77
23
13.27
14.15
1504
15.92
16.81
17.69
18.58
24
13.85
14.77
15.69
16.62
17.54
18.46
19.38
25
14.42
15.38
16.35
17.31
18.27
19.23"
20.19
26
15.00
16.00
17.00
18.00
19.00
20.00
21.00
D
$22
$23
$24
$25
$26
$27
$28
1
0.85
0.88
0.92
0.96
1.00
1.04
1.08
2
1.70
1.77
1.85
1.92
2.00
2.07
2.15
3
2.54
2.65
2.77
2.89
3.00
3.11
3.23
4
3.38
3.53
3.84
4.00
4.15
4.31
5
4.23
4.42
4.62
4.81
5.00
5.19
5.38
6
5.08
5.30
5.54
5.77
6.00
6.23
6.46
7
5.92
6.19
6.46
6.73
7.00
7.27
7.54
8
6.77
7.08
7.38
8.00
8.30
8.62
9
7.61
7.96
8.31
8.65
9.00
9.34
9.69
10
8.46
8.85
9.23
9.61
10.00
10.38
10.77
11
9.30
9.93
10.15
10.57
11.00
11.42
11.84
12
10.15
10.62
11.08
11.54
12.00
12.46
12.92
13
11.00
11.50
12.00
12.50
13.00
13.50
14.00
14
11.84
12.38
12.92
13.46
14.00
14.54
15.08
15
12.69
13.27
13.85
14.42
15.00
15.58
16.15
16
13.54
14.15
14.77
15.38
16.00
16.61
17.23
17
14.38
15.03
15.70
16.34
17.00
17.65
18.31
18
15.23
15.91
16.62
17.31
18.00
18.68
19.38
19
16.07
16.79
17.54
18.27
19.00
19.72
20.46
20
16.92
17.69
18.46
19.23
20.00
20.76
21.54
21
17.77
18.56
19.38
20.19
21.00
21.80
22.61
22
18.61
19.46
20.31
21.15
22.00
22.84
23.69
23
19.46
20.34
21.23
22.11
23.00
23.88
24.77
24
20.30
21.22
22.16
23.08
24.00
24.91
25.85
25
21.15
22.12
23.08
24.04
25.00
25.95
26.92
26
22.00
23.00
24.00
25.00
26.00
27.00
28.00
300 A MANUAL FOR NORTHERN WOODSMEN
TABLE OF WAGES AT GIVEN RATES PER MONTH
OF TWENTY-SIX DAYS — continued
D
$29
$30
$31
$32
$35
$40
$45
1
1.12
1.15
1.19
1.23
1.35
1.54
1.73 i
2
2.23
2.30
2.38
2.46
2.69
3.08
3.46 !
3
3.34
3.46
3.58
3.69
4.04
4.62
5.19 i
4
4.46
4.62
4.77
4.92
5.38
6.15
6.92
5
5.58
5.77
5.96
6.15
673
7.69
8.65
6
6.69
6.92
7.15
7.38
8.07
9.23
10.39
7
7.80
8.08
8.35
8.61
9.42
10.77
12.12
8
8.92
9.23
9.53
9.85
10.77
12.31
13.85
9
10.04
10.38
10.73
11.08
12.11
13.84
15.58
10
11.15
11.54
11.92
12.31
13.46
15.38
17.31
11
12.27
12.69
13.12
13.54
14.81
16.92
19.04
12
13.38
13.85
14.32
14.77
16.15
18.46
20.77
13
14.50
15.00
15.50
16.00
17.50
20.00
22.50
14
15.61
16.15
16.70
17.23
18.84
21.54
24.23
15
16.73
17.31
17.88
18.46
20.19
23.07
25.96
16
17.84
18.46
19.07
19.69
21.54
24.61
27.70
17
18.96
19.62
20.27
20.92
22.88
26.15
29.43
18
20.07
20.77
21.47
22.15
24.23
27.69
31.16
19
21.19
21.92
22.65
23.38
25.57
29.23
33.89
20
22.30
23.08
23.85
24.62
26.92
30.77
34.62
21
23.42
24.23
25.04
25.85
28.27
32.31
36.35
22
24.53
25.38
26.23
27.08
29.61
3.3.84
38.08
23
25.65
26.54
27.42
28.31
30.96
35.38
39.81
24
25
26^6
27*8
27.69
28.85
28.61
29.81
29.54
30.77
32.31
33.65
36.92
38.46
41.54
43.27
26
29.00
30.00
31.00
32.00
3500
40.00
45.00
D
850
$60
$70.
$75
$80
$90
$100
1
1.92
2.31
2.69
2.88
3.08
3.46
3.85
2
3.85
4.62
5.38
5.77
6.15
6.92
7.69
3
5.77
6.92
8.08
8.65
9.23
10.38
11.54
4
7.69
9.23
10.77
11.54
12.31
13.85
15.38
5
9.61
11.54
13.46
14.42
15.38
17.31
19.23
6
11.54
13.85
16.15
17.11
18.46
20.77
23.08
7
13.46
16.15
18.84
19.19
21.54
24.23
26.92
8
15.38
18.46
21.54
23.08
24.62
27.69
30.77
9
17.31
20.77
24.23
25.96
27.69
31.16
34.61
10
19.23
23.08
26.92
28.85
30.77
34.62
38.46
11
21.15
25.38
29.61
31.73
33.84
38.08
42.31
12
23.08
27.69
32.31
34.61
36.92
41.54
46.15
13
25.00
30.00
35.00
37.50
40.00
45.00
50.00
14
26.92
32.31
37.69
40.38
43.08
48.46
53.85
15
28.85
34.61
40.38
43.27
46.15
51.92
57.69
16
30.77
36.92
43.08
46.15
49.23
55.38
61.54
17
32.69
39.23
45.77
49.04
52.31
58.85
65.38
18
34.61
41.54
48.46
51.92
55.38
62.31
69.23
19
36.54
43.84
51.15
54.81
58.46
65.77
73.08
20
38.46
46.15
53.85
57.69
61.54
69.23
76.92
21
40.38
48.46
56.54
60.58
64.61
72.69
80.77
22
42.31
50.77
59.23
63.46
67.69
76.15
84.61
23
44.23
53.08
61.92
66.35
70.77
79.61
88.46
24
46.15
55.38
64.62
69.23
73.85
83.08
92.31
25
48.08
57.69
67.31
72.12
76.92
86.54
96.15
26
50.00
60.00
70.00
75.00
80.00
90.00
100.00
THE BILTMORE STICK
301
THE BILTMORE STICK
This implement, employed to ascertain the diameter of
standing timber when held at arm's length tangent to the
trees to be measured, was briefly described on page 163.
Relations between tree, stick, and eye when the stick is
in use are made clear in the figure, the circle representing
a section of a tree -breast high, B X the Biltmore stick,
A T the distance from the stick to the eye, and 0 M a
radius vertical to the line of sight passing on one side of
the tree. With this for a pattern it is clear how the woods-
man, after having determined A T as a matter of practice,
can plot circles of different diameters, draw tangents to
them from A, and ascertain by measurement in each case
B C, the proper stick graduation.
The geometry of the matter is that of similar right-
angled triangles, and consideration will show the soundness
of the formula appended, from which may be derived
AT(AT+D)
the value of B C for circles of any size and for any arm
reach. When .the latter, A T, has been determined by
trial, the formula becomes simpler. Thus with A T = 25
BC
25 D
or, for D = 10 inches
V25 (25 + D)
250 250
V625 + 250 29.58
= 8.45 inches.
Values of B C for tree diameters from 6 to 60 inches and
distances of 23 to 27 inches have been worked out and
are published in the- "Proceedings of the Society of Amer-
ican Foresters " for 1914, page 48.
302 A MANUAL FOR NORTHERN WOODSMEN
The Forest Service has employed the Biltmore stick in
measuring large timber on the Pacific Coast and else-
where, and the tests applied have shown reasonable
accuracy. A careful analysis of sources of error 1 has devel-
oped the following:
(a) Tilting the stick and holding it other than vertical
to the line of sight to the trees' center are practices to be
guarded against, but if reasonable care is used in manipula-
tion, errors are negligible.
(6) In applying values derived from plots or tables to
the stick itself, regard must be had to its thickness. The
stick may well be beveled, or a steel spline may be inserted
into it to carry the graduations.
(c) Errors arising from measuring a tree the narrow or
the wide way are greater than with the c'aliper; hence
cross measures are the more desirable.
(d) It is very easy in practice to vary the distance
between the stick and the eye, and this introduces error
that is material, though in continued work successive
errors tend to balance.
(e) Men of ordinary height have a constant tendency
to measure tree diameter not breast high, but higher, near
the eye level.
To conclude, the Biltmore stick requires to be practi-
cally tested before use and constant care in application.
More liable to error than the caliper, in ordinary timber
it works less rapidly as well. While serviceable in its
field, its general use is not to be recommended.
1 Bruce at previous reference.
CENTRAL UNIVERSITY LIBRARY
University of California, San Diego
DATE DUE
UtC 171983
JuN * 2 R£C1
JUN27IQPT
a 39
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