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Full text of "A manual for northern woodsmen"

Presented to 

THE BILTMORE ROOM 

HOWARD R. KRINBILTi B ft"S'. |<jfOfj 

t)ate Modern h&r i*?5Y 



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A MANUAL 
FOR NORTHERN WOODSMEN 



Digitized by tine Internet Arciiive 

in 2009 witii funding from 

NCSU Libraries 



littp://www.arcliive.org/details/manualfornortlierOOcary 



A MANUAL 

FOR , 

NORTHERN WOODSMEN 



BY 



AUSTIN GARY 

Recently Assistant Professor of Forestry 
in Harvard University 




REVISED EDITION 



CAMBRIDGE 

HARVARD UNIVERSITY PRESS 

1918 



FIRST EDITION 

Copyright, 1909 

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 



PRINTED AT THE 

HARVARD UNIVERSITY PRESS 

CAMBRIDGE, MASS., U. S. A. 



f 



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, chiefiy 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 Sueveyor's Compass 

1. The Instrument 1 

2. Adjustments of the Compass 4 

3. Keeping the Compass in Order 6 

Section II. The ISL\gnetic 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. jNIarking Lines and Corners 23 

4. Original Surveys and Resurseys 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 \TII. The United States Public Land 

Surveys 60 



VIU 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 M!. 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 subdi\'ided 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 MEASUREIVIENT 

Section I. Cubic Contents 137 

Section II. Cord Wood Rule 138 

Section III. New IL\^ipshire 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 St.^jstdard Rule 147 

Section VI. Scaling Practice 148 

Section VII. Mill T.^llies 151 

Section VLQ. Cord Measure 157 



CONTENTS IX 
PART IV. TIMBER ESTIMATING 

PAGE 

Section I. Introduction lgl 

Section II. Instruiviental Helps 162 

Section HI. Height Measurement 165 

Section IV. Volu:me T.\bles and Tree Form ... 167 

Section V. Pkictice of Timber Estbla-ting . . . 173 

A. Small and Valuable Tracts I74 

B. Larger and Less Valuable Tracts 186 

1. T}T)e and Plot System 187 

2. The Strip System 188 

3. Line and Plot System 192 

C. Summary I95 

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. LoGARiTiEvnc Sines, Cosines, Tangents, and Co- 

tangents 222 

6. Supplementary Tables of Sal^ll Angles .... 228 

7. Natural Sines and Cosines 230 

8. Natural Tangents and Cotangents 232 

9. Specimen Lettering 234 

Section II. Tables relating to Parts III and IV 

1. Volumes of Cylinders (Logs) in Cubic Feet . . 236 

2. Are-\s of Circles or Basal Areas 238 

3. Cord Wood Rule 239 

4. New H.AMPSHIRE Rule 240 

5. New York Standard Rule 242 

6. Scribner Log Rule, Legal in Minnesota . . . 243 

7. DECIM.A.L 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 



CONTENTS 



PAGE 

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 W^oods in Cords .... 270 

15. Form Height Factors for Southern Hard Woods 271 
16, 17. Northern Hard Woods in Board Measure . 272, 273 

18 
19 



B. 



Longleaf Pine in Board Measure . . 
Loblolly Pine by the Scribner Rule 

Western; Notes on Western Volume Tables 



20. Western White Pine in Board Feet 

21. Western Yellow Pine in Board Feet 

22. Western Yellow Pine (16-foot log lengths) 

23. Lodgepole Pine in Feet, Board Measure, and 

in Railroad Ties 

24. Western Larch in Board INIeasure . . 

25. Engelmann Spruce in Board Measure 

26. Douglas Fir of the Coast 

27. Douglas Fir of the Interior 

28. Washington Hemlock in Board Measure 

29. Washington Red Cedar in Board Measure 

30. California Sugar Pine in Board Measure . 



274 
275 

276 

281 
282 
283 

284 
285 
286 
287 
288 
289 
290 
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 SUR\^YING 



PART I. LAND SURVEYING 

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. ]\Ie-\sueewent of Distance 9 

1. The Surveyor's Chain 9 

2. The Tape 10 

3. Marking Pins 11 

4. Chaining Practice 11 

5. INIeasuring 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 SurA^eys 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 VIL On Obtaining the ]'>iERiDiAN .... 51 
Section VIII. The Unhted States Public Land 

Surveys 60 



A MANUAL 

FOR NORTHERN WOODSMEN 
Part I. Land Surveying 

Surveying in forest land as compared with work done in 
towns and on farms is carried out under unfavorable cir- 
cumstances. In the first place, timber and brush growth 
offer an obstruction to sighting; second, the work is often 
done far from a well supplied base; third, the limits of 
cost allowed are often the lowest practicable. These con- 
ditions have a strong effect upon the methods employed, 
and they also affect the choice of outfit. Equipment for 
such work should not usually be expensive, it should be 
as compact and portable as possible, and it should not 
be so delicate or so complicated as to be likely to get 
seriously out of order and so hold up a job. 

SECTION I 

THE SURVEYOR'S COIMPASS 

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. 

1 



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 haK 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. Adjustivients of the Compass 

A compass in first-class order will meet the following 
tests : 

a. The plate must be perpendicular to the axis of the 
socket. 

b. The plane of the level bubbles must be perpendicular 
to the same axis. 

c. The point of the pivot must be in the center of the 
graduated circle. 

d. The needle must be straight. 

e. The sights must be perpendicular to the plane of the 
bubbles. 

In these tests it is presupposed that the circle is accurately 
graduated and that the plane of the sights passes through 
the zero marks. These are matters that belong to the 
maker of instruments, and in all modern compasses accu- 
rate adjustment of them may be assumed. 

The general principle of almost all instrumental adjust- 
ments is the Principle of Reversion, whereby the error 
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. W hen 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 AIAGNETIC 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 ISIAGNETIC 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 thi^t occurs during the 
course of the year, is in woods work commonly disregarded. 

Irregular Changes. The needle is subject occasionally 
to sudden and irregular changes in direction. They some- 
times occur during thunder storms, and at other times are 
attributed to so-called magnetic storms, related perhaps 
to the aurora horealis. 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. 

^ See page 21. 




105 Longitude 100 West fi 



Lines of Equal Magnetic Declination and of Equal An? 

United States Coasi 




li Change in the United States for 1915. (From Report of 
d Geodetic Survey.) 



MEASUREMENT OF DISTANCE 9 

Electricity, A little caution is necessary in handling 
the compass in order that the glass cover shall not be elec- 
trified by the friction of cloth or the hand, so as to attract 
the needle to its under surface. If, however, the glass does 
become electric, the trouble may be removed by breathing 
upon it, or by touching different parts of its surface with 
the moistened finger. 

Difference in Instruments. It is a well-known fact that 
different instruments do not always give the same bearing 
when read on the same marks at the same time. A differ- 
ence of 15' is not uncommon. 

Summary. The magnetic needle is thus seen to be sub- 
ject to numerous variations and irregularities, and on that 
account work with the needle compass cannot be expected 
to give the most accurate results. The instrument has 
great advantages, however, and a very large field of legiti- 
mate use. It gives an approximately true direction from a 
detached point. Except on open ground, it furnishes the 
quickest and cheapest means of turning an angle or pro- 
longing a line. Most authoritative land surveys have 
been made with the needle compass and their renewal is 
best accomplished by use of the same instrument. The 
special advantages of the compass in forest conditions and 
its most effective use therein are discussed under the head 
of Surveying Practice. 

SECTION III 

MEASUREMENT OF DISTANCE 

1. The Surveyor's Chain 

The word "chain" in connection with land surveying is 
used to represent two things: a distance of 4 rods or 66 
feet, and an instrument for measuring distance. The 
chain in use for general land surveying is 66 feet long and 
divided into 100 links, but woodsmen working in rough 
ground find the 33 foot or half chain with 50 links much 
more convenient. 

A chain for surveying purposes should be made of steel 
wire, and its links should be brazed to prevent stretching 



10 A MANUAL 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 hnks 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 | 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. IVIarking Pins 

Woodsmen frequently manufacture their own marking 
pins of wood or wire. Those bought from dealers are 
made of hea\'y 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. Chaixing 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 tw^o 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. 


In feet 
per 100. 


In degrees. 


In feet 
per mile. 


In links 
per chain. 


2 


u 


1.0 


.02 


4 


2i 


4.3 


.1 


6 


31 


9.5 


.2 


8 


4^ 


16.7 


.3 


9 


5i 


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. 




--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 ab = 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 Cy 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 ab c = 30°, 
setting a stake c in the range 
a X. Then ab = 2 a c. 
5. Method by Tangents. (D) With the compass at a 

set a stake at b, 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 

a c 
look up the tangent of this angle. Then ab = 




Fig. C 



tan abc 





Fig. D 



Fig. E 



6. Method by Oblique Triangle. (E) The stake c may 
be set at any convenient point visible from both a and b 
and the angles at a and b measured. Measure also the side 
a c OT b c, whichever is easier. Then a b may be computed 
as the side of an oblique triangle. For formulas neces- 
sary, see pages 212-213. 

7. Method by Traverse. (F) In the case of a large lake 
or stream, several courses may be run along its banks, and 
when the range of the line is again struck, as at e, the dis- 



MEASUREMENT OF DISTANCE 



17 




tance a e may be computed by traverse. If a e runs N and 
S, the distance a e will be the latitude of the traverse, or, 
stated in other words, it will be the sum of 
the products of the cosines of the several 
courses into their respective distances. The 
departure of such a traverse should be zero. 
Thus, if e is not visible from a, or if it is not 
convenient to take the range a e, e may be 
set when the sum of the departures figures 
up 0. This process of surveying a lake or 
river shore is called " meandering." It is the 
method pursued in the United States land 
surveys on considerable bodies of water. The 
same method may also be employed to get 
round a precipitous hill or some other inac- 
cessible object. 

An example of the computation necessary 
for solving a problem of this kind is given on 
page 33. 

8. Method by 60° Angles. (G) A precipitous bluff or 
impassable swamp may occasionally be passed most read- 
ily in the following manner. With 
the compass at a, lay off a 60° 
angle and run out a c, carefully 
chaining. Next, making an angle 
of 60° at c, run out c 6 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 




Fig. G 



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 w^ill readily 
be understood from its 
construction and from 
consideration of the ad- 
justments required for the 
transit. 

The advantages of this 
instrument in land sur- 
veying are as follows : — 

1. Sights may be taken 
on steeper ground, either 
up or down hill, than can 
be covered through com- 
pass sights. 

2. Distances over very 
steep ground can be 
measured more accurately 
and quickly than by use 
of the chain. 

3. Distance across 
and bodies of water can be obtained 




A Telescopic Sight 



gorges, swamps 
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 33^ 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 mav be to find out what 
course to run by an observation for the true meridian, or 
by finding the bearing of an old line. With the starting 
point and course determined, the method of procedure is 
about as follows. 



£0 a manual for northern woodsmen 

1. Running a Compass Line 

Set up the compass at the point from which the hne 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. 

Aji 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 conmionly 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 
leams his exact duties, and all hands, particularly the com- 
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 when an assumed or trial 
course has been started, it is prolonged by backsight en- 
tirely, reference to the needle not necessarily being made. 
In order to do this, either a rear rodman is employed or a 
stake is set in line at each station occupied by the compass. 

Picketing. The compass after the start, indeed, may not 
be used at all, but straight stakes, preferably four to five 
feet high and sharpened at both ends, may be ranged in 
one after another along the line. This method of running 
a line is frequently resorted to, and is called picketing. 

To clear out in most woods a line open enough for con- 
tinuous backsighting or picketing is an expensive process, 
and, further, this method for long distances and uneven 
ground is not to be relied on. If, in those circumstances, 
close accuracy of alignment must still be had, resort must 
be made to another class of instrument, a transit or solar, 
which may carry the work out of the hands of the woods 
sun'eyor. 

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. ^Yhen 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'. 



jTrial Line 
5ch, 10 ch. 15 ch. 20 ch. 26 ch. 30 ch. 

Diagram Showing the Method bt 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 23 

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 J 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 1 5-chain mark should evidently be 
half that at the finish, or 16 links. At the 5-chain mark it 
is J 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 FOR 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 hne, 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 hues 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 wiU 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, hovi^ever, 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 runnmg 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. He 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- 
Hable 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.^ 

5. Age of Spots or Blazes 

A subject of special interest to the forest surveyor is 
the determination of the age ot 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 



27 




20 25 17 30 32 35 40 43 

c 



A. B. Blaze Five Years after Cut was Made : A, Front Vietv 
Showing Rim of Callus ; B, Cross Section 

C. Blaze Twenty-thbee 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 



f ffene)Y(7/of3ouf/>///76 of Tnp., S/?.4, Ox/v/t:/ Co., Afa/'/Te ^pt-25;/90S. 
l./ne onj//?a//y ri//? ^ £.Ba//arsf J/7 /794, /7a5 6ee/7 i^/a;!ec/oyer so/7?e s//7ce ,6uf 



never 



resurveyecf. 



£.5. Deardor/7, rearc/7o//7. 



Naye tmcec/ cforvn a/?cf prv^^ec/ f^'re east ///;& of//7e tDyy/7s/7//:> to a ///re 



Of3po 



ts ruj7r?/'/?o west supposed fv^/'/3 ^oa/tr //'/re . •Sean^ a/o/7i^ /^/s ^f/oivs 



wMw 



Zorvds a spruce and a ^/rch mW? yery oM jp/azes w/^/c/? prove <7s 



neor cs Mer/'/^s ca/7 be coa/7fsdfv de ///years o/c/. /^d/aze of Me 



age /s 



a /so foi//7d 3 rods /v f/?e easfyYand. y\/o s/^/? see/? of /f?e or^//7a/ 



Cor/?e, r noted as 6e//7g //? d /?/rz:/7. 



1/7 raq(7e oft/7e spots east and yvesf a/7d //? //re ///7e comZ/Tg^so/d/? 



seta 



cedar post a/7ds/v//es. 7h/s /'s /'/? f/af spruce /a/?d a/7d S rods 



iro/n 



rs/andfbrdto ///e easfyyard. AfarAed/f/epasf Od /\(IV. TS /?.4-, 



on //.£. 



T4- fl4-j 0/7 5. TS P.3 , a/so 'i/.J.B. /30S. T/?e m'/ncss frees, a/so /narfed 



sJ.d.B. 



/90S, Ore a cedar s/s/7d//7^ /V /ff°£ /Q ////As fro/77//;epost, a/7od?er 



3.SO''£ 



/8///7AS, a spruce S.S0°>Y.£0///7As & a d//c// /V.^S YY /2///iAs. 



Fro/n /Aepostra/7 afr/a///re A:83°>r. at n'^At a/7^/es to/t/e //a 6 ///re 



Af/er 



dSrods found a/7otAer or/p/da/ d/aze £0 ////As /o t//e /eft fr'e/vrred /o 



post , 



ar/dra/? //.8330fY. 



fJods 



80 



/^arAed a i>/'rcA rifft/ of ///re ^Af' 



120 



ffis/np o/rfo tte //e/p/zt ofar/c^e yyd/cA fa//s of/- pnsc/p/'/ous/y 



2. rods to the Sou/A. Or/'q/'//a/ t//?//>er />/oyy/? doyy/r a/zd ro//e// A/ere 



a/7d so/ne rods aAead. fou/7d3ofBa//a/?d5 spof^ c/ose /of/^siya/7/j^ 



-///p a/7d30/7?e spots i>y /u/r/Aer/T/e// offe/7 w/de of t/?e ////e. 



B/azec/ tArou^/? strv/pAt. 



/SO 



AfarAed a spruce ri^At of //de. ^ /</>-» S/ope 2- IV 



210 



Doyfn a stro/zp s/o//e S. IV. O/d spots Aaye dee/? Aau////p to /Ae r/gAt 



and dotv o/7e o// a A/rcA yy/tA ///r/nps over /t /s so AAAs r/^At 



Offset to it, f/// /n fAe //ne AacA oi^er /Ae o/d spots, a/rd co/Ttdi/e 



on sa/ne dear/'/^g- 



a4€ 



Set a cec/ar StaAe /r/arAed ^ A/>^ 



256 



iVatsr crosses to Sou AA west 



2.7S 



Last 'M rods tAroupAr syya/np yy/tA /na/n//jou//pproyY/A and/zo 



Spots to Ae seed. 



O/d 6/aze prod a A// Ba//ards found noyy or a dead and do yyn cedar 



29S 



Cross Canada A/ ay road. 



3Z0 



A spot of 3a//ards ape on a spruce just AacA 2 rods SoutA ans 
spots of tnucA /ess a^e yyA/cA co/ne /d/a tAerz/z/gre a feiv rods 



furtAero/7. ff/azedtde //de tdrou^dsArg/^df Set a//ost tor 
///e cor/zer of sect/'ons 3S a. 36 /narAed on A/.kV "S. A/? 3S. " 



o n A(£. "3.//°36."y on 3. "t.S /f.3" z^^arAed /t and tde yy/tness 
frees ^.d.S. /^OS^ 



30 



A MANUAL FOR NORTHERN WCK)DSMEN 



1 Woodstock, Mass. , Afa^£0, /£>£>? Purvey made for C/arA L umi>er Co of 
^elr f^rker lof SO ca//eaf Dec/. ofneec//e as /rear as Anotv/? //° mvkona/^Mn 


Beg//? at 


Souff7\ 


vest cor/7er crt /ot afjuncf/o/? ofsfu/7e yYa//s marA/'/Ty 


recogr?/z 


'.J bo 


/ndar/es of t/re /ot: 7?7er7ce — 


Bear/>r,g 


D/'st 




N/O'E 


847' 


A/ong yva//to /fs e/7c/ 




19/7' 


t/7roi/£j/7 p/ne f//77/?er do/fs/^/es yr/TA /7o s/g/7 ofprvperfy 




(fofa/) 


///7e, f> a ro/fe^n fe/rce n/nn/pg easfer/y. T/7e c/eec/s ccrZ/zhp 






for a///7e ru/7mAg' "/A a /7orAAer/y o/jrecf/o/r" / 6/azGc/ 






■/■/re/Z/re-AAroi/e^Ar o/?/Ae. rap^e offAe ivaA/ o/7dseA aposf 






a/7o/sfD/7&5 at /As /7orAA e/7a/. 






This is on /edgy (^rounc/ W/tA a drop off /O feet yy&st 


S79°3S'£. 


/0S4' 


A /org tAe o/d fence //ne Sma// brooA njns A/ at 680 ft 






to 5 E correr of the /ot/y/np norffy, as /rd/cotsd &/ 






range of o/d far/n iva// run//? from fAe /7or/A to /A/s po//7t 






Set a stone b/ocA onend and sarroarc/ed /A tv/tAstones 






Set se vera / Aeaps of stones a/o/rp fAe //ne. 


A//0°£ 


sso' 


Onranpe of farm wa// menA'o/vedand roc/pA/y a/onp AAe 






bound off/?e Ci//t/np, /n Sivampy /and after £00 '. 






Set s/uAes a/on_p tAe //ne eacA 200 'and at AAe e/7c/ a 






post w/fA heap of Stones. 


sao'E 


SO' 


Atr/pAt anp/es to AAerarge A/ne to CoAasse ArooA. 






7A/S d/sAance As AAe one (3 rods) Ca//ed for An tAe deed 






and /s AAe on/y means of f/X/nj A/re /ast named corner 






0/7 tAe nor/A and SoatA Ane . 


SJS'f 


/7^^ 




5SJ£ 


3/9'!) 


A/ono CoAasse brooA as per ca// of c/ee^f. 


S80°E 


33S 


Across brook, ffen on soutA border of f/e/d /n /posses- 






sion of owners nor/A, to west s/de ofA/pAyvay. 






Tn/spo/nt/s 7/6 ft soa/Aer/y from f/re forks of AAe A/pAivny, 






the deed ca///np for "about ^M rods " Set post andstones. 


v5"£5V 


/6 a'- 


dJoyvn A/pAtvay to br/dje oyer CoAasse brook as ca//ed 


S^o''30'£ 


ZSO 


•for /n deed 


-S4C°30'£ 


/33'- 




Stew 


7/2'- 


|//7 t/7e swamp c/ose to foot of tAe r/d^e 


5/aiY 


Z8S' 


Offset fre(^uenf/y fopet exact area of tAe "bard /and" 


538 W 


720' 


yvb/c/7 yyas coni/'eyed/n/Ae deed 7b stone i'va//,tAe 


SE^W 


S6Z'- 


recopn/zecA Soutb bound of tAe /of 


/V84°yv 


zee' 


Alon^ yva//, up a predp'fous s/ope 


Nva'dow 


/066' 


A/onp tAe yva// to p/ac e of Aepfnn/npr 


Th/s survey 


ib//ow^ 


fte fernrs ott/7e deeds as near as tAe/ can be /nferpre^d 


Jo//r7 /^rmsf/ 


?/?^,ar 


';s/dent cf/Ae /oca//^ SOyears and fam/f/ar >v/tb /fs hnp/runsfe/^ 


andocwpa/TC 


' nasp 


■Bsent and says /fe/acaf/of? apnxs as near as /?& A/?oyrs wttfte a/r- 


ckrstandifjq c 


"/^e 0) 


ipart/es and facts ofpossess/on. locaf/on, ffye/iefore.^ood The 


\,j)ostssef 


7 re mo 


'■fedond^e sicfe surre/edC.L Co /S07 "and a/so >v///> /ny /n///a/s 



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 
Comers, 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 diflBculty 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 mfluencing 
cost. The main thing is to have suflScient 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 
COiMPUTATION AND OFFICE WORK 

1. Traverse 

To " traverse" a line or route is to surs'ey 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 comes 
to a lake shore. Setting there a post, duly marked, he runs 
round the lake near the shore by the following courses : 

N 50° E 12 chains. 

N 9° 30' E 20 

N 40° W 9 " 

S 80° W 6.81 " 

Reckoning up his courses by the traverse table, he finds 



COMPUTATION AND OFFICE WORK 



33 



that his E and W departures balance, hence he should be 
in line. The difference between northing and southing 
gives him the distance. He may then set a second post, 
add the distance to his previous chainage, and proceed with 
his survey. 



COMPUTED TRAVERSE 



Field Notes. 


From Traverse Tables. 


Bearing. 


Distance. 


Latitude. 


Departure. 






N. 


S. 


E. 


. w. 


N. 50° E. 


12.0 chains 


7.71 




9.19 


... 


N. 9° 30' E. 


20.0 


19.73 


, 


3.30 




N. 40° W. 


9.0 


6.89 


. . 




5.78 i 


S. 80° W. 


6.81 




1.18 




6.71 1 




34.33 


1.18 


12.49 12.49 1 

1 




1.18 






Distance d 


ue 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 appHed 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. = 
log dep. == 


1.3010 


1.1790 


1.0910 


1.2109 


1.3444 


1.2396 


0.9394 


0.6250 


1.1664 


0.8607 


Departure = 
log cos = 


17.36 


8.70 


4.22 


14.67 


7.26 


9.6957 


9.9125 


9.9730 


9.6340 


9.9752 


log dist. = 
log lat. = 


1.3010 


1.1790 


1.0910 


1.2109 


1.3444 


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 



35 













.—1 


lO 


rt< 


o 


. 








^ 


• 


• 




1— 1 




I— 1 

d 


^1 






00 


(N 








o 


2 p 








CO 


t^ 


• 


* 


• 


1-1 




-d 


a 


l>^ 


00 




1 


] 


d 




"5 




1—1 










(N 








lO 








1— 1 


O 




« 


M 


CJ 








d 


00 

d 


















IM 


CO 




















3 !0 




























(N 


l^ 


t^ 




CO 


=^T3 






^ 




CO 


.»o 






00 

d 

CO 
























Sc 












(M 


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CD 


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o 


c-3 






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IM 




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d d 


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(N (N 




§o 




















oc*^ 
















OT3 


Q. 




o 


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CO 


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Pi 

w. 




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03 ,D 


















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33 


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32 

03 
















p.^ .a 


















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si 


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+ 






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02 


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-gt « 




















5 =s fci 




















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t^ J 




















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a 


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b >_ b 




















KH 


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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 ^ we have 

tan. ^EZ=^| = ^ =.3411. 
EX 21.02 

A E X from the table of tangents = 18° 50'. 
S 18° 50' W is therefore the bearing required. 

The length oi 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. 

V2I.O22 + 7.172 = 22.21, 

the distance required. That this value and that for the 
angle differ somewhat from the true ones is due to the 
errors of compass surveying. 

In a similar way the course and distance of an inacces- 
sible line may be computed or omissions supplied in notes. 



COMPUTATION AND OFFICE WORK 37 

That is a very undesirable thing to do, however, as it in- 
fringes on the tests which serve to verify the work. 

2. Area 

Rectangles. The woodsman in his land work has 
most frequently to do with rectangular figures, and com- 
putation of area is simple. If the average of the chained 
east and west sides of a rectangular piece of land is 201 
rods or 50.25 chains, and the north and south dimension 
40 chains, the area equals 50.25 X 40 ^ 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 = yis{s — a) (s — b) (s — c), 

where a, b> and c are the three sides and s is half their sum. 

Or, lastly, an irregular figure when plotted may be re- 
duced graphically to the triangular form and the area ob- 
tained at one computation by either of the methods just 
given. 

The relations between units of distance and of area are 
given on page 19. 

By Offsets. In surveying around the borders of a body 
of water, and in some cases when the exact border of a 
property presents great difficulties, it is customary to run 
as near the border as is practicable and to take rectangu- 
lar offsets to it at selected intervals along the line. These 
offsets should be measured to angles in the border, or 
placed near enough together so that the border between 
offsets may be considered a straight line. The area of 
the figure between each two offsets may then be computed 
by multiplying the distance along the base by half the 
sum of the two offsets. 



38 



A MANUAL FOR NORTHERN WOODSMEN 



Another way is to take the offsets at regular distances 
along the base, 10 rods apart for instance. In that 
case the rule for the area is : — Add together all the in- 
termediate offsets and half the end offsets, and multiply 
the sum by the constant interval between them. 

By 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 6 is a meridian through its 
most westerly point, b ByC C, 
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 Bb equals the area oi 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/\s the 
latitude oi E A. These latitudes, it is to be noted, are 
negative and, to correspond, the areas oi A B b and of 
E A e are to be deducted from b B C D E e to give the area 
oi 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 oi A B b. b B + 
c C, the two bases of the trapezoid b B C c, = twice the 
departure of ^ jB + the departure oi B C. c C -\- d D 
= the same expression as the last + the departure oi 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 FOR 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 


-f 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 



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 





E 


"^^D 


-.24 1 


\. 


1 ^ 
/ ^ 


21.89 

CO 

26,10 


\ 






Ml 




/ 




17.38 ' £ 


\ 




Fig. 1 Fig. 2 

Methods of 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 m 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. 



(W% 




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 



H 1 1 h 



Stone Wall ocx:Xoccccccx3CCX13Coooocc)ccg 

Fence 

Telephone Line ,,,,,, 

Field or Prairie . . . 



Open Swamp 

Dam 



.diL, '\;, ulJlL. -ih- JUL. 

■ III! I.- ^^)/, _»v. .»■ 

■ M.^ '\l* \l/ \ll/» N\/ ^, 



Topographic Symbols 

SECTION \T 
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° 10' 
E ought to reproduce the line. 

3. By Tables. The following tables, derived from 
publications of the United States Coast and Geodetic 
Survey, are very convenient for determining change in 
declination. They give for many localities well distrib- 
uted throughout the United States declination at ten- 
year intervals as far back as it has been recorded. The 
change found to have taken place at a given locahty 
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-l 
ments. It is well known that two compasses on thej 
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 r* 



i 



ON THE BEARING OF LLNES 



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 


New 


Ver- 


Mass. 


Mass. 


(Jan. 1) 


N'theast 


S'thwest 


Hamp. 


mont 


East 


West 




o / 


o / 


o / 


o / 


o / 


o / 


1750 


12 05W 


8 34W 


8 02W 


7 43W 


7 46W 


6 21W 


1760 


11 53 


8 15 


7 28 


7 09 


7 19 


5 52 


1770 


11 53 


8 10 


7 03 


6 44 


7 00 


5 31 


1780 


12 05 


8 10 


6 47 


6 28 


6 50 


5 19 


17&0 


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 


18^0 


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 


1830 


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 


18G0 


18 44 


13 51 


12 03 


11 39 


12 02 


10 25 


iroo 


19 02 


14 21 


12 31 


12 08 


12 .'^4 


10 59 


1910 


19 45W 


15 06 W 


13 16W 


12 57W 


13 21W 


11 42 W 



Year 


Rhode 


Conn. 


N. Y. 


N. Y. 


Penn. 


Penn. 


(Jan. 1) 


Island 


East 


West 


East 


West 




o / 


o / 


o / 


o / 


o / 


o / 


1750 


7 04W 


5 47W 


7 35W 


4 40W 


4 47W 




1760 


6 37 


5 18 


6 53 


3 57 


4 01 




1770 


6 18 


4 57 


6 17 


3 18 


3 19 




1780 


6 08 


4 45 


5 50 


2 46 


2 44 


1 16W 


1790 


6 08 


4 43 


5 34 


2 24 


2 21 


52 


1800 


6 19 


4 51 


5 28 


2 13 


2 08 


37 


1810 


6 38 


5 08 


5 34 


2 13 


2 09 


31 


1820 


7 05 


5 34 


5 50 


2 24 


2 22 


37 


1830 


7 40 


6 07 


6 17 


2 46 


2 47 


52 


1840 


8 22 


6 47 


6 53 


3 18 


3 21 


1 16 


1850 


9 06 


7 31 


7 39 


3 57 


4 04 


1 48 


1860 


9 46 


8 09 


8 25 


4 46 


4 46 


2 26 


1870 


10 19 


8 43 


9 04 


5 23 


5 32 


3 06 


1880 


10 50 


9 24 


9 51 


6 16 


6 16 


3 50 


1890 


11 20 


9 51 


10 14 


6 57 


6 50 


4 28 


1900 


11 ^1 


10 25 


10 48 


7 37 


7 25 


5 07 


1910 


12 40W 


11 IIW 


11 31W 


8 12W 


8 07W 


5 45W 



46 



A MANUAL FOR NORTHERN WOODSMEN 



TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC- 
LINATION IN THE UNITED STATES 
(From U. S. Coast and Geodetic Survey Reports) 



Year 

(Jan. 1) 


New 

Jersey 


Ohio 


Indiana 


Illinois 


Iowa 


Mich. 
North 




/ 


o / 


o / 


o / 


o / 


o / 


1750 


4 43W 












17bO 


4 04 












1770 


3 31 












1780 


3 C6 












17^0 


2 £0 












1800 


2 45 


3 13E 


4 44E 


5 54E 






1810 
1820 


2 fO 

3 06 


3 22 
3 22 


4 59 

5 04 


6 18 
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 
1870 


5 22 

6 01 


1 50 
1 14 


3 50 
3 13 


5 54 

5 26 


10 09 

9 44 


5 25 
4 38 


1880 


6 41 


37E 


2 35 


4 44 


9 06 


3 47 


1890 


7 14 


02W 


1 57 


4 05 


8 21 


2 58 


1900 
1910 


7 49 

8 33W 


42 

1 low 


1 24 
1 08E 


3 36 
3 25E 


7 52 
7 57E 


2 20 
2 05E 



Year ' 
fjan. 1) 


Michigan 
South 


Wisconsin 


Minnesota 

North 


Minnesota 
South 


1750 


o / 


o / 


/ 


o / 


1760 










1770 










1780 










1790 










1800 










1810 
1820 


4 lOE 


8 34E 


10 27E 


11 20E 


1830 


4 04 


8 40 


10 44 


11 36 


1840 


3 46 


8 34 


10 50 


11 42 


1850 


3 20 


8 16 


10 44 


11 36 


1860 


2 46 


7 49 


10 27 


11 20 


1870 


2 04 


7 14 


9 59 . 


10 54 


1880 


1 17 


6 25 


9 17 


10 22 


1890 


32E 


5 36 


8 33 


9 32 


If'OO 


02W 


5 01 


7 58 


8 57 


1910 


27W 


4 51E 


8 03E 


9 OOE 



ON THE BEARING OF LINES 



47 



TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
TION IN THE UNITED STATES 

(From U. S. Coast and Geodetic Survey Reports) 





a 


,_^ 


^-^ 


^ 


^^ 




■ 1 


^ 


o 


"H 5 


(A 'a 


03 h 


o3 n 


2--? 


2^^ 


t-'-l 

2d 
^3 


CO 

Id 

S3 


oj 2 


Virgini 

East 

(Richmo 


Virgini 

West 

(Lynchbi 


West 

Virgini 

(Chariest 


North Ca 
lina Eas 
(Newber 


North Ca 

lina Wef 

(Salisbur 




o / 


o / 


/ 


o / 


o / 


o / 


o / 


1750 


1 41W 


3 05W 


1 13W 






18W 


1 31E 


1760 


1 02 


2 26 


37 


08E 




18E 


2 08 


1770 


28 


1 52 


05 W 


42 




50 


2 42 


1780 


OOIW 


1 25 


20E 


1 11 




1 17 


3 12 


1790 


19E 


1 05 


38 


1 33 


2 DOE 


1 35 


3 34 


1800 


28 


56 


47 


1 46 


2 15 


1 44 


3 48 


1810 


28 


56 


47 


1 51 


2 20 


1 44 


3 52 


1820 


19E 


1 05 


38 


1 46 


2 15 


1 35 


3 48 


1830 


01 W 


1 25 


20E 


1 33 


2 00 


1 16 


3 33 


1840 


28 


1 52 


05W 


1 11 


1 37 


50 


3 10 


1850 


1 02 


2 26 


36 


45 


1 05 


17E 


2 40 


1860 


1 41 


3 05 


1 12 


lOE 


30E 


19W 


2 06 


1870 


2 21 


3 45 


1 51 


29W 


12 W 


58 


1 29 


1880 


3 00 


4 24 


2 29 


1 09 


51 


1 35 


51 


1890 


3 36 


5 00 


3 06 


1 46 


1 28 


2 14 


13E 


1900 


4 11 


5 35 


3 40 


2 22 


2 06 


2 51 


23 W 


1910 


4 olW 


6 loW 


4 13W 


2 53W 


2 39W 


3 25W 


47W 





1 --^ 




. 


__^ 


1 


1 




^3 


South 

Carolina 

(Columbia 


■11 
1? 


Florida 

East (Jack 

sonville) 


Florida 

West 

(Pensacola 


Florida 

South 

(Tampa ) 


Alabama 
(Montgom- 
ery) 


.1? 

<n CO 

§3 




/ _ 


o / 


o / 


o / 


o / 


o / 


o / 


1750 


2 04E 


3 16E 


2 27E 


5 00E 


5 00E 


2 52E 




1760 


2 41 


3 53 


3 04 


5 37 


5 30 


3 28 




1770 


3 15 


4 29 


3 40 


6 13 


5 55 


4 03 




1780 


3 44 


5 01 


4 12 


6 44 


6 15 


4 34 




1790 


4 06 


5 26 


4 37 


7 11 


6 26 


5 02 




1800 


4 19 


5 44 


4 55 


7 32 


6 30 


5 24 


7 54E 


1810 


4 24 


5 53 


5 04 


7 45 


6 26 


5 39 


8 13 


1820 


4 19 


5 53 


5 04 


7 50 


6 15 


5 47 


8 24 


1830 


4 05 


5 44 


4 55 


7 45 


5 55 


5 46 


8 28 


1840 


3 44 


5 26 


4 37 


7 31 


5 30 


5 38 


8 24 


1850 


3 15 


5 01 


4 12 


7 12 


5 00 


5 22 


8 13 


1860 


2 41 


4 29 


3 40 


6 45 


4 28 


5 00 


7 57 


1870 


2 03 


3 53 


3 04 


6 13 


3 53 


4 32 


7 31 


1880 


1 25 


3 14 


2 25 


5 34 


3 16 


3 54 


6 55 


1890 


47 


2 39 


1 50 


4 57 


2 48 


3 15 


6 21 


1900 


HE 


?08 


1 19 


4 2P 


2 19 


2 49 


5 58 


1910 


12W 


1 52E 


1 05E 


4 22£ 


2 06E 1 


2 45E 


6 OSE 



48 



A MANUAL FOR NORTHERN WOODSMEN 



TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
TION IN THE UNITED STATES 

(From U. S. Coast and Geodetic Survey Reports) 



Year 
(Jan. 1) 


Tennessee 
East (Chat- 
tanooga) 


Tennessee 
West (Hun- 
tingdon) 


Kentucky 

East 
(Lexington ) 


Kentucky 

West 
(Princeton) 


Louisiana 
(Alexandria) 


W2 


Texas Mid- 
dle (San 
Antonio) 


1750 


' 


/ 


o / 


o / 


o / 


o / 


o / 


1760 
















1770 
















1780 
















1790 
















1800 


5 07E 




4 22E 


6 32E 


8 04E 






1810 
1820 


5 16 
5 16 


7 24E 


4 31 
4 31 


6 50 
6 59 


8 25 
8 41 


8 55E 




1830 
1840 


5 07 


7 24 


4 22 


6 59 


8 49 


9 10 


9 37E 


4 49 


7 16 


4 04 


6 50 


8 48 


9 19 


9 48 


1850 


4 24 


6 59 


3 39 


6 32 


8 40 


9 19 


9 53 


1860 


3 52 


6 35 


3 07 


6 07 


8 24 


9 12 


9 48 


1870 
1880 
1890 


3 16 


6 05 


2 31 


5 37 


8 02 


8 56 


9 37 


2 36 
2 01 


5 29 
4 53 


1 53 
1 15 


4 57 
4 20 


7 26 
6 53 


8 29 
7 56 


9 19 
8 52 


1(^00 
1910 


1 30 
1 12E 


4 24 
4 18E 


41 
19E 


3 51 
3 36E 


6 33 

6 50E 


7 44 

8 05E 


8 43 

9 09E 



^5 


Texas 
West 
(Pecos) 


Arkansas 
(Little 
Rock) 


Oklahoma 
(Okmulgee) 


Missouri 
(Sedalia) 


Kansas East 
(Emporia) 


Kansas 

West (Ness 

City) 


Nebraska 

East 
(Hastings) 




o / 


/ 


o / 


o / 


o / 


<a / 


o / 


1750 
















1760 
















1770 
















1780 
















1790 
















1800 




8 13E 












1810 
1820 
1830 
1840 


10 46E 

11 00 


8 36 

8 51 

9 00 

8 59 




10 03E 
10 13 
10 13 






11 39E 

11 57 

12 07 


1850 
1860 
1870 
1880 
1890 


11 08 
11 07 
11 00 
10 48 
10 24 


8 51 
8 34 
8 14 
7 38 
7 01 


10 15E 

10 06 

9 51 

9 33 

9 07 


10 04 
9 46 
9 24 
8 44 
8 02 


11 34E 
11 28 
11 12 
10 45 
10 07 


12 24E 
12 23 
12 12 
11 54 
11 21 


12 07 
11 59 
11 41 
11 10 
10 31 


iroo 

1910 


10 18 
10 50E 


6 38 
6 49E 


8 42 
8 55E 


7 38 
7 46E 


9 50 
10 08E 


' 11 OR 
11 27E 


10 14 

10 28E 



ON THE BEARING OF LINES 



49 



FABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA- 
TION IN THE UNITED STATES 

(From U. S. Coast and Geodetic Survey Reports) 









^-^ 


,_^ 










raska 

est 

ance) 


J. -^^ 


1 *3 >> 


^^t 


h Da- 
West 
inson) 


e8 -rt 


<3 ^ 


<u a 


^ 1-. 


Q|3 


Q »5 o 


Montan 
East 
(Forsyt 


tan 

est 

ena 


^3 




Sout 

kota 

(Hi 


Sout 
kota 
Rapi< 


Nort 

kota 

Jame 


Nort 
kota 
(Dick 










^^ — ' 


^' — ' 










o / 


o / 


o / 


O / 


/ 


o / 


o / 


1750 
















1760 
















1770 
















1780 
















1790 
















1800 
















1810 
















1820 
















1830 
















1840 




13 06E 








18 09E 


18 53E 


1850 


15 27E 


13 06 


16 26E 


14 31E 


17 37E 


18 27 


19 18 


1860 


15 27 


12 57 


16 26 


14 21 


17 37 


18 36 


19 36 


1870 


15 18 


12 39 


16 16 


14 02 


17 27 


18 36 


19 45 


1880 


14 50 


12 07 


15 50 


13 31 


17 00 


18 21 


19 34 


1890 


14 20 


11 25 


15 17 


12 43 


16 21 


17 53 


19 23 


1900 


14 10 


11 07 


15 07 


12 24 


16 10 


17 50 


19 31 


1910 


14 31E 


11 28E 


15 27E 


12 44E 


16 36E 


18 17E 


20 02E 





M ^ 


(4 




c c 
o o 


c 


-1^ 

rr. --^ 


1^ 


03 • 

^'3 


Vyomin 

East 

Dougla 


Vyomin 

West 
reenRi-v 


2a 


ashingt 
St (Wils 
Creek) 


ashingt 
West 
Seattle 


o S 
Ma 






f" ^~■ 


^ o 




^3 


^ ' 




O 




O 1 


o / 


o / 


o / 


o / 


o / 


o / 


1750 
















1760 
















1770 
















1780 










17 19E 






1790 










17 62 






1800 










18 27 




16 05E 


1810 










19 04 




16 43 


1820 










19 41 




17 22 


1830 










20 16 




18 01 


1840 










20 49 




18 38 


1850 


15 51E 


16 45E 


18 OOE 


21 16E 


21 19 


19 15E 


19 12 


1860 


15 59 


16 58 


18 30 


21 37 


21 45 


19 40 


19 41 


1870 


15 59 


17 02 


18 45 


21 52 


22 06 


19 58 


20 06 


1880 


15 47 


16 54 


18 45 


21 56 


22 19 


20 09 


20 24 


1890 


15 24 


16 36 


18 39 


22 06 


22 38 


20 11 


20 32 


1900 


15 19 


16 37 


18 51 


22 22 


22 58 


20 26 


20 50 


1910 


15 43E 


17 08E 


19 31E 


23 OOE 


23 40E 


21 07E 


21 33E 



50 



A MANUAL FOR NORTHERN WOODSMEN 



TABLE GIVING SECULAR CHANGE OF THE IVIAGNETIC DECLINA- 
TION IN THE UNITED STATES 

(From U. S. Coast and Geodetic Survey Reports) 





.3 o-r- 


■- ^^ 


.S 'm 


d ,-s 


4.^ 






c^ S 




c^ c 


-c-^^ o 




-5 =« 


2 c 

^5 




:t: 0-T3 


1^ - 








o / 


o / 


o / 


o f 


O 1 


o / 


1750 














1760 














1770 














1780 


10 24E 


13 37E 


14 07E 








1790 


10 58 


14 03 


14 35 








1800 


11 32 


14 32 


15 04 








1810 


12 07 


15 01 


15 34 








1820 


12 39 


15 30 


16 04 








1830 


13 09 


15 57 


16 33 








1840 


13 36 


16 22 


17 01 








1850 


13 57 


16 45 


17 26 


17 20E 


16 16E 


16 25E 


1860 


14 13 


17 05 


17 47 


17 36 


16 37 


16 36 


1870 


14 24 


17 20 


18 06 


17 41 


16 52 


16 40 


1880 


{ 14 33 


17 28 


18 15 


17 44 


17 00 


16 30 


1890 


1 14 36 


17 32 


18 20 


17 38 


17 02 


16 20 


1900 


! 14 52 


17 51 


18 39 


17 49 


17 17 


16 28 1 


1910 


15 35E 


18 32E 


19 22E 


18 27E 


17 58E 


17 03E 1 



1 




1 


o 1? 1 


o 1 


^ 1 




Year 
(Jan. 1) 


Colorado 

East 
(Pueblo) 


I!olorado 
est (Glen 
wood 
Springs) 


ew Mexic 

East 
anta Ros 


ew Mexic 

West 
(Laguna) 


Arizona 

East 
Holbrook 


Arizona 

West 
(Prescott 






^ 


'Z ^ 


Z 








o / 


o / 


o / 


o / 


o / 


o / 


1750 














1760 














1770 














1780 














1790 














1800 














1810 














1820 














1830 
1840 
1850 














13 47E 


16 07E 


12 43E 


13 26E 


13 33E 


13 19E 


1860 


13 50 


16 15 


12 47 


13 33 


13 44 


13 33 


1870 


13 46 


16 16 


12 43 


13 34 


13 47 


13 40 


1880 


13 31 


16 04 


12 29 


13 22 


13 40 


13 36 


1890 


13 00 


15 40 


12 03 


13 02 


13 25 


13 32 


1900 


12 53 


15 39 


11 59 


13 02 


13 29 


13 44 


1910 


13 19E 


16 lOE 


12 29E 


13 36E 


li 0.5E 


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 
sw^ung 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. 

WTien the north star is farthest from the meridian it is 
said to be in elongation, east when the star is east of the 
meridian, west when on the opposite side. A plane through 
the observer, the zenith, and the north star when at elonga- 
tion, prolonged downward to the horizon, makes an angle 
with the meridian which is called the azimuth of the star 
at that time. This angle may be obtained for any time and 
position from tables, and setting off the angle, the true 
meridian is found. Upon this meridian the needle can be 
read or marks can be left for reference at any future time. 

The operation of bringing down the star may be per- 
formed either with the plumb line or, more accurately and 
conveniently, with a well-adjusted transit. When the 
transit is used it is necessary to illuminate the cross wires. 
This may often be done by holding a lantern or candle 
in front of the transit tube and a little to one side, when 
the field should appear light with the cross hairs show- 



52 



A MANUAL 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 diflicult 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 Une. « 
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 Polaris i '' 

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) Cassiopeise is on the me- 
ridian below Polaris and the pole, at 
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. 



Great 



. .North Pole 



Delta • ■ * 



Cassio 



Zeta 



Bear 



peia 



10.6 " { increase 

14.7 " ( .41 min. 

7.1 min. ( annual 

11.0 " { increase 



ON OBTAINING THE MERIDIAN 53 

Six months later the star Zeta (f), 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- 
siopeise, Zeta (^) Ursae 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 .... 6.5 min. ( annual 
* For Zeta Urs. Maj. { 1920 
(1930 

(1910 
For Delta Cass. \ 1920 

( 1930 .... 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 

Instru:ment 

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 bemg du-ected into the object end of the telescope by an 
assistant ; while great care will be taken, by perfect leveling, to 
insure that the hne x)i collimation describe a trulv 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- 
trarv to its former motion; thus indicating the time of elongation. 

Then while the star appears to thread the vertical wire, depress 



54 A MANUAL FOR NORTHERN WOODSMEN 

the telescope to a horizontal position; five chains north of the 
place of observation set a stone or drive a firm peg, upon which 
by a strongly illuminated pencil or other slender object, exactly 
coincident with the vertical wire, mark a point and drive a tack 
in the line of sight thus determined; then, to eliminate possible 
errors of coUimation or imperfect verticaUty 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 dayUght 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 decUnation, 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 Deterahne a Meridian without a Telescope 

Attach a plumb line to a support situated as far above the 
ground as practicable, such as the Hmb of a tree, a piece of board 
nailed or otherwise fastened to a telegraph pole, a house, barn, 
or other building, affording a clear \aew 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 wiU hold the plumb fine vertical, fully as well as one of 
finished metal. 

Strongly illuminate the plumb fine just below its support by a 
lamp or candle, care being taken to obscure the source of light 
from the \Tlew of the observer by a screen. 

For a peep sight, cut a slot about one-sixteenth of an inch wide 
in a thin piece of board, or nail two strips of tin, with straight 
edges, to a square block of wood, so arranged that they will stand 
vertical when the block is placed flat on its base upon a smooth 
horizontal rest, which u411 be placed at a convenient height south 
of the plumb Une and firmly secured in an east and west direction, 
in such a position that, when \iewed through the peep sight, Po- 
laris will appear about a foot below the support of the plmnb 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 fine 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 mo\ing 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 w ith its exact position marked on the rest, and all fmlher 
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 sufl5- 
cient accuracy for the needs of local surveyors. 

Example: Sept. 10, 1915, in latitude 45° N, longitude 
71° W, it is desired to obtain the declination of the needle. 

From the table giving times of elongation it is found that 
Polaris is at eastern elongation on Sept. 1st at 53.2 minutes past 
8 p. M. 

Correction A is not required in this case. 

Correction B, for the 9 days elapsed since Sept. 1st, is 35.3 min., 
to be subtracted. 

Correction C, for 71° longitude, is 16 min., to be subtracted. 

Correction D, for 45° latitude, is 0.85 min., to be added. 

Correction E is 0.2 min., to be added. 

8 hrs. 53.2 min. — 35.3 min. — 16 min. + .85 min. -\- .2 min. 
= 8 hrs. 3 min., time of elongation by the watch. 

The star having been observed at the time indicated and brought 
down to the horizon, its azimuth is ascertained from the table of 
azimuths. For 1915 and latitude 45°, this value is 1° 37.4' and 
there is no appreciable correction for apparent place. The merid- 
ian then is that much to the west of the line determined. In this 
case, with the instrument on the azimuth line the needle was 
allowed to settle and a reading of N 17° 50' E obtained. 17° 50' — 
1° 37.4,' = 16° 12.6'. 16° 12.6' is therefore the magnetic decUnation 
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 observ-ation. Then, watching the star, when satisfied by its 
motion that it has reached elongation he ^ill 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 



00 
.-1 


/ 

1 ll.G 
12.2 
12.S 
13.5 
14.2 


qt-q-<*q 

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(N IN IN (N IN 


Xdr^lNTl^ 

c^ CO CO CO CO 


rHXr^COO 

dt>^dr4fo 

COCOCOtJ* T}< 


d 


1—1 


qqqqrH 
- «oc6cot>^3C 

o ^ 


xi^»o ■<*<■* 
00 d d r.; c^ 

rH -HIMINC^l 


q Tin q q X 
CO -^ d d t>^ 

CllNININiN 


rHT}<0>-*q 

d d -3 CO r)5 

(N CO CO CO CO 


CD CO rH O rH 

d 00 d c<i T)< 

CO CO ^ ■^ "^ 


(N 

d 


03 


o o o o o 

•cor^ooo 

(NevIIN(NiN 


O O O o 

OrH(NeO-* 

CO CO COCO CO 


o o o o o 

iCcOt>.X05 
CO CO CO CO CO 


o o o o o 

OrHINCO-* 


o o o o o 

iOCOt>»X05 





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 bv 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 1 


For Middle of 

i 


Correction 


January- 


/ 1 
— 0.5 ! 


1 

July 


+ 0.2 


February 


— 0.4 ! 


August 


+ 0.1 


March 


— 0.3 


September 


— 0.1 


April 


— 0.0 


October 


— 0.4 


Mav 


+ 0.1 


November 


— 0.6 


June 


+ 0.2 


December 


— 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 ^^EST 
OF GREENWICH) 

(From L'nited States Coast and Geodetic Survey) 



Date 


Eastern Elongation 


Western Elongation 


1915 


h. 


m. 


h. 


m. 


January' 1 





51.7 P. M. 





46.0 P. M. 


January 15 


11 


56.4 A. M. 


11 


46.8 P. M. 


February 1 


10 


49.2 A. M. 


10 


39.7 P. M. 


February' 15 


9 


54.0 A. M. 


9 


44.4 P. M. 


March 1 


8 


58.7 A. M. 


8 


49.2 P. M. 


March 15 


8 


3.5 A. M. 


7 


54.0 P. M. 


April 1 


6 


56.6 A. M. 


6 


47.1 P. M. 


April 15 


6 


1.6 A. M. 


5 


52.0 P. M. 


May 1 


4 


58.7 A. M. 


4 


49.2 P. M. 


May 15 


4 


3.8 A. M. 


3 


54.2 P. M. 


June 1 


2 


57.2 A. M. 


2 


47.6 P. M. 


June 15 


2 


2.4 A. M. 


1 


52.8 P. M. 


July 1 





59.8 A. M. 





50.2 P. M. 


July 15 





5.0 A. M. 


11 


55.4 A. M. 


August 1 


10 


54.5 P. M. 


10 


48.8 A. M. 


August 15 


9 


59.8 P. M. 


9 


54.1 A. M. 


September 1 


8 


53.2 P. M. 


8 


47.5 A. M. 


September 15 


7 


58.3 P. M. 


7 


52.6 A. M. 


October 1 


6 


55.5 P. M. 


6 


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 

1918 add 

1919 add 

1920 {^dd 

1921 add 

1922 add 

1923 add 

1924 {^^^ 

1925 add 

1926 add 

1927 add 
f add 



1928 



add 



0.7 minute 
0.9 minute 

2.5 minutes 

4.0 minutes 
0.1 minute 

1.6 minutes 

3.1 minutes 

4.5 minutes 
5.9 minutes 
2.0 minutes 
3.3 minutes 

4.6 minutes 
5.9 minutes 

7.2 minutes 

3.3 minutes 



up to March 1 

on and after March 1 



up to March 1 

on and after March 1 



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° ajid 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 ]\Iarch 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 loth it occurs at 2 a. m. 

From early October to middle January use upper cul- 
mination with Zeta of the Great Bear. 



60 A MANUAL FOR NORTHERN WOODSMEN 

SECTION VIII 
THE UNITED STATES 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 surveyed or patented, or the course of navigable rivers, 
may render this impracticable; and in that case this rule must 
be departed from no fiui^^her 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 subdi\'ided 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 tlie 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 ^^•ithin 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 hnes from east to west, or from north 
to south ; the sections and half-sections bounded on the northern 
and western hnes 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, subdi\'ided into twenty-five equal hnks; and the chain 
shall be adjusted to a standard to be kept for that pinpose. 

Sec. 100. The boundaries and contents of the several sections, 
half-sections, and quarter-sections of the pubHc 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 estabhshed 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 Une. 

Second. The boundary hnes, actually run and marked in the 
sur\'eys returned by the sm-veyor-general, shall be estabhshed as 
the proper boundary Hnes of the sections or subdivisions for which 
they were intended, and the length of such Hnes as returned shaU 
be held and considered as the true length thereof. And the 
boundary Hnes which have not been actually run and marked 
shaU be ascertained by running straight Hnes from the estabhshed 
corners to the opposite corresponding corners; but in those por- 
tions of the fractional townships, where no such opix)site corre- 
sponding corners have been or can be fixed, the boundary Hnes 
shall be ascertained by running from the estabhshed corners due 
north and south or east and west Hnes, as the case may be, to the 
water-course, Indian boundary Hue, or other external boundary 
of such fractional to^\^lship. 

Third. Each section or subdi\ision 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 shaU not have been thus returned, shall be held 
and considered as containing the one-half or the one-fourth part, 
respectivelv, 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 di\'ision of a quarter-section 
the Hne for the division thereof shah run north and south, and the 
corners and contents of half-quarter-sections which may there- 
after be sold shaU 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 Unes, 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 pubUc 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 impossibihty 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 \aew of these facts, and under the pro\asions 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 w^here the 
exterior lines of the townships, thus to be subdi\dded 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 w^estern or northern ranges of sections or half- 
sections in such township, according as the error may be iln run- 
ning lines from east to west, or from south to north ; the sections 
and half-sections bounded on the northern and western hues 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 incompatibihties 
of the requirements of law and practice, as follows : 

First. The establishment of a principal meridian conforming 
to the true merichan, 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-foiu- 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 subdidded into thirty-sLx tracts, called 
sections, each of which shall contain 640 acres, as nearly as may 
be, by two sets of parallel hues, 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 sur\'eyed 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 fine is defective, the section lines 
should be run by a reversed method. 

For convenience the well-surveyed lines on which subdi\a- 
sions are to be based wiU 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 hne; 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 siu"veys 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 nmnbers 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 hne, 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 



i 

Standard 3 


J 

2 

Principal 


! 1 


J 


1 

/ 1 


-I e 
1 11^ 






1 1 


ft 


Base 


"^ Line 

% 

% 





standard Parallel 
1 1 1 




c 










13 

.s 

13 

*c 

o 






c 




to 

c 


to 

c 


a 

c 




■a 
c 
o 


i 


3 
o 


(i: 











FiKST Subdivision of 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 comers 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 



W 



6 


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. M 
160 acres 


N. E. H 
160 acres 


of S.W. 

H 
80 acres 


of S.W. 

H 

80 acres 


N.W. ^ 

of S.E. 

H 


40 acres 


40 acres 


S.E.^ 

of S.E. 

H 



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 suflicient 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 towTiship 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 OflBce 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 to^Tiship, a section, or a quarter-section 
corner, the marks upon it indicating what the corner is. 

1. Stone w4th 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 comers 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 towaiship or section corners 
is plainly scribed with the towTiship number and range and 
that of the section in which it stands. Thus, T 10 S R 
6 E S 2-4 B T (B T for bearmg tree). 

There are several exceptions to the system of rectan- 
gular surveying and the regular scheme of monuments 
resulting therefrom, which it is necessary for the woodsman 
to understand. 

1. Township and Section Corners on Standard Parallels. 

It will be noted after careful reading of the above that 
towTiship or section corners are common to four townships 
or sections, with the exception of those on the standard 
parallels which are four tov.Tiships 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 Ij'ing south of the parallel are marked 
C C, "closing corner." This last term is also applied in 
other connections, as when a rectangular survey closes on 
the boundary of a state, a reservation, or a previous land 
claim, while occasions for its application have often been 
found in connection with errors or departures from instruc- 
tions in the system of surveying. 

2. Meander Lines and Corners. 

Ownership of considerable streams or lakes, with the 
exception of certain "riparian rights," is not conveyed 
with a land title, the legal limit being high- water mark, or 
the line at which continuous vegetation ends and the sandy 



68 A MANUAL FOR NORTHERN WOODSMEN 

or muddy shore begins. This Hne 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 
comer" is established and marked in the same way. 

3. Witness Corners and Witness Points. 

A key to the location and meaning of these will be found 
in the following sections from the " Instructions." 

49. Under circumstances where the survey of a township or 
section line is obstructed by an impassable obstacle, such as a 
pond, swamp, or marsh (not meanderable), the line will be pro- 
longed across such obstruction by making the necessary right- 
angle offsets; or, if such proceeding be impracticable, a traverse 
line will be run, or some proper trigonometrical operation em- 
ployed to locate the line on the opposite side of the obstruction; 
and in case the line, either meridional or latitudinal, thus regained, 
is recovered beyond the intervening obstacle, said Hne will be siu- 
veyed back to the margin of the obstruction. 

50. As a guide in aUgnment 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 tv^'enty chains of the inac- 
cessible comer point, such ^\^tness corner will be established. 

97. The point for a corner faUing on a railroad, street, or 
wagon road, will be perpetuated by a marked stone (charred stake 
or quart of charcoal), deposited tv^enty-four inches in the ground, 
and vatnessed by tT\ o witness corners, one of which will be estab- 
lished on each limiting line of the highway. 

In case tlie point for any regular corner falls at the intersection 
of two or more streets or roads, it vdll 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 comer described in these 
instructions falls where prevailing conditions would insure its 
destruction by natural causes, a witness corner wiU 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, 
win have the letters W C (for witness comer) conspicuously dis- 
played above the regular markings on the NE. face when witness- 
ing in towTiship or section corner; such witness corners will be 
established, in all other respects, like a regular corner, marking 
bearing trees ^-ith 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, viith the marking W P 
(for \\'itness point), in place of \, or \ S, as the case may be. 

K bearing trees are available as accessories to witness points, 
each tree will 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 tow^ard the north is crowded, 
are called fractional as well. Within these sections again, 
the westerly quarters and forties w ill 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 w ith the east or north, with seven 
lots for Section 6. In timbered country, however, they 
are seldom run out on the groimd. 

WMle 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 in 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 Surv^ey combined 123 

D. Western Topography. Use of the Clinometer 129 
Section VIII. Advantages of a Map System ... 133 



Part II. Forest Maps 

SECTION I 

THE TRANSIT 

The transit in general engineering work is the most 
useful and most frequently employed of surveying instru- 
ments. It is commonly used to measure horizontal and 
vertical angles, but, having a magnetic needle, it may be 
used to take bearings, and, when provided with stadia 
wires, to measure distances. It may also be used as a 
levelling instrument. A cut of a transit is shown here- 
with, also a sectional view through the axis of the same 
instrument. 

The essential parts of an engineer's transit are described 
below. The telescope is attached by means of a hori- 
zontal axis and standards to the upper of two circular 
plates. The two plates move freely on one another, the 
lower being graduated, while the upper has a vernier 
which allows readings to be made with accuracy. A 
compass circle is also attached to the upper plate. A 
clamp fixes the upper to the lower plate, and a tangent 
screw secures a slow adjusting movement between the 
two. A similar arrangement is placed between the lower 
plate and the head of the instrument. 

The whole instrument is supported on a tripod ; levelling 
screws serve with the aid of cross levels to fix the plates in 
a horizontal position ; and a finely turned spindle and socket 
arrangement guides the plates in their movement on one 
another. By means of a plumb line attached to the lower 
end of the spindle the instrument may be set with its axis 
exactly over any desired point. 

1. Adjustments of the Transit 

The object of these adjustments is to cause (1) the 
instrument to revolve in a horizontal plane; (2) the line 
of sight to generate a vertical plane when the telescope is 

73 



74 



A MANUAL FOR NORTHERN WOODSMEN 



revolved on its axis; (3) the axis of the telescope bubble 
to be parallel to the line of sight, thus enabling the instru- 
ment to be used as a level ; (4) the vernier on the vertical 




The Transit 



circle to be so adjusted as to give the true altitude of the 
line of sight. These results may be secured as follows: 
a. To adjust the plate levels so that each is in a plane 



THE TRANSIT 



75 



perpendicular to the vertical axis of the instrument. Set 
up the transit and bring the bubbles to the center of their 
respective tubes. Turn the plate 180° about its vertical 
axis, and see if the bubbles remain in the center. If they 
move from the center, turn the capstan-headed screws on 
the bubble tube until the bubble moves half-way back to 
the center, or as nearly so as this can be estimated. Each 
bubble must be adjusted independently. The adjust- 
ment should be tested again by relevelling and reversing 
as before, and the process continued until the bubbles re- 
main in the center when reversed. When both levels are 
adjusted, the bubbles should remain in the center during 
the entire revolution about the vertical axis. 




Cross-section op the Transit Head 

b. To make the line of sight perpendicular to the hori- 
zontal axis so that the telescope when revolved will 
generate a plane. To do this choose open and nearly level 
ground. Set up the transit carefully over a point A, sight 
accurately at a point B at about the same level and 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 £", one- 
fourth the distance from D toward C, since, in this case, 
a double reversal has been made. 

The cross-hair ring is moved by loosening one of the 
screws which hold it in the telescope tube and tightening 
the opposite screw. The process of reversal should be 
repeated until no further adjustment is required. When 
finally adjusted, the screws should hold the ring firmly but 
without straining it. 

c. To make the horizontal axis of the telescope per- 
pendicular to the vertical axis of the instrument, so that 
the telescope in its revolution will generate a vertical 
plane. Set up the instrument and level it carefully. Sus- 
pend a fine, smooth plumb line twenty or thirty feet long 
some twenty feet away from the instrument with a weight 
on the lower end hanging freely in a pail of water. Set the 
line of sight carefully on the cord at its upper end. Clamp 
both plates and bring the telescope down until it reads on 
the lower end of the cord. If the line of sight does not cut 
the cord, raise or lower the adjustable end of the horizon- 
tal axis until the line of sight does revolve in a vertical 
plane. Constant attention must be given to the plate 
bubbles to see that they do not indicate an inclined' verti- 
cal axis. 

If more convenient two points in a vertical line may be 
used, as points on a building. Set on the top point and turn 
down to the bottom one, marking it carefully. Revolve 
both plate and telescope 180° and set again on the bottom 
point. Raise the telescope again and read on the top point. 
The second pointing at the top point should correspond 
with the first. If it does not, adjust as above for half the 
difference. 

d. To make the telescope bubble parallel to the line o£ 
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 bein^ 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 bein^ 
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 TR.\NS1T 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 endugh 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. 



Obser\'ed 


Computed 


Bearing 


Rod 
Reading 


Vert. 
Angle 


Distance 


Diff. 
Elev. 


Elev. 


N. 5° E. 
N. 5° E. 
N. 5° E. 

N. 5° E. 


2.00' 
1.80' 
1.05' 
1.50' 


+ 1° 30' 
+ 4° 10' 
+ 8° 
— 30' 


200.86' 
179.84' 
103.94' 
150.98' 


+ 5.27' 
-h 13.12' 
+ 14.61' 
— 1.31' 


5.27' 
18.39' 
33.00' 
31.69' 


635.62' 


31.69' 



Computation. First shot, with v. a. of 1° 30', rod reading 2.00'. 
Add .01' for instrument constant, making 2,01', for corrected rod 
reading. From table the horizontal distance for 1' rod reading is 
found to be 99.93' the difference of elevation 2.62'. For 2.01' rod 
reading the elements are 99.93 X 2.01 and 2.62 X 2.01 or 200.86' 
and 5.27', as above. 

Second shot, 1.80 + .01, = 1.81, corrected rod reading. 

For V. a. 4° 10' and rod reading 1', horizontal distance 99.47 
and diff. 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. 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 

^ 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. Read 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: 



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Instead of interior angles, deflection angles may be 
read, a deflection angle being the angle which any course 
makes with the prolongation of the one preceding. To 
get this, after the instrument has been turned on the rear 
point, revolve the telescope on its axis and turn to the point 
ahead. The deflection must be recorded as right or left, 



84 A MANUAL 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 




1 
2 


89° 19' L. 
84° 8' R. 


N. 81° E. 

N. 8° 15' W. 

N. 75° 45' E. 


N. 81° E. 

N. 8° 19' W. 

N. 75° 49' E. 


518.63 ft. 

48.19 ft. 

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 
tiansits 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 


A 


limvith 


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. 



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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, usmg 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 89 

adjusting screws. When the two axes are in the same 
plane, the bubble will remain in the center while the 
telescope is revolving, 

(c.) Make the level tube parallel to the line of sight. 
This may be done in two ways. The first or indirect 
method is as follows : 

Clamp the instrument over a pair of levelling screws ; 
then bring the bubble to the center of the tube, lift the tele- 
scope out of the wyes, turn it end for end, and set it down 
in the wyes again. The eye end now is where the objective 
was originally. This operation must be performed with 
the greatest care, as the slightest jar of the instrument will 
vitiate the result. If the bubble returns to the center of the 
tube the axis of the tube is in the correct position. If it does 
not return to the center, the end of the tube provided with 
the vertical adjustment should be moved until the bubble 
moves half-way back to the center. This test must be 
repeated to make sure that the movement is due to defec- 
tive adjustment and not to the jarring of the instrument. 

For the second, the direct or peg adjustment, select the 
points A and B, say 200 feet apart. The distance need not 
be measured. Set up the level close to A so that when the 
rod is held upon it the eyepiece of the telescope will swing 
within about half an inch of its face. Bring the bubble to 
the middle of the tube and looking through the telescope 
wrong end to, put a pencil mark on the rod at the center 
of the small field of view. Note the rod reading thus ob- 
tained. Then turn the telescope toward B and take a rod 
reading in the usual way, making sure that the bubble is 
in the middle of the tube. The difference between these 
two rod readings is the difference in elevation of the two 
points + or — the error of adjustment. Next take the 
level to B and repeat the above operation. The result here 
gained is the difference in elevation — or + the error 
of adjustment, and the mean of the two results is the differ- 
ence of elevation between points A and B. Now, knowing 
the difference between A and B and the height of the in- 
strument above B, the rod reading at A which will bring 
the target on the same level as the instrument may be com- 
puted. With the horizontal cross-hair on the target, the 



90 A MANUAL 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 

Diflf. elev. of B and A = 0.949 
Mean of the two results = 1.067 +0-949 = 1.008, true difif. 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. K 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 reqmred. 
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- 



92 



A MANUAL FOR NORTHERN WOODSMEN 



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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 workc 



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°. Directlv over the wire and mirror is a 
spirit tube (c), shown inclined in the ^^ure. 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 w^ith 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 stafE 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; decimation can be set off by means of a 
vernier; mside 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 1^ 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 
ON MOUNTAIN TRAILS 



Slope 


Length of step ascending 


Length of step descending 


0° 


2.53 


2.53 


5° 


2.30 


2.43 


10° 


2.03 


2.36 


15° 


1.84 


2.30 


20° 


1.64 


2.20 


25° 


1.48 


1.97 


30° 


1.25 


1.64 



but for practical work it is better for each man to train 
himself on measured distances and learn to discount on 
slopes by experience and the sense that he develops. Sim- 
ilarly, rough bottom and bushes have an effect on the pace. 
This is best dealt with in the same way. 

Harder perhaps to allow for, are the errors arising from 
a man's own condition. A man steps shorter when trav- 
elling slowly than when going at a good rate ; he steps 
shorter when tired unless he forces himself to the work; 
he is not sure of himself in the morning or after a longer 
rest until he gets " into his gait " ; he has his " off times " 
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 
ill the head and take down the hundreds on a "clicker," 
in a note book, or by breaking an elbow in a tough twig 
carried in the teeth or hand. 

Accuracy. With all its limitations, pacing is a very ser- 
viceable means of measurement and a man who has duly 
trained himself can get very good results. Johnson's 
" Surveying " says, that when a man's gait has been stand- 
ardized and on the work he walks at a constant rate, " dis- 
tances can be determined by pedometer or by counting the 
paces to within 2 per cent of the truth." That refers, 
without doubt, to open land. In woods work too there 



Outlet 




Section Lines 
Compass Bearings 
Pacing Traverses 



^M. J^M. %M. IM. 

Pond Sur\teyed from Section Lines bt Cross Bearings and the 
Compass and Pacing Method 

are many men who can be depended on for results as close 
as that, but errors up to 5 per cent in a straight mile on 
uneven land is for the writer the usual standard of work. 
This is not serious. \Yhen 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 BO.\RD 



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 



Seventy-four 




Plane Table Map 

of 

ROUND LAKE 

Washington Co. 

Maine 

C. A. Gary 1907 

Area 3 43 Acres 

Scale of Feet 
1 



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 suflfice. 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 sur^^ey 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 h 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 6 a at ^1 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, f, and g. 

Board at D 



Board at C 


■JL^b 


WJ ! 


lulA^ 


^ffl^ 



1 


e 



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 x by a ray brought back in the 
range A a until it cuts c x. 



Board at X 


\ ^ 


x\ • -b 


) 


■■ 


• d 


■ e 


f- 



Board at Y 




a 

.b 


'■ 1^' ] 




■ d 




g- 


f -^ 



(c) By setting up the board on any desired point on the 
shore as F, 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 \1 

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 
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 



Aneroid Barometer 



104 A MANUAL FOR NORTHERN WOODSMEN 

face is graduated to correspond with the height of column of 
a mercurial barometer, 30, 29, 28, etc., inches, these even 
inches being divided into fractional parts. 

This change in pressure corresponds with definite change 
in altitude. One inch on the scale means roughly 900 feet 
in altitude; a half inch means 450 feet, and so on. As 
a matter of fact, there is a foot scale on most aneroids 
outside the inch scale, movable and graduated from zero 
up to the capacity of the instrument. Thus, if one knows 
how high he is above sea level, he may turn the foot scale 
of his instrument until the registering hand points to that 
height, and, going either up or down hill, read directly the 
elevation of any station which he may occupy. 

Just this process answers many purposes, but when best 
results are sought for, the operation is not quite so simple. 
First, there is the Correction for the Temperature of the 
Air. An inch difference in pressure at a temperature of 
32°, for instance, converted into height, means one thing; 
at 70° it means a good deal more. In order to get accu- 
rate results, therefore, on considerable elevations, it is 
necessary to read the inner or inch scale of the instrument, 
take the temperature of the air at the two points, and 
obtain the elevation from tables. Such tables will be 
found on pages 111 and 112 and full directions for their 
use accompany them. 

Correction for Weather Change. The other liability to 
error arises from the fact that the air pressure is frequently 
changing with the weather. This does not hamper work 
seriously in the western country where the weather and 
pressure remain steady for long periods at a time, but diffi- 
culty does arise from this source throughout the East. 
With an approaching storm the air grows lighter, and the 
reverse in clearing weather. This effect is best seen on a 
stationary barometer, but it has a like effect on one that 
is in motion. Thus, if an explorer starts at a lake of known 
elevation and takes two hours in going to the top of a hill, 
the air pressure meanwhile may have changed so as to 
throw his height readings off materially. 

There are three ways of obviating this, outside the evi- 
dent one of working only in steady weather. One is to 



THE ANEROID BAROMETER 



105 



return to the lake and take a second reading, using the 
average of the two to compare with that observed at the 
summit. A second, often available in cruising timber, is 
to read on the same point two or more times during the 
day and so ascertain the course of the barometer. The 
third method of correction is by means of another instru- 
ment which is left at the base station or some other 
convenient point, and read by another person every hour 
or half hour while the observer is in the field. Since in 
ordinary weather the air changes are the same over large 
areas, this arrangement tells what the field barometer 
would have read on the base station at any hour during 
the day. Better than this, however, is a self-recording 
barometer, or barograph, which makes a continuous record 
of pressure. The explorer compares his pocket instru- 




Barograph 



ment with this as he starts out on his work, and again 
when he comes in. If these comparisons are satisfactory, 
he has the means of telling what his field instrument would 
have read on the base station at any time while he was 
gone, and so obtains the correct figure for comparison 
with any given field observation. This arrangement en- 
ables him to stay away from known elevations half a day 



106 A MANUAL FOR NORTHERN WOODSMEN 

or a day at a time and still make fairly satisfactory height 
determinations. 

This is all good in theory, but it must be said that in 
practice it does not always work out to one's entire sat- 
isfaction. The 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 from damage, also from extreme heat and 
rapid changes of temperature. 



THE ANEROID B.-VROMETER 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 .vnd 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 differeiice in elevation 
of the two points. 

Ride. — Enter the first column of Table T with the read- 
ings of the barometer on the two stations, and take out the 
corresponding numbers from column '2 (column 3 is for 
help in interpolating). Take the difference between these 
two figures. Call this result for the present a. 

Add the two temperatures together (or if the tempera- 
tures of the two stations do not differ materially, multiply 
that of the region by two). With this enter Table II, that 
for temperature correction, and find in column 1 the near- 
est number of degrees given. Take out of column 2 the 
number corresponding, noting the + or — sign, and 



108 A MANUAL FOR NORTHERN WOODSMEN 

multiply a above by this percentage. Let us call this h. 
If h 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 



DifiFerence {a above) 692 feet 

From Table II we have for t+ t' = 135°, C= + .042. 
b therefore = 692 X .042, is = 29 feet. This must be 
added to a, since the sign of the factor is +, and the 
result (692+ 29= 721) gives 721 feet as the required 
answer. 

A short cut to the same result, which is accurate enough 
and which will save much labor in reducing a number of 
readings referred to the same base station, is as follows: 
Between 29.500 and 28.760 inches the difference of eleva- 
tion corresponding to .1 inch pressure is 94 feet. This 
is obtained instantly by inspection of column 3 of Table 
I. Stated another way, the difference of elevation in feet 
is 6 per cent less than the difference between barometric 
readings expressed in thousandths of an inch. But the 
temperature correction for the conditions is + 4 per cent, 
leaving a net loss of 2 per cent on the difference in the 
barometric readings. 

Now 29.500- 28.760= .740, and 740- 2 per cent = 
725. Answer, 725 feet. 

Problem II. — To correct for changes of pressure due 
to the iveather, 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 29.100. That difference in pressure 
corresponds to nearly 150 feet in elevation, and height 
observations made during the day would be uncertain to 
very wide limits if the change could not be allowed for. 

THURSDA Y FRIDA Y 

8 1.0 A/T 2 4 6 8 1 X;/ 2 4 6 8 10 M^ 2 4 6 8 10 XII 2 ^ B 8 lOAf ^ 2 




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 w^as left there. 

The field barometer may not read the same as the 
barograph when they are brought together, but that 
" index error," as it is called, does not matter if the differ- 
ence between the two remains constant. In this case the 
field barometer at camp in the morning read 29.350 and at 
night 29.200, .1 inch higher than the barograph. One 
may, therefore, when he gets to computing, draw on the 



110 A MANUAL FOR NORTHERN WOODSMEN 

barograph sheet a curve through these two new points 
and parallel to the one made by the barograph pen. 
From this curve he may take off the reading for any hour 
in the day to compare with a field reading taken at the 
same time. Such a supplementing curve is shown on the 
sheet illustrated. 

Example. — At 11 a. m. on the day in question at a 
point two miles away from camp the field barometer 
read 29.270. What was the elevation relative to the base 
station ? 

The field reading can not be compared with the morning 
reading at camp because the barometric pressure is known 
to have been changing. Neither can it be compared with 
the night reading, for the same reason. The short curve 
on the sheet, however, does tell what the field instrument 
would presumably have read at camp at any hour in the 
day. The curve at 11 a. m. is at 29.270, and the two points, 
therefore, are of equal elevation. 

In view of the low accuracy of aneroid work, different 
users of the instrument have devised schemes for shorten- 
ing or obviating the labor of computation. One that is 
serviceable where temperature at different seasons shows 
wide variation is as follows: 

On the foot scale of most instruments 1000 feet at the 
higher elevations will be found to occupy a smaller sector 
on the scale than 1000 feet at low elevations — as 5000- 
6000 as against 0-1000. This can be tested by comparing 
against identical marks on the inner scale. 

Now, being at a known or assumed elevation, set the 
corresponding graduation against the movable hand and 
observe where the thousand-foot marks above and below 
cut the inner or inch scale; next, take the values so ob- 
tained and compute difference of elevation accurately, 
correcting for temperature. If the result obtained varies 
seriously from 1000 feet, shift the foot scale by even 
thousands until a portion is found so graduated that it 
does correspond. With a constant correction of even 
thousands, elevations may now be had directly. Correc- 
tion is not thus made for weather changes, however. 



THE ANEROID BAROMETER 



111 



TABLES FOR REDUCING READINGS OF THE ANEROID 
BAROMETER i 

I — Barometric Elevation 







Difference 






Difference 


Reading 


Elevation 


for .01 inch 


Reading 


Elevation 


for .01 inch 


Inches 


Feet 


Feet 


Inches 


Feet 


Feet 


20.0 


11047 


—13.6 


23.4 


6770 


— LI. 7 
—11.6 


20.1 


10911 


—13.5 


23.5 


6654 


—11.6 


20.2 


10776 


—13.4 


23.6 


6538 


—11.5 


20.3 


10642 


—13.4 


23.7 


6423 


— 11.5 


20.4 


10508 


—13.3 


23.8 


6308 


—11.4 


20.5 


10375 


—13.3 


23.9 


6194 


—11.4 


20.6 


10242 


—13.2 


24.0 


6080 


—11.3 


20.7 


10110 


—13.1 


24.1 


5967 


—11.3 


20.8 


9979 




24.2 


5854 




20.9 


9848 


—13.1 
—13.0 


24.3 


5741 


-11.3 
—11.2 


21.0 


9718 


—12.9 


24.4 


5629 


—11.1 


21.1 


9589 


—12.9 


24.5 


5518 


—11.1 


21.2 


9460 




24.6 


5407 




21.3 


9332 


—12.8 


24.7 


5296 


-11.1 


21.4 


9204 


—12.8 


24.8 


5186 


—11.0 


21.5 


9077 


—12.7 


24.9 


5077 


—10.9 


21.6 


8951 


—12.6 


25.0 


4968 


—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 


8327 


—12.4 


25.5 


4428 


—10.7 


22.2 


8204 


—12.3 
—12.2 


25.6 


4321 


—10.6 
—10.6 


22.3 


8082 


— 12.2 


25.7 


4215 


—10.5 


22.4 


7960 


• — 12.2 


25.8 


4109 


—10.5 


22.5 


7838 


—12.1 


25.9 


4004 


—10.5 


22.6 


7717 


—12.0 


26.0 


3899 


—10.4 


22.7 


7597 


—12.0 


26.1 


3794 


—10.4 


22.8 


7477 


—11.9 


26.2 


3690 


—10.3 


22.9 


7358 


—11.9 


26.3 


3586 


—10.3 


23.0 


7239 


—11.8 


26.4 


3483 


—10.3 


23.1 


7121 


—11.7 


26.5 


3380 


—10.2 


23.2 


7004 


—11.7 


26.6 


3277 


—10.2 


23.3 


6887 




26.7 


3175 





^ Taken from John'^on's "Surveying " and Report of U. S. Coast and 
Geodetic Survey for 1881. 



112 A MANUAL FOR NORTHERN WOODSMEN 



I — Barometer Elevation — continued. 







Difference 






Difference 


Reading 


Elevation 


for .01 inch 


j Reading 


Elevation 


for .01 inch 


Inches 


Feet 


Feet 


Inches 


Feet 


Feet 






—10 1 






—9.5 


26.8 


3073 


—10 1 


28.7 


1207 


—9 4 


26.9 


2972 


—10 1 


28.8 


1112 


—9 4 


27.0 


2871 


—10 


28.9 


1018 


—9.4 


27.1 


2770 


—10 


29.0 


924 


—9.4 


27.2 


2670 


—10 


29.1 


830 


—9.3 


27.3 


2570 


— 9 9 ' 


29.2 


736 


—9 3 


27.4 


2470 


— 9 9 


29.3 


643 


—9.2 


27.5 


2371 


— 9 9 


29.4 


550 


—9.2 


27.6 


2272 


— 9 8 


29.5 


458 


—9.2 


27.7 


2173 


— 9 8 


29.6 


366 


—9 2 


27.8 


2075 


-9.7 


29.7 


274 


—9 1 


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 


GO 


—9 


28.2 


1686 


— 9 6 


30.1 


— 91 


—90 


28.3 


1589 


— 9 6 


30.2 


181 


—9 


28.4 


1493 


— 9 5 


30.3 


271 


—9 


28.5 


1397 


— 9 5 


30.4 


361 


— 9 


28.6 


1302 


V.O J 


30.5 


—451 





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 


5° 


— 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 


eo 


— 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° 


—0.04.33 


115 


+ 0.0209 


175 


+ 0.0829 


C0° 


— 0.0380 


120 


+ 0.0262 


ISO 


+ 0.0879 



METHODS OF MAP MAKING 113 

SECTION VII 

METHODS OF ^lAP 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 accompanpng 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 efficient 
map. 



116 A MANUAL FOR 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 w^ere 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 w^ithin reach, 
one might sav, 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 against methods which can be carried 
on under the cover of the woods. 

■S. 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 Forestrv 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 difBculty 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 i§ 
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 • 
Harvard Forest School 

May, I 907 
Datum Plane Assumed 
Contour Interval 10 ft. 




Scale of Feet 



600 400 300 200 100 



500 



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 S: chained 
Points marked for reference 
Levelled lines 
Bench marks. 
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 

Stri'p 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 fm'nish the most eflficient 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 :=o= 



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 MAKESTG 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 way, 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 renew^ed 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 wTitten 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 

920 Trail 9T5 



876 860 




980 9T0 



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 re.'^dings, and 
then work around that. 



METHODS OF MAP MAKING 



127 



■Sf-grfi^q af>5ou/:h ///7e of Totvns/r/p, 2Srocfs £ 0/7 /■/7e S ///fis. 



of6e 



zf/'o/? as g/Ve/7 /'/? sarv^sy /7o/t^s. £/evay-/o/7 370ft 



as as cerfa/A ec/ from po/7c/ /7ear^/ c/efer/77//7ec/ S'/ /eye/. 



T/7eJ7ce //7 sec/y'0/7 2S 



Bearing 



fbces 



/V£0''£ 



200 



A/0/7^ easy s/Oyoe r/q/rf,//7^oo</f/mder. 



A/S^S 



3SO 



fo 



syvamp 



/VSO£ 



7S 



fo sma// brooA r6//7f?//7q 6£. S/ei/af/0/7 34c' 



N8ZE 



2S0 



af /OO ' //r/v /7/77der crffo//? 



//73£ 



/SO 



Up s/ope, fo pass b&fween h/f/s 



//6S£ 



32S 



r/ghf S /eff £/ey /O60 ' 



//4Z£ 



/7S 



on a genera/ s/ope £asf of aSoaf /oZ 



/V2S£ 



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fo f/af /one/ anc/ 



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1/7 f/af /and w/f/7 t/7/cA spruc& ^qroyyfh 



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fo Norf/7 //ne sec/yon 2S. /SO roc/s £asf 



on // as g/yen dy Sc/rvey /rofes. 



£/ey.BdOff C/;ec/redon B.Af. /fa/f an/^c/r/afsr 



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 



r" 






Bar Camp. (£/ey. dy /eve/ 30/') 6 AM. 23. 3S0 




TA. 60° Baro^rc^pfy 6A/^. 23.2S0 ' Bar ^^5^ 




Canai/a roac/ 0/7 /^. ///re secf/on 2S T/me 7/0 B3.360 -68/' 


3tTsps 


6a yVes/- o/j Sec/-/o/7 ///7e 


/90 


i/r7//e /r?ar/( af-5^ryey. P/a/- .Spruce ^roa/x/. 23. 36S 8 76 


S/0 


i m//e mar/(. slope M£. t/?en N. 29. 295 935 


S/S 


Secf/ofJ corner Oe/?/-/e5/a/>e A/.y/. A// spri/ce 




r/ml?er. 3ar 7.4o E9.30S 920 




Return fa /OO steps £. of ^ mVe mar/^ anc/ 




go S. 7° iV. /n 3ec//o/7. Start at Z5^A/>t. 


3S0 


Oert/e S/ope A< //./!/ Sprcfce ^roy/tt? 29. EOS /o/6 


400 


lbpot/7///,fa//s steep// £.a^£/W. 28.990 1220 


470 


Dom? strops ^raa/e 3. yy. 7//ni)ero/7/?////77/xea^ 




a/?£t ^strort. 3o/tam rau^/; 29. /7S /03S 


/7S 


Camc/a tay road or easy /a/7c/ 29. /95 /o/S 


J7S 


Down easi/y /r tar^e /77/yed^royvt/7 to ec/^e 




of .5)vampy tare/ 29.260 350 


E80 


Toyyr5t7/p tine 50 steps fast of^/n/temarA 




Bar 9.3S (TA.es'j 29.280 930 




Bar Camp //A. A/. (TA. 69j 29. 280 




Baro^rap/7 //, 29. /7S 







Stkaight Tkaverse across Section. Elevations by Barometer 

CORRECTED BY BaROGEAPH 

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 




vti 




'oxiM ! 



: EtBl u-ob \ 
^^ .oi» otiuiq* • *-, 






' * V-ss*'^'^* 




^'^' 




\ 





, T33H3 fl^aMIT ■ -^-^ 

a«inM fioitoaa ^d b9>)i£rn etsb ts^t aoniz sn.tJO OOe I b9iolq«3 




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 emplo;vTnent 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 widel}" encountered, which makes almost impossible 
the clear sighting necessary for the employment of any 
other height-determining instrument. On the contrary, 
the temptation is to rely on the aneroid for work that it 
should not be called upon to do. Where, as is the case 
here, railroads are employed for nearly all main transpor- 
tation, heights with a reliable basis are essential if a 
map is to be widely serviceable. Frequently the ground 
lies in such a way that the routes of future railroad de- 
velopment are evident. Levels run along these routes, 
with aneroid work for the rest, is then the natural treat- 
ment. Just this method has been employed m 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 pomts 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. Complamts of the results of 
aneroid work frequently arise from unskilled use and from 
employment of instruments of inferior character. The 
quaHty 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 
Hghtly 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 w^ith 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 Imes 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.^ Both instruments have, however, 
been subjected to modification. The clinometer has been 
made more efficient in numerous ways; m particular the 
arc has been enlarged and so graduated that instead of 
degree or per cent of slope it gives diiference 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, tw^o 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 

^ For a fuller description of this method see "The Timbennan/' 
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. 




2 Chains >J 



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 rims 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, m 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 m length aroimd either subdivisions of 



/ocbs. 




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 acre as a 
total for topography and cruise. Some commercial work 
is done on the same general plan, a five-chain tape being 
used and correction for distance made from tables in the 
field. 

The accompanying map of mountainous land in Idaho 
shows at the left the topography along two miles of section 
line as developed by a survey for control purposes which 
surrounded four sections. This control work naturally is 
performed and checked m 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 IMAP 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 Imes, 
map the cutting of successive years, and watch the con- 
dition of the timber. 

1. Great saving in the aggregate can be effected through 
the detection of small losses, such as windfalls and insect 
depredations, also by finding bodies of unhealthy timber, 
and as far as possible having such material cut and hauled. 

2. The location of all sorts of roads, whether railroads, 
logging roads, or supply roads, is greatly facilitated. 
Exploring is saved, and distances are accurately known. 

3. Operations can be planned and largely controlled 
from a center with all sources of information at hand. 



134 A MANUAL FOR NORTHERN WOODSMEN 

The timber resources are known; also their location, and 
all related facts. The cut can be located for years ahead 
to the best advantage, so as to make driving and the haul- 
ing of supplies, for instance, come cheapest and handiest. 

4. A map system preserves information about the land. 
An old lumberman or cruiser has a lot of information in 
his head that is lost to a business when he dies or steps out, 
unless it is fixed in some permanent form. 

5. A concern knows what it is possessed of, and has that 
information in the form most easily taken in by all intelli- 
gent men whom it may be desirable to inform ; for instance, 
stockholders, and possible money lenders. 

6. A good map system in a business may pay for itself at 
the first change of management. A new manager coming 
into a business is in the hands of his employees for years 
until he can get first-hand knowledge of his country. With 
the aid of a good map system w^orking command of a big 
property may be had in a year. 

7. A reliable map system followed up for a term of 
years through a series of pictures of the land furnishes a 
record of its growth, and so enables a concern to grapple 
with the question of future supplies. 



PART III 
LOG AND WOOD MEASUREMENT 



PART m. LOG AND WOOD MEASUREMENT 

Section I. Cubic Contents 137 

Section II. Cord Wood Rule 138 

Section III. New H.\mpshire 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 B^unsw^ck Rule 144 

7. Quebec Rule 145 

8. Theory of Scale Rules and Clark's International 

Log Rule 145 

Section V. New York Standard Rjile 147 

Section VT. Scai.ing Practice 148 

Section VII. Mill Tallies 151 

Section VIII. Cord Measure 157 



Part III. Log and Wood Measurement 

SECTION I 

CUBIC CONTENTS 

The simplest way to measure the contents of a log is to 
take its length and mid-diameter and ascertain the cubic 
contents of a cylinder having those dimensions. Bark may 
be taken in or left out. By the use of a caliper and tape, 
a very close result may be had on logs that are not too 
long, provided care is taken either by inspection or by cross 
measurement to get a true mid-diameter. Trees cut nearly 
full length are given as a rule too large a value when 
measured in this way, — larger, that is to say, than their 
actual cubic contents. The percentage of overrun for large 
spruce cut off at o 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 J 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 tlirow 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 measm-ement for logs that 
are to be converted into pulp, shingles, excelsior, etc. It 
is not a diflScult 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 w^hich wood 
will occupy in a pile. 128 of these make a cord. Like the 
preceding, these figures are ordinarily placed for conven- 
ient use on the bar of a caliper rule. 

These figures have been long and widely tested in prac- 
tice, and when used as designed have given satisfaction. 
Logs should not be measured in too long lengths, for whole 
trees measured in this way may not hold out. Again, 
small, crooked, and knotty timber will pile up rather more 
cords than the rule gives. On a good quality of pulp wood 
these figures yield just about the same return as the re- 
sults of piling. For further details see Section VIII, on 
cord measure. 

SECTION m 
THE NEW HA^lPSfflRE 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 foUowing 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 IMEASURE 

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 1 6-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 w^ith little 
taper. When logs are long enough to be cut in two for 
sawing, or to yield side boards for a part of their length, 
to derive contents from length and top diameter is not a 
fair thing. In such cases a second measure of diameter 
should be taken, and this can be done accurately only with 
a caliper. Allowance for " rise " or taper, whether for each 
log by judgment or according to some rule agreed upon, 
is more or less inaccurate and should be resorted to only 
in case of necessity. It may be said as a general rule that 
20-foot lengths are as long as it is safe to scale logs in.^ 

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- 

^ Except in the case of Pacific Coast timber. 



BOARD MEASURE 



141 



factory results. In some matters, especially culling for 
defects, latitude must be allowed to the scaler. In general, 
however, practice is weak in the direction of strict mechan- 
ical accuracy. Reference is made to section VI following. 
The method of construction, field of use, and relation to 
saw product of the above named rules are as follows : 

2. Scribner and Decimal Rules. The figures of the 
original Scribner rule were obtained by drawing diagrams 
of the end sections of logs 12 to 48 inches in diameter and 
the boards which in the mill practice of the time could be 
sawed out of them. It is a very old rule and in wide use. 
As printed, extended down to 6 inches, it is the legal rule 
in the state of Minnesota. 

Omitting unit figures of the Scribner rule and taking the 
nearest tens has given the Decimal rule, so called, legal in 
Wisconsin and adopted by the United States Forest 
Service. 

3. Spaulding or Columbia River Rule. This rule was 
derived by similar methods as the preceding, i inch being 
allowed for saw kerf. It is in more extensive use on the 
Pacific Coast than any other. 

4. Doyle Rule. This rule was constructed by the fol- 
lowing formula : — Deduct 4 inches from the diameter of 



Diameter 


No. Logs 


Doyle 
Scale 


Product 


Overrun 


6-8 in. 


28 


289 


903 


213% 


7-9 in. 


54 


831 


2159 


159% 


8-12 in. 


101 


2603 


5471 


110% 


10-17 in. 


104 


6324 


9976 


58% 


18-20 in. 


90 


15440 


20215 


31% 


21-24 in. 


126 


30929 


37744 


22% 


25-33 in. 


31 


11866 


13368 


12% 



the log for slab, square I of the remainder, and multiply 
by the length of the log in feet. This is a very illogical 
rule and gives results widely varying from saw product in 



142 A MANUAL FOR NORTHERN WOODSMEN 

logs of different sizes, though in a run of logs the results 
obtained may approximate a fair thing. Very small values 
are given to small logs, too small by far for normal logs 
economically manufactured, while beyond about 36 inches 
in diameter values are given that are above the product of 
the saw. It crosses the Scribner rule at 25 inches in 
diameter, the Maine rule at 34. A test made by Dr. J. F. 
Clark in 1905 in a Canadian band mill cutting sound, 
straight pine into boards resulted as shown on page 141. 

The Doyle rule is in more general use than any other in 
the United States and Canada, and is the one printed in 
recent editions of Scribner 's " Lumber and Log Book." 

This rule has been combined with the Scribner into the 
Doyle -Scribner rule, the figures of the Doyle rule being 
taken for small logs where the Doyle figures are lower, 
and of the Scribner rule on the largest logs where these 
figures are less. This Doyle-Scribner rule has been used 
largely on hard woods. 

5. Maine, also called Holland Rule. The figures of this 
rule were derived from diagrams. That is to say, circles 
6, 7, 8, etc. inches in diameter were plotted and within 
these the boards that could be sawed, an inch thick with 
J inch for saw kerf. Not only the boards derived from the 
inscribed square were reckoned, but the side boards if 
they were as much as 6 inches wide. No rounding off of 
the figures was done, so they are a little irregular, but that 
takes care of itself in a run of logs. 

This rule is used largely in Maine and to some extent 
elsewhere. It has been carefully tested at the saw, and 
the conclusions are as follows : — Sound spruce and pine 
logs 12 to 18 feet long, of best merchantable quality, 
manufactured at a circular saw cutting |-inch kerf will 
yield in the shape of inch boards just about the number of 
feet of edged lumber that the rule gives. A band saw will 
get more, and there will be a larger product if the logs are 
put into plank or timber. More will also be got the longer 
the logs run, up to the point where they are scaled in two 
pieces. 

How sawing practice affects the product at the saw was 
clearly shown by a test made by the United States Forest 



BOARD MEASURE 



143 



Service in various spruce mills of Maine. Some results of 
this test are given in tabular form. All logs were straight 
and sound, and exact conditions were as follows : 

Band Mill No. 1, |-inch saw kerf, lumber cut just 1 inch 
thick. Mill run for economy and utmost product of long 
lumber, giving product of about 40 M daily. 

Band Mill No. 2, same saw kerf. Mill run for speed 
rather than economy, product being 58 M a day. 

Rotary Mill, j^-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 Ifi FEET 
LONG AS SAWED IN DIFFERENT MILLS 





1-1 


i-i 


(N 








Top 
Diam. 






II 

— cS 
•--3 


> 

O OJ 


Gang 


Scale by 

Maine 

Log 




-hI 


-^l 


-^^ 


^1 




Rule 




g^ 


%^ 


= '^ 


ai 








« 


« 


fi 








6 in. 


30 


26 


20 


18 


24 


20 


Tin. 


41 


36 


29 


25 


34 


31 


Sin. 


53 


47 


39 


.35 


43 


44 


9 in. 


66 


59 


51 


46 


54 


52 


10 in. 

1 


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. 



Top 
Diam. 


Lengths in Feet 


8 


10 


12 


14 


16 


18 


20 


22 


24 


6 in. 

Sin. 
10 in. 
12 in. 
14 in. 
16 in. 


13 
25 
39 
54 
73 
95 


17 
32 
49 
68 
92 
120 


22 
39 
59 
83 
111 
145 


26 
46 
70 
97 
130 
170 


30 

53 

81 

112 

149 

196 


34 

60 

91 

126 

170 

223 


39 
68 
101 
141 
190 
250 


44 
76 
113 
156 
211 
278 


50 

84 
124 
172 
232 
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 
17-20 ft. 
21-24 ft. 


10 in. 

10 in. 

8^ in. 


24% 
23% 
37% 


16 ft. and under 
17-20 ft. 
21-24 ft. 
25-28 ft. 


10 in. 

lOh in. 

12 in. 

9h in. 


0% 
6% 

11% 
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 
3} 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 ^ than by anyone else, and a rule 
called the International Log Rule was devised by him, 
on the basis of this reasoning, which he also tested at 
the saw. The main points in this study are as follows : 

Taper of Logs. While logs exhibit a great variety of 
taper, it has been found (1) that rough logs taper more 
than clear, smooth logs, so that quality tends to neutralize 
taper; (2) that average taper does not differ greatly in dif- 
ferent localities or with different species. This average 
taper as a result of much measurement is found to be 
safely 1 inch in 8 feet. This in modern economical mill 
practice increases the yield of lumber in the form of side 
boards, and the above stated allowance for taper is there- 
fore introduced into the rule for all lengths over 8 feet. 

Crook and Sweep. In this study due allowance was 
made for irregularity of surface, and crook averaging 1^ 
inches in 12 feet of length, found to be characteristic of 
white pine logs on the Ottawa River, was counted normal. 
Above the limit of \\ 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 tlu-ows 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, w^hile 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 l^V inch thick to allow for this. 

^ See Forestry Quarterly, Vol. IV, No. 2. 



146 A MANUAL FOR NORTHERN WOODSMEN 

Saw Kerf. This loss in logs of different sizes is pro- 
portional to the area of their cross-section, or to the square 
of the diameter. It varies in proportion to the thickness 
of saw kerf as well. As embodying an average of good 
present practice, ^ inch was allowed. 

Loss in Edging Lumber. This includes not only that 
portion of a log which is thrown away in the form of edg- 
ings, but also the fractions of inches in the width of boards, 
which in Dr. Clark's studies were uniformly thrown off'. 
It is counted to be in all logs proportional to the surface, 
or, what amounts to the same thing, to the diameter. 
Counting boards to be merchantable down to the size of 
2 ft. B. M,, Dr. Clark found that an allowance of .8 foot 
board measure for each square foot of surface under the 
bark, or, what amounts to much the same, a layer .8 inch 
in thickness around the surface, would justly allow for 
this waste. 

Formula for the Rule. The above elements being put 
into mathemetical form with D representing top diameter 
inside bark, there is obtained for 4-foot sections the formula 
(D- X .22) - .71 D = contents B. M. 

Adaptation to Other Conditions. The product for other 
widths of saw kerf than ^ inch may be obtained by apply- 
ing the following per cents: 

For ^ inch kerf add 1.3 per cent. 

For 3^ inch kerf subtract .5 per cent. 

For 5 inch kerf subtract 9.5 p)er cent. 

For Y^6 inch kerf subtract 13.6 per cent. 

For I inch kerf subtract 17.4 per cent. 

For -{^ inch kerf subtract 20.8 per cent. 

Should the y^'ii^ch allowance for shrinkage not be made 
in the mill practice in question, this may be allowed for 
in a similar way. According to Dr. Clark's assumptions, 
each board with its saw kerf means 1^^ inch in thickness 
taken out of the log. 

If mill practice in other ways is not so economical as 
the rule presupposes, that is to say, if logs are sawed 
with more waste in slab and edging than has been assumed, 
or if logs vary in taper and straightness from the standard, 
that is considered by Dr. Clark to be proportional to the 



THE NEW YORK STANDARD RULE 147 

surface or diameter, and he recommends that it be allowed 
for by making a comparison between the scale and mill 
product, and then adjusting the zero mark on the scale 
stick more than one inch from the inch mark on the stick 
in accordance with the results of that comparison. Dr. 
Clarke's rule will be found on page 254 in the same section 
with the other board rules. 

SECTION V 
THE NEW YORK STANDARD RULE 

In northern New York logs are cut as a rule 1 3 feet long, 
and a log of that length and 19 inches in diameter at the 
top, inside bark, is the common unit of log measure- 
ment. It is called a " market " or " standard," and logs 
of other dimensions are valued in proportion. 

The " standard " is thus another artificial unit of log 
measurement, more artificial, perhaps, than any other here 
dealt with. Standard measure in logs of the same length 
runs very close to cubic measure. Thus a log 19 inches in 
diameter at the top and 13 feet long has 26 cubic feet in it; 
four logs 9^ inches in diameter and 13 feet long, also 
making one standard, contain the same amount of wood 
approximately, while a 38-inch log of the same length has 
four standards and 104 cubic feet of contents. A log 26 
feet long, however, has more than twice the wood contents 
of a 13-foot log on account of taper. For that reason the 
use of standard measure outside of a region where short 
standard lengths are cut would be likely to make trouble. 

Standard measure does not run parallel to board measure 
or to the yield of logs of different sizes at the saw. The 
standard log, — a log, that is to say, 19 inches in top diameter 
and 13 feet long, — scales by the Scribner rule 195 feet, and, 
in practice, five standards are often reckoned as the equiv- 
alent of a thousand. Four 9^-inch logs, together making 
one standard, scale but 144 feet by the rule, or seven stand- 
ards to the thousand, and the actual ratio between stand- 
ards and thousands is stated to run all the way from 4 
to 14. 



148 A MANUAL FOR NORTHERN WOODSMEN 

The ratio between cords and standards is nearly con- 
stant in logs of all sizes if cut of equal length. In the 
Adirondack woods 2.92 standards are commonly reckoned 
as one cord. 

SECTION VI 
SCALING PRACTICE 

Logs are best scaled when they are being handled over, 
as on a landing or mill brow, for then all parts can be seen 
and got at. Measurement in the pile, especially for long 
logs, is both diflScult and unsatisfactory. 

1, Length. A tape worked by two men is an accurate 
measure of length. Short logs may be accurately measured 
with a marked pole, and for long logs a carefully adjusted 
wheel with brads in the ends of its spokes is cheap to use 
and reasonably accurate. Measurement with a four-foot 
stick has a very wide range of accuracy, according to 
the way it is done. 




German Numbering Hammer 

Valuable timber cut into standard log lengths is com- 
monly allowed two inches extra to permit trimming at 
the saw, this amount being disregarded in the scale. If 
logs are cut without measuring, in which case they are as 
likely to be ten inches over foot lengths as two inches, the 
extra inches are commonly thrown off just the same. That 
practice, however, means in 16-foot logs a loss of 2 J per 
cent on the scale or the timber. On 30-foot logs, it means 
1^ 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 scalers 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 d efects, 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 ^^Titten 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. Scalers 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, 

i while there is very little of it in spruce. In large measm^e, 
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 

Tpitch 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 ^ 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 scalers have that ; some do not, and have to rely either 

^ Graves' " Forest Mensuration." 



MILL TALLIES 



151 



TABLE OF LOSS BY HOLES OR ROT NEAR THE CENTER 

OF LOGS, GOOD FOR DEFECTS MORE THAN 4 

INCHES FROM THE BARK 







Length of Logs in Feet 




Diam. 












of Hole 
















10 


12 


14 


16 


18 


20 


Inches 


Board Feet 

1 


o 


5 


6 


7 


8 


9 


10 


3 


9 


11 


13 


15 


16 


18 


4 


14 


17 


20 


23 


25 


28 


5 


20 


24 


28 


32 


36 


40 


6 


27 


33 


38 


44 


49 


55 


7 


36 


43 


50 


57 


65 


72 


8 


45 


54 


63 


72 


81 


90 


9 


56 


67 


78 


89 


100 


112 


10 


67 


81 


93 


107 


120 


133 



on arbitrary rules or on guesswork. Proper discount may 
vary greatly, too, with the mill practice and product. A 
mill with a box factory attached, or sawing round-edged 
stuff which is measured regardless of crooks, wastes little 
or nothing on account of defective form. For a mill 
which can market only three-inch deals at a profit, an 
entirely different system of scaling is appropriate. 

SECTION VII 
MILL TALLIES 

Thousands of unrecorded tests of scale rules have doubt- 
less been made at the saw, using local and current scaling 
and sawing methods. During the last few years a number 
of such tests have been made under stated conditions so 
carefully guarded that they may serve a general purpose. 
Reference is made to the tests recorded on pages 143 and 
144 of this work. The following also are reliable and of 
interest to northern workers in timber. 

The wide variation in the yield of logs as sawed under 
different conditions is a matter of great importance in 
several ways to the worker in timber, chiefly, perhaps, for 
its bearing upon timber estimates. The relative compe- 



152 A MANUAL FOR NORTHERN WOODSMEN 



tence of sawyers is one cause of this, and that, according to 
careful mill men, may readily amount to 10 per cent. Then 
market demand affects the matter, some mills being so 
situated that they can market only the larger sizes of lumber. 
The type of saw employed and the methods of handling 
on the carriage also have their effect. 

TABLE 1 

Yield in inch boards, squared, of second growth white pine 
logs. Based on 740 logs; study by Harvard Forest ScJwol. 

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 
Diameter 


Yield B.M. 


12-foot Logs 


14-foot Logs 


5 inches 

6 inches 

7 inches 

8 inches 

9 inches 

10 inches 

11 inches 

12 inches 

13 inches 

14 inches 

15 inches 

16 inches 

17 inches 

18 inches 


14 

20 

26 

34 

43 

53 

67 

81 

95 

110 

128 

147 

170 

202 


15 

23 

30 

39 

50 

61 

76 

90 

105 

122 

139 

160 



A practice that in some localities of recent years has 
greatly increased the merchantable product of logs is that 
of sawing waney or round-edged boards. Portable mills in 
southern New England sawing lumber for boxes or finish 
follow this practice largely, and stationary mills in many 
localities have a box or other saw to which they can turn 
over the small and crooked logs for this most economical 



MILL TALLIES 



153 



form of manufacture. WTien boards in this form are sur- 
veyed thev 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 groicth white pine logs, 
sawed tuith a circular saiv cutting \-inch kerf. Greater part 
of boards not edged, but measured for width at an average 
ividth, inside bark, on narrow side, without discount for 
crook. 

Based on 1180 logs. From Massachusetts State Forester. 



Top 


Length of Log — Feet 


10 


12 


14 


16 


Diam. 


* 








Inches 










Vol. 


Vol. 


Vol. 


Vol. 




Bd. ft. 


Bd. ft. 


Bd. ft. 


Bd. ft. 


4 


9 


13 


17 


21 


5 


13 


17 


21 


26 


6 


17 


22 


27 


32 


7 


23 


29 


35 


40 


8 


30 


37 


44 


51 


9 


39 


47 


55 


64 


10 


48 


58 


68 


79 


11 


58 


70 


82 


98 


12 


69 


83 


97 


115 


13 


80 


96 


113 


136 


14 


92 


111 


131 


158 


15 


104 


129 


150 


180 


16 


117 


146 


170 


205 


17 


131 


1G5 


192 


230 


18 


. 


184 


220 


250 



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 FOR NORTHERN WOODSMEN 



TABLE m 



Same logs but grouped according to inid diameter outside 
hark. 







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 




V3 


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 
^-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 savnng 
as shmvn in Tables I arid II. 1^-foot logs. 



Top Diameter 


Maine Log 


Results of Sawing 


1 


Inches 


Rule 


VTA^ 1 T „r,,K^^ Round-edged 

"^^T^vJr"^ Lumber 
Table 1 rp^^jig II 

1 


4 






13 


5 




14 


17 


6 


15 


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 



T.\BLE V 



Yield in ^-inch boards of pine logs 4 feet long (+ 2 inches 
for trimming). 



Diameter 


Yield 


Basis 


Surface Measure 


4 inches 

5 inches 

6 inches 

7 inches 

8 inches 

9 inches 

10 inches 

11 inches 

12 inches 

13 inches 

14 inches 

15 inches 

16 inches 


4 feet 
6 feet 
9 feet 
13 feet 
17 feet 
22 feet 
28 feet 
34 feet 
41 feet 
49 feet 
57 feet 
66 feet 
75 feet 


3 logs 
48 logs 

121 logs 
109 logs 
75 logs 
84 logs 
40 logs 
36 logs 
21 logs 
11 logs 
6 logs 

4 logs 
6 logs 



156 A MANUAL FOR 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 this fashion 
yields about 1000 feet of box boards. Sawed one inch 
thick, it is counted by Massachusetts box board men to 
yield about 650 feet surface measure. 



TABLE VI 



Yield in round-edged boards of second growth hard 
wood logs 12 feet long cut 1^ inch thick ivith circular saw 
Based on 1831 logs. 



cutting \-inch kerf 

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 



8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 



nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 
nches 



Yield, Surface 
Measure, of 12- 
foot Logs 



11 feet 

15 feet 

21 feet 

29 feet 

37 feet 

49 feet 

61 feet 

75 feet 

91 feet 

107 feet 

126 feet 

143 feet 

165 feet 

187 feet 

210 feet 



From New Hampshire Forestry Report for 1905-1906. 



CORD MEASURE 157 

SECTION \t:ii 

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 1'28 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 90 



158 A MANUAL FOR 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 wood is more or less than 4 feet 
long, multiply length, width, and height of the pile together, 
and divide by 128. If wood is piled on sloping ground, 
the length and height should be measured perpendicular 
to one another. 

For measurement of logs into cord measure, see page 138. 

The French cord of the Province of Quebec is 8' 6" X 4' 
X 4' 3", containing, therefore, 144 cubic feet, as against 
128 for the cord current elsewhere. *- 

* See Zon on this subject in Forestry Quarterly, Vol. I, No. IV. 



PART IV 
TIMBER ESTIMATING 



PART IV. TIMBER ESTIMATING 

Section I. Introduction 161 

Section II. Instrumental Helps 162 

Section III. Height Me.\surement 165 

Section IV. Volume Tables and Tree Form . . . 167 

Section V. Practice of Timber Estial^ting . . . 173 

A. Small and Valuable Tracts 174 

B. Larger and Less Valuable Tracts 186 

1. Type and Plot System 187 

2. The Strip System 188 

3. Line and Plot System 192 

C. Summary 195 

D. Pacific Coast Methods 196 



Part IV. Timber Estimating 

SECTION I 

INTRODUCTION 

Methods of estimating timber vary greatly in different 
regions and with different men. They vary also with the 
value of the timber involved and with the purpose for 
which the work is done. In this last connection cost is 
a guiding principle; in general, that method of doing a 
piece of work is best which secures a result sufficiently 
accurate for the purpose with the smallest expenditure 
of time and money. 

Lump Estimate by the eye has not gone out of use, and 
in fact never will cease to be employed. The immediate 
judgment that a good lumberman forms, simply by walk- 
mg 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 m 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 ahgned 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.^ 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 cahper in steady work on 
timber of" ordinary dimensions. 



■ I'M Pi'lM'IM'l'l 'I'IM'i'l 

3« 33 33 31 30 29 28 21 26 25 2« 23 22 21 20 



i I I i M I ' I ' I ' I ■ I I I ■ I I I I M I M I I ' I ' 

5 14 13 12 II 10 9 9 7 t S « 3 1 I 



Tree Caliper 

2. Counter or Tallying ]\Iachine. Teniber 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- 

^ See Appendix on theory and accuracy of this instrument. 



164 A MANUAL FOR NORTHERN WOODSMEN 



man has no concern. Such a man when he wishes to 
know the diameter of a standing tree at a point out of 
reach will ordinarily either estimate it or cut the tree 
down. 




Bark Blazer 

Occasionally, however, timber 
may be met with which is of suf- 
ficient value for special purposes 
to require measurement in this 
way. In such a case the engineer's 
transit may be employed, and by 
its aid it is not a difficult matter 
to determine either the height at 
which any given diameter is at- 
tained or the diameter at any given 
height. A very simple little in- 
strument for diameter measure- 
ment has been devised, which is described by its inventor 
as follows : ^ 




Counter 




Timber Scribe 



" The Biltmore pachymeter is used in connection with 
a target or piece of board graduated in inches, marked 

^ 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 1^ inches wide, containing a longi- 
tudinal slot about ^ inch wide and 17 inches long. The 
edges of this slot must be strictly parallel. Its actual 
width is entirely irrelevant from the mathematical stand- 
point. 

" It might be stated that any stick or pole, even a walking- 
cane, having parallel edges, will answer the purpose of 
establishing and measuring upper diameters. The Bilt- 
more pachymeter is merely a device convenient to handle. 

" The observer holds the pachymeter pendulum fashion 
by the hand of the outstretched arm in a position parallel 
to the tree trunk, and moves the instrument backward 
or forward until the edges of the slot cut off even with the 
desired diameter shown on the target. Then, the eye 
following upward along the trunk and sighting through 
the slot, that point on the tree bole is readily obtained 
where the bole cuts off with the edges of the slot. The 
position of this point above ground can be ascertained 
easily with the help of any hypsometer." 

SECTION III 

HEIGHT MEASUREMENT 

There are many methods of measuring the height of 
trees. As serviceable as any are the following: 

1. Windfalls are often of great assistance in ascertain- 
ing the height of timber, 

2. A pole 15 or 20 feet in length may be set up along- 
side the tree to be estimated and then, standing some dis- 
tance away, the cruiser may run his eye up the tree and 
judge how many times the length of the pole will be con- 
tained in it. A pencil held erect at arm's length in range 
of the pole and then run up the tree will help the eye in 
making the judgment. 

3. A cane or staff may be used on the principle of similar 
triangles. Hold the staff firmly in the hand with the arm 
straight and horizontal. Swing the end of the staff down 



166 A MANUAL. FOR NORTHERN WOODSMEN 

by the face and adjust the hold till the end of the staflF 
just comes by the eye. The distance from the eye to the 
staff and from the hand up to the end of the staff are now 
equal. Go off from the tree to be measured, holding the 
staff erect, until you can sight by the fist to the base of the 
tree and by the top of the staff to the top of the tree. Pace 
or measure to the tree and this will give its height. 

4, The Abney clinometer, shown on page 93 of this 
work, may be used for height measurement in much the 
same manner. Set the level tube at an angle of 45° with 
the line of sight and go off from the tree on a level with 




Faustmann's Height Measure 

its base until, sighting at the top of the tree, you see by 
the bubble that the tube is level. The distance from the 
observer to the tree is then equal to the tree's height. 

5. A second method employing the same instrument 
is as follows : Stand at a point where both the top and the 
base of the tree can be seen and at some convenient dis- 
tance from it, as 100 feet. Sight to the top of the tree and 
observe the angle of inclination, and again to the base of 
the tree, observing that angle also. Go into the table of 
tangents with the angles in turn, find the decimals corre- 
sponding, and multiply by the length of base. The sum 
of the two figures is the total height of the tree. 



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 8^° 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 increasmg 

toward the top. 

(6) Of two trees having the same breast diameter, ttie 
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 

(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 ot 
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 
hei-ht 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 bemg 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,^ 
be considered safe for most purposes. It is true, however, 
that some Pacific Coast timbers, with a very variable 
thickness of bark and the root swelling of large trees run- 
ning above a man's height oftentimes, have to be handled 
with special caution. 

The other variety of tables classifies trees in height by 
the number of standard log lengths they will yield or the 
height at which their boles attain a specified diameter. 
Under this plan the point to be observed is brought nearer 
the estimator. It is not, however, as sharply defined a 
point as in the other case, while, as explained on pages 
274-275, special opportunities for error arise through vari- 
ability in lumbering practice. 

Another matter that has to be reckoned with in the 
valuation of standing timber, and vv^hich 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 161, 262, and 277. 



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 di^ersity. 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: 









Feet in 


Height 






Breast 
Diana. 


























Inches 


50 


55 


eo 


65 


70 


75 


11 


52 


56 


64 


72 


84 


92 


12 


60 


68 


80 


88 


96 


108 


13 


72 


80 


92 


100 


112 


125 


14 


85 


100 


110 


125 


140 


155 


15 


100 


115 


130 


145 


160 


175 


16 




130 


143 


155 


175 


190 


17 




142 


158 


175 


190 


210 


18 




155 


175 


195 


210 


230 


19 




175 


195 


215 


240 


265 


20 




195 


220 


245 


270 


295 



SECTION V 

PRACTICE OF TIMBER ESTIMATING 

The methods that should be employed in a survey of 
standing timber depend on a great variety of facts of which 
the main ones are these: the size of the tract to be ex- 
amined, the method and fineness of its subdivision, the 
variety in its stand of timber, the value of the timber, and 
the experience and qualifications of the estimator. These 
methods are best discussed in two divisions, — first, 
methods for small tracts with valuable timber as a rule; 
and second, those for large tracts where more extensive 
processes must be employed. 



174 A MANUAL FOR NORTHERN WOODSMEN 

A. Small Tracts 

1. In the case of very valuable timber it may pay the 
owner or purchaser to examine each tree individually, 
ascertain its contents carefully, and study it for defects. 
The net contents of each tree as so ascertained will then 
be put down separately in the notes, and in case several 
parties are interested, each tree may be stamped with a 
number to correspond with one in the notes. At any rate, 
blazing each tree examined is a good means to make sure 
that all are taken and to prevent measuring any twice. 

Such procedure as this is appropriate to very large and 
valuable pine or to valuable but over-mature hard woods, 
which are especially liable to be defective. Volume tables 
might help in such cases, but they cannot be fully trusted ; 
a scale rule at hand would be to many men of quite as 
much assistance. For instruments, a caliper would come 
in play along with an instrument to measure heights 
accurately, while use might be found for some form of 
the dendrometer. But the best part of the equipment of 
the estimator in such cases is local experience in cutting 
and sawing the same class of timber. 

2. When timber in good stand and of considerable 
value is involved, it may be advisable to caliper each of 
the trees and measure a sufficient number to obtain the 
range of heights. After the stand is measured, sample 
trees of different sizes may be estimated after careful 
examination, or such trees may be felled and measured. 
Better than either of these methods, however, is a volume 
table giving the yield of trees of the given kind and dimen- 
sions. Volume tables, however, cannot be depended on 
to allow justly for defects. That is a matter for the judg- 
ment of the estimator. 

The above method works well in woods of approximately 
even type. When, however, the stand has a great variety 
of form and quality, the difficulty in making a true valua- 
tion is greater. In that case it may be practicable to cut 
it up into nearly homogeneous parts. 

The following example taken from practice will illus- 
trate the methods of working in a simple case. 



PRACTICE OF TIMBER ESTIMATING 



175 



Estimate of about 7 acres of land, covered nearly throughout 
with white pine standing fairly evenly, but not as a rule very dense. 
Concluded after inspection that no such differences of type or 



Field Observations 


Computed Volumes 


Breast 


No. 


Observed Heights 


Deduced 


Scale 


Total 


Diam. 


Trees 




Height 


Each 


Scale 


8" 


85 


51-47-50-54-59 


50' 


50' 


4250' 


9 


70 


50-47-52-48-56-57 


55 


70 


4fe00 


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—7 1—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 






Tota 


1 




252938 



Plot of Obsen^ed Heights and 
Deduced Height Cun^e 



1)0 


























1 




85 




















• 






[ [ 


Dedu 


ced 
















r'"''!^ 
















-Heig 
^Cun 


ht 

re. 


C3 l5 

^70 












x" 




1 
































y 


































g,60 








/ 








































p/1 






































W^ 


1/ 








































50 


"" 


i 






































45 


I 
1 










































8 9 



10 11 12 la 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

Diameter Breast High —Inches 



form existed' as to call for differentiation of treatment. Instru- 
ments employed, cahper and Faustmann's hypsometer. Steps of 
the survey as follows: 

a. Merchantable trees (those 8 inches and over in diameter 
breast high) cahpered 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 multipUed by the number of trees 
in the class. For the tract in question Table No. 4 gives the 
figures wanted, the product of the trees in boards, both round-edged 
and square-edged lumber. In this table the contents of a tree 8 
inches in breast diameter and 50 feet high is given as 50 feet B. M. ; 
that of a tree 9 inches x 55 feet, 70 feet, and so on. No discount 
appearing necessary for defects, by addition of the contents of the 
size classes the total stand of the lot is obtained. This comes to 
253 M feet, of which in the practice of the locality 20 per cent may 
be sawed into good plank, 30 per cent into edged boards, and the 
balance of 50 per cent, the smaller trees and rougher logs, put into 
round-edged box-board lumber. The recorded figures, the plot 
and height curve, and a table showing the way the figures are put 
together, are given on the preceding page. 

The estimate after this fashion of 250 M feet of timber 
of this size is a light day's work for two men. Three men 
form an economical crew for big jobs. 

3. In the valuable timber lands of the Lake States and 
South it is customary to estimate each forty acres by 
itself, and the methods of estimation frequently cover 
the whole stand. Pacing is largely used as a measure of 
distance, and the cruiser is generally equipped with some 
kind of volume table giving as often as not the board 
contents of trees of different diameters yielding 2, 3, 4, or 
5 16-ft. logs. Usually two men work together. In that case 
the helper may run a compass line across one end of the 
" forty," ten rods or so from its boundary, leaving marks 
enough so that on the return trip it can be followed. 
Through the strip so cut off the cruiser circulates, keep- 
ing watch of his other bound and scoring down, as he 
passes, the merchantable trees according to species and 
in appropriate classes. As a rule very little measurement 
of height or diameter has been done in the past. The two 
men keep abreast of one another. When one strip has 
been covered another is taken in the same way. After 
the whole " forty " has been covered addition of the 



PRACTICE OF TIMBER ESTIMATING 



177 



figures obtained gives its timber stand. In well-timbered 
land two to four " forties " a day can usually be covered 
by these methods. 

In recording the results of such an estimate the size 
and quality of the timber are of course noted as well as 
its amount, and general notes on the growth, topography, 
and lumbering conditions of the land are also recorded. 
Following are sample notes of such an exploration: 

Twp. 29 N. R. 7 W. S. E. i of S. E. i of Sec. 8. 



White Pine, 7 logs average to M.; 30% uppers 
Norway Pine, 8 logs to M. 
Hemlock, 11 logs to M. 
Basswood, 7 logs to M. 
Maple, 14 logs to M. 
Total 



835.000 

110,000 

175.000 

15,000 

65.000 

1,200,000 



Plot 



VI 



Plot 



Plot 



YII 



Plot 



IV 



Land slopes to North. Clay soil; very stony. Tv\o ra\Tnes 
running N. \Y. 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 oOO of his natural 
paces are required to go 80 
rods. He begins at the cor- 
ner of a " forty," say at the 
southeast corner, and steps 
off 125 paces on the south 
line, and so covers one- 
quarter of the side. He then 
stops and, facing north, 
counts the trees of the 
** forty," first to an estimated 
distance of 125 paces on the 
right hand, and then to an 
estimated distance of 125 
paces on the left hand, and 
in each case to a distance 
of 100 paces in front of him. thus including the area represented 
in the diagram as Plot I. He then steps north 100 paces, and 
in the same way counts the trees in Plot II, and repeats the opera- 
tion successively for Plots III, IV, and V. He has then a complete 
count of the trees on the eastern half of the " forty." He then 
walks west 250 paces along the north line of the " forty." Facing 
south, he now counts all the trees on Plots \T^, \TI, \Tn, IX, 
and X in the same way as before, and thus completes counting 
the trees on the entire " forty. " 



Plot 



Plot 



Plot 



VIII 



IX 



X 



Plot 



Plot 



Plot 



III 



II 



125 paces 



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 w^oods, 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 wiU 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 " apphes to a forty-acre tract. 

ArrivTing at the tract to be examined, I usually first go entirely 
around th^ 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 jx)ints at each 125 paces on the 
boundary. If the land is uniformly level, it is immaterial at which 
point on the boundary Hne the work is commenced. If the tract 
is very roUing, the strips taken must be run so as to cross the ridges 
at as nearly right angles as is possible. 



Sec.J?P._- T^3_N R3.1F— 

Co. .Cheboygan S>ta.te.MicJi 




Suppose we are at the southeast corner of the section and that we 
have an entire section of fahly level land to examine. My pacer 
and compassman (I have but one assistant) steps off 125 paces, 
say in a westerly du-ection, along the south hne 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 Une drawn dhectly north 
from this point should be parallel with the east line of the lot, also 
parallel with the center Une, if one were in existence, and 20 rods 
distant from each of them. We proceed north from this pomt. 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 talhes each kind under the proper heading. 



180 



A MANUAL FOR NORTHERN WOODSMEN 



Examination Lot. 1 Sec. _2£ 


} 






Made by. — May, 


1908.. 


C.L. 


Maple 


Bass 


Beech 


Hemlock \ 


12-1 
12-2 


III 


1 




























13-1 
13-2 


1 
II 






19 
6i 
























13-3 
14-1 


tH. 


'III 




ISO 
400 


1 






50 


HI nil 




450 


1 






50 


14-2 
14-3 


Ill 


1 




no 










1 






110 


1 




110 

1 


15-1 
15-2 


III 

tH 


ItHJI 




216 
1320 










III 




390 


1 
II 




72 
140 


15-3 
16-1 


































16-2 
16-3 


tWtHj 1 


III 


S64 
2520 


1 




180 


11, 1 
III 




576 
540 


III 




d32 


16-4 
































1 



As soon as the assistant reports that he is ready I take the 
nearest tree and put the calipers upon it at a point where it would 
be cut in ordinary logging operations. 1 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 fine. My caU})er blade is graduated to 57 
inches from the stationary arm, just ^th of two rods, and if there is 
any question as to a tree's being in the strip it is very quickly set- 
tled by taking seven lengths of the caliper blade as I walk toward 
the tree from the compass fine. 

Having taken the trees to a point a httle 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 fine 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 Une of the 
section, at a point 20 rods west of the northeast corner. As it 
rarely occurs that our compass line has been so accurate as to 
bring us out at exactly this point, we find the mark made during 



PRACTICE OF TIMBER ESTI^L\TING 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 1^411 be parallel with the center hne 
of lots 1, 8, 9, and 16, and with the west Hne 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. Arri\ing 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 caUper 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 exery 10 rods instead of 20 rods, which 
gives 5th 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 dumber of the strips taken. 

My volume table is of my own making. During the last twenty 
years I have been called upon verv 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 dm-ing 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 stmnp 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 caUper ehminates 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 \vdll get over a half -section in a day, and do it 
well if the timber is not too small and the undergrowi;h is not too 
dense. 

Sometimes I am called upon to give a rough estimate of a tract 
in a hurr}\ 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 w-e 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 suflS- 
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 WOODSMEN 

the appearance of timber; a man's condition also varies 
from day to day, affecting his judgment in this matter, as 
in every other. 

The above is the faculty of the old lumberman. On 
the other hand, the forester who has studied the rate of 
growth and the yield of timber has, in area, soil quality, 
and density of stocking, factors which he can profitably 
use to help him in his estimate of quantity. A fully stocked 
acre of white pine on good soil in Massachusetts, for in- 
stance, will yield at forty to sixty years of age a thousand 
feet of lumber for each year it has been growing, — a 
standard which a man may use to check the judgment 
through a considerable range of conditions. 

Ocular estimate has been spoken of as especially ap- 
propriate to small tracts of land, but as a matter of fact 
the methods and principles here stated are still employed 
to a large extent in the valuation of the largest tracts as 
well, and even for the purposes of sale and purchase. 
This is perhaps not as it should be, but it has at least 
partial justification in the fact that as business goes the 
amount of timber on a tract is not the only element in 
value ; often it is not the largest, even, for in addition 
availability, safety, the suitability of a tract to given pur- 
poses, and the financial situation of the parties concerned 
must all be considered. Sometimes a tract by reason of 
its relation to a given investment or manufacturing enter- 
prise really must be had, almost regardless of its timber 
resources ; while, on the other hand, though rich in timber, 
another tract may be dear at a small price. Accurate es- 
timates of the quantity of timber, therefore, may be a 
secondary matter. 

When large tracts are estimated by the eye, it is com- 
monly done on the basis of so much to the acre, either 
from the looks of the stand or by comparison with some 
similar tract already cut. Subdivisions, if they exist, might 
be estimated separately, and the estimated area of waste 
lands would then be thrown out of account. Some old 
lumbermen might also estimate by valleys, judging quan- 
tity from the density of the timber and the length of the 
roads necessary to operate it. 

6. Recount of the work done on a tract of 89 acres 



PRACTICE OF 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. 

6. 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 stafiF 
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 I'^OO acres. It lay in the 
form shown, with a ridge running down 
the middle of it, which naturally formed 
the first line of subdivision. The tract was 
therefore surveyed with compass and chain and a dividing 
line run along the ridge top. 

Then on each side of the ridge three distinct types of 
timber stand were recognized. The heaviest timber, red 
fir of good size, was in the middle; the north end was 
lighter, with a mixture of lodgepole pine; the south end 
had been damaged and rendered very thin by fire. These 
blocks were therefore blazed out and roughly surveyed. 
Thus the land was divided into six compartments of ap- 
proximately even stand and of known area. 




188 A MANUAL FOR NORTHERN WOODSMEN 

Then with a party of three men the supervisor ran 4-rod 
strip surveys ^ through each compartment, covering in each 
from 10 to 15 per cent of the area. Having no volume 
tables, he scored down instead the logs judged to be in the 
trees passed, in 16-ft lengths and by inch-diameter classes. 
In the office the contents of these logs were ascertained 
from the scale rule, multiplied by the number of each size, 
and added together. If then 10 per cent of a compartment 
had been covered, multiplying by 10 gave the stand of 
the compartment, which was the result desired. 

With trustworthy volume tables and calipers better re- 
sults could probably be had, but those here obtained were 
satisfactory. General good judgment is essential in carry- 
ing out such a survey, but, that given, a man can do it 
who has not had long woods and mill training. In fact, 
in the same forest one or two green but intelligent men are 
said to have been quickly trained so that their figures 
could be relied on within 10 or 15 per cent. 

2. The Strip System 

The strip system of estimating has been used rather 
widely in woods work, not infrequently in connection with 
land subdivision. As a survey party is running through 
the woods, it is sometimes made the duty of the chainmen 
to count the merchantable trees for a stated distance on 
each side of the line run, the contents of the trees being 
determined oftenest by an estimate of the number neces- 
sary to make up a thousand feet. The same system in 
effect is sometimes used by the cruiser who counts the 
trees passed within a certain distance as he travels across 
a lot, or the work may be done more elaborately, and the 
caliper and hypsometer introduced to any extent thought 
advisable. 

The methods of a Michigan cruiser who employs this 
system were described on page 178. Following are 
methods pursued on tracts of considerable size by a 
number of progressive concerns at the South dealing with 
pine and a variety of hard wood timbers. 

The strip lines are usually yi mile apart; they may be 
^ 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 caHper 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 dowTi 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 utihzation, 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 


4 


5 


6 


Contents in Feet Board Measure 


15 
16 

17 
IS 


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 ^ 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 forw'ard 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 caUpered 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 cahpered 
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 measm'ed principally in studying 
the question of future growth. 

FORM OF NOTES 

lj0ca\\tj..T.5.E.lS^Jj:.E..L.S.^Maine 

Tjipe-Hardwood. Slope.. J)a,te-Sept..TZ^1901 

Sheet '^o. A. 41 



D.B.H. 


Spruce 


Dead 


Fir 


White 
Birch 


Beech 


Hard 
Maple 


— ' 
Pine 


Popl. 


2 in. 


i^n 




N 












3 " 


r:. 
















4 " 


M . 






• 










5 " 


M. 
















6 " 








1^.. 








• 


7 " 


n 






M' 


. 








8 " 








^. 










9 " 


• 






i^:. 




. 




M. ■_ 


10 " 








, 










11 " 












• 




• 



On large tracts satisfactory estimates can be made by the 
measurement of about 1 out of every 30 acres. In very extensive 
forest tracts the Bureau of Forestry usually measures not more 
than one or two out of every hundred acres. 

This method is clearly adapted to securing knowledge 
of the make-up of a forest, and of its stand of merchant- 
able timber if good volume tables are at hand to go w'ith 
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 inches 
stump diameter in board feet; (6) smaller spruce down 
to 6 inches breast diameter in cords; (c) fir in cords; 
(d) cedar in feet B. M.; (e) pine; (/) good hard- wood 
logs. Number and contents of trees both given. 

This method of timber cruising may be employed on 
land areas of any size, and has been largely employed on 
areas of a mile square, or " sections." 



194 



A MANUAL FOR NORTHERN WOODSMEN 



To travel the boundaries of a square mile and twice 
across it, taking quarter acres each 20 rods as determined 
by pacing, gives about 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. 



f 


Sp. Logs 


Sp.Pij/p 


Fjr 


Cedar 


P/ne 


NardWood 




4- 4O0 


3 -.3 


/6-/S 


/2 -300 








9-/200 


2S-4- 












8-/80O 


2 


8-/ 






Soff wo 


ods or? f/af 


3-400 


7-1 






/-/oo 


/and, S/o 


ny dat 


3-SOO 


7-1 


34-4- 






5fnoof/7 


/o^gw^. 


10-2000 


7-.e 


24-3 


4-/00 




Adunc/an 


f reproducf-- 


3 -/300 


2-- 


9-/. 3 






/on of f/ 


7 yv/f/7 spruce 


8-/000 


7-1 


/2-/k 




2-300 


cS occasio. 


7a/p/r7e /> 


//- tsoo 


23- 2k 


8- / 






Ope/7//?^i 




8 - /OOO 


37-3 












S-800 


/S-2 


s-i 


Aastec 


• rods //7 


2-300 




3 -7 GO 


6:6 


4-.3 


mixed 


groiYi^/? 


S-900 




^!^.^^oo' 


S.4C 


4.7c 


/33' 


/33' 



























































































The last two methods described as usually employed 
are alike in this, that in the endeavor to get at a fair sample 
of the country they depend mainly on mechanical arrange- 
ments rather than choice. This as a general rule is a 
safe thing to do. There will always be enough things left 
to exercise the best judgment of the estimator. On the 
other hand, neither this nor any other system should be 
followed blindly. If part of the tract is especially valua- 
ble, especial pains should be taken with it. As a rule it 
will be found safe to ascertain the area of such tracts and 



' 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 are well tried methods of timber 
estimating and survey, but what has been wTitten 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 t>^e. 

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. QuaHty 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 
m the mill and m the woods to mere measuring." ^ The 
same is true where great differences in value are dependent 
upon quahty or grade. 

» Schenck's "Forest Mensuration." 



196 



A MANUAL FOR NORTHERN WOODSMEN 



8. Very bunchy timber can be estimated only in bmiches 
or tree by tree. No general system of lines or plots can 
be trusted to give safe results. 

9. In the emergencies which arise in actual business, 
a little rough and ready land surveying is often the most 
vital part of a reliable timber estimate. One or two lines 
run with compass and chain will frequently check areas 
of waste land or of different stand in effective fashion. 
Transit and stadia work on streams or roads often 
affords very material help. There is continual call for 
the sort of results that can best be obtained by means of 
compass and pacing. _^ 



D. Pacific Coast Methods 

Much Pacific Coast timber is 200 feet and over in height 
and of diameter to correspond, while the stand sometimes 
passes 20 million feet per quarter section. It is evident, 
therefore, that because of the values involved intensive 
methods of cruising are appropriate, while peculiarities 
of method are suggested by the very size and height of 
the timber. Of the region as a whole the portion west of 
the Cascade Mountains in Washington and Oregon, pro- 
ducing Douglas fir, "Oregon pine" as it was called form- 
erly, is most active and characteristic, and the following 
refers to that region unless specified otherwise. 

SUCCESSIVE LOGS IN A FIR 





Top 
Diam. 


Scale 


% of 
Total 


1st 32-foot log 

2nd 32-foot log 

3rd 32-foot log 

4th 32-foot log 

5th 32-foot log 

Total 


31 

28 
25 
20 
14 


1420 

1160 

920 

560 

230 


33 
27 
21 
14 
5 




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 ^ 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- 

^ Tables based on 16-foot logs are also in existence. 



198 A MANUAL FOR NORTHERN WOODSMEN 

tance measure; a vernier compass is usually employed 
for the sake of more accurate line running. Twenty to 
fifty per cent of the gross area is commonly covered by 
actual estimate, one hundred per cent in some cases. 
The unit party for the work consists of two men, compass- 
man and cruiser, of whom one handles distance, area, 
and topography, while the other is responsible for the 
timber. Details of practice vary much, as elsewhere, in 
accordance with the purpose of a cruise, conditions 
found, and the training of different estimators. Follow- 
ing is a description of a method as near standard as any, 
widely employed in work of high responsibility. 

a. Section lines are usually freshened up and re- 
chained, and a center line may be run through each sec- 
tion. The main purpose of this work is to set stakes for 
the guidance of the cruising party. It is so laid out that 
the actual cruise or estimating lines will run as nearly 
as may be across the features of the topography. 

b. The cruising party, starting at one corner of the 
section to be examined, proceeds to the nearest stake, 
2}/2 chains from it, whence the compassman, with the 
declination set off in his staff compass, travels parallel 
to the side line of the section, keeping account of his 
pacing, taking aneroid readings at changes of the ground, 
and sketching topography. Behind him follows the cruiser, 
who for a wadth 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, 73^ chains from the corner, from which point a 
parallel line is run in the opposite direction. Four such 
lines are run across each tier of forties. With 16 such 
lines the cruise of the section is completed. 

c. The detail of the estimating work is as foUows: — 
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. Li 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 teUs something 
as to log quaUty 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 XOTES 
(Usually made on celluloid sheets) 



Fir 


Dead 

& 
Down 


Cedar 


D&D 


Hem. 


Spruce 


Poles 


Fir 


Hem. 


Cedar 


2-6 M 
1-2.5 
6-30 
2-7.5 


2 
1.5 


1-.7 
1-.4 
1-3. 


.s 


1-1.5 
2-2.5 
1-.3 
1-1. 


1-5 M 


1 

Ave 
9'di 


1 

Tage 45 
am. at i 


111 

'long 
niddle 



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 ad\'ice or directions. 

Two miles of line per day are the standard product 
for tliis method of cruising, giving eight working days to 



200 A MANUAL FOR NORTHERN WOODSMEN 

the section, which involves a cost of about 25 cents per 
acre outside of the checking, overhead and office work. 
Ordinary variations are : — 

a. Double running each forty instead of running four 
times through it as above, a method widely practiced as 
costing less and considered sufficiently accurate in many 
circumstances. The cruise lines in this case are started 
5, 15, 25, etc. chains from the section corner to divide 
the area equally. Sometimes, also, the strip is widened. 

b. 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 foUow 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 miiform 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 half the width, and we find that the basis of much of the 
error that occurs in our work is due to inaccurate tree counting. 

If the timber is large and particularly accurate results are de- 
sired, we now run 12 times through each forty and frequently work 
between blazed lines. That is, instead of running through the 
middle of the strip, the 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, imder certain conditions where we have a uniform 
stand of large timber, we run 4 times, taking strips equivalent 
to one-tweKth of a forty. This plan, we believe, gives better results 
than two strips each covering ^ 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 ^Tong. 

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 w^hich 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 scaler contain at least 50 j>er 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 scaler, 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 scaler, suitable 
for the manufacture of Common lumber. 

Cull logs shall be any logs which in the judgment of 
the scaler will not cut 333/^ per cent of sound timber. 

An essential to reliable timber grading is experience, a 
background of knowledge of the out-turn of similar tim- 
ber. In the next place, close examination of the stand 
is required as to the number and size of limbs and knots 
and for indications of these, or of other defects, that 
may lie beneath the surface. Age is a help here (these 
stands are commonly even-aged over considerable areas). 
Many cruisers go no farther than this and set percentage 
figures for log grades as the result of a broad judgment. 

When further detail is thought desirable, the volume 
tables before mentioned are of assistance, giving as some 
of them do for a tree of given diameter, taper, and mer- 
chantable length the percentage each successive 32-foot 
log bears to total contents. One standard volume table 
contains the following directions : — 

"Determine the percentages of the different grades as 
contained in a given percentage of the trees on each 40 
acres by selecting, for instance, an average tree on each 
tally and carefully determining the percentage of the 
different grades of logs contained in these sample trees 
and applying the average to all trees on the forty." 

To illustrate, in the notes on page 199, 11 trees, 46 M 
feet, are scored down in the column of living fir, giving an 
average volume of 4200. 4 inches taper and 4 logs may fit 
this timber; if so, a tree yielding 4330 feet (see extract from 
taper table) gives a close approximation. Of such a tree 
a 32' butt log constitutes 37 per cent, the second log 28 



204 



A MANUAL FOR NORTHERN WOODSMEN 



per cent, and the third 21 per cent, while top diameters 
are approximately 33, 29 and 25 inches respectively. 
One of these logs is large enough for No. 1 ; it may or may 
not be clear enough. Second and third logs are of suffi- 
cient size, and likely to be of a quality, to put them in 
the second grade. 

Methods in this branch of the work, however, vary 
greatly. A few, in the endeavor to reduce the field of 
judgment, have gone into much detail and devised forms 
of notes which record trees by sizes and log grades in each 
tree as its contents is estimated. Of the percentage of 
successive logs, it may be said that the above relations 
are fairly typical — that is to say in normal fir timber 
large enough so that log grades are of importance, about 
35 per cent of the total contents of trees is contained in 
the butt log if cut 32 feet long, the second log will add 
25 to 30 per cent more, and about 20 per cent will be 
in the third log. Breakage and defect may throw out 
these relations, and they are different in extremely tall 
or short timber. 



Butt 
Diam. 

Inches 


fa 

CO 

.9 

u 


3 Logs or 96 Feet 


4 Logs or 128 Feet 






Logs 






Logs 


















Is 




Contents 


-ki 








Contents 






Ti 


J 




H 


S 

03 


B. M 


t» 


-3 


CO 


s 


B. M 


03 


-a 


CO 


■* 




3 


Q 




65 




^ 


Q 




65 


65 

27 


65 
22 


65 
18 




28 


4230 


40 


33 


27 


25 


5128 


33 




4 


25 


3714 


43 


33 


24 


21 


4330 


37 


28 


21 


14 




6 


22 


3234 


46 


33 


21 


17 


3610 


42 


29 


19 


10 


37 


6 

7 
8 
9 


19 
16 
13 
10 


2790 
2386 
2029 
1729 


50 
55 
60 
66 


32 
32 
31 

28 


18 
11 
09 
06 


13 


2979 


47 


30 


17 


06 



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 quaUty 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 been found already that logs graded by the same man 
under the same rules vary considerably by locality in 
their yield of high grade lumber. 

Yellow Pine Log Grades of the U. S. Forest Service. 

Clear logs shall be 22 inches or over in diameter inside 
the bark at the small end and not less than 10 feet long. 
They shall be reasonably straight-grained, practically 
surface clear, and of a character which m the judgment 
of the scaler 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 scaler 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 scaler 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 foregomg 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 
quahty, play in the value of timber is an essential service. 
Then it is true and worthy of regard that in these cir- 
cumstances simple methods may actually give the best 
results. 

A man may learn much in a logging operation where 
timber similar to that he is concerned with can be ex- 
amined after it is felled and bucked into logs. He can 
see how much is broken up, whether the timber is rotten 
or sound, and from the cross cuts and surface indications 
of the logs examined at close range get an idea of the prev- 
alence of knots, shakes and other blemishes. Then he 
can scale up the logs from a number of trees, ascertain- 
ing the total length utilized and the quantity of mer- 
chantable timber derived from each tree. This he will 
attach to its length and base diameter and endeavor to 
link up with trees of similar dimensions standing. 

Such work as this will enable a man to understand a 
volume table, and he may even get enough measures to 
make one for himself in some size groups, with which he 
may check published volume tables. Or old devices and 
short cuts^ may be tried out with the idea of sharpening 

^ 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 tliis 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.^ 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 cruismg, is only an expedient; still, carried out by 
a clear-headed man, it might really be worth more than 
what passes oftentimes as somethmg more ambitious. 
Such a man, too, can sometimes find out what he wants 
to know, or manage to protect his otsti 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. 

^ 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 Tri.angles 212 

3. Traverse Tables 214 

4. Logarithms of Nuimbers 220 

o. Logarithmic Sixes, Cosines, Tangents, and Co- 

t-angents 222 

6. Supplementary Tables of Small Angles .... 228 

7. Natural Sines and Cosines 230 

8. Natural Tangents and Cotangents 232 

9. SpEcr\iEN Lettering 234 



TABLES RELATING TO PARTS I AND II 211. 



STADIA REDUCTIONS 

Horizontal Distance 



0' 

1 


10' 


20' 


30' 


40' 


50' 




0' 


10' 20' 30' I 40' 1 50' 


I ' ! 

0= 100.0 100.0 100.0 100.0 


100.0 


100 16° 


92.4 


! 1 
92.3 92.1 91.9 


91.8 91.6 


1° 100.0 


100.0 


99.9 


99.9 


99.9 


99.9 


117° 91.5 


91.3 91.1 91.0 


S0.8 90.6 


2°l 99.9 


99.8 


99.8 


99.8 


99.8 


99.8 


il8° 90.4 


90.3 90.1 89.9 


89.8 89.6 


3° 


99.7 


99.7 


99.7 


99.6 


99.6 


99.6 


;19° 89.4 


89.2 89.0 88.9 


88.7 88.5 


4° 


99.5 


99.5 


99.4 


99.4 


99.3 


99.3 


20° 88.3 


88.1 87.9 


87.7 


87.5 87.3 


5° 


99.2 


99.2 


99.1 


99.1 


99.0 


99.0 


21° 87.2 


87.0 86.8 


86.6 


86.4 86.2 


6° 


98,9 


98.9 


98.8 


98.7 


98.6 


98.6 


22° 86.0 


85.8 85.6 


85.4 


85.2 84.9 


7° 


98.5 


98.4 


98.4 


98.3 


98.2 


98.1 


!23°'84.7 


84.5 84.3 


84.1 


83.983.7 


8° 


98.1 


98 


97.9 


97.8 


97.7 


97.6 


24° 83.5 


83.2 83.0 


82.8 


82.6 82.4 


9° 


97.5 


97 5 


974 


97.3 


97.2 


97.1 


25° 82.1 


81.9 81.7 


81.5 


81.2181.0 


10= 


97 


96.9 


96.8 


96.7 


96.6 


96.5 


26° 80.8 


80.6 80.3 


80.1 


79.9179.6 


11° 


96.4 


96.3 


96.1 


96.0 


95.9 


95.8 


27°i79.4 


79.2 78.9 


78.7 


78.478.2 


12° 


95.7 


95.6 


95.4 


95.3 


95.2 


95.1 


28° 178.0 


77.7 77.5 


77.2 


77.0|76.7 


13° 


94.9 


94*8 


94.7 


94.5 


94.4 


94.3 


29°;76.5 


76.2176.0 


75.7 


75.5i75.2 


14° 


94.2 


94.0 


93.9 


93.7 


93.6 


93.4 


30°i75.0 


74.7 74.5 


74.2 


74.0 


V3.V 


15° 


93.3 


93.2 


93.0 


92.9 


92.7 


92.6 















Difference of Elevation 





Proportional Parts 




0' 


10' 


20' 


30' 


40' 


50' 


1' 


2' 


3' 


4' 


5' 


6' 


7' 


8' 


9' 


0° 


0.00 ' 0.29 


i 1 ! 

0.58' 0.87 1.16 1.45 


.03 '.06 


.09 


.12 


.14 


.17 


.20 


.23 


.26 


1° 


1.74 2.04! 2.331 2.62 2.9li 3.20| 


.03 .06 .09 


.12 .14 


.18 .20.23 


.26 


2° 


3.49 3.78 4.07 


4.36 


4.65, 4.94 


.03 .06 .09 


.12 .14 .171.20 .23 


.26 


3° 


5.23 5.52 5.80 


6.09 


6.381 6.67 


.03 .06 .09 


.12, .14 


.17 .20 .23.26 


4° 


6.96 7.25; 7.53 


7.82 


8.111 8.40 


.03 .06 .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 .231.25 


6° 


10.40 10.6810.96 11.25 11.53 11.81 1 


.03 .06 .08 .111.14 


.17 .20 .23 


.25 


7° 


12.10,12.38 12.66 12.94 13.22 13.50 


.03 .06 .08 .11 


.14 


.17 


.201.22 


.25 


8° 


13.78|l4.06ll4.34 14.62 14.90 15.17 


.03 .06 .08 .11 


.14 


.17 


•19-22 


.25 


9° 


15.45 15.73 16.00 16.28 


16.55 16.83 


.03 .06 .08 


.11 


.14 


.17 


.19 


.22 


.25 


10° 17.10 17.37 17.65 17.92 


18.19 18.46 


.03 .05 .08 


.11 


.14 


.16 


.19 


.22 


.24 


11° 18.73 19.00 19.27 19.54 


19.80 20.07 


1.03 .05 .08 


.11 


.13 


.16 


.19 


.21 


.24 


12° 20.34 20.80 20.87 21.13 


21.39 21.66 


j.03 .05 .08 .11 


.13 


.16 


.18 


.21 


.24 


13° 21.92 22.18 22.44 22.70 22.96 23.22 


1.03.05 .08 .10 .13 


.16 .18 .211.23 


14° 23.47 23.73 23.99 24.24 24.49 24.75 


.03 .05 .08.10 .13 


.15 .18 .20 .23 


15° 25.00 25.25 25.50 25.75 26.00 26.25 


.03 .05 .07 .10 .13 


.15.17 .20.23 


16° 26.50 26.74 26.99 27.23 27.48 27.72 


.02 .05 .07 .10 .12 .15 .17.20 


.22 


17° 127.96 28.20 28.44 28.68 28.92 29.15 


.02 .05L07j.lO .12 .141.17 


.19 


.21 


18° '29.39 29.62 29.86 30.09 30.32 30.55 


.02 .05 .07i.09 .121.141.16 


.19 


.21 


19° 30.78 31.01 31.24 31.47 31.69131. 92 


1.02 .05 .07 .09 .11:. 141 16 .18 


.21 


20° 32.14 32.36 32.58 32.80 33.02133.24 


.02.04 .07 .09 .11 .13 .15i.l8 


.20 


21° 


33.46 '33.67 33.89 34.10 34.31 34.52 


.02 .04 .06 .08 .111.13 .15 


.17 


.19 


22° 


34.73 34.94 35.15 35.36 35.56 35.76 


.02 .04 .06 .08 .10 .12 .14 


.16 


.19 


23° 


35.97 36.17 36.37 36.57 36.77i36.96 


.02 .04 .06 .08 .10,. 12 .14 


.16 


.18 


24° 


37.16 37.35 37.54 37.74 37.93 38.11 


.02 .04 .06 .08 .09 .11 .13 


.15 


.17 


25° 


38.30 38.49 38.67 38.86 .39.04|39.22 


.02 .04 .06 .07 .091.11 .13 


.15 


.17 


26° 


39.40 39.58 39.76 39.93 40.11 40.28 


.02 .04 .05 .07 .09 .11 .121.14 


.16 


27° 


40.45 40.62 40.79 40.96 41.12 41.29 


.02 .03 .05 .07 .08 .10.12.13 


.15 


28° 


41.45 41.61141.77,41.93 42.09 42.25 


i.02 .03 .05 .06 .081.10 .11 .13 


.14 


29° 


42.40 42.56 42.71 42.86 43.01 43.16 


.02 .03 .05 .06 .08 .09 .11 .12 .14 


30° 143.30 43.45 43.59 43.73 43.87 44.01 

1 


.01 .03 .04 .06 .07 .09 .10 .11|.13 

1 1:1 



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 
BAC are respect- 





of the angle 
triangle ABC are as follows : 



ively the sme, 

secant, and tangent of CAD, the 

complement of BAC. 

Represented as ratios, the functions 
A in the right-angled 



Sine A = 



CB 
AC 



Cosine A 



AB 
AC 



Tangent -^ = — 



Secant A = —r= 
AB 



By these formulas, and the use of the tables of sines and 
tangents, all the parts of any right-angled triangle may be 
obtained if two sides, or an acute angle and a side, are 
given. 

All the parts and the area of an 
oblique triangle may be obtained if 
any three parts including one side 
are given. Let A, B, C represent 
the angles, and a, 6, c the opposite 
sides, of any oblique triangle ; then . 
the solutions are as given on the 
next page. 




TABLES RELATING TO PARTS I AND II 213 



Given 



A, B, a 



A, a, b 



A,B,C,a 

C, a, h 



a, 6, c 



Sought 



C,h,c 



B,C,c 



Area 

m+B) 

i{A-B) 

A 
B 



Area 
A 



B, C 
Area 



C = 180° - (A + B) 
6= ^ 



c = 



sin B = 
C 



sin B 

. sin C 
sin A 

b sin A 



sin ^ 
a 



180° - (.4 + B) 
a sin C 



c = 



sin A 

. €? sin B sin C 

Area = ; 

2 sin A 

J (^ + 5) = 90° - i C 






cos \{A ^tB) 



= {a-b) 



cos i (vl - B) 
sin i (A + 5) 



sin i{A - B) 
Area = ^ o 6 sin C 
Let s = i (a + 6 + c) 



rw,, . 1 X i/(* — b) (s — c) 

Then sin iA = V ^ ^ 

be 



cos ^^ 



./ g (g - g) 
^ be 



5 (5 — a) 
Similar formulas 
Vs (5 — a) {s — b) (5 — c) 



214 



TRAVERSE TABLE 



Course 


Dist. 1 1 


j Dist. 2 1 


Dist. 3 1 


Dist. 4 1 


Dist. 5 


89 45 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


O ' 

15 


1.0000 


0.0044 


2.0000 


0.0087 


3 0000 


0.0131 


4.0000 0.0175 


5.0000 


0.0218 


30 


0000 


0087 


19999 


0175 


2.9999 


0262 


3.9998 


0347, 


4.9998 


0436 


30 


45 


0.9999 


0131 


9998 


0262 


9997 


0393 


9997 


0524 [ 


9990 


0654 


15 


1 


9998 


0175 


9997 


0349 


9995 


0524 


9994 


0698; 


9992 


0873 


89 


15 


9998 


0218 


9995 


0436 


9993 


0654 


9990 


0873 


9988 


1091 


45 


30 


9997 


0262 


9993 


0524 


9990 


0785 


9986 


1047} 


9983 


1309 


30 


45 


9995 


0305 


9991 


0611 


9986 


0916 


9981 


1222 


9977 


1527 


15 


2 


9994 


0349 


9988 


0698 


9982 


1047 


9976 


1396 


9970 


1745 


88 


15 


9992 


0393 


9985 


0785 


9977 


1178 


9969 


1570 


9961 


1963 


45 


30 


9990 


0436 


9981 


0872 


9971 


1309 


9962 


1745 


9952 


2181 


30 


45 


0.9988 


0.0480 


1.9977 


0.0960 


2.9965 


0.1439 


3.9964 


0.1919 


4.9942 


0.2399 


15 


3 


9986 


0523 


9973 


1047 


9959 


1570 


9945 


2093 


9931 


2617 


87 


15 


9984 


0507 


99G8 


1134 


9952 


1701 


9936 


2268 


9920 


2835 


45 


30 


9981 


0610 


9963 


1221 


9944 


1831 


9925 


2442 


9907 


3052 


30 


45 


9979 


0654 


9957 


1308 


9936 


1962 


9914 


2616 


9893 


3270 


15 


4 


9976 


0698 


9951 


1395 


9927 


2093, 


9903 


2790 


9878 


3488 


86 


15 


9973 


0741 


9945 


1482 


9918 


2223 


9890 


2964 


9863 


3705 


45 


30 


9969 


0785 


9938 


1569 


9908 


2354; 


9877 


3138 


9846 


3923 


30 


45 


9966 


0828; 


9931 


1656 


9897 


2484 


9863 


3312 


9828 


4140 


15 


5 


9962 


0872 


9924 


1743 


9886 


2615 


9848 


3486 


9819 


4358 


85 


15 


0.9958 


0.0915 


1.9916 


0.1830 


2.9874 


0.2745 


3.9832 


0.3660 


4.9790 


0.4575 


45 


30 


9954 


0958 


9908 


1917 


9862 


2875 


9816 


3834 


9770 


4792 


30 


45 


9950 


1002 


9899 


2004 


9849 


3006 


9799 


4008 


9748 


5009 


15 


6 


9945 


1045 


9890 


2091 


9836 


3136 


9781 


4181 


9726 


5226 


84 


15 


9941 


1089 


9881 


2177 


9822 


3266 


9762 


4355 


9703 


5443 


45 


30 


9936 


1132 


9871 


2264 


9807 


3396 


9743 


4528 


9679 


5660 


30 


45 


9931 


1175 


9861 


2351 


9792 


3526 


9723 


4701 


9653 


5877 


15 


7 


9925 


1219 


9851 


2437 


9776 


3656 


9702 


4875 


9627 


6013 


83 


15 


9920 


1262 


9840 


2524 


9760 


3786 


9680 


5048 


9600 


6390 


45 


30 


,, 991* 


1305 


9829 


2611 


9743 


3916 


9658 


5221 


9572 


6526 


30 


45 


0.9909 


0.1349 


1.9817 


0.2697 


2.9726 


0.4040 


3.9635 


0.5394 


4.9543 


0.6743 


15 


8 


9903 


1392 


9805 


2783 


9708 


4175 


9611 


5561 


9513 


6959 


82 


15 


9897 


1435: 


9793 


2870 


9G90 


4305 


9586 


5740 


9483 


7175 


45 


30 


9890 


1478 


9780 


2956 


9670 


4434 


9561 


5912 


9451 


7390 


30 


45 


9884 


1521 


9767 


3042 


9651 


4564 


9534 


6085 


9418 


7606 


15 


9 


9877 


1504 


9754 


3129 


9631 


4693 


9508 


6256 


9384 


7822 


81 


15 


9870 


1607 


9740 


3215 


9610 


4822 


9480 


6430 


9350 


8037 


45 


30 


9863 


1050 


9726 


3301 


9589 


4951 


9451 


6602 


9314 


8252 


30 


45 


9856 


1693 


9711 


3387 


9567 


5080 


9422 


6774 


9278 


8467 


15 


10 


9848 


1736 


9696 


3473 


9544 


5209 


9392 


6946 


9240 


8682 


80 


15 


0.9840 


0.1779 


1.9681 


0.3559 


2.9521 


0.5338 


3.9362 


0.7118 


4.9202 


0.8897 


45 


30 


9833 


1822! 


9665 


3645 


9498 


5467 


9330 


7289 


9163 


9112 


30 


45 


9825 


1865 


9849 


3730 


9474 


5596 


9298 


7461 


9123 


9326 


16 


11 


9816 


1908, 


9633 


3816 


9449 


5724 


9265 


7632 


9081 


9540 


79 


15 


9808 


1951 


9616 


3902 


9424 


5853 


9231 


7804 


9039 


9755 


45 


30 


9799 


1994 


9598 


3987 


9398 


5981 


9197 


7975 


8996 


9968 


30 


45 


9790 


2036 


9581 


4073 


9371 


6109 


9162 


8146 


8952 


1.0182 


16 


12 


9781 


2079 


9563 


4158 


9344 


6237 


9126 


8316 


8907 


0390 


78 


15 


9772 


3122 


9545 


4244 


9317 


6365 


9089 


8487 


8862 


0609 


45 


30 


9763 


2164. 


9526 


4329 


9289 


6493 


9052 


8658 


8815 


0822 


30 


45 


0.9753 


0.2207 


1.9507 


0.4414 


2.9260 


0.6621 


3.9014 


0.8828 


4.8767il.l035 


15 


13 


9744 


2250; 


9487 


4499 


6231 


6749 


8975 


8998 


8719 


1248 


77 


15 


9734 


2292 


9468 


4584 


9201 


6876 


8935 


9168 


8069 


1460 


45 


30 


9724 


2334 


9447 


4669 


9171 


7003 


8895 


9338 


8618 


1672 


30 


45 


9713 


2377 


9427 


4754 


9140 


7131 


8854 


9507 


8567 


1884 


15 


14 


9703 


2419 


9406 


4838 


9109 


7258 


8812 


9677 


8515 


2096 


76 


15 


9692 


24G2 


9385 


4923 


9077 


7385 


8769 


9846 


8462 


2308 


45 


30 


9681 


2504 


9363 


5008 


9044 


7511 


8726 


1.0015 


84(.7 


2519 


30 


45 


9670 


2546 


9341 


5092 


9041 


7638 


8682 


0184 


8352 


2730 


15 


15 


9659 


2588 


9319 


5176 


8978 


7765 


8637 


0353 


8296 


2941 


75 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Course 




Dist. 1 


Dis 


t. 2 


Dist. 3 


Dist. 4 


1 Dist. 5 



TRAVERSE TABLE 



215 



Course 


1 Dist. 6 


Dist. 7 


1 Dist. 8 1 


Diet. 9 


' Dist. 10 




Lat. 


Dep. 


Lat. , Dep. 


Lat. 


Dep. 


Lat. 
8.9999 


Dep. 
0.0393 


Lat. 
9.9999 


Dep. 


^0 15 15. 9999 


0.0262 


6.9999 0.0305 


7.9999 


0.0349 


0.0436189 45 


30 


9998 


0524 


9997 0611 


9997 


0698 


9997 


0785 


9996 


0873 30 


45 


9995 


0785i 


9994 0916 


i 9993 


1047 


9992 


1178 


9991 


1309 15 


1 


9991 


10471 


9989 1222 


9988 


1396 


9986 


1571 


9985 


1745 89 


15 


9986 


1309 


9983 


15271 


9981 


1745 


9979 


1963 


9976 


2181 


45 


30 


9979 


1571 1 


9976 


1832 


9973 


2094 


9969 


2356 


9966 


2618 


30 


45 


9972 


1832 


9967 


2138 


1 9963 


2443 


9958 


2748 


9953 


3054 


15 


2 


9963 


20941 


9957 


2443 


9951 


2792 


9945 


3141 


9939 


3490 


88 


15 


9954 


2356 


9946 


2748 


t 993S 


3141 


9931 


3533 


9923 


3926 


45 


30 


9943 


2617 


9933 1 3053 


9924 


3490 


9914 


3926 


9905 


4362 


30 


45 


5.9931 


0.2879 


6.9919 0.3358 


7.9908 


0.3838 


8.9896 


0.4318 


9.9885 


0.4798 


15 


3 


9918 


3140; 


9904 


3664 


i 9890 


4187 


9877 


4710 


9863 


5234 37 


15 


9904 


3402 


9887 


3968 


■ 9871 


4535 


9855 


5102 


9839 


5669 45 


30 


9888 


3663 


9869 


4273 


9851 


4884 


9832 


5494 


9813 


6105 30 


45 


9872 


3924 


9850 


4578' 


1 9829 


5232 


9807 


5886 


9786 


6540 15 


4 


9854 


4185 


9829 


4883 


! 9805 


5581 


9781 


0278 


9756 


6976 80 


15 


9S35 


4447 


9808 


5188 


9780 


5929 


9753 


6670 


9725 


7411 


45 


30 


4815 


4708 


9784 


5492 


9753 


6277 


9723 


7061 


9692 


7846 


30 


45 


9794 


4968 


9760 


5797 


9725 


6625 


9691 


7453 


9657 


8281 


15 


5 


9772 


5229 


9734 


6101 ; 


9696 


6972 


9658 


7844 


9619 


8716 85 


15 5.9748 


0.5490 


6.9706 0.6405 


7.9664 


0.7320 


8.9022 


0.8235 


9.9580 


0.9150 45 


30 9724 


5751 


9678 


6709 


! 9632 


7668 


9586 


8626 


9540 


9585 30 


45 9698 


6011 


9648 


7013; 


9597 


8015 


9547 


9017 


9497 


1.0019 15 


6 9671 


6272 


9617 


7317: 


9562' 8362 


9507 


9408 


9452 


0453 84 


15 9643 


6532 


9584 


7621 1 


9525! 8709 


94C5 


9798 


9406 


0887 45 


30 9014 


6792 


9550 


7924 


t 94S6 9056 


9421 


1.01S8 


9357 


1320 30 


45 9584 


7052 


9515 


8228; 


9445 


9403 


5378 


0578 


9307 


1754 15 


7 9553 


7312 


9478 8531' 


9404 


9750 


9329 


0968 


9255 


2187 83 


15 9520 


7572 


9440 


8S34 


9360 


1.C096 


9280 


1358 


9200 


2620 : 45 


30 9487 


7832 


9401 


9137 


9316 


0442 


9230 


1747 


9144 


3053 30 


45 5.9452 


0.8091 


6.9361 0.9440' 


7.9269 


1.0788 


8.9178 


1.2137 


9.9087 


1.3485 15 


8 


9416 


8350 


93191 9742 


9221 


1134 


9124 


2526 


9027 


3917 82 


15 


9379 


8610 


927611.0044 


' 9172 


1479 


9069 


2914 


8965 


43491 45 


30 


9341 


8869 


9231 


0347 


9121 


1825 


9011 


3303 


8902 


4781 30 


45 


9302 


9127 


9185 


0649 


, 9009 


2170 


8953 


3G91 


8836 


5212I 15 


9 


9261 


9386 


9138 


0950 


9015 


2515 


8892 


4079 


8769 


5643 81 


15 


9220 


9645 


9090 


1252 


i 8960 


2859' 


8830 


4467 


8700 


6074 45 


30 


9177 


9903 


9040 


1553 


8903 


3204 


8766 


4854 


8629 


65051 30 


45 


9133 


1.0101 


8989 


1S54 


8844 


3548 


8700 


5241 


8556 


6935 15 


10 


9088 


0419 


8937 


2155 


8785 


3892| 


8033 


5628 


8481 


7365 80 


15 5.9042 


1.0677 


6.8883 


1.2456 


7.8723 


1.4235 


8.8564 


1.6015 


9.8404 


1.7794j 45 


30 


8995 


0934 


8728 


2756 


8660 


4579 


8493 


6401 


8325 


82241 30 


45 


8947 


1191 


8772 


3057 


1 8696 


4922 


8421 


6787 


8245 


8652' 15 


11 


8S98 


1449 


8714 


3357 


8530 5265 


8346 


7173 


8163 


9081 79 


15 


8847 


1705 


8655 


3656 


8463 5607 


8271 


7558 


8079 


9509 45 


30 


8795 


1962 


8595 


3956 


8394 


5949 


8193 


7943 


7992 


9937: 30 


45 


8743 


2219 


8533 


4255 


8324 


6291 


8114 


8328 


7905 


2.0364 15 


12 


8689 


2475 


8470 


4554 


8252 


6633 


8033 


8712 


7815 


079178 


15 


8634 


2731 


8406 


4852 


8178 


6974 


7951 


9096 


7723 


1218i 45 


30 


8578 


2986 


8341 


5151 


8104 7315 


7867 


9480 


7630 


1644 30 


45 5.8521 


1.3242 


6.8274 1.5449 


7.8027 


1.7656 


8.7781 


1.9863 


9.7534 


2.2070' 15 


13 0; 8462 


3497 


8206 5747 


7950 


7996: 


7693 


2.0246 


7437 


2495 77 


15; 8403 


3752 


8137 6044 


7870 


8336' 


7604 


0628 


7338' 


2920 45 


301 8342 


4007 


8066 


6341 


7790] 8676' 


7513 


1010 


7237: 


3345 30 


45 j 8281 


4261 


7994 


6638 


, 77071 9015 


7421 


1392 


7134! 


3769 15 


14 8218 


4515 


7921 


6935 


7624' 9354 


7327 


1773 


7030 


4192 76 


15 [ 8154 


4709 


7846 


7231 


. 7538: 9692 


7231 


2154 


6923 


4615 45 


30, 8089 


5023 


7770 


7527 


7452 2.0030 


7133 


2534 


6815 


5038 30 


45 


8023 


5276 


7693 


7822 


7364, 0368 


7034 


2914 


6705 


5460 15 


15 


7956 


5529 


7615 


8117 


7274' 0706; 
1 


6933 


3294 


6593 


5882,75 





Dep. 


Lat. 


Dep. 


Lat. 


Dep.|, Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


jQurse 


Dist. 6 1 


1 Dist. 7 1 


Diet. 8 


Dist. 9 1 


Dist. 10 1 



216 



TRAVERSE TABLE 



Course 


Dist. 1 


Dist. 2 


Dist. 3 


Dist. 4 


Dist. 5 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
2.8944 


Dep. 


Lat. 


Dep. 


Lat. 
4.8239 


Dep. 
1.3152 




15 15 


0.9648 


0.2630 


1.9296 


0.5261 


0.7891 


3.8591 


1.0521 


74 45 


30 


9636 


2672 


9273 


5345 


8909 


8017 


8545 


0690 


8182 


3362 


30 


45 


9625 


2714 


9249 


5429 


8874 


8143 


8498 


0858 


8123 


3572 


15 


16 


9613 


2756 


9225 


5513 


8838 


8269 


8450 


1025 


8063 


3782 


74 


15 


9600 


2798 


9201 


5597 


8801 


8395 


8402 


1193 


8002 


3991 


45 


30 


9588 


2840, 


9176 


5680 


8765 


8520 


8353 


1361 


7941 


4201 


30 


45 


9576 


2882 


9151 


5764 


8727 


8646 


8303 


1528 


7879 


4410 


15 


17 


9563 


2924' 


9126 


5847 


8689 


8771 


8252 


1695 


7815 


4619 


73 


15 


9550 


2965 


9100 


5931 


8651 


8896 


8201 


1862 


7751 


4827 


45 


30 


9537 


3007 


9074 


6014 


8612 


9021 


8149 


2028 


7686 


6035 


30 


45 


0.9524 


0.3049 


1.9048 


0.6097 


2.8572 


0.9146 


3.8096 


1.2195 


4.7620 


1.5243 


15 


18 


9511 


3090 


9021 


6180 


8532 


9271 


8042 


2361 


7553 


5451 


72 


15 


9497 


3132 


8994 


6263 


8491 


9395 


7988 


2527 


7485 


5678 


45 


30 


9483 


3173 


8966 


6346 


8450 


9519 


7933 


2692 


7416 


5865 


30 


45 


9469 


3214 


8939 


G429 


8408 


9643 


7877 


2858 


7347 


C072 


15 


19 


9455 


3256 


8910 


6511 


8366 


9767 


7821 


3023 


7276 


6278 


71 


15 


9441 


3297 


8882 


6594 


8323 


9891 


7764 


3188 


7204 


6485 


45 


30 


9426 


3333 


8853 


6676 


8279 


1.0014 


7706 


3352 


7132 


6690 


30 


45 


9412 


3379 


8824 


6758 


8235 


0138 


7647 


3517 


7059 


6896 


15 


20 


9397 


3420 


8794 


6840 


8191 


0261 


7588 


3681 


6985 


7101 


70 


15 


0.9382 


0.3461 


1.8764 


0.6922 


2.8146 


1.0384 


3.7528 


1 .3845 


4.6910 


1.7306 


45 


30 


9367 


3502 


8733 


7004 


8100 


0506 


7467 


4008 


6834 


7510 


30 


45 


9351 


3543 


8703 


7086 


8054 


0629 


7405 


4172 


6757 


7715 


15 


21 


9336 


3584 


8672 


7167 


8007 


0751 


7343 


4335 


6679 


7918 


69 


15 


9320 


3624 


8640 


7249 


7960 


0873 


7280 


4498 


6600 


8122 


45 


30 


9304 


3666 


8608 


7330 


7913 


0995 


7217 


4660 


6521 


8325 


30 


45 


9288 


3706 


8576 


7411 


7864 


1117: 


7152 


4822 


6440 


8528 


15 


22 


9272 


3746 


8544 


7492 


7816 


1238! 


7087 


4984 


6359 


8730 


68 


15 


9255 


3786 


8511 


7573 


7766 


1359 


7022 


6146 


6277 


8932 


45 


30 


9239 


3827 


8478 


7654 


7726 


1481 j 


6955 


5307 


6194 


9134 


30 


45|0.9222'0.3867l 


1.8444 


0.7734 


2.7666 


1.1601 


3.6888 


1.5468 


4.6110 


1.9336 


15 


23 


9205 


3907 


8410 


7815 


7615 


1722 


6820 


5029 


6025 


9537 


67 


15 


9188 


3947 


8376 


7895 


7564 


1842 


6752 


5790 


5940 


9737 


45 


30 


9171 


3987 


8341 


7975 


7512 


1962 


6682 


5950 


5853 


9937 


30 


45 


9153 


4027 


8306 


8055 


7459 


2082 


6612 


6110 


5766 


2.0137 


15 


24 


9135 


4067 


8271 


8135 


7406 


2202, 


6542 


6569 


5677 


0337 


66 


15 


9118 


4107 


8235 


8214 


7353 


2322 


6470 


6429 


5588 


0536 


45 


30 


9100 


4147 


8199 


8294 


7299 


2441 


6398 


6588 


5498 


0735 


30 


45 


9081 


4187 


8163 


8373 


7214 


2560 i 


6326 


6746 


6407 


0933 


15 


25 


9063 


4226 


8126 


8452 


7189 


2679 


6252 


6905 


5315 


1131 


65 


15 0.9045 


0.4266 


1.8089 


0.8531 


2.7034 


1.2797 


3.6178 


1.7063 


4.5223 


2.1328 


45 


30 


9026 


4305 


8052 


8610 


7078 


2915 


6103 


7220 


5129 


1526 


30 


45 


9007 


4344 


8014 


8689 


7021 


3033 


6028 


7378 


5035 


1722 


5 


2G 


8988 


4384 


7976 


8767 


6964 


3151 


5952 


7535 


4940 


1919 


64 


15 


8969 


4423 


7937 


8846 


6906 


3269 


5875 


7692 


4844 


2114 


45 


30 


8949 


4462 


7899 


8924 


6848 


3386 


5797 


7848 


4747 


2310 


30 


45 


8930 


4501 


7860 


9002 


6789 


3503 


5719 


8004 


4649 


2505 


15 


27 


8910 


4540 


7820 


9080 


6730 


3620 


5640 


8160 


4550 


2700 


63 


15 


8890 


4579 


7780 


9157 


6671 


3736 


5561 


8315 


4451 


2894 


45 


30 


8870 


4617 


7740 


9235 


6610 


3852 J 


5480 


8470 


4351 


3087 


30 


45 


0.8850 


0.4656 


1.7700 


9312^ 


2.6550 


1.3968 


3.5400 


1.8625 


4.4249 


2.3281 


15 


28 


8889 


4695 


7659 


9389 


6488 


4084 


5318 


8779 


4147 


3474 


62 


15 


8809 


4733 


7618 


9466 


6427 


4200| 


5236 


8933 


4045 


3666 


45 


30 


8788 


4772 


7576 


9543 


6305 


4315 


5153 


9086 


3941 


3858 


30 


45 


8767 


4810 


7535 


9620 


6302 


4430 


5069 


9240 


3836 


4049 


15 


29 


8746 


4848 


7492 


9696 


6239 


45441 


4985 


9392 


3731 


4240 


SI 


15 


8725 


4886 


7460 


9772 


6175 


4659 


4900 


9545 


3625 


4431 


45 


30 


8704 


4924 


7407 


9848 


6111 


4773 


4814 


9697 


3518 


4621 


30 


45 


8682 


4962 


7364 


9924 


6046 


4886 


4728 


9849 


3410 


4811 


15 


30 


8660 


5000 


7321 


1.0000 


5981 


5000 


4641 


2.0000 


3301 


5000 60 




Dep. 


Lat. 


Dep. 


Lat. ( 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dist. 1 1 


Dist. 2 1 


Dist. 3 1 1 


Dist. 4 1 1 


Dist 


.5 ^ 


juursB 



TRAVERSE TABLE 



217 



Course 


Diet. 6 


Dist. 7 


Dist. 8 1 


Dist. 9 


Dist. 10 




Lat. 1 Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


15 15 5.7887 1.5782 


6.7335 


1.8412 


7.7183 


2.1042 


S.6831 


2.3673 


9.6479 


2.6303 


74 45 


30 7818 


60a4 


7454 


8707 


7090 


1379 


6727 


4051 


6363 


6724 


30 


45' 7747 


6286 


7372 


9001 


6996 


1715 


6621 


4430 


6246 


7144 


15 


16 7676 


6538 


7288 


92951 


6901 


2051 


6514 


4807 


6126 


7564 


74 


15 7603 


6790 


7203 


9588: 


6804 


2386 


6404 


5185 


6005 


7983 


45 


30; 7529 


7041 


7117 


9881 


6706 


2721 


6294 


5561 


5882 


8402 


30 


45! 7454 


7292 


7030 


2.0174 


6C06 


3056 


6181 


5938 


5757 


8820 


15 


17 7378 


7542 


6941 


0466 


6504 


3390 


6067 


6313 


5630 


9237 


73 


15' 7301 


7792 


6851 


0758! 


6402 


3723 


5952 


6689 


5502 


9654 


45 


30 7223 


8040 


6760 


1049 


6297 


4056 


5835 


70&4 


5372 


3.0071 


30 


45 5.7144 


1.8292 


6.6668 


2.1341 


7.6192 


2.4389 


8.5716 


2.7438 


9.5240 


3.0486 


15 


18 


7063 


8541 


6574 


1631 


6085 


4721 


5595 


7812 


5106 


0902 


72 


15 


6982 


8790 


6479 


1921' 


5976 


5053 


5473 


8185 


4970 


1316 


45 


30 


6899 


9038 


6383 


2211 


5866 


5384 


5349 


8557 


4832 


1730 


30 


45 


6816 


9386 


6285 


2501 


5754 


5715 


5224 


8930 


4693 


2144 


15 


19 


6731 


9534 


6186 


2790, 


5641 


6045 


5097 


9301 


4552 


2557 


71 


15 


6645 


9781 


6086 


3078 


5527 


6375 


4968 


9672 


4409 


2969 


45 


30 


6658 


2.0028 


5985 


3366 


5411 


6705 


4838 


3.0043 


4264 


3381 


30 


45 


6471 


0275 


5S82 


3654 


5294 


7033 


4706 


0413 


4118 


3792 


15 


20 


6382 


0521 


5778 


3941 1 


5175 


7362 


4562 


0782 


3969 


4202 


70 


15 


5.6291 


2.0767 


6 5673 


2.4228 


7.5055 


2.7689 


8.4437 


3.1151 


9.3819 


3.4612 


45 


30 


6200 


1012 


5565 


4515; 


4934 


8017 


4300 


1519 


3767 


5021 


30 


45 


6108 


1257 


5459 


4800 


4811 


8343 


4162 


1886 


3514 


5429 


15 


21 


6015 


1502 


5351 


5086 


4686 


8669 


4022 


2253 


3358 


5837 


69 


15 


5920 


1746 


5241 


5371 


4561 


8995 


3881 


2619 


3201 


6244 


45 


30 


5825 


1990 


5129 


5655 


4433 


9320 


3738 


2985 


3042 


6650 


30 


45 


5729 


2233 


5017 


6939 


4305 


9045 


3593 


3350 


2881 


7056 


15 


22 


5631 


2476 


4903 


6222 


4176 


9969 


3447 


3715 


2718 


7461 


68 


15 


5532 


2719 


4788 


6505 


4043 


3.0292' 


3299 


4078 


2554 


7865 


45 


30 


5433 


2961 


4672 


6788 


3910 


0015 


3149 


4442 


2388 


8268 


30 


45 


5.5332 


2.3203 


6.4554 


2.7070 


7.3776 


3.0937 


8.2998 3.4804 


9.2220 


3.8671 


15 


23 


5230 


3414 


4435 


7351 


3640 


1258 


2845 5166 


2050 


9073 


67 


15 


5127 


3685 


4315 


7632 


3503 


1580 


2691 5527 


1879 


9474 


45 


30 


5024 


3925 


41y4 


7912 


3365 


1900 


2535 5887 


1706 


9875 


30 


45 


4919 


4165 


4072 


8192 


3225 


2220 1 


2375 


6247 


1531 


4.0275 


15 


24 


4813 


4404 


3948 


8472 


3084 


25391 


2219 


6606 


1355 


0674 


66 


15 


4706 


4643 


3823 


8750 


2941 


2858; 


2059 


6965 1 1176 


1072 


45 


30 


4598 


4882 


3697 


9029 


2797 


3175 i 


1897 


7322 


0996 


1469 


30 


45 


4489 


5120 


3570 


9306 


2651 


3493; 


1733 


7679 


0814 


1866 


15 


25 


4378 


5357 


3442 


9583 


2505 


3809 


1568 


8036 


0631 


2262 


65 


15 


5.42G7 


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 0259 


3051 


30 


45 


4042 


6067 


3049 


0411 


2056 


4756 


1063 


9100' 1 0070 


3445 


15 


26 


3928 


6302 


2916 


0686 


1904 


5070 


0891 


9453 8.9879 


3837 


64 


15 


3812 


6537 


2781 


0960 


1750 


5383 


0719 


9806 


9687 


4229 


45 


30 


3696 


6772 


2645 


1234 


1595 


5696 


0644 


4.0158' 


9493 


4620 


30 


45 


3579 


7006 


2509 


1507 


1438 


6008 


0368 


0509 


9298 


5010 


15 


27 


3460 


7239 


2370 


1779 


1281 


6319 


0191 


0859 


9101 


5399 


63 


15 


3341 


7472 


2231 


2051 


1121 


6630 


0012 


1209: 


8902 


5787 


45 


30 


3221 


7705 


2091 


2322 


0961 


6940 


7.9831 


1557 


8701 


6175 


30 


46 


5.3099 


2.7937 


6.1949 3.2593 


7.0799 


3.7249 


7.9649 


4.1905 8 8499'4.6561 


15 


28 


2977 


8168 


18(6 


2863 


0636 


7558 


9465 


2252 8295; 6947 


62 


15 


2853 


8399 


1662 


3132 


6471 


7866 


9280 


2599 8089 1 


7332 


45 


30 


2729 


8630 


1517 


3401 


0305 


8173; 


9094 


2944 


7882 


7716 


30 


45 


2604 


8859 


1371 


3669 


0138 


8479 


8905 


3289 


7673 


8099 


15 


29 


2477 


9089 


1223 


3937 


6.9970 


87851 


8716 


3683 


7462 


8481 


61 


15 


2350 


9317 


1075 


4203 


9800 


9090 


8525 


3976 


7250 


8862 


45 


30 


2221 


9545 


0925 


4470 


9628 


9394 


8332 


4318 


7036 


9242 


30 


45 


2092 


9773 


0774 


4735 


9456 


9697 


8148 


4659 


6820 9622 


15 


30 


1962 


3.0000 


0622 


5000 


9282 4.0000 


7942 5000 


6603 5.0000 


60 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. j 


Dep. 1 Lat. 


Dep. Lat. 






Dist. 6 1 


Dist. 7 


Diet. 8 


Dist. 9 i 


Dist. 10 


Course 



218 



TRAVERSE TABLE 



Course 


Dist. 1 


Pist. 2 


Pist. 3 


Piet. 4 1 


Pist. 5 




Lat. 


Pep. 
0.5038 


Lat. 


Pep. 


Lat. 


Pep. 
1.5113 


Lat. 


Pep. 


Lat. 


Pep. 


30 15 


0.8638 


1.7277 


1.0075 


2.5915 


3.4553 


2.0151 


4.3192 


2.5189 


o / 

59 45 


30 


8616 


5075 


7223 


0151 


5849 


5226 


4465 


0302 


3081 


5377 


30 


45 


8594 


5113 


7188 


0226 


5782 


5339 


4376 


0452 


2970 


5565 


15 


31 


8572 


5150 


7142 


0301 


5715 


5451 


4287 


0602 


2858 


5752 


59 


15 


8549 


5188! 


7098] 0375 


5647 


5563 


4196 


0751 


2746 


5939 


45 


30 


8526 


5225 


7053 j 0450 


5579 


5675 


4106 


0900 


2632 


6125 


30 


45 


8504 


52G2 


70071 0524 


5511 


5786 


4014 


1049 


2518 


6311 


15 


32 


8480 


5299 


6961 0598 


5441 


5898 


3922 


1197 


2402 


6496 


58 


15 


8457 


5336 


69151 0672 


5372 


6008 


3829 


1345 


2286 


6681 


45 


30 


8434 


5373 


6868 0746 


5302 


0119 


3736 


1492 


2170 


6865 


30 


45 


0.8410 


0.5410 


1.6821:1.0819 


2 5231 


1.6229 


3.3642 


2.1639 


4.2052 


2.7049 


15 


33 


8387 


5446 


6773 


0893 


5160 


6339 


3547 


1786 


1934 


7232 


57 


15 


8363 


5483 


6726 


0966 


5089 


6449 


3451 


1932 


1814 


7415 


45 


30 


8339 


5519 


6678 


1039 


5017 


6558 


3355 


2077 


1694 


7597 


30 


45 


8315 


5556 


6629 


1111 


4944 


6067 


3259 


2223 


1573 


7779 


15 


34 


8290 


5592 


6581 


1184 


4871 


6776 


3162 


2368 


1452 


7960 


50 


15 


8266 


5628 


6532 


1256 


4798 


6884 


3064 


2512 


1329 


3140 


45 


30 


8241 


5664 


6483 


1328 


4724 


6992 


2965 


2656 


1206 


8323 


30 


45 


8216 


5700 


6433 


1400 


4649 


7100 


2866 


2800 


1082 


8500 


15 


35 


8192 


5736 


6383 


1472 


4575 


7207 


2766 


2943 


0958 


8679 


55 


15 


0.8166 


0.5771 


1.6333^1. 1543! 


2.4499 


1.7314 


3.2666 


2.3086 


4.0832 


2.8857 


45 


30 


8141 


5807 


6282 


1614 


4423 


7421 


2565 


3228 


0706 


9035 


30 


45 


8116 


5842 


6231 


1685 


4347 


7527 


2463 


3370 


0579 


9212 


15 


36 


8090 


5878; 


6180 


1756 


4271 


7634 


2361 


3511 


0451 


9389 


54 


15 


8064 


5913 


6129 


1826 


4193 


7739 


2258 


3652 


0322 


9505 


45 


30 


8039 


5948 


6077 


1896 


4116 


7845 


2154 


3793 


0193 


9741 


30 


45 


8013 


5983 


6025 


1966 


4038 


7950 


2050 


3933 


0063 


9916 


15 


37 


7986 


6018 


5973 


2036 


3959 


8054 


1945 


4073 


3.9932 


3.0091 


53 


15 


7960 


6053 


5920 


2106 


3880 


8159 


1840 


4212 


9800 


0365 


45 


30 


7934 


6088 


5867 


2175 


3801 


8263 


1734 


4350 


9668 


0438 


30 


45 


0.7907 


0.6122 


1.5814 


1.2244 


2.3721 


1.8367 


3.1028 


2.4489 


3.9534 


3.0611 


15 


38 


7880 


6157; 


57(K) 


2313 


3640 


8470 


1520 


4626 


9400 


0783 


52 


15 


7853 


6191 


5706 


2482 


3500 


8573 


1413 


47641 


9266 


0955 


45 


30 


7826 


6225 


5652 


2450 


3478 


8675 


1304 


4901 


9130 


1126 


30 


45 


7799 


6259 


5598 


2518 


3397 


8778; 


1195 


5037 


8994 


1296 


15 


39 


7771 


6293 


5.543 


2586 


3314 


8880 


1086 


5173 


8857 


1466 


51 


15 


7744 


6327, 


5488 


2654 


3232 


8981 


0976 


5308 


1 8720 


1635 


45 


30 


7716 


6361, 


5432 


2722 


3149 


9082 


0865 


5443 


8581 


1804 


30 


45 


7688 


6394' 


5377 


2789 


3065 


9183 


0754 


5578 i 


8442 


1972 


15 


40 


7660 


6428: 


5321 


2856 


2981 


9284 


0642 


5512 


8302 


2139 


50 


15 0.7632 


0.6461 


1.5265 


1.2922 


2.2897 


1.9384 


3.0529 


2.5845 


3.8162 


3.2306 


45 


30 7604 


6494 


5208 


2989 


2812 


9463 


0416 


5978 


8020 


2472 


30 


45 


7576 


6528 


5151 


3055 


2727 


9583 


0303 


6110 


7878 


2638 


15 


41 


7547 


6561 


5094 


3121 


2641 


9682 


0188 


6242 


7735 


2803 


49 


15 


7518 


6593 


5037 


3187 


2555 


9780 


0074 


6374 


7592 


2967 


45 


30 


7490 


6626 


4979 


3252 


24(59 


9879 


2.9958 


6505 


7448 


3131 


30 


45 


7461 


6659 


4921 


3318 


2382 


9976 


9842 


6635 


7303 


3294 


15 


42 


7431 


6891 


4863 


3383 


2294 


2.0074 


9726 


6765 


7157 


3457 


48 


15 


7402 


6724 


4-04 


3447 


2207 


0171 


9609 


6895 


7011 


3618 


45 


30 


7373 


6756' 


4746 


3512 


2118 


0268 


9491 


7024 


6864 


3780 


30 


45 


0.7343 


0.6788' 


1.4686 1.3576 


2.2030 


2.0364 


2.9373 


2.7152 


3.6716 


3.3940 


15 


43 


7314 


6820 


4627 3640 


1941 


04(;0 


9254 


7280 


6568 


4100 


47 


15 


7284 


6852, 


4567 


3704 


1851 


0555 


9135 


7407 


6419 


4259 


45 


30 


7254 


6884 


4507 


3767 


1701 


0651 


9015 


7534 


6268 


4418 


30 


43 


7224 


6915 


4447 


3830 


1671 


0745 


8895 


7661 ; 


6118 


4576 


15 


44 


7193 


6947 


4387 


3893 


1580 


0840 


8774 


7786 


5967 


4733 


46 


15 


7163 


6978 


4326 


3956 


1489 


0934 


8652 


7912 


5815 


4890 


45 


30 


7133 


7009 i 


4265 


4018 


1398 


1027 


8530 


8036 


5663 


5045 


30 


45 


7102 


70401 


4204 


4080 


1306 


1120 


8407 


8161 


5509 


5201 


15 


45 


7071 


7071 


4142 j 4142 


1213 


1213 


8284 


8284 


5355 


5355 


45 




Pep. 


Lat. 


i Pep. i Lat. 


Pep. 


Lat. 


, Pep. 


Lat. 


Pep. 


Lat. 


Course 


Pis 


t. 1 


1 Dist. 2 


Pist. 3 1 


j Pis 


t.4 1 


Pist. 5 1 



TRAVERSE TABLE 



219 



Course 


Dist. 6 1 


Dist. 7 j 


Dist. 8 


Dist. 9 


Dist. 10 




Lat. 


Dep. 
3.0226 


Lat. 
6.0468 


Dep. 

3.5264 


Lat. 


Dep. 


Lat. 


Dep. 
4 5340 


Lat. Dep. 


30 15 


5.1830 


6.9107 


4.0302 


7.7745 


8.6384 5.0377 


o / 
59 45 


30 


1G9S 


0452 


0314 


55281 


8930 


0603 


7547 


5678 


6163! 0754 


30 


45 


1564 


0678 


0158 


5791 


8753 


0903 


7347 


6016 


5941 1 1129 


15 


31 


1430 


0902 


0002 


6053 


8573 


1203 


7145 


6353 


5717 1 1504 


59 


15 


1295 


1126 


5.9844 


6314 


8393 


1502 


6942 


6690 


5491 


1877 


45 


30 


1158 


1350 


9685 


6575 


8211 


1800 


6738 


7025 


5264 


2250 


30 


45 


1021 


1573 


9525 


68351 


8028 


2097 


6532 


7359 


5035 


2621 


15 


32 


0883 


1795 


9363 


7094 


7844 


2394 


6324 


7693 


4805 


2992 


58 


15 


0744 


2017 


9201 


7353 


7658 


2689 


6116 


8025 


4573 1 3361 


45 


30 


0603 


2238 


9037 


7611 


7471 


2984 


5905 


8357 


4339 3730 


30 


45 


5.0462 


3.2458 


5.8873 


3.7868 


6.7283 


4.3278 


7.5694 


4.8688 


8.4104 5.4097 


15 


3? 


0320 


2678 


8707 


8125; 


7094 


3571 


5480 


9018 


3867 


4464 


57 


15 


0177 


2898 


8540 


8381 


6903 


3863 


5266 


9340 


3629 


4829 


45 


30 


0033 


3116 


8372 


8636 1 


6711 


4155 


5050 


9674 


3389 


5194 


30 


45 


4.9888 


3334 


8203 


8890 


6518 


4446 


4832 


5.0001 


3147 


5557 


15 


34 


9742 


3552 


8033 


9144 


6323 


4735 


4613 


0327 


2904 


5919 


56 


15 


9595 


3768 


7861 


9396 


6127 


5024 


4393 


0652 


2659 


6280 


45 


30 


9448 


3984 


7689 


9648 


5930 


5312 


4171 


0977! 


2413 


6641 


30 


45 


9299 


4200 


7515 


9900 1 


5732 


5600 


3948 


1300 


2165 


7000 


15 


35 


9149 


4415 


7341 


4.0150; 


5532 


5886 


3724 


1622 


1915 7358 


55 


15 


4.8998 


3.4629 


5.7165 


4.0400 


6.5331 


4.6172 


7.3498 


5.1943 


8.16645.7715 


45 


30 


8847 


4842 


6988 


0649 


5129 


6456 


3270 


2263 


1412 


8070 


30 


45 


8694 


5055 


6810 


0897 


4926 


6740 


3042 


2582 


1157 


8425 


15 


36 


8541 


5267 


6631 


1145 


4721 


7023 


2812 


2901 


0902 


8779 


54 


15 


8387 


5479 


6451 


1392 


4516 


7305 


2580 


3218 


0644 


9131 


45 


30 


8231 


5689 


6270 


1638 


4309 


7586 


2347 


3534 


0386 


9482 


30 


45 


8075 


5899 


6088 


1883 


4100 


7866 


2113 


3849 


0125! 9832 


15 


37 


7918 


6109 


5904 


2127 


3891 


8145 


1877 


4193 


7.9864!6.0182 


53 


15 


7760 


6318 


5720 


2371 


3080 


8424 


1640 


4476 


9600 


0529 


45 


30 


7001 


6526 


5535 


2613 


3468 


8701 


1402 


4789 


9335 


0876 


30 


45 


4.7441 


3.6733 


5.5348 


4.2855 


6.3255 


4.8977 


7.1162 


5.5100 


7.9069 


6.1222 


15 


38 


7281 


6940 


5161 


3096 


3041 


9253 


0921 


5410 


8801 


1566 


52 


15 


7119 


7146 


4972 


3337 


2829 


9528' 


0679 


5718 


8532 


1909 


45 


30 


6956 


7351 


4783 


3576 


2609 


9801 


0435 


6026 


8261 


2251 


30 


45 


6793 


7555 


4592 


3815 


2391 


5.0074 


0190 


6333 


7988 


2592 


15 


39 


6629 


7759 


4400 


4052 


2172 


0346 


6.9943 


6639 


7715 


2932 


51 


15 


6464 


7962 


4207 


4289 


1951 


0616 


9695 


69431 


7439 


3271 


45 


30 


6297 


8165 


4014 


4525 


1730 


0886 


9446 


7247 


7162 


3608 


30 


45 


6131 


8366 


3819 


4761 


1507 


1155 


9196 


7550 1 


6884 


3944 


15 


40 


5963 


8567 


3623 


4995 


1284 


1423 


8944 


7851 


6604 


4279 


50 


15 


4.5794 


3.8767 


5.3426 


4.5229 


6.1059 


5.1690 


0.8091 


5.8151 


7.6323'6.4612 


45 


30 


5624 


89671 


3228 


5461 


0832 


1956' 


8437 


8450 


6041 1 4945 


30 


45 


5454 


9166 


3030 


5693 


0605 


2221 1 


8181 


8748 


5756 


5276 


15 


41 


5283 


9364 


2830 


5924 


0377 


2485 


7924 


9045 


5471 


5606 


49 


15 


5110 


95611 


2629 


6154 


0147 


2748 


7666 


9341 


5184 


5935 


45 


30 


4937 


9757 


2427 


6383 


5.9916 


3010 


7406 


9638 


4896 


6282 


30 


45 


4763 


9953 


2224 


6612 


9685 


3271 


7145 


9929 


4606 


6588 


15 


42 


4589 


4.0148 


2020 


6839! 


9452 


3530 


6883 


6.0222 


4314 


6913 


48 


15 


4413 


0342! 


1815 


7066 


9217 


3789 


6620 


0513 


4022 


7237 


45 


30 


4237 


0535; 


1609 


7291! 


8982 


4047 


6355 


0803 


3728 


7559 


30 


45 


4.4059 


4.0728' 


5.1403 


4.7516 


5.8746 


5.4304 


6.6089 


6.1092 


7.3432 


6.7880 


15 


43 


3881 


0920 


1195 


7740! 


8508 


4560 


5822 


1380 


3135 


8200 


47 


15 


3702 


nil 


0986 


7963 


8270 


4815 


5553 


1666 


2837 


8518 


45 


30 


3522 


1301 


0776 


8185 


8030 


5068 


5284 


1952 


2537 


8835 


30 


45 


3342 


1491 


0565 


8406 


7789 


5321 


5013 


2236 


2236 


9151 


15 


44 


3160 


1680 


0354 


86261 


7547 


5573 


4741 


2519 


1934 


9466 


46 


15 


2978 


1867; 


0141 


8845: 


7304 


5823 


4467 


2801 


1630 


9779 


45 


30 


2795 


2055; 


4.9928 


9064! 


7000 


6073 


4193 


3082 


1325 


7.0091 


30 


45 


2611 


22411 


9713 


9281 1 


6815 


63211 


3917 


3361 


1019 


0401 


15 


45 


2426 


2426 


9477 


9497 


6569 


6569 


3640 


36401 


0711 
'Dep. 


0711 


45 




Dep. 


Lat. ' 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


Course 


Dist. 6 1 


Dis 


t. 7 


Dist. 8 1 


Dist. 9 1 


Dist. 10 1 



220 



A MANUAL FOR NORTHERN WOODSMEN 



LOGARITHMS OF NUMBERS 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


0000 


0043 


0086 


0128 


0170 


0212 


0253 


0294 


0334 


0374 


11 


0414 


0453 


0492 


0531 


0569 


0607 


0645 


0682 


0719 


0755 


12 


0792 


0828 


0864 


0899 


0934 


0969 


1004 


1038 


1072 


1106 


13 


1139 


1173 


1206 


1239 


1271 


1303 


1335 


1367 


1399 


1430 


14 


1461 


1492 


1523 


1553 


1584 


1614 


1644 


1673 


1703 


1732 


15 


1761 


1790 


1818 


1847 


1875 


1903 


1931 


1959 


1987 


2014 


16 


2041 


2068 


2095 


2122 


2148 


2175 


2201 


2227 


2253 


2279 


17 


2304 


2330 


2355 


2380 


2405 


2430 


2455 


2480 


2504 


2529 


18 


2553 


2577 


2601 


2625 


2648 


2672 


2695 


2718 


2742 


2765 


19 


2788 


2810 


2833 


2856 


2878 


2900 


2923 


2945 


2967 


2989 


20 


3010 


3032 


3054 


3075 


3096 


3118 


3139 


3160 


3181 


3201 


21 


3222 


3243 


3263 


3284 


3304 


3324 


3345 


3365 


3385 


3404 


22 


3424 


3444 


3464 


3483 


3502 


3522 


3541 


3560 


3579 


3598 


23 


3617 


3636 


3655 


3674 


3692 


3711 


3729 


3747 


3766 


3784 


24 


3802 


3820 


3838 


3856 


3874 


3892 


3909 


3927 


3945 


3962 


25 


3979 


3997 


4014 


4031 


4048 


4065 


4082 


4099 


4116 


4133 


26 


4150 


4166 


4183 


4200 


4216 


4232 


4249 


4265 


4281 


4298 


27 


4314 


4330 


4346 


4362 


4378 


4393 


4409 


4425 


4440 


4456 


28 


4472 


4487 


4502 


4518 


4533 


4548 


4564 


4579 


4594 


4609 


29 


4624 


4639 


4654 


4669 


4683 


4698 


4713 


4728 


4742 


4757 


30 


4771 


4786 


4800 


4814 


4829 


4843 


4857 


4871 


4886 


4900 


31 


4914 


4928 


4942 


4955 


4969 


4983 


4997 


5011 


6024 


5038 


32 


5051 


5065 


5079 


5092 


5105 


5119 


5132 


5145 


5159 


5172 


33 


5185 


5198 


5211 


5224 


5237 


5250 


5263 


5276 


5289 


5302 


34 


5315 


5328 


5340 


5353 


5366 


5378 


5391 


5403 


5416 


5428 


35 


5441 


5453 


5465 


5478 


5490 


5502 


5514 


5527 


5539 


5551 


36 


5563 


5575 


5587 


5599 


5611 


5623 


5635 


5647 


5658 


5670 


37 


5682 


5694 


5705 


5717 


5729 


5740 


5752 


5763 


5775 


5786 


38 


5798 


5809 


5821 


5832 


5843 


5855 


5866 


5877 


5888 


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 


6385 


6395 


6405 


6415 


6425 


44 


6435 


6444 


6454 


6464 


6474 


6484 


6493 


6503 


6513 


6522 


45 


6532 


6542 


6551 


6561 


6571 


6580 


6590 


6599 


6609 


6618 


46 


6628 


6637 


6646 


6656 


6665 


6675 


6684 


6693 


6702 


6712 


47 


6721 


6730 


6739 


6749 


6758 


6767 


6776 


6785 


6794 


6803 


48 


6812 


6821 


6830 


6839 


6848 


6857 


6866 


6875 


6884 


6893 


49 


6902 


6911 


6920 


6928 


6937 


6946 


6955 


6964 


6972 


6981 


60 


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 


63 


7243 


7251 


7259 


7267 


7275 


7284 


7292 


7300 


7308 


7316 


54 


7324 


7332 


7340 


7348 


7356 


7364 


7372 


7380 


7388 


7396 


No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 



TABLES RELATING TO P.\RTS I AND II 



221 



LOGARITHMS OF NUMBERS 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


55 


7404 


7412 


7419 


7427 


7435 


7443 


7451 


7459 


7466 


7474 


66 


74S2 


7490 


7497 


7505 


7513 


7520 


7528 


7536 


7543 


7551 


57 


7559 


7566 


7574 


7582 


7589 


7597 


7604 


7612 


7619 


7627 


58 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7694 


7701 


59 


7709 


7716 


7723 


7731 


7738 


7745 


7752 


7760 


7767 


7774 


60 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 


61 


7853 


7860 


7868 


7875 


7882 


7889 


7896 


7903 


7910 


7917 


62 


7924 


7931 


7938 


7945 


7952 


7959 


7966 


7973 


7980 


7987 


63 


7993 


8000 


8007 


8014 


8021 


8028 


8035 


8041 


8048 


8055 


64 


8062 


8069 


8075 


8082 


8089 


8096 


8102 


8109 


8116 


8122 


65 


8129 


8136 


8142 


8149 


8156 


8162 


8169 


8176 


8182 


8189 


66 


8195 


8202 


8209 


8215 


8222 


8228 


8235 


8241 


8248 


8254 


67 


8261 


8267 


8274 


8280 


8287 


8293 


8299 


8306 


8312 


8319 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


8382 


69 


8388 


8395 


8401 


8407 


8414 


8420 


8426 


8432 


8439 


8445 


70 


8451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8506 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


8555 


8561 


8567 


72 


8573 


8579 


8585 


8591 


8597 


8603 


8609 


8615 


8621 


8627 


73 


8633 


8639 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 


74 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


8739 


8745 


75 


8751 


8756 


8762 


8768 


8774 


8779 


8785 


8791 


8797 


8802 


76 


8808 


8814 


8820 


8825 


8831 


8837 


8842 


8848 


8854 


8859 


77 


8865 


8871 


8876 


8882 


8887 


8893 


8899 


8904 


8910 


8915 


78 


8921 


8927 


8932 


8938 


8943 


8949 


8954 


8960 


8965 


8971 


79 


8976 


8982 


8987 


8993 


8998 


9004 


9009 


9015 


9020 


9025 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


81 


9085 


9090 


9096 


9101 


9106 


9112 


9117 


9122 


9128 


9133 


82 


9138 


9143 


9149 


9154 


9159 


9165 


9170 


9175 


9180 


9186 


83 


9191 


9196 


9201 


9206 


9212 


9217 


9222 


9227 


9232 


9238 


84 


9243 


9248 


9253 


9258 


9263 


9269 


9274 


9279 


9284 


9289 


85 


9294 


9299 


9304 


9309 


9315 


9320 


9325 


9330 


9335 


7340 


86 


9345 


9350 


9355 


9360 


9365 


9370 


9375 


9380 


9385 


9390 


87 


9395 


9400 


9405 


9410 


9415 


9420 


9425 


9430 


9435 


9440 


88 


9445 


9450 


9455 


9460 


9465 


9469 


9474 


9479 


9484 


9489 


89 


9494 


9499 


9504 


9509 


9513 


9518 


9523 


9528 


9533 


9538 


90 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


91 


9590 


9595 


9600 


9605 


9609 


9614 


9619 


9624 


9628 


9633 


92 


9638 


9643 


9647 


6952 


9657 


9661 


9666 


9671 


9675 


9680 


93 


9685 


9689 


9694 


9699 


9703 


9708 


9713 


9717 


9722 


9727 


94 


9731 


9736 


9741 


9745 


9750 


9754 


9759 


9763 


9768 


9773 


95 


9777 


9782 


9786 


9791 


9795 


9800 


9805 


9809 


9814 


9818 


96 


9823 


9827 


9832 


9836 


9841 


9845 


9850 


9854 


9859 


9863 


97 


9868 


9872 


9877 


9881 


9886 


9890 


9894 


9899 


9903 


9908 


98 


9912 


9917 


9921 


9926 


9930 


9934 


9939 


9943 


9948 


9952 


99 


9956 


9961 


9965 


9969 


9974 


9978 


9983 


9987 


9991 


9996 


No. 





1 2 


3 


4 


5 


6 


7 


8 


9 



222 



A MANUAL FOR NORTHERN WOODSMEN 



LOGARITHMIC SINES, COSINES, 



Angle 



0° 0' 

0° 10' 
0° 20' 
0° 30' 
0° 40' 
0° 50' 
1° 0' 

1° 10' 
1° 20' 
1° 30' 
1° 40' 
1° 50' 

2° 0' 

2° 10' 

2° 20' 

2° 30' 

2° 40' 

2° 50' 

3° 0' 

3° 10' 
3° 20' 
3° 30' 
3° 40' 
3° 50' 
4° 0' 

4° 10' 
4° 20' 
4° 30' 
4° 40' 
4° 50' 

5° 0' 

5° 10' 
5° 20' 
5° 30' 
5° 40' 
5° 50' 
6° 0' 
6° 10' 
6° 20' 
6° 30' 
6° 40' 
6'=' 50' 

7° 0' 

7° 10' 
7° 20' 
7° 30' 



Sin. 



00 



7.4637 
.7648 
.9408 

8.0656 
.1627 



8.2419 



.3088 
.3668 
.4179 
.4637 
.5050 



8.5428 



.5776 
.6097 
.6397 
.6677 
.6940 



8.7188 



.7423 
.7645 
.7857 
.8059 
.8251 



8.8436 



.8613 
.8783 
.8946 
.9104 
.9256 



D. r 



8.9403 



.9545 
.9682 
.9816 
.9945 
9.0070 



9.0192 



.0311 
.0426 
.0539 
.0648 
.0755 



9.085.^ 



.0961 
.1060 
.1157 



Cos. 



301.1 

176.0 

125.0 

96.9 

79.2 

66.9 
58.0 
51.1 

45.8 
41.3 
37.8 

34.8 
32.1 
30.0 
28.0 
26.3 
24.8 

23.5 

22.2 
21.2 
20.2 
19.2 
18.5 
17.7 
17.0 
16.3 
15.8 
15.2 
14.7 
14.2 

13.7 
13.4 
12.9 
12.5 
12.2 

11.9 

11.5 
11.3 
10.9 
10.7 
10.4 

10.2 

9.9 

9.7 



D.r 



Cos. 



10.0000 



.0000 
.0000 
.0000 
.0000 
.0000 



9.9999 



.9999 
.9999 
.9999 
.9998 
.9998 



9.9997 



.9997 
.9996 
.9996 
.9995 
.9995 



9.9994 



.9993 
.9993 
.9992 
.9991 
.9990 



9.9989 



.9989 
.9988 
.9987 
.9986 
.9985 



9.9983 



.9982 
.9981 
.9980 
.9979 
.9977 



9.9976 



.9975 
.9973 
.9972 
.9971 
.9969 



9.9968 



.9966 
.9964 
.9963 



Sin. 



D.l 



.0 
.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.1 

.0 ■ 

.1 

.1 

.1 

.1 

.0 

.1 
.1 
.1 
.1 

.2 
.1 
.1 

.1 
.1 

.2 
.1 

.1 
.2 
.1 
.1 
.2 
.1 

.2 

.2 
.1 



D.l 



Tan. 



00 



7.4637 
.7648 
.9409 
8.0658 
_^1J327 
8.2419 



.3089 
.3669 
.4181 
.4638 
.5053 

8.5431 



.5779 
.6101 
.6401 

.6682 
.6945 



8.7194 



.7429 
.7652 
.7865 
.8067 
.8261 



8.8446 



.8624 
.8795 
.8960 
.9118 
.9272 



8.9420 



.9563 
.9701 
.9836 
.9966 
9.0093 



9.0216 



.0336 
.0453 
.0567 
.0678 
.0786 



9.0891 



.0995 
.1096 
.1194 



Cot. 



D.r 



301.1 

176.1 

124.9 

96.9 

79.2 

67.0 

58.0 
51.2 
45.7 
41.5 
37.8 

34.8 
32.2 
30.0 
28.1 
26.3 
24.9 

23.5 
22.3 
21.3 
20.2 
19.4 
18.5 
17.8 
17.1 
16.5 
15.8 
15.4 
14.8 
14.3 

13.8 
13.5 
13.0 
12.7 
12.3 

12.0 

11.7 
11.4 
11.1 
10.8 
10.5 
10.4 

10.1 

9.8 



D.r 



Cot. 



00 



2.5363 
.2352 
.0591 

1.9342 
.8373 



1.7581 



.6911 
.6331 
.5819 
.5362 
■4947 
1.4569 



.4221 
.3899 
.3599 
.3318 
■3055 
1.2806 



.2571. 
.2348 
.2135 
■ 1933 
.1739 



1.1554 



.1376 
.1205 
.1040 

.0882 
.0728 



1.058 

.0437' 
.0299 
.0164 
.0034 
0.9907 



0.9784 
■9664 
■9547 
.9433 
■9322 
■9214 

0.9109 



.9005 
■8904 
■8806 



Tan. 



89 



88° 

87° 
87° 
87° 

J-70 



90° 0' 

89° 50' 
89° 40' 
89° 30' 
89° 20' 
89° 10' 

C 

50' 
40' 
30' 
20' 
10' 
C 

50' 
40' 
30' 
87° 20' 
87° 10' 

87° 0' 

86° 50' 

86° 40' 

86° 30' 

86° 20' 

86° 10' 

86° 0' 

85° 50'. 

85° 40' 

85° 30' 

85° 20' 

85° 10' 

85° 0' 

84° 50' 

84° 40' 

84° 30' 

84° 20' 

84° 10' 

84° C 

83° 50' 
83° 40' 
83° 30' 
83° 20' 
83° 10' 

83° 0' 

82° 50' 
82° 40' 
82° 30' 



Angle 



TABLES RELATING TO PARTS I AND II 



223 



TANGENTS, AND COTANGENTS 



Angle 


Sin. 


D.r 


Cos. 


D.r 


Tan. 


D.r 


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' 
15° 0' 


9.1157 

.1252 
.1345 


9.6 
9.3 
9.1 

8.9 

8.7 
8.6 
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 

6.1 
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 
6.6 
6.4 
6.3 
6.3 
6.1 
6.1 
6.1 
5.9 
6.9 

5.8 

5.7 
6.7 
5.6 
5.6 
6.6 
5.4 

6.3 
5.3 
5.3 
5.1 
5.2 

6.1 


0.8806 
.8709 
.8616 


82° 30' 
82° 20' 
82° 10' 
82° 0' 

81° 60' 
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° 60' 
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° 60' 
75° 40' 
75° 30' 
75° 20' 
75° 10' 
75° 0' 


9.1436 


9.9958 


9.1478 


0.8522 


.1525 
.1612 
.1697 
.1781 
.1863 

9.1943 


.9956 
.9954 
.9952 
.9960 
.9948 


.1569 
.1658 
.1745 
.1831 
.1916 


.8431 
.8342 
.8255 
.8169 
.8085 


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 


0.7637 


.2468 
.2538 
.2606 
.2674 
.2740 
9.2806 


.9931 
.9929 
.9927 
.9924 
.9922 


.2636 
.2609 
.2680 
.2750 
.2819 


.7464 
.7391 
.7320 
.7250 
.7181 


9.9919 


9.2887 


0.7113 


.2870 
.2934 
.2997 
.3058 
.3119 


.9917 
.9914 
.9912 
.9909 
.9907 


.2953 
.3020 
.3086 
.3149 
.3212 


.7047 
.6980 
.6915 
.6861 

.6788 


9.3179 


9.9904 


9.3275 


0.6726 


.3238 
.3296 
.3353 
.3410 
.3466 


.9901 
.9899 
.9896 
.9893 
.9890 


.3336 
.3397 
.3458 
.3517 
.3576 


.6664 
.6603 
.6642 
.6483 
.6424 


9.3521 

.3575 
.3629 
.3682 
.3734 
.3786 


9.9887 


9.3634 


0.6366 


.9884 
.9881 
.9878 
.9876 
.9872 

9.9869 


.3691 
.3748 
.3804 
.3859 
.3914 


.6309 
.6252 
.6196 
.6141 
.6086 


9.3837 


9.3968 


0.6032 


.3887 
.3937 
.3986 
.4035 
.4083 


.9866 
.9863 
.9859 
.9856 
.9853 


.4021 
.4074 
.4127 
.4178 
.4230 


.5979 
.5926 
.5873 

.6822 
.6770 


9.4130 


9.9849 


9.4281 


0.5719 




Cos. 


D.r 


Sin. 


D.r 


Cot. 


D.r 


Tan. 


Angle 



224 



A MANUAL FOR NORTHERN WOODSMEN 



LOGARITHMIC SINES, COSINES, 



Angle 


Sin. 


D. r 


Cos. 


D.r 


Tan. 


D.r 


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 
.9846 
.9843 
.9839 
.9836 
.9832 


.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 


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 
3.6 
3.6 


0.5719 


75° 0' 

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' 

71° 50' 
71° 40' 
71° 30' 
71° 20' 
71° 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 


.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 

9.4900 


.9802 
.9798 
.9794 
.9790 
.9786 


.4898 
.4943 
.4987 
.5031 
.5075 


.5102 
.5057 
.5013 
.4969 
.4925 


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 
.5306 


.9752 
.9748 
.9743 
.9739 
.9734 


.5411 
.5451 
.5491 
.5531 
.5571 
9.5611 


.4589 
.4549 
.4509 
.4469 
.4429 


9.5341 


9.9730 


0.4389 


.5375 
.5409 
.5443 
.5477 
.5510 


.9725 
.9721 
.9716 
.9711 
.9706 


.5650 
.5689 
.5727 
.5766 
.5804 


.4350 
.4311 
.4273 
.4234 
.4196 


9.5543 


9.9702 


9.5842 


0.4158 


.5576 
.5609 
.5341 
.5673 
.5704 


.9697 
.9692 
.9687 
.9682 
.9677 


.5879 
.5917 
.5954 
.5991 
.6028 
9.6064 


.4121 
.4083 
.4046 
.4009 
.3972 


9.5736 


9.9672 


0.3936 


.5767 
.5798 

.5828 


.9667 
.9861 
.9656 


.6100 
.6136 
.6172 


.3900 
.3864 
.3828 




Cos. 


D.r 


Sin. 


D.l' 


Cot. 


D.r 


Tan. 


Angle 



TABLES RELATING TO PARTS I AND II 



225 



TANGENTS, AND COTANGENTS 



Angle 



22° 30' 
22° 40' 
22° 50' 

23° 0' 

23° 10' 
23° 20' 
23° 30' 
23° 40' 
23° 50' 
24° 0' 

24° 10' 
24° 20' 
24° 30' 
24° 40' 
24° 50' 

25° 0' 

25° 10' 
25° 20' 
25° 30' 
25° 40' 
25° 50' 
26° 0' 
26° 10' 
26° 20' 
26° 30' 
26° 40' 
26° 50' 



27° 

27° 
27° 
27° 
27° 
27° 
28° 

28' 
28' 



0' 

lOf 
20' 
30' 
40' 
50' 
0' 
10' 
20' 



28° 30' 
28° 40' 
28° 50' 
29° 0' 
29° 10' 
29° 20' 
29° 30' 
29° 40' 
29° 50' 
30° 0' 



Sin. 



9.5828 
.5859 
.5889 



9.5919 

.5948 
.5978 
.6007 
.6036 
.6065 



9.6093 



.6121 
.6149 
.6177 
.6205 
.6232 



9.6259 



.6286 
.6313 
.6340 
.6366 
.6392 



9.6418 



.6444 
.6470 
.6495 
.6521 
.6546 



9.6570 



.6595 
.6620 
.6644 
.6668 
.6692 

9.6716 

.6740 
.6763 
.6787 
.6810 
.6833 



9.6856 



.6878 
.6901 
.6923 
.6946 
.6968 



9.6990 



Cos. 



D.l 



3.1 
3.0 
3.0 

2.9 

3.0 

2.9 
2.9 
2.9 
2.8 
2.8 

2.8 
2.8 
2.8 
2.7 
2.7 

2.7 

2.7 
2.7 
2.6 
2.6 
2.6 
2.6 
2.6 
2.5 
2.6 
2.5 
2.4 

2.5 

2.5 
2.4 
2.4 
2.4 
2.4 

2.4 

2.3 
2.4 
2.3 
2.3 
2.3 
2.2 

2.3 
2.2 
2.3 

2.2 
2.2 



D.l 



Cos. 



9.9656 
.9651 
.9646 



9.9640 



.9635 
.9629 
.9624 
.9618 
.9613 



9.9607 



.9602 
.9596 
.9590 
.9584 
.9579 



9.9573 



.9567 
.9561 
.9555 
.9549 
.9543 



9.9537 

.9530 
.9524 
.9518 
.9512 
.9505 



9.9499 



.9492 
.9486 
.9479 
.9473 
.9466 



9.9459 



.9453 
.9446 
.9439 
.9432 
.9425 



9 .9418 



.9411 
.9404 
.9397 
.9390 
.9383 

9.9375 



Sin. 



D.r 



D.r 



Tan. 



9.6172 
.6208 
.6243 



9.6279 



.6314 
.6348 
.6383 
.6417 
.6452 



9.6486 



.6520 
.6553 
.6587 
.6620 
.6654 



9.668'; 



.6720 
.6752 
.6785 
.6817 
.6850 



9.6882 



.6914 
.6946 
.6977 
.7009 
.7040 



9.7072 



.7103 
.7134 
.7165 
.7196 
.7226 



9.7257 



.7287 
.7317 
.7348 
.7378 
.7408 



9.7438 



.7467 
.7497 
.7526 
.7556 
.7585 



9.7614 



Cot. 



D.l 



3.6 
3.5 
3.6 

3.5 
3.4 
3.5 
3.4 
3.5 
3.4 

3.4 

3.3 
3.4 
3.3 
3.4 
3.3 

3.3 
3.2 
3.3 
3.2 
3.3 
3.2 
3.2 

3.2 
3 1 
3.2 
3.1 
3.2 

3.1 

3.1 
3.1 
3.1 
3.0 
3.1 
3.0 

3.0 
3.1 
3.0 
3.0 
3.0 

2.9 

3.0 
2.9 
3.0 
2.9 
2.9 



D.r 



Cot. 



.3828 
.3792 
.3757 



0.3721 



.3686 
.3652 
.3617 
.3583 
■3548 

0.3514 



.3480 
.3447 
.3413 
.3380 
.3346 



0.3313 



.3280 
.3248 
.3215 
.3183 
.3150 



0.3118 



.3086 
.3054 
.3023 
.2991 
.2960 



0.2928 



.2897 
.2866 
.2835 
.2804 
.2774 



0.2743 



.2713 
.2683 
.2652 
.2622 
.2592 



.2562 
.2533 
.2503 
.2474 
.2444 
.2415 



0.2386 



Tan. 



67° 30' 
67° 20' 
67° 10' 
67° C 

66° 50' 
66° 40' 
66° 30' 
66° 20' 
66° 10' 

66° C 

65° 50' 
65° 40' 
65° 30' 
65° 20' 
65° 10' 

65° 0' 

64° 50' 
64° 40' 
64° 30' 
64° 20' 
64° 10' 
64° C 

63 50' 
63° 40' 
63° 30' 
63° 20' 
63° 10' 
63° C 

62° 50' 
62° 40' 
62° 30' 
62° 20' 
62° 10' 
62° C 

61° 50' 
61° 40' 
61° 30' 
61° 20' 
61° 10' 
61° C 
60° 50' 
60° 40' 
60° 30' 
60° 20' 
60° 10' 
60° 0' 



Angle 



226 



A MANUAL FOR NORTHERN WOODSMEN 



LOGARITHMIC SINES, COSINES, 



Angle 


Sin. 


D.r 


Cos. D 


r 


Tan. 


D.l' 


Cot. 


i 


30° 


0' 


9.6990 


2 2 


9.9375 


7 


9.7614 


3 


0.2386 


60° 


0' 


80° 


10' 


.7012 


2.1 
2.2 
2.1 
2.1 
2 1 


.9868 


7 
8 
7 
8 

7 


.7644 


2.9 
2.8 
2.9 
2.9 
2 9 


.2356 


59° 


,50' 


30° 


20' 


.7088 


.9861 


.7673 


.2327 


59° 


40' 


80° 


30' 


.7055 


.9353 


.7701 


.2299 


59° 


,80' 


80° 


40' 


.7076 


.9346 


.7730 


.2270 


59° 


20' 


30° 


50' 


.7097 


.9338 


.7759 


.2241 


59° 


10' 


31° 


0' 


9.7118 


2 1 


9.9331 


8 


9.7788 


2 8 


0.2212 


59° 


0' 


81° 


10' 


.7139 


2.1 
2.1 
2.0 
2.1 
2 


.9828 


8 
7 
8 
8 
8 


.7816 


2.9 

2.8 
2.9 
2.8 
2 8 


.2184 


58° 


.50' 


31° 


20' 


.7160 


.9815 


.7845 


.2155 


58° 


40' 


81° 


80' 


.7181 


.9808 


.7873 


.2127 


,58° 


30' 


31° 


40' 


.7201 


.9:^00 


.7902 


.2098 


58° 


20' 


31° 


50' 


.7222 


.9292 


.7930 


.2070 


58° 


10' 


32° 


0' 


9.7242 


2 0- 


9.9284 


8 


9.7958 


2 8 


0.2042 


58° 


0' 


32° 


10' 


.7262 


2.0 
2.0 
2.0 
2.0 
1.9 


.9276 


8 
8 
8 
8 

s 


.7986 


2.8 
2.8 
2.8 
2.7 
2 8 


.2014 


57° 


.50' 


32° 


20' 


.7282 


.9268 


.8014 


.1986 


57° 


40' 


32° 


80' 


.7302 


.9260 


.8042 


.1958 


57° 


.30' 


32° 


40' 


.7822 


.9252 


.8070 


.1930 


57° 


20' 


82° 


50' 


.7342 


.9244 


.8097 


.1908 


57° 


10' 


33° 


0' 


9.7361 


1 9 


9.9236 


8 


9.8125 


2 8 


0.1875 


57° 


C 


33° 


10' 


.7380 


2.0 
1.9 
1.9 
1.9 
1 9 


.9228 


9 

8 
8 
9 

8 


.8153 


2.7 
2.8 
2.7 
2.8 
2 7 


.1847 


56° 


50' 


33° 


20' 


.7400 


.9219 


.8180 


.1820 


56° 


40' 


33° 


30' 


.7419 


.9211 


.8208 


.1792 


56° 


30' 


33° 


40' 


.7438 


.9203 


.8235 


.1765 


56° 


20' 


33° 


50' 


.7457 


.9194 


.8263 


.1737 


56° 


10' 


34° 


0' 


9.7476 


1 8 


9.9186 





9.8290 


2 7 


0.1710 


56° 


0' 


34° 


10' 


.7494 


1.9 

1.8 
1.9 
1.8 
1 8 


.9177 


8 
9 
9 
9 

s 


.8317 


2.7 

2.7 
2.7 


.1683 


55° 


50' 


84° 


20' 


.7513 


.9169 


.8344 


.1656 


55° 


40' 


84'^ 


80' 


.7581 


.9160 


.8371 


.1629 


55° 


80' 


34° 


40' 


.7550 


.9151 


.8398 


.1602 


55° 


20' 


34° 


50' 


.7568 


.9142 


.8425 


2 7 


.1575 


55° 


10' 


35° 


0' 


9.7586 


1 8 


9.9134 


9 


9.8452 


2 7 


0.1548 


55° 


0' 


35° 


10' 


.7604 


1.8 
1.8 
1.7 
1.8 
1 7 


.9125 


9 
9 
9 
9 
q 


.8479 


2.7 
2.7 
2.6 
2.7 
2 7 


.1521 


54° 


50' 


85° 


20' 


.7622 


.9116 


.8506 


.1494 


54° 


40' 


35° 


80' 


.7640 


.9107 


.8588 


.1467 


54° 


,30' 


85° 


40' 


.7657 


.9098 


.8559 


.1441 


54° 


20' 


85° 


50' 


.7675 


.9089 


.8586 


.1414 


54° 


10' 


36" 


0' 


9.7692 


1 8 


9.9080 J 





9.8613 


2 6 


0.1387 


54° 


0' 


36" 


10' 


.7710 


1.7 
1.7 
1.7 
1.7 
1.7 
1.6 

1.7 
1.6 


.9070 


9 
9 

9 


9 



9 


.8639 




.1361 


58° 


50' 


86° 


20' 


.7727 


.9061 


.8666 


2.6 
2.6 
2.7 
2.6 

2.6 

2.7 
2.6 


.1334 


.53° 


40' 


86^ 


30' 


.7744 


.9052 1 
.9042 ^ 


.8692 


.1308 


53° 


,30' 


86° 


40' 


.7761 


.8718 


.1282 


,58° 


20' 


86" 
37° 

87° 


60' 
0' 

10' 


.7778 


.9033 ^ 
9.9023 
.9014 , 
.9004 ^ 


.8745 
9.8771 


.1255 


53° 
53° 

52° 


10' 
0' 

.50' 


9.7795 
.7811 


0.1229 


.8797 


.1203 


87° 


20' 


.7828 


.8824 


.1176 


52° 


40' 


87° 


80' 


.7844 


.8995 


.8850 


.1150 


52° 


80' 




Cos. 


D.l' 


Sin. D 


r 


Cot. 


D.r 


Tan. 


Angle 



TABLES RELATING TO PARTS I AND II 



227 



TANGENTS, AND COTANGENTS 



Angle 



37° 30' 
37° 40' 
37° 50' 

38° 0' 

38° 10' 
38° 20' 
38° 30' 
38° 40' 
38° 50' 

39° 0' 

39° 10' 
39° 20' 
39° 30' 
39° 40' 
39° 50' 
40° 0' 

40° 10' 

40° 20' 
40° 30' 
40° 40' 
40° 50' 

41° 0' 

41° 10' 
41° 20' 
41° 30' 
41° 40' 
41° 50' 
42° 0' 

42° 10' 
42° 20' 
42° 30' 
42° 40' 
42° 50' 

43° 0' 

43° 10' 
43° 20' 
43° 30' 
43° 40' 
43° 50' 
44° 0' 

44° 10' 

44° 20' 

44° 30' 

44° 40' 

44° 50' 

45° 0' 



Sin. 



9.7844 
.7861 

.7877 



9.7893 



.7910 
.7926 
.7941 
.7957 
.7973 



9.7989 



.8004 
.8020 
.8035 
.8050 
.8066 



9.8081 



.8096 
.8111 
.8125 
.8140 
.8155 



9.8169 



.8184 
.8198 
.8213 
.8227 
.8241 



9.8255 



.8269 
.8283 
.8297 
.8311 
.8324 



9.8338 



.8351 
.8365 

.8378 
.8391 
.8405 



9.8418 



.8431 

.8444 
.8457 
.8469 
.8482 

9.8495 



Cos. 



D. 1 



1.7 
1.6 
1.6 

1.7 
1.6 
1.5 
1.6 
1.6 
1.6 

1.5 
1.6 
1.5 
1.5 
1.6 
1.5 
1.5 

1.5 
1.4 
1.5 
1.5 
1.4 

1.5 
1.4 
1.5 
1.4 
1.4 
1.4 

1.4 

1.4 
1.4 
1.4 
1.3 
1.4 

1.3 
1.4 
1.3 
1.3 
1.4 
1.3 

1.3 
1.3 
1.3 
1.2 
1.3 
1.3 



D. 1 



Cos 



.8995 
.8985 
.8975 



9.8965 



.8955 
.8945 
.8935 
.8925 
.8915 



9.8905 



9. 



8895 
8884 
8874 
8864 
8853 
8843 



.8832 
.8821 
.8810 
.8800 
.8789 



9.8778 



.8767 
.8756 
.8745 
.8733 
.8722 



9.8711 



.8699 
.8688 
.8676 
.8665 
.8653 



9.8641 



.8629 
.8618 
.8606 
.8594 

.8582 



9.8569 



.8557 
.8545 
.8532 
.8520 
.8507 



9.8495 



Sin. 



D.r 



1.0 
1.0 
1.0 
1.0 

1.0 
1.0 
1.0 
1.0 
1.0 

1.0 

1.1 

1.0 
1.0 

1.1 

1.0 

1.1 

1.1 
1.1 

1.0 

1.1 
1.1 

1.1 

1.1 
1.1 

1.2 

1.1 
1.1 

1.2 

1.1 
1.2 
1.1 
1.2 
1.2 

1.2 

1.1 



1.2 
1.3 

1.2 



D.r 



Tan. 



9.8850 

.8876 
.8902 



9.8928 



.8954 
.8980 
.9006 
.9032 
.9058 



9.9084 



.9110 
.9135 
.9161 
.9187 
.9212 



9.9238 



.9264 
.9289 
.9315 
.9341 
.9366 



9.9392 



.9417 
.9443 
.9468 
.9494 
.9519 
9.9544 



.9570 
.9535 
.9621 
.9646 
.9671 



9.969'; 



.9722 
.9747 
.9772 
.9798 
.9823 



9.9848 
.9874 
.9899 
.9924 
.9949 
_^9975 
O.OOOO' 



D.r 



2.6 
2.6 
2.6 

2.6 
2.6 
2.6 
2.6 
2.6 
2.6 

2.6 

2.5 
2.6 
2.6 
2.5 
2.6 

2.6 

2.5 
2.6 
2.6 
2.5 
2.6 

2.5 
2.6 
2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.5 
2.5 
2.6 
2.5 
2.5 
2.6 

2.5 
2.5 
2.5 
2.6 

2.5 



Cot. 



Cot. 'D, 1' 



0.1150 
.1124 
.1098 



0.1072 



.1046 
.1020 
.0994 
.0968 
.0942 



0.0916 



.0890 
.0865 
.0839 
.0813 
0788 
0.0762 



.0736 
.0711 
.0685 
.0659 
.0634 



0.0608 



.0583 
.0557 
.0532 
.0506 
.0481 



0.0456' 



.0430 
.0405 
.0379 
.0354 
.0329 



0.0303 



.0278 
.0253 
.0228 
.0202 
.0177 



0.0152 



.0126 
.0101 
.0076 
.0051 
.0025 



0.0000 



Tan. 



52° 30' 
52° 20' 
52° 10' 

52° C 

51° 50 
51° 40' 
51° 30' 
51° 20' 
51° 10' 
51° 0' 

50° 50' 
50° 40' 
50° 30' 
50° 20' 
50° 10' 
50° 0' 

49° 50' 
49° 40' 
49° 30' 
49° 20' 
49° 10' 

49° 0' 

48° 50' 

48° 40' 

48° 30' 

48° 20' 

48° 10' 

48° 0' 

47° 50' 
47° 40' 
47° 30' 
47° 20' 
47° 10' 
47° 0' 

46° 50' 
46° 40' 
46° 30' 
46° 20' 
46° 10' 
46° 0' 

45° 50' 
45° 40' 
45° 30' 
45° 20' 
45° 10' 
45° 0' 



Angle 



2^ A MANUAL FOR. NORTHERN WOODSMEN 



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^29 



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18 80 

19 62 

20 41 

21 19 

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17 97 

18 80 

19 61 

20 41 

21 19 

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22 71 

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230 A MANUAL FOR NORTHERN WOODSMEN 



NATURAL SINES AND COSINES 



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' 



Sin. 



.000000 



.002909 
.005818 
.008727 
.011635 
.014544 



.017452 



.02036 
.02327 
.02618 
.02908 
.03199 



.03490 



.03781 
.04071 
.04362 
.04653 
.04943 



.05234 



.05524 
.05814 
.06105 
.06395 
.06685 



.06976 



.07266 
.07556 
.07846 
.08136 
.08426 



.08716 



.09005 
.09295 
.09585 
.09874 
.10164 



.10453 



.10742 
.11031 
.11320 
.11609 
.11898 



.12187 



.12476 
.12764 
.13053 



Cos. 



Cos. 



1.0000 
1.0000 
1.0000 
1.0000 
.9999 
.9999 



.9998 



.9998 
.9997 
.9997 
.9996 
.9995 



.9994 



.9993 
.9992 
.9990 
.9989 
.9988 



.9986 



.9985 
.9983 
.9981 
.9980 
.9978 



.9976 



.9974 
.9971 
.9969 
.9967 
.9964 



.9962 



.9959 
.9957 
.9954 
.9951 

.9948 



.9925 



.9922 
.9918 
.9914 



Sin. 



90° 

50' 
40' 
30' 
20' 
10' 
89° 

50' 
40' 
30' 
20' 
10' 
88° 

50' 
40' 
30' 
20' 
10' 

87° 

50' 
40' 
30' 
20' 
10' 

86° 

50' 
40' 
30' 
20' 
10' 
85° 

50' 
40' 
30' 
20' 
10' 

84° 

50' 
40' 
30' 
20' 
10' 

83° 

50' 
40' 
30' 



A. 



30' 
40' 
50' 

8° 

10' 
20' 
30' 
40' 
50' 

9° 

10' 
20' 
30' 
40' 
50' 

10° 

10' 
20' 
30' 
40' 
50' 

11° 

10' 
20' 
30' 
40' 
50' 
12° 

10' 

20' 
30' 
40' 
50' 

13° 

10' 
20' 
30' 
40' 
50' 
14° 

10' 
20' 
30' 
40' 
50' 

15° 



Sin. 



1305 
1334 
1363 



1392 

1421 
1449 
,1478 
,1507 
1536 



1564 



1593 
1622 
1650 
1679 
1708 



1736 



1765 
1794 
,1822 
.1851 
,1880 



,1908 



,1937 
,1965 
,1994 
,2022 
2051 



,2079 



.2108 
.2136 
.2164 
.2193 
.2221 



2250 



.2278 
.2306 
.2334 
.2363 
.2391 



,2419 



Cos. 



Cos. 



9914 
9911 
9907 

9903 

,9899 
,9894 
,9890 

,9886 
.9881 



.9877 
.9872 
.9868 
.9863 
.9858 
.9853 



^48 
.9843 
.9838 
.9833 
.9827 
.9822 



.9816 



.9811 
.9805 
.9799 
.9793 

.9787 



.9781 



.9775 
.9769 
.9763 
.9757 
S)750 
.9744 



.9737 
.9730 
,9724 
,9717 
9710 



.9703 



,9696 
9689 
9681 
9674 
9667 



9659 



Sin. 



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° 



A. 



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' 



Sin. 



2588 



2616 
2644 
2672 
2700 

,2728 



,2756 



,2784 
2812 
2840 
,2868 
2896 



,2924 

2952 
,2979 
,3007 
.3035 
.3062 



.3090 



.3118 
.3145 
.3173 
.3201 
^228 
.3256 



.3283 
.3311 
.3338 
.3365 
.3393 



,3420 



.3448 
.3475 
.3502 
.3529 
^5^ 
.3584 



.3611 
.3638 
.3665 
.3692 
.3719 
.3746 



3773 
.3800 

3827 



Cos. 



Cos. 



.9659 



9652 
9644 
,9636 
.9628 
.9621 

.9613 



.9605 
.9596 
.9588 
.9580 
.9572 



.9563 



.9555 
.9546 
.953 i 
.9528 
.9520 



.9511 



.9502 
.9492 
.9483 
.9474 
.9465 



.9455 



.9446 
.9436 
.9426 
.9417 
.9407 



.9397 



.9387 
.9377 
.9367 
.9356 
.9346 



.9336 



.9325 
.9315 
.9304 
,9293 
,9283 

9272 



9261 
,9250 
9239 



Sin. 



TABLES RELATING TO PARTS I AND II 



^31 



NATURAL SINES AND COSINES — continued 



A. 


Sin. 


Cos. 




A. 


Sin. 


Cos. 




A. 


Sin. 


Cos. 




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° 


.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' 

36° 

10' 
20' 
30' 
40' 
50' 
37° 

10' 
20' 
30' 


.5000 


.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' 
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° 


.6088 
.6111 
.6134 


.7934 
.7916 

.7898 


30' 
20' 
10' 

52° 

50' 
40' 
30' 
20' 
10' 
51° 

50' 
40' 
30' 
20' 
10' 
50° 

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° 

A. 


.5025 
.5050 
.5075 
.5100 
.5125 


.8646 
.8631 
.8616 
.8601 

.8587 


.3907 


.9205 


.6157 


.7880 


.3934 
.3961 
.3987 
.4014 
.4041 


.9194 
.9182 
.9171 
.9159 
.9147 


.6180 
.6202 
.6225 
.6248 
.6271 


.7862 
.7844 
.7826 
.7808 
.7790 


.5150 


.8572 


.5175 
.5200 
.5225 
.5250 
.5275 


.8557 
.8542 
.8526 
.8511 
,8496 


.4067 


.9135 

.9124 
.9112 
.9100 
.9088 
.9075 


.6293 


.7771 


.4094 
.4120 
.4147 
.4173 
.4200 


.6316 
.6338 
.6361 
.6383 
.6406 


.7753 
.7735 
.7716 
.7698 
.7679 


.5299 


.8480 


.5324 
.5348 
.5373 
.5398 
.5422 


.8465 
.8450 
.8434 
.8418 
.8403 


.4226 


.9063 


.6428 


.7660 


.4253 
.4279 
.4305 


.9051 
.9038 
.9026 


.6450 
.6472 
.6494 
.6517 
.6539 


.7642 
.7623 
.7604 
.7585 
.7566 


.5446 


.8387 


.4331 
.4358 


.9013 
.9001 

.8988 


.5471 
.5495 
.5519 
.5544 
.5568 


.8371 
.8355 
.8339 
.8323 
.8307 


.4384 


.6561 

.6583 
.6604 
.6626 
.6648 
.6670 


.7547 


.4410 .8975 
.4436 .8962 
.4462 .8949 
.4488 .8936 
.4514 .8923 


.7528 
.7509 
.7490 
.7470 
.7451 


.5592 


.8290 


.5616 
.5640 
.5664 
.5688 
.5712 


.8274 
.8258 
.8241 
.8225 
.8208 

.8192 


.4540 .8910 


.6691 


.7431 
.7412 
.7392 
.7373 
.7353 
.7333 


.4566 .8897 
.4592 .8884 
.4617 .8870 


.6713 
.6734 
.6756 
.6777 
.6799 


.5736 


.4643 
.4669 

.4695 


.8857 
.8843 


.5760 
.5783 
.5807 
.5831 
.5854 


.8175 
.8158 
.8141 
.8124 
.8107 
.8090 


.8829 


.6820 


.7314 


.4720 
.4746 
.4772 


.8816 
.8802 
.8788 


.6841 
.6862 
.6884 
.6905 
.6926 


.7294 
.7274 
.7254 
.7234 
.7214 


.5878 


.4797 : .8774 
.4823 .8760 


.5901 
.5925 
.5948 
.5972 
.5995 


.8073 
.8056 
.8039 
.8021 
.8004 


.4848 .8746 


.6947 


.7193 


.4874 1 .8732 
.4899 ' .8718 
.4924 .8704 
.4950 .8689 
.4975 .8675 


.6967 
.6988 
.7009 
.7030 
.7050 


.7173 
.7153 
.7133 
.7112 
.7092 

.7071 


.6018 


.7986 


.6041 
.6065 
.6088 


.7969 
.7951 


.5000 j .8660 


.7934 30' 


.7071 




Cos. Sin. 


A. 




Cos. 


Sin. 


A. 




Cos. 


Sin. 



232 



A MANUAL FOR NORTHERN WOODSMEN 



NATURAL TANGENTS AND COTANGENTS 



A. 



0° 

10' 
20' 
30' 
40' 
50' 

1° 

10' 
20' 
30' 
40' 
50' 
2° 

10' 
20' 
30' 
40' 
50' 

3° 

10' 
20' 
30' 
40' 
50' 

4° 

10' 
20' 
30' 
40' 
50' 
5° 

10' 
20' 
30' 
40' 
50' 

6° 

10' 
20' 
30' 
40' 
50' 

7° 

10' 
20' 
30' 



Tan. 



,000000 



.002909 
.005818 
.008727 
.011636 
.014545 



.017455 



.02036 
.02328 
02619 
02910 
03201 



03492 



.03783 
.04075 
.04366 
.04658 
■04949 
.05241 



05533 
05824 
06116 
06408 
06700 



06993 



07285 
07578 
07870 
08163 
08456 



.08749 



.09042 
09335 
.09629 
.09923 
10216 



10510 



10805 
11099 
11394 
11688 
11983 



12278 



.12574 
.12869 
13165 



Cot. 



Cot. 



00 



343.7737 

171.8854 

114.5887 

85.9398 

68.7501 



57.2900 



49.1039 
42.9641 
38.1885 
34.3678 
31.2416 



28.6363 



26.4316 
24.5418 
22.9038 
21.4704 
20.2056 



19.0811 



18.0750 
17.1693 
16.3499 
15.6048 
14.9244 



14.300^ 



13.7267 
13.1969 
12.7062 
12.2505 
11.8262 

11.4301 



11.0594 
10.7119 
10.3854 
10.0780 

9.7882 



9.5144 



9.2553 
9.0098 
8.7769 
8.5555 
8.3450 



8.1443 



7.9630 
7.7704 
7.5958 



Tan. 



90° 

50' 
40' 
30' 
20' 
10' 
89° 

60' 
40' 
30' 
20' 
10' 
88° 

50' 
40' 
30' 
20' 
10' 
87° 

50' 
40' 
30' 
20' 
10' 

86° 

50' 
40' 
30' 
20' 
10' 

85° 

50' 
40' 
30' 
20' 
10' 
84° 
50' 
40' 
30' 
20' 
10' 

83° 

50' 
40' 
30' 



A. 



30' 
40' 
50' 

8° 

10' 
20' 
30' 
40' 
50' 

9° 

10' 
20' 
30' 
40' 
50' 

10° 

10' 
20' 
30' 
40' 
50' 
11° 

10' 
20' 
30' 
40' 
50' 
12° 

10' 
20' 
30' 
40' 
50' 

13° 

10' 
20' 
30' 
40' 
60' 
14° 

10' 
20' 
30' 
40' 
50' 
15° 



Tan. 



1317 
,1346 
.1376 



.1405 



1436 
1466 
1496 
1524 
1654 



1684 



.1614 
.1644 
.1673 
.1703 
.1733 



1763 



,1793 
,1823 
,1863 
,1883 
.1914 



1944 



1974 
,2004 
2036 
2066 
3095 



2126 



.2156 
.2186 
2217 
,2247 

2278 



.2309 



2339 
2370 
2401 
2432 
2462 



2493 



2524 
2555 
2586 
2617 
2648 



2679 



Cot. 



Cot. 



7.5958 

7.4287 
7.2687 



7.1164 



6.9682t 
6.8269 
6.6912 
6.5606 
6.4348 



6.3138 



6.1970 
6.0844 
5.9768 
6.8708 
6.7694 



6.6713 



6.6764 
6.4845 
6.3956 
6.3093 
5.2257 



5.1446 



6.0658 
4.9894 
4.9162 
4.8430 
4.7729 



4.7046 



4.6382 
4.5736 
4.6107 
4.4494 
4.3897 



4.3315 



4.2747 
4.2193 
4.1653 
4.1126 
4.0611 

4.0108 



3.9617 
3.9136 
3.8667 
3.8208 
4.7760 



3.7321 



Tan. 



30' 
20' 
10' 

82° 

60' 
40' 
30' 
20' 
10' 

81° 

60' 
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' 
60' 

16° 

10' 
20' 
30' 
40' 
50' 

17° 

10' 
20' 
30' 
40' 
60' 
18° 
10' 
20' 
30' 
40' 
60' 

19° 

10' 
20' 
30' 
40' 
60' 

20° 

10' 
20' 
30' 
40' 
60' 
21° 

10' 
20' 
30' 
40' 
60' 

22° 

10' 
20' 
30' 



Tan. 



2679 



2711 

2742 
.2773 
.2805 
.2836 



.2867 



.2899 
.2931 
.2962 
.2994 
.3026 
.3057 



.3089 
.3121 
.3163 
.3186 
.3217 



.3249 



.3281 
.3314 
.3346 
.3378 
.3411 



.3443 



.3476 
.3508 
.3541 
.3574 
.3607 



.3640 



.3673 
.3706 
.3739 
,3772 
.3806 



3839 
3872 
3906 
3939 
3973 
4006 



4040 



4074 
4108 
4142 



Cot. 



Cot. 



3.7321 



3.6891 
3.6470 
3.6059 
3.5666 
3.6261 



3.4874 



3.4496 
3.4124 
3.3759 
3.3402 
3.3062 



3.2709 



3.2371 
3.2041 
3.1716 
3.1397 
3.1084 



3.0777 



3.0475 

3.01' 

2.9887 

2.9600 

2.9319 



2.9042 



2.8770 
2.8602 
2.8239 
2.7980 
2.7725 



2.7476 



2.7228 
2.6986 
2.6746 
2.6611 
2.6279 

2.6051 



2.6826 
2-6606 
2 6386 
2.6172 
2.4960 



2.4751 



2.4546 
2.4342 
2.4142 



Tan. 



TABLES RELATING TO PARTS I AND II 



233 



NATURAL TANGENTS AND COTANGENTS 



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° 



Tan. 



,4142 
,4176 
,4210 



4245 



,4279 
4314 
4348 
,4383 
4417 



,4452 



,4487 
,4522 
,4557 
,4592 
,4628 



,4663 



,4699 
,4734 
,4770 
.4806 
.4841 



.4877 



.4913 
4950 
.4986 
.5022 
.5059 



.5095 



.5132 
.5169 
.5206 
.5243 
.5280 
^53 17 



.5774 



Cot. 



Cot. 



2.4142 
2.3945 
2.3750 



2.3559 



2.3369 
2.3183 
2.2998 
2.2817 
2.2637 



2.2460 



2.22S6 
2.2113 
2.1943 
2.1775 
2.1609 



2.1445 



2.1283 
2.1123 
2.0965 
2.0809 
2.0655 
2.0503 



2.0353 
2.0204 
2.0057 
1.9912 
1.9768 



1.9626 



1.9486 
1.9347 
1.9210 
1.9074 
1.8940 



1.880; 



1.8676 
1.8546 
1.8418 
1.8291 
1.8165 



1.8040 



1.7917 
1.7796 
1.7675 
1.7556 
1.7437 



1.7321 



Tan. 



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° 



A. 



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' 
36° 

10' 
20' 
30' 
40' 
50' 

37° 

10' 
20' 
30' 



Tan. 



,5774 

,5812 
,5851 
,5890 
5930 
,5969 

6009 



.6048 
.6088 
.6129 
,6168 
.6208 



,6249 



6289 
,6330 
,6371 
,6412 
,6453 



,6494 



,6787 
,6830 
,6873 
,6916 
,6959 
,7002 



7046 
7089 
7133 
7177 
7221 



r265 



r3io 

'355 
r400 
r445 
r490 



r536 

r58i 

r627 
r673 



Cot. 



Cot. 



1.7321 



1.7205 
1.7090 
1.6977 
1 .6864 
1.6753 



1 .6643 



1.6534 
1.6426 
1.6319 
1.6212 
1.6107 



1.6003 



1 .5900 
1.6798 
1.5697 
1.5597 
1.5497 



1.5399 

1.5301 
1.5204 
1.5108 
1.5013 
1.4919 



1.4826 

1.4733' 
1.4641 
1.4550 
1.4460 
1.4370 



1.4281 



1.4193 
1.4106 
1.4019 
1.3934 
1.3848 



1.3764 



1.3680 
1.3597 
1.3514 
1.3432 
1.3351 



1.3270 



1.3190 
1.3111 
1.3032 



Tan. 



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' 



A. 



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° 



Tan. 



.7860 
.7907 
.7954 
.8002 
.8050 

.8098 



.8146 
.8195 
.8243 
.8292 
.8342 



.8391 



.8441 
.8491 
.8541 
.8591 
.8642 



.8693 



.8744 
.8796 
.8847 
.8899 
.8952 



.8004 



.9057 
.9110 
.9163 
.9217 
.9271 



.9325 
.9380 
.9435 
.9490 
.9545 
.9601 

.9657 
.9713 
.9770 
.9827 
.9884 
.9942 



Cot. 



1.0000 



Cot. 



1.3032 
1.2954 
1.2876 



1.2799 



1.2723 
1.2647 
1.2572 
1.2497 
1.2423 



1 .2349 



1.2276 
1.2203 
1.2131 
1.2059 
1.1988 



1.1918 



1.1847 
1.1778 
1.1708 
1.1640 
1.1571 



1.1504 



1.1436 
1.1369 
1.1303 
1.1237 
1.1171 



1.1106 



1.1041 
1.0977 
1.0913 
1.0850 
1.0786 



1.0724 

1.0661 
1.0599 
1.0538 
1.0477 
1.0416 



1.0355 



1.0295 
1.0235 
1.0176 
1.0117 
1.0058 



1.0000 



Tan. 



234 A MANUAL FOR NORTHERN WOODSMEN 




04 



C3 
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SECTION II 
TABLES RELATING TO PARTS UI AND IV 

1. Volumes of Cylindebs (Logs) in Cubic Feet . . 236 

2. Are-\s of Circles or Basal Areas 238 

3. Cord Wood Rule 239 

4. New Ha^vipshire 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. W'hite 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. W^estern 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 



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238 A IVIANUAL FOR NORTHERN WOODSME2S 



AREA OF CIRCLES OR BASAL AREAS 
(Gives also Contents of Cylinders one foot long) 



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1.0 


.005 


13.0 


0.92 


25.0 


3.41 


37.0 


7.47 


49.0 


13.10 


1.5 


.012 


13.5 


0.99 


25.5 


3.55 


37.5 


7.67 


49.5 


13.37 


2.0 


.022 


14.0 


1.07 


26.0 


3.69 


38.0 


7.88 


50.0 


13.64 


2.5 


.034 


14.5 


1.15 


26.5 


3.83 


38.5 


8.08 


50.5 


13.91 


3.0 


.049 


15.0 


1.23 


27.0 


3.98 


39.0 


8.30 


51.0 


14.19 


3.5 


.067 


15.5 


1.31 


27.5 


4.12 


39.5 


8.51 


51.5 


14.47 


4.0 


.087 


16.0 


1.40 


28.0 


4.28 


40.0 


8.73 


52.0 


14.75 


4.5 


.111 


16.5 


1.48 


28.5 


4.43 


40.5 


8.95 


52.5 


15.03 


5.0 


.136 


17.0 


1.58 


29.0 


4.59 


41.0 


9.17 


53.0 


15.32 


5.5 


.165 


17.5 


1.67 


29.5 


4.75 


41.5 


9.39 


53.5 


15.59 


6.0 


.196 


18.0 


1.77 


30.0 


4.91 


42.0 


9.62 


54.0 


15.90 


6.5 


.230 


18.5 


1.87 


30.5 


5.07 


42.5 


9.85 


54.5 


16.20 


7.0 


.267 


19.0 


1.97 


31.0 


5.24 


43.0 


10.08 


55.0 


16.50 


-2-5 


.307 


19.5 


2.07 


31.5 


5.41 


43.5 


10.32 


55.5 


16.80 


^.0 


.349 


20.0 


2.18 


32.0 


5.59 


44.0 


10.56 


56.0 


17.10 


8.5 


.394 


20.5 


2.29 


32.5 


5.76 


44.5 


10.80 


56.5 


17.41 


9.0 


.442 


21.0 


2.41 


33.0 


5.94 


45.0 


11.04 


57.0 


17.72 


9.5 


.492 


21.5 


2.52 


33.5 


6.12 


45.5 


11.29 


57.5 


18.03 


10.0 


.545 


22.0 


2.64 


34.0 


6.30 


46.0 


11.54 


58.0 


18.35 


10.5 


.601 


22.5 


2.76 


34.5 


6.49 


46.5 


11.79 


68.5 


18.67 


11.0 


.660 


23.0 


2.89 


35.0 


6.68 


47.0 


12.05 


39.5 


18.99 


11.5 


.721 


23.5 


3.01 


35.5 


6.87 


47.5 


12.26 


59.5 


19.31 


12.0 


.785 


^4.0 


3.14 


36.0 


7.07 


48.0 


12.57 


60.0 


19.63 


12.5 


.852 


24.5 


3.27 


36.5 


7.27 


48.5 


12.83 


60.5 


19.96 



TABLES RELATING TO PARTS III AND IV 239 



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OSOO(Nt^05<©'Ot^05(NTt<CD05.-lf<5»Ot^O<N-<*<OCir-iCO«0000 
i-i(N (N (N CO ■* •* ■* »0 »0 lO »0 CO CO CO CO t^ t^ t> t^ t^ 00 00 00 00 0» 


i-H 


°^2g^S??^^^'^^SSS§g8SSSg^F^^^^§ 


CO 

1-1 


^^2c3g5?5^J?^5$^^^§SS:§^§§SSSSgF: 


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2222S^j;??;S^??^5^^^^^g;^f;5S5g§§5S 




2-:;22?^^^gj;5??^JS?:5^^^^^^^^^SS3S 


CO 
t-l 


5S22;22g^ss^?5S?;?:???^i?5?^^5^^g^^^ 




-^^S^SSgj^g^^^^^S^g^g^^;?????^^???;?^^^ 


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^oq»oo5co 

C^iOCOo60'-H'<*»f5lOCOt^r-0005050— <iM<NfCTjHTtlOCOCDt-00 

,_l,-(,_l^_l_l_l_(^,_l(^^(^^c<,c^o^o^c^c^c^,c^c^(^^, 


OS 


CC lO CD 00 CC 

(^i•<l<lOcbt>o■-^<N(^^^5^o■*lOlOoco^^^^ooo5CiOO^^<N(:c 

,-l,-(r-l^i-lrt^^^i-(.-(r-t.-l,-lr-<(NCN(N(N<N(N 


00 


00 lO •^_ ro 00 1-; 05 ec 00 

i-JeC-*'»0>OI>o605CsO'-"-i'-'(N<NMC«5-*-<*iOiOCOcDcDt^t^OO 


t^ 


■*t-.Tj^,-;T}<iooq<N»ooq<N'Ooqc<iioo3 

r-4C<icO-^'-*"»OcOt^t^t-^o6oo'odci05C50'-<'-i.-<(N(NC<IMfOfO-* 


CO 


ooiooc^oo<N»ooqpc<i»ooqp(N»ooqp<Nioooo(Nioooo 
i-4(N(NMcoTjiiokO»o»ocdcocdco't^i>t^r^ododo6o6a>oioioid 


»o 


i^-*t^^(MooiocqooO(NfCioN;oqo<N 

O ^ 1-^ C<1 Ci (N CO CO C<3 •*'"*■*■*■*■ Tf<' »0 "5 


■* 


■* 05 1-" CO ■* 00 <N CO ■* CO t^ 00 05 o 

O d -< ^' ^' ^ oi (N (N (N (N ci IN ^i 


n 


(NiOcOt^OOO 

<6d>dd><6^ 


m 




■^oooc^cocoo— i(Nr0'*»ocoi^00C5O^cic0'*»ocit^00CiO 
^^_i,_((MCv^c^c<j(MC^<N(N(N(Ncocococorororococoro-* 



240 



A MANUAL FOR NORTHERN WOODSMEN 



I>0 • CO 
(N(N • CO 



• CO -co -co 






Cqf0-*iOc0l:^00C5O^<Nf0'*i0i©t^C00>O'-i(NC0'*iOC0t^00a>O 
^^^^,_t^^^(N(N(M(N(N(N<N(N(M<NCOCOCOCOCOCOCOCOCOC0'^ 



i-i.-lC^C0^i0Ot^0000C5O^<Nr0-*iO'CcOt^00CiO'-i(N<NC0-*»O 
^rt^^^,_i^^^rH,-H(N(N(N(N(N<N(NlN(N(N(NC0COCOCOCOCOCO 



00 -OO •'-((N •CO'^ -lOCO -1^00 -OiO 'r-KN • CO '^ -lOO 

.ii .,-lrH -i-^rH -rH^ -l-H,-! -.-((N -CaC^ -(NM -IMIN 



t^ -00 -Oi -O -^(N -CO ••* -lOCO •!%• -00 -O) •0'-< -IN 
. ,-H .,— I.— I •■<-{ • i-( -i-li-l 'i-H •i-l 'i-H 'C^C^ -W 



■CD • t^ -OO -05 



■.-H -(N -CO 



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iN?0'l<>CcOt^0005 0^C<lCO-*"^CDf-0005 0'^(NCO'*>OCOt^OOOSO 
^^^^^,_(^^(M(M(M(M(N(NIN(M<NC^COCOC0COCOCOC0COCOC0-* 



TABLES RELATING TO PARTS III AND IV 241 



l^00000500'-iT-i(NMCO'*iOiO«0<Ot^OOOOCiOO'-<^WCCCO'*»C 
rH^,-l,-(,-H,-H,-irt,-irt— i^^,-<,-i,-H01(M(N<M(N(N<N(NCS 



oo 



■O • — t^^^^5^0 — t>(N«Tj<OO(N0C-<*OcD(NQ0rf<OcD(N00 

•C5 •OO'-i'-i<NC0CC-*-^i0CDOt^t^00w3OOO-^<N(N:CC0 

. rt ,_, ^ ,_ ^ ^ ,_, ^ ^ ^ ^ ^ ^ ^ ^ ^ „ C^l Cvj (N (N <N (N (N 



00 



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<©t^t^00C2C3OO'-H^(N^0r0'<1<Tj<ir)iCC0Ot^XXC;OOO— i(N(N 



■*C5»OOkO-HcD'-it^<N00CC00'*0i'*OiCO<O^r^(NI>C<l00C0C0-^ 
«0«Dt>OOOOC5C500'-^^iM(NfOM-*"5»C5D<r>t^I>«XCrjOOO" 

rt,-H^,-(r-^rHl-(l-Hl-H,-l,-l,-l,-l,-l,-l,-lr-ll-H^(N(N(N 



,-HOi-iiO'-'CD^CO-^CO-<CC^CO(Nt^(Nr^(Nr^(Nr>-<Nr-'Mt^C<)t^lM 

,-|^rtr-lr-lr-(r-(,-HT-l.-ll-(T-lT-l,-l,-,r^.-l.-H,-H^(N 



r^<Nt^C<U^-H(O^OOiOO'OOi005Tti05-<tXc<;XCCI^(Nt^(NI>»-i 
i0OOI>I>XX0S05OO^'-^lM!NC^C0r0-*-^'0i0i©Ot>l>XX0i 



s 

S3 

p 

c 



qqqqqqqqqqqopqqqpqqqpppp>oqqqq 

iOiOcOCOt>l>XXw5CiOOO^^<N(NrCCClTTj<-<*i»0»OCOCCt^t^X 






«(NcOO-*XC<IOO-*XlNi©0'*X<NCOO-*X(N?DO-*X(NiriO 
■<ti»OiOCicO<©I>I>XXXC50000^^04(N(NCOCC'T'-*TfiO>00 



»OOfO<CiO-*«'-<iOOfCCOO'*X'-<»005C«5COO-<*'X'-i»OOCOCOO 
■^Tj<iOiO!£)COCOI>I>l>«XC»05C5000^'--<N<N<NCOCCrO'*'*iO 



•^■^T^io»oo«occn>t>t>xxxoo30;ooo-^'-'-^c^c^rcccrcT 



C0'^'3<'3<'*»0i0i0ir>i«ir)t^t^l>XXXXC5C5©OOO-^'-i^<N(N 



■*^^O^ocox^'*^-oco>ox— '■*r^OcciCX'-i-<*<r^o<NioX'— ■<*' 

eOCO'<l"<*-*"<l'iOiO»OCOtOCOOt>t>I>XXXXOi0300000-^'H 



■ ■<}. .10 • -o 



•o -o 
■o -o 






MfC-*iCcOt^XOO'-^<NM-*>0«C«^XC50-<C<lr?Tf<»OOt^«00 



242 



A MANUAL FOR NORTHERN WOODSMEN 



NEW YORK STANDARD, DIMICK, OR 
GLENN'S FALLS RULE 



Hi 


Diameter in Inches 




3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


ft. 

4 


.009 


.01 


.02 


.03 


.04 


.06 


.07 


.09 


.10 


.12 


.14 


.17 


.19 


5 


.01 


.02 


.03 


.04 


.05 


.07 


.08 


.11 


.13 


.15 


.18 


.21 


.24 


6 


.01 


.02 


.03 


.05 


.06 


.08 


.10 


.13 


.16 


.18 


.22 


.25 


.29 


7 


.02 


.02 


.04 


.05 


.08 


.10 


.12 


.15 


.18 


.22 


.25 


.29 


.33 


8 


.02 


.02 


.04 


.06 


.09 


.11 


.14 


.17 


.21 


.25 


.29 


.33 


.38 


9 


.02 


.03 


.05 


.07 


.10 


.12 


.15 


.19 


.24 


.28 


.33 


.37 


.43 


10 


.02 


.03 


.05 


.08 


.11 


.14 


.17 


.22 


.26 


.31 


.36 


.42 


.48 


11 


.03 


.03 


.06 


.08 


.12 


.15 


.19 


.24 


.29 


.34 


.40 


.46 


.52 


12 


.03 


.04 


.06 


.09 


.13 


.17 


.20 


.26 


.31 


.37 


.43 


.50 


.57 


13 


.03 


.04 


.07 


.10 


.14 


.18 


.22 


.28 


.34 


.40 


.47 


.54 


.62 




16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


4 


.22 


.25 


.28 


.31 


.34 


.38 


.41 


.45 


.49 


.53 


.58 


.62 


.67 


5 


.27 


.31 


.35 


.38 


.43 


.47 


.52 


.57 


.62 


.67 


.72 


.78 


.83 


6 


.33 


.37 


.42 


.46 


.51 


.56 


.62 


.68 


.74 


.80 


.86 


.93 


1.00 


7 


.38 


.43 


.48 


.54 


.60 


.66 


.72 


.79 


.86 


.93 


1.01 


1.09 


1.17 


8 


.44 


.49 


.55 


.62 


.68 


.75 


.82 


.90 


.98 


1.06 


1.15 


1.24 


1.34 


9 


.49 


.55 


.62 


.69 


.77 


.84 


.93 


1.02 


1.11 


1.20 


1.29 


1.40 


1.50 


10 


.55 


.62 


.69 


.77 


.85 


.94 


1.03 


1.13 


1.23 


1.33 


1.44 


1.55 


1.67 


11 


.60 


.68 


.76 


.85 


.94 


1.03 


1.13 


1.24 


1.35 


1.46 


1.58 


1.71 


1.84 


12 


.66 


.74 


.83 


.92 


1.02 


1.13 


1.24 


1.36 


1.48 


1.60 


1.73 


1.86 


2.00 


13 


.71 


.80 


.90 


1.00 


1.11 


1.22 


1.34 


1.47 


1.60 


1.73 


1.87 


2.02 


2.17 




29 


30 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 




4 


.72 


.77 


.82 


.87 


.93 


.98 


1.04 


1.10 


1.17 


1.23 


1.30 


1.36 




5 


.90 


.96 


1.02 


1.09 


1.16 


1.23 


1.30 


1.38 


1.46 


1.54 


1.62 


1.70 




6 


1.08 


1.15 


1.23 


1.31 


1.39 


1.48 


1.56 


1.66 


1.75 


1,85 


1.94 


2.04 




7 


1.25 


1.34 1.43 


1.53 


1.63 


1.72 


1.83 


1.93 


2.04 


2.15 


2.27 


2.39 




8 


1.43 


1.53 1.64 


1.75 


1.86 


1.97 


2.09 


2.21 


2.33 


2.46 


2.59 


2.73 




9 


1.61 


1.72 


1.84 


1.97 


2.09 


2.22 


2.35 


2.49 


2.62 


2.77 


2.91 


3.07 




10 


1.79 


1.92 


2.05 


2.18 


2.32 


2.46 


2.61 


2.76 


2.92 


3.08 


3.24 


3.41 




11 


1.97 


2.11 


2.25 


2.40 


2.56 


2.71 


2.87 


3.04 


3.21 


3.38 


3.56 


3.75 




12 


2.15 


2.30 


2.46 


2.62 


2.79 2.95 


3.13 


3.31 


3.50 


3.69 


3.89 


4.09 




13 


2.33 


2.49 


2.66 


2.84 


3.02 3.20 


3.39 


3.59 


3.79 


4.00 


4.21 


4.43 





TABLES RELATING TO PARTS III AND IV 243 



i-i 
O 

o 

Pi 

I— I 

O 
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TTicoor^ooci 



COOlMTf «ooo 
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t^ re O to <M X lO 
CO ■^ iC lO CO CD t--. 



Tf -- ri CO ro —I X 
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C«5 ■^ ■* iQ »0 CO CO 



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CO CO T TT »0 »0 CO 



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(N ec CO ■* •* lO lo 



r-HC^-^CCXC^ 

lO 05 CO t^ ^^ CO o 
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XcOTf COOXcD 
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ooooooo 

X -^ -^ t- O ^t CO 
i-H M (N (N CO CO CO 



Ot^coo t^rco 

CO X -H Tj< CO C5 C<1 
T-H -< IN (N (N (N CO 



O (N lO X C^l iC X 

CO CO X o ro o t^ 

—I T-H .-H (N <N (M IM 



OC5C5XXXX 
■— I CO lO t^ C5 '— I CO 
T-H rt ,-( ,-1 ,-H (N (N 



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1-t C<J (N CO CO CO 






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CO c^ 00 •* o CO e< 

05 ^ IN Tji CD t^ Ol 
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1-1 .-< ^ ^ IN IN (N 



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1-1 CO ic r- C3 1— I CO 



c; c; X i^ X X X 
CO c^ — ' o c: X r^ 
1-1 cc ic t- X O (N 
1-1 rt -< 1-1 .-I IN (N 



0>00i00'*0 

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^IN-TCOXOiN 
rt ^-H-^^(NIN 



CO IN CO -^ lO X (N 

rr N w3 r^ T ^ ci 
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t^ »0 CO 1-1 O X •* 

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1-1 rH 1-1 1-1 r-l rt IN 



■^ CO IN -^ O X X 
lO -H r> CO cr. -* o 
c: ^ (N Tt lo t^ Oi 



CO CO ■^ Tf lO CO CO 
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X C5 1-1 IN -* lO CD 



1-1 Tj< X 1-1 to X <N 
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<N —H O X I^ CD ■<* 
l> O IN lO X 1-1 -^ 

t^ c:5 o -^ IN ■<*< lO 



<NI>COXlNXO 

C50iNCOiOcO X 
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r^ CO CD to lO ■<# •* 

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CO t^ X cr. o — I (N 



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lO CO t^ X 05 O i-H 



<N Tji CO X O <N ■<* 
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lO CD t^ X 05 O 1-1 



ININOOXCOH? 

CO IN 1-1 CI X r^ 2 
»ocot^t^xc55 



CO "3 r~ C5 r-< Tj< CO 
c;r-ioco<Nox 

Tj< lO CO t^ 0^ 05 OS 






(N •* CO X O (N r}< 
•-I ^ 1-1 rH W <N M 

_J 



244 



A MANUAL FOR NORTHERN WOODSMEN 



c3 d 






(NCCTjH-^iOCOCOt^GOOOOTO'-l 



oieccc-*ioioco<ot^ooooo50 



C0 05-^OCDINt^e0CT>»0OOCV| 
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i-tCNfNIMeCCC-^'^iOkCiCOO 
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,-ir-i.-i(N(N(Nc<:)coeoc<3'^'<i<'^ 

i-Hf0C00>i-H'*<t^05(Ni0t>.OC0 

T-lrHrHt-HrH(N(N(NC<l(NCOCO 

t^05T-i(NTf<COOOO^fOiOI:^00 



COCOOOT}<COCOt>XOiOiO'-iN 



c<ieocoec'<*'<*Tt<»o«0(r>i>ooo5 



i-i(NC<l(NC0e0C0-*'*»O;D«0t> 



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rt^^^_iC<j(MC^(MCOCOCO 




co'^'tiooor^oococioO'-H 

00OlM-«^OC»OC^rJ<OaJ'-iC0 
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O5C5CT>O5O500000O00GOGOt^t^ 

t^05^coict>oi^eoior^05'-i 

rt^^,_i^lM(MC<j(MC^CO 




<DiO-rt<COiM^OOCOt^OOrl4 
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o 

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CO^Oit~CO-^(NOOSI>i-OCO'-* 
COTtTftiOtOt^OOOiOiO'-HiMCO 




i-HoocDcO'-ioocoTt<'-io>t^'*'c^ 
eocO'<*<'Cco<©t^ooo5 05 0'-iiM 



TABLES RELATING TO PARTS III AND IV 245 












'-HIM(NCOCO^-<tii-OiCOcOOt> 















C5 05C5 05000 0000 00 OOOOI>t^ 

lOOicot^-Hiooscot^^ioocc 



■^fOfNOOSOOt^iO-^fO-HOO 
iOO>OOt^OTt<OOlMOO-^00^ 



•-iC5t^iO(NO00CD'*<NOaCiO 
COCCrftiOCOt^t^OOOlO^'HC^ 



oaococ<5<-iC5t>.TfiiNot~-io:o 
eocc-<t»ocoot^ooc5CO-H(N 



»-ir^(Mi>.oooofoc5Tf05icoic 
Or>.i.O(NOt^ioiNOi>.ioroo 

C<3CO'*iOOOt>000050'-<(M 

I-H 1— ( 1— ( 



Ot^Tf-^OCDM^OOmcOOt^ 
■*CC(NOC5fOI>^-<*'X<NOO 



iO'-<t^0002iC(NXTfOO(NCi 

T}<x-Hi.oooiMOOfor^OTtn> 



oocicoioomoicoioo 

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»005C0t^O->*X(NOO-<J<I>^ 
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OOO'CQ'COiO'— lO"— 'O*-" 
(NINCOCC^-^OiOCDOt^t^X 



XOfN-JfOXOC^fOXOIN 



246 A MANUAL itcJR NORTHERN WOODSMEN 



B 



^99 J Ut 



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•<tit^OCOCDCiC^kO»H^t^OrOOOi<N»OCOi--(-<*i|>OCOCOC!lC^iCOOi-iT}iOO^ 
WM CO C0C0C0'*'*'3<fO>O»Oi©<O©CDt^t^I> 000000050505 0500 1-1 rH^IM 



000«OM'-tOOcOCO*-ip5<OTt<.-i05CO-*^05t^-^(N05t^'*(NOt:^»0(NOt^'0(N 

(NTtir^OfO'000>-iM<tOO>(MiOt^OCC<r>00'-H-«J<t^C5(N»000'-iCO«005<N^l^O 
C<I<N(NCCOOC*5CO'*M<'*Tt<«OiC»OiCCDCO<©t^I>I>t^0000000505050>000'-i 



0»00»COi«0'ob(OOiOOiOO'00"50iOO>00'OOiOO»00»00»00 
O(N»0t^OiMi0t^ptN»0t^O(N'0r^O(N'0t^OiN»0t^OIMi0t^OlM'0t^O 

(N!N(M<NCCCOCOfOS^rf*'*'»OiO"5>0«3i©COCDt>I>t>t^OOOOOOOOC505C5050 



OCOCOOO'-iCOOOCDb5fOC005<NeOt005^(NCOCOC005(N»000(NCOC5(MUOI>OCO 
000(N'*l>05^CoC5pCO<N'Ot>05^TjicOOOOC^'*t^C5i-iTt<cOOO.-irO>COOO 
.-H(N(N(N(NC^CCOOtofO^-<l<-^'*'*»0>0'OiOcO«DiOcDcOt^t^t^t^0000000005 



lMlN(NCCC«5COCOCO^h»'"*"*"*"^''5"'<C>COCOCOOCOCDI>OOOOOOOOC5050500 
iaDOOOC^'*«OOOOP<lr*tOOOOC^'*'5DOOOlN'*COOOO<N'<T'COOOO(NTtiiri(:r->-( 
rHT-((N(N<N(N(NfCt0MC0C<:-*'*-<3<-^TMO»0>Ok0i0«C'CDO<£>C0t-l>t-t>t^00 




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)iOCDOOC50<MCC'OcD00050iNCOiO;Or--050(NCO-<ti;0 
l(N(N(N(NCOCOCOCCC<5COCO-<*'*'*-<ti'<*-rPT}<iO»0»0>00 



000(N>OI>Oi-i-^toboOCO»OI>05iN'*COOO^C<:»OI>0(NTj<cOC5'-HCO>COOO 
05>-i(NOQ-*":)J^OOt50 0)r0^kO^OOC;0^00'*'OCD00050'-<<N'*'CcCI>C5 



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N -H O 05 00 t^ ?D »0 M< CO (N 1-1 O C5 « r^ I© "5 •* CO (N ^ O 05 00 t^ «D »0 TfCC N 1-H O 

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rHrHt-ir-(U-<t-HT^i-li-H.-(.-((M(N(NlN(N(NC^(M(NC^(NCOC0C0COC0C0C0 



000>OCOi-lOO<OCOMbOCDCO^OOCD-^^05tf5-*(N05<ri-*(N05«0»0(NOt^»0<N 
CO<£>t^0005050'-HrNIMCO'*iC»0<©t^XOOOO^'-i(NfO'*-<*<'OOt^«00050 

rH,-(fHl-Hr-li-(,-li-l.-li-lr-(rHr-l(N(N(N(N(N(N(NM<N(N(NC^C<lCO 



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■" i(NCO:0'*>0>OCOCOt^OOOOC500^'-i(N~:!CO'*>0 



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<N CO O ■* 00 (N CO O,'^ DO IM CO O ■* 00 iM O O •* 00 IN to O 'f 00 (N CD O -^ 00 (N «5 O 
COCO^^'<J<»0>Oco'©C01>t-00000005C5000^'-i(M(N<NCOrO-^-*'*iOlOCD 



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lN(NCOCOCO-^-<l'-<l<'^»0»OiOCOCOcDl>t>t^00000000050505000-H,-Hi-(TH(N 



OOOCOiOr^C5(NTf<cOOOT-H^OCDOCON-^cOO)— <C0>C00O<N'*t^<35^C0»O00O 
i-HC^C^lOl<NC<lC0C0C0C0'*-*'^-*'O»O»OiOiOCDCOCDCOt^t^t^I>t^00000000Oi 



<(N(NlM(N?^(NC0C0COC0C0C0C0'*'^-*'*'*'*'O»O»O'OlO»OW5COCO 



m ooo50'-l(^^co•*lOco^^ooaJO^(N^5•>*llOcD^^ooo50^(Nco•*>ocot^ooo50 

,-t,-H,-(.-(,-lTH.-(^rH,-((N(NM(NlN<N(N(N(N(NC0C0COCOC0C0C0COCO:O-^ 



199J ni 



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,-(^r-li-lrH>-H;,-(p-i,-(^(M(NC>^(N(M(N(N(NIN(NCOCOCOCOCOCCCOCOCOfO-<*' 



TABLES RELATING TO PARTS III AND IV 247 






CO 05 0- 



i(NCO"*lO;Ot^OOOO^<NfO'5f<lOCOI>OOC30'-<<NCO-*»OOt^00050 



ooooooooooooooooooooooooooooooooo 
ooooooooooooooooooooooooooooooooo 
oocnO'-HiNeci'^'O^r^oocjO'-iiMco'^'Oot^cocjO^CMcO'^'Ocot^ooosO 

^^^rt,_H,-i,-l,-Hi-HT-(N(NCv>IMIM(N(N(N(N(NCOeOCOeOeOeOCOCOCCCC-V 



i-i(©'-tC0'-it^'-i<O^«0^<D<Nt:^i-it^C^C0<Nt^(NcD(NCOlNt^C^t^fCt^C<H>(N 

<OlOlO^'*COCO(M(Ni-ir-iOOa>CiOOOCl>l>CDO'OlO'<tTfiCOCO(N(Ni-ir-iOO 

t^OOOO'-llMfOTfi lOOt^OOC^dO'-^tNCO-^'OCO t^OQ,0>0'-i(NfC-*iO<OI>QO 

^ ^ ^ rt r-(i-i ^ .-1 --H rt rt <N (N (N (N (N <N (N Cvl C^ (N CO C<0 CO CO CO CO CO M CO 



<NN(NCOCOCO'*"*'*'*"'5"3»OU5cD<OCOCOCOt^t^I>t^000000000505C>0500 

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t^0005050'^(NCO'*'OCOI>000000'-i<NCO'3"OCOt^I>XC50'-^INCO-<S"OcO 

,-ii-Hi-Hi-ti-li-irH,-HrHi-HrH(M(N(N(N(N(M(N(NC^(N(NCOCOCOCOCOeOCO 



■*OcO^t^<N00-*C:«5O«DTHl>C<100C00S»COC0i-il^(N00'>*0iVOOCD>-it^C0 

OOI>lO'<*(N'-l0500CDiO'<ti(N'-<0500<©>OCO(Ni-HOOOCD'OCO(NOC50CCC«CCO(N 

^t^000iO^'-HlNC0'*i0CDt^r^XC5O'-ilMr0C0-^»OCCt^Q0C;CiO'-iCNC0'* 

,-H,-li-l,-(.-i.-irtr-ir-irHMi-H(N(N(NIN(N(N(MIN(N(N(N(NCOCOCOCOCO 



00C5O— KNCO-^iOCOt^WOO— i<NCO'*iOOt^OCC50'-iC^fO-*»0<©t^0005< 
T}<(N-^C::l>'0C0^Ol^»O:0<MO00C0TriMO00O-*C0'-iCr-I>'0C0'^C5t^'0' 



C^05lO<NOd005»OC^05»OOI>'*'-<00>0(Mr^T}<,-iOOCOOcD'*r-iCOCOO><CC<l 

i-iOO«0-<*<^Ot^-*(NOI>»OrOOOOOCO^C3CD-*<NC5I:^»0<MOXiOC000050 

«);Ot^0005C50'-i<NCOCO'*»COCDI>OOC500'-<(N(NCOTriC<ricDI>OOC500 

^rtrt^rHr-<^.-i.-ir-i,-H,-(,-i(N(N(N(N(N(NCSl(NlN(N(N(N(NCO 



aOCO»Ot^05^COOOOO(NCOQCOC<lTf;0000<N>0<DO(NCDC005'-iCO'0000 

r^»0(NOi©rO^X»CllMOt^Tj>,-(0;cDcOOt^>OlM05COCO^OC»OiMOt^'*^05 

»0«Or^I>OOC500i-i<NCOCO-^lOiOCDt^OOOOC>OO^C^COCO"*»COCDt>XOO 

rtr-(i-ii-i.-irH.-(i-*.-H,-i,-(^rH^iM<N<N(NiN(N(N(N(MiM(N(N(N 



■*ro>-i05t^'*co>-i05r^ioro^Ot^<C'*iMXX<0':fiNOXcO'*rooxcO'*<N 

■^.-iX-<**'-iXiO(MX'OlNOCDC005CDCOOC)COOI>"*'-it^'*'-iX'O^X«0(N 

iOco<Oi>XX0500'-<c^c^co-^'^»OOt^t^XOOO^'-H(N:oro'roio-xit^ 

^^_T-lrtr-(^rH,-lr-l,-lrt.-H,-(THC^C4(NlNINC^MC-4(N(N(M 



MCOO'^»iMcDO-*X<NcOO-*XlNOO-^X<NCOO'*«<NCDO'^00<NCOO 

,-it^TtiO'©C0OCD(NXi0'-iX'*Ot^C0OCDlN0:i0lNX'^i-H>T}HOCDC005C0 

»0»0?OC^l>XX050C>'-i<N(NCO'^'*'»OcCCOt>t^XC5050'-^»-iC<)COCO-*'<*"»0 

rt^^^^^^^^,-HT-<,-<rH,-H,-i,-i(N(N(NC^iN(N(N(N(N 



00^^'-''-<'--''--"'-'.--i»-ii--i(Nr-<<N.--i(N^(N(N(N(N(N(N(N<MM(N<N(NlM(N(N 

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■*iOcDCDl>I>WOi0500'-'<NC^COCO'*iOiOCDCDI^«aC:020'-H'-c(N(NCO'^ 



oco(Na5»Or-(t^Tfo«0(N©'0-<r^coo<r>(NX>o^t^foo«0(NX>o^«-<*o 

OOO^r^COX-^O'O'-HOiMXrOC-. iOOCCi'-it^COX-*0»Oi-iO(NX^?05>0 

TfiiC'0C0i©t^t>XCiC5OO^'-iC<)iMC0"^'* »CiC tOOt^XX050lOO'-''-i(N 

,_,^^^,-i,-i,-(^,-(,-(,-ii-H,-<i-i.-(i-Hf-(.-((N-<J'iMC^<N 



OC0C0X'-<r0O05>-l->*C0C5'-^'*OO(N'*l^O(Nrf<t^05<N»0t^O(N»0«O<N 
C^r-(Nr^COXCOX'^C5'*C:'00'00'©'-<CDC4l>(Nr^iMXCOX"T'C5Tj<05»00 
T}<rtiif5iCcO<OI>t>XXC5050'-i^(N(MrOCO-^'<tiO»Oi©COr^t^XX05030-< 

.— II— II— (I— (1— (i—Ci— (1— (,— (,— li-Hi— Ir-li— (I— <T-<T-«i-Hi-<C^C^ 



(Ni-iOOXr^«Di0-*C0(N--OX0il>CD»0'<tiC00Ji-iO0>Xt^«D«CT}'C0<N'-'O 
Ci'^OCOXCOXCOXCOXCOXC^l^<Mt^lMt^<Nt^<NI>'-'tO'-HCO'-iCi.-iCD'-iCO 
COTtiTtii/5»0<OCOC^t~-XXOOiOO^^<N(NCOCO'*'*»C2COCOt^t^XX0505 



TfOcO<Nt^C<)«C005-*OkOMt^'*C>-^C5Tj'OcO^CO(NXfOX-<*<OCO'-i«<N 
0^iOO^C5COX(Nl>iM^^»00'*OCOXCOt^(NCO'-'>CO'*0'*Xcor^<N 

co'*'*"0'Cio;ocot^t^xxa5cr. ooO'-i'-'(N(Ncocc-<*<-*'Oioioco«c>t^t^x 

XO<NiOt^O^COCDX--CO'OI:^0<N'^«OXO(NTfOC5C<>'tcD05(NrOCOXO 
COXClcCO-^OCOr^i— iCDO'*XC^jr^'-ilOC5-^XIMCOO'OC-COt^<NCCO'*"05 
COCO'*'*»0'0»OCDOI>t>XXX05C5000-H.-i(NiNrCCOCO-*'*>0>0«DCD<0 



(NIM— i005Xt^<0«0-^COIN<NOO««t^'-0»0-*eO(N— lOOlWt^CDiO-^COIN 
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COCOCO'*<'<*iiO»OiOCOOt-t^t^XXX0305000'-<'-<iM<N<NCOCO-^'^'*>0»0 



Q0-*OCO<NX-*OOC<>«M'0^(NX'*00<NO'*OCD(NX-*0«0<NX'<*0 
XC<)O0iC0C0O'^t^»-i'*X(Ni0C5<NC0OC0t^X'^X^»0X<NCDOC0<OO'S' 
C^C0C0C0'<*'^'0»0»0CDCDiOt>t>t^XX0i050iOOO'— I"— '•— 'IN(N(NCOCO'*'^ 



'»'t^OCOt^OCOOOCOCOO-^COCOO'*t— OCOCOC5C<ICDOrOC0 05iMrOCD05IN 
OC5'^<Od'^OC:"^trOCOC005C^tOw5C^005(N>005C^Oai(N»CO:01'CX<N 
C<IC^MCOCO'Ti'^'^«0»0»OOcOCOt~-t-t>XXX050iC5000'-i^^(M(N(NCO 






QOOsO'-<C<CO-*>OOt^»a>0-^NCO'4'iCcDt^X050-^iNCO'*»OcOt^X050 

*''^|r;^ii;ji-;;-i,Hi-^i-(.H^c^(NiNC^c^<N(N(NC^(NcocorocococofoeococO'i< 



248 A MANUAL FOR NORTHERN WOODSMEN 



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o— <(McO'#iccot^xciO'-i(Nc«;-*»ccc>t^ooc;o 



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OOOO— i(NCO-*iOy3COt>00050-H(N:«5rt<'*oO 



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r- 00 o C2 o —I C4 (N CO ■* ko lO CO r^ .X « C5 o —"-I IN 



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I-^OCOCOOi-^'*'t^O<Nifl«^CCCOOi(NTj<i©C5iN 
IMCOfCCCfO"*"*'*'OiOiOiOcO«0©COI>t^t:^t^X 



ci-<*ict^xc500ic*5-^icr^xa)0<NfCir}<coi^x 

,_(^^^,-(rH(N(N<NlN<MIMiM(MCCCCCC«tCP:>CO 



0^iMfo-*iLOcoi>xo30-<(NeoTt<mcot^xc50 

^,_l^,_i,-irH,-(r-i^,-((NiM(N(N(N(N(N(N<NlMCC 



TABLES RELATING TO PARTS III AND IV 249 



C0C:;O'-i(Mr0TrTi0CCI>C0C:O'-<-^<N^:"^'0C0 

Tj*i>,-iir305<NOC5C0c0Of0r^O'n't^O'^l^'-|'* 
ec^ooocoio^ri-iOxr^io^rcMOXt^ocoiNfC 

000500^<M^f*iOiCcOt-X~. OO — iMCOTinO 
XOT(NOXCC-^-^C:t^'OrC'-<C:i^Ti<(NOXCC 

t^xcio — ^cs^:c■*■*lOcot>xxc■.o^(N(N^^ 
cC— <t^rc^:'Tfc:>oo«oc~5r^coX'<*<c;»o — co<Nt^ 

iO:COXiO^:OX-,C^: — XcCCO^XO-^^CiO 
OXCICIO — C^lC^^C'TlO^OcC^^XXC7;0'-''-l<N 

c;o--ojrC'f»oor^xC50-^<Ncc'*-<r»ocDi^x 

OXiCuMOCC^COr^Ti— C^CC^JOt^"*'— XiOiM 

r^t^X3;ClO^^c^^;•v*»0cDl>^>xc5C:o — 
x^ — xio-MXioc^cr-ccrcoicorcor^^oot^-* 

Ot^XX^CO— 'CsKNCC-^-tiOcOt^t^XClCr. O 

i-'ioo-<i'XM^O»oC5rci^^iocr:rcxc^'wC:'* 



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193 J m 



0-^(NM'<*'iOOt^XOO — lNr^'<*'>OCOr*XCiO 



250. A MANUAL FOR NORTHERN WOODSMEN 



PROVINCE OF QUEBEC 

Table of Contents of Saw Logs, Boom and Dimension Timber in 
Feet Board Measure 



DlAJMETER IN INCHES 



10 



11 



12 



13 



14 



15 



16 



17 



18 



19 



20 



28 

31 
34 
37 
40 

42 

45 
48 
51 
54 
57 

59 
62 
65 
68 

71 

74 
76 
79 
82 
85 



91 
93 
96 
99 

102 
105 
108 
111 
114 



37 

40 
44 
48 
51 
55 

59 
62 
66 
70 
73 

77 
81 
84 
88 
92 

95 

99 

103 

106 

110 

114 
117 
121 
125 
128 

132 
136 
139 
143 
147 



42 

46 
50 
54 
58 
62 

67 
71 
75 
79 
83 

87 

92 

96 

100 

104 

108 
112 
117 
121 
125 

129 
133 
137 
142 
146 

150 
154 
158 
162 
167 



50 

55 
60 
65 
70 
75 

80 
85 
90 
95 
100 

105 
110 
115 
120 
125 

130 
135 
140 
145 
150 

155 
160 
165 
170 
175 

180 
185 
190 
195 
200 



62 

69 

75 
81 
87 
94 

100 
106 
112 
119 
125 

131 
137 
144 
150 
156 

162 
169 
175 
181 
187 

194 
200 
206 
212 
219 

225 
231 
237 
244 
250 



75 

82 

90 

97 

105 

112 

120 
127 
135 
142 
150 

157 
165 
172 
180 
187 

195 
202 
210 
217 
225 

232 
240 
247 
225 
262 

270 
277 
285 
292 
300 



83 

92 
100 
108 
117 
125 

133 
142 
150 
158 
167 

175 

183 
192 
200 
208 

217 
225 
233 
242 
250 

258 
267 
275 
283 
292 

300 
308 
317 
325 
333 



100 117 



110 
120 
130 
140 
150 

160 
170 
180 
190 
200 

210 
220 
230 
240 
250 

260 
270 
280 
290 
300 

310 
320 
330 
340 
350 

360 
370 
380 
390 
400 



133 



128 147 
140 160 



152 
163 
175 

187 
198 
210 
222 
233 

245 
257 
268 
280 
292 

303 
315 
327 
338 
350 

362 
373 
385 
397 
408 

420 
432 
443 
455 



173 

187 
200 

213 
227 
240 
253 
267 

280 
293 
307 
320 
333 

347 
360 
373 
387 
400 

413 
427 
440 
453 
467 

480 
493 
507 
520 



467 533 



154 

170 

185 
200 
216 
231 

247 
262 
277 
293 
308 

324 
339 
355 
370 
385 

401 
416 
432 
447 
462 

478 
493 
509 
524 
540 

555 
570 
586 
601 
617 



175 

192 
210 

227 
245 
262 

280 
297 
315 
332 
350 

367 
385 
402 
420 
437 

455 i 
472' 
490 ! 
507 j 
525 
1 
542, 
560 
577 1 
595! 
612 

630 

647 
665 
682 
700 



TABLES RELATING TO PARTS III AND IV 251 



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 


475 


ft? 
10 


211 


238 


264 


289 


312 


348 


367 


399 


431 


463 


495 


522 


11 


230 


260 


288 


315 


340 


380 


400 


435 


470 


505 


540 


570 


12 


249 


282 


312 


341 


368 


412 


433 


471 


509 


547 


585 


617 


13 


268 


303 


336 


367 


397 


443 


467 


507 


548 


589 


630 


665 


14 


287 


325 


360 


394 


425 


475 


500 


544 


587 


631 


675 


712 


15 


307 


347 


384 


420 


453 


507 


533 


580 


627 


673 


720 


760 


16 


326 


368 


408 


446 


482 


538 


567 


616 


666 


715 


765 


807 


17 


345 


390 


432 


472 


510 


570 


600 


652 


705 


757 


810 


855 


18 


364 


412 


456 


499 


538 


602 


633 


689 


744 


800 


855 


902 


19 


383 


433 


480 


525 


567 


633 


667 


725 


783 


842 


900 


950 


20 


402 


455 


504 


551 


595 


665 


700 


761 


822 


884 


945 


997 


21 


422 


477 


528 


577 


623 


697 


733 


797 


862 


926 


990 


1045 


22 


441 


498 


552 


604 


652 


728 


767 


834 


901 


968 


1035 


1092 


23 


460 


520 


576 


630 


680 


760 


800 


870 


940 


1010 


1080 


1140 


24 


479 


542 


600 


656 


708 


792 


833 


906 


979 


1052 


1125 


1187 


25 


498 


563 


624 


682 


737 


823 


867 


942 


1018 


1094 


1170 


1235 


26 


517 


585 


648 


709 


765 


855 


900 


979 


1057 


1136 


1215 


1282 


27 


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 


594 


672 


744 


814 


878 


982 


1033 


1124 


1214 


1305 


1395 


1472 


31 


613 


693 


768 


840 


907 


1013 


1067 


1160 


1253 


1347 


1440 


1520 


32 


632 


715 


792 


866 


935 


1045 


1100 


1196 


1292 


1389 


1485 


1567 


33 


652 


737 


816 


892 


963 


1077 


1133 


1232 


1332 


1431 


1530 


1615 


34 


671 


758 


840 


919 


992 


1108 


1167 


1269 


1371 


1473 


1575 


1662 


35 


690 


780 


864 


945 


1020 


1140 


1200 


1305 


1410 


1515 


1620 


1710 


36 


709 


802 888 


971 


1048 


1172 


1233 


1341 


1449 


1557 


1665 


1757 


37 


728 


823 912 


997 


1077 


1203 


1267 


1377 


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 



^52 A MANUAL FOR NORTHERN WOODSMEN 



PROVINCE OF QUEBEC 

Table of Contents of Saw Logs, Boom and Dimension Timber in 
Feet Board Measure 





Diameter in Inches 




H 
1-1 


33 


34 


35 


36 


37 


38 


39 


40 


41 


42 


43 


ftT 

10 


525 


542 


567 


592 


617 


655 


692 


733 


758 


792 


833 


11 


577 


596 


623 


651 


678 


715 


761 


807 


834 


871 


917 


12 


630 


650 


680 


710 


740 


780 


830 


880 


910 


950 


1000 


13 


682 


704 


737 


769 


802 


845 


899 


953 


986 


1029 


1083 


14 


735 


758 


793 


828 


863 


910 


968 


1027 


1062 


1108 


1177 


15 


787 


812 


850 


887 


925 


975 


1037 


1100 


1137 


1187 


1250 


16 


840 


867 


907 


947 


987 


1040 


1107 


1173 


1213 


1267 


1333 


17 


892 


921 


963 


1006 


1048 


1105 


1176 


1247 


1289 


1346 


1417 


18 


945 


975 


1020 


1065 


1110 


1170 


1245 


1320 


1365 


1425 


1500 


19 


997 


1029 


1077 


1124 


1172 


1235 


1314 


1393 


1441 


1504 


1583 


20 


1050 


1083 


1133 


1183 


1233 


1300 


1383 


1467 


1517 


1583 


1667 


21 


1102 


1137 


1190 


1242 


1295 


1365 


1452 


1540 


1592 


1662 


1750 


22 


1155 


1192 


1247 


1302 


1357 


1430 


1522 


1613 


1668 


1742 


1833 


23 


1207 


1246 


1303 


1361 


1418 


1495 


1591 


1687 


1744 


1821 


1917 


24 


1260 


1300 


1360 


1420 


1480 


1550 


1660 


1760 


1820 


1900 


2000 


25 


1312 


1354 


1417 


1479 


1542 


1625 


1728 


1833 


1896 


1979 


2083 


26 


1365 


1408 


1473 


1538 


1603 


1690 


1796 


1907 


1972 


2058 


2167 


27 


1417 


1462 


1530 


1597 


1665 


1755 


1867 


1980 


2047 


2137 


2250 


28 


1470 


1517 


1587 


1657 


1727 


1820 


1937 


2053 


2123 


2217 


2333 


29 


1522 


1571 


1643 


1716 


1788 


1885 


2006 


2127 


2199 


2296 


2417 


30 


1575 


1625 


1700 


1775 


1850 


1950 


2075 


2200 


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 


2833 


35 


1837 


1896 


1983 


2071 


2158 


2275 


2421 


2567 


2654 


2771 


2917 


36 


1890 


1950 


2040 


2130 


2220 


2340 


2490 


2640 


2730 


2850 


3000 


37 


1942 


2004 


2097 


2189 


2282 


2405 


2559 


2713 


2806 


2929 


3083 


38 


1995 


2058 


2153 


2248 


2343 


2470 


2628 


2787 


2882 


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 



1^ 

1-3 


Diameter at Top in Inches 


11 


12 


13 


14; 

1 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


12 


60 


72 


84 


98 


112 


128 


149 


172 


196 


225 


247 


272 


297 


324 


14 


70 


84 


98 


114 


131 


149 


174 


200 


228 


262 


288 


317 


336 


380 


16 


80 


96 


112 


130 


150 


170 


198 


229 


261 


300 


327 


362 


376 


432 


18 


90 


108 


126 


147 


168 


192 


223 


258 


294 


337 


370 


408 


445 


486 


20 


100 


120 


140 


163 


187 


213 


248 


286 


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 


196 


226 


259 


298 


346 


396 


453 


509 


560 


614 


660 


730 


28 


154 


182 


212 


245 


280 


323 


374 


428 


490 


550 


605 


653 


716 


788 


30 


164 


194 


226 


261 


299 


344 


398 


457 


523 


588 


644 


698 


756 


840 


32 


176 


208 


242 


280 


320 


368 


427 


490 


561 


627 


689 


738 


808 


898 


34 


186 


220 


256 


297 


336 


390 


452 


519 


594 


664 


732 


784 


877 


952 


36 


198 


234 


273 


315 


360 


415 


481 


552 


631 


707 


778 


853 


931 


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 


'1O88 


1181 


44 


242 


286 


333 


384 


'439 


509 


590 


674 


771 


865 


951 


1042 


1138 


1235 


46 


252 


298 


347 


401 


458 

i 


531 


613 


703 


804 


903 


992 


1088 


1188 


1289 


48 


264 


312 


364 


420 


480 


554 


642 


736 


842 


944 


1038 


1138 


1242 


1348 


50 


286 


336 


392 

1 


450 


515 


596 


690 


788 


903 


1003 


1104 


1208 


1308 


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 



u 

0) 
0) 

a 

S3 

Q 






Length — 


Feet 


8 


' 


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 


26 


25 


30 


30 


7 


15 


15 


15 


20 


20 


25 


25 


30 


30 


36 


36 


40 


45 


8 


20 


20 


25 


25 


30 


35 


35 


40 


46 


45 


60 


56 


60 


9 


25 


30 


30 


35 


40 


45 


50 


50 


55 


60 


65 


70 


76 


10 


30 


35 


40 


45 


50 


65 


60 


65 


70 


76 


85 


90 


96 


11 


40 


45 


50 


55 


65 


70 


75 


80 


90 


95 


106 


110 


116 


12 


50 


55 


65 


70 


75 


85 


90 


100 


105 


115 


126 


130 


140 


13 


60 


65 


75 


85 


90 


100 


110 


120 


130 


140 


146 


165 


165 


14 


70 


80 


90 


100 


110 


120 


130 


140 


175 


160 


175 


185 


196 


15 


80 


90 


105 


115 


125 


140 


150 


160 


185 


200 


215 


226 


16 


95 


105 


120 


130 


145 


160 


170 


185 


200 


215 


230 


246 


260 


17 


105 


120 


135 


150 


165 


180 


195 


210 


225 


245 


260 


276 


296 


18 


120 


135 


155 


170 


185 


205 


220 


240 


255 


276 


295 


310 


330 


19 


135 


155 


175 


190 


210 


230 


250 


270 


290 


310 


330 


360 


370 


20 


150 


170 


195 


215 


235 


255 


275 


300 


320 


346 


366 


390 


410 


21 


170 


190 


215 


235 


260 


285 


305 


330 


355 


380 


406 


430 


465 


22 


185 


210 


235 


260 


285 


315 


340 


365 


390 


420 


446 


475 


600 


23 


205 


230 


260 


285 


315 


345 


370 


400 


430 


460 


490 


620 


660 


24 


225 


255 


285 


315 


345 


375 


405 


440 


470 


600 


635 


666 


600 


25 


245 


275 


310 


345 


375 


410 


445 


475 


610 


645 


680 


615 


660 


26 


265 


300 


335 


370 


405 


445 


480 


520 


665 


596 


630 


670 


706 


27 


290 


325 


365 


405 


440 


480 


520 


560 


600 


640 


680 


726 


766 


28 


310 


3501 395 


435 


475 


520 


560 


605 


645 


690 


736 


780 


826 


29 


335 


380 425 


470 


510 


560 


605 


650 


696 


740 


790 


836 


886 


30 


360 


405 


455 


500 


550 


600 


645 


695 


746 


796 


845 


896 


950 


31 


385 


435 


485 


540 


590 


640 


695 


745 


800 


850 


905 


960 


1016 


32 


410 


465 


520 


575 


630 


685 


740 


796 


860 


910 


966 


1025 


1080 


33 


440 


495 


555 


610 


670 


730 


790 


850 


906 


970 


1030 


1090 


1150 


34 


470 


530 


590 


650 


715 


775 


840 


900 


966 


1030 


1096 


1160 


1226 


35 


495 


560 


625 


690 


755 


825 


890 


955 


1026 


1096 


1160 


1230 


1300 


36 


525 


595 


665 


735 


800 


875 


945 


1015 


1085 


1160 


1230 


1305 


1376 


37 


560 


630 


705 


775 


850 


925 


1000 


1075 


1150 


1226 


1300 


1380 


1455 


38 


590 


665 


745 


820 


895 


975 


1055 


1135 


1210 


1295 


1375 


1465 


1536 


39 


620 


705 


785 


865 


945 


1030 


1110 


1196 


1280 


1365 


1450 


1635 


1620 


40 


655 


740 


825 


910 


995 


1085 


1170 


1260 


1346 


1436 


1525 


1616 


1706 


41 


690 


780 


870 


960 


1050 


1140 


1230 


1326 


1416 


1610 


1605 


1700 


1796 


42 


725 


820 


915 


1010 


1100 


1200 


1295 


1390 


1490 


1685 


1685 


1786 


1885 


43 


760 


860 


960 


1060 


1155 


1260 


1360 


1460 


1660 


1665 


1770 


1870 


1976 


44 


800 


900 


1005 1110 


1215 


1320 


1425 


1530 


1636 


1745 


1855 


1960 


2070 


45 


835 


945 


1055 1160 


1270 


1380 


1490 


1600 1715 


1826 


1940 


2060 2166 


46 


875 


990 


1100 


1215 


1330 


1445 


1560 


1675 1790 


1910 


2030 


2145 2266 


47 


915 


1035 


1150 


1270 


1390 


1510 


1630 


1750 


1870 


1996 


2120 2240 23661 


48 


955 


1080 


1205 


1325 


1450 


1575 


1700 


1830 


1965 


2086 


2210 2340 


2470 



TABLES RELATING TO PARTS III AND IV 255 



SPAULDING LOG RULE OF COLUMBIA RIVER 



O 
Z 


Diameter in Inches 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


K 

12 


38 


47 


58 


71 


86 


103 


121 


141 


162 


184 


207 231 


256 


14 


44 


55 


67 


82 


100 


120 


141 


164 


189 


214 


241 


269 


298 


16 


50 


63 


77 


94 


114 


137 


161 


188 


216 


245 


276 


308 


341 


18 


57 


70 


87 


106 


129 


154 


181 


211 


243 


276 


310 


346 


384 


20 


63 


78 


96 


118 


143 


171 


201 


235 


270 


306 


345 


385 


426 


22 


69 


86 


106 


130 


157 


188 


221 


258 


297 


337 


379 


423 


469 


24 


76 


94 


116 


142 


172 


206 


242 


282 


324 


368 


414 


462 


512 


26 


82 


101 


125 


153 


186 


223 


262 


305 


351 


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 


291 


342 


399 


459 


521 


586 


654 


725 


36 


113 


140 


174 


212 


258 


308 


362 


422 


486 


552 


620 


692 


768 


38 


120 


148 


183 


224 


272 


325 


382 


446 


513 


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 


594 


674 


758 


846 


938 


46 


145 


179 


222 


272 


329 


394 


463 


540 


621 


705 


793 


885 


981 


48 


151 


187 


232 


284 


344 


412 


484 


564 


648 


736 


828 


924 


1024 


60 


157 


195 


241 


295 


358 


429 


504 


587 


675 


766 


862 


962 


1066 




23 


24 


25 


26 


27 28 


29 


30 


31 


32 


33 


34 


ft: 

12 


282 


309 


337 


366 


) 396 


427 


459 


492 


526 


561 


597 


634 


14 


329 


360 


393 


427 


' 462 


498 


535 


574 


613 


654 


696 


739 


16 


376 


412 


449 


485 


; 528 


569 


612 


656 


701 


748 


796 


845 


18 


423 


463 


505 


54S 


594 


640 


688 


738 


789 


841 


895 


951 


20 


470 


515 


561 


61C 


660 


711 


765 


820 


876 


935 


995 


1056 


22 


517 


566 


617 


671 


726 


782 


841 


902 


964 


1028 


1094 


1162 


24 


564 


618 


674 


732 


792 


854 


918 


984 


1052 


1122 


1194 


1268 


26 


611 


669 


730 


793 


858 


925 


994 


1066 


1139 


1215 


1293 


1373 


28 


658 


720 


786 


854 


924 


996 


1070 


1148 


1226 


1308 


1392 


1478 


30 


705 


772 


842 


915 


990 


1067 


1147 


1230 


1314 


1402 


1492 


1584 


32 


752 


824 


898 


976 


1056 


1138 


1224 


1312 


1402 


1496 


1592 


1690 


34 


799 


875 


954 


1037 


1122 


1209 


1300 


1394 


1490 


1589 


1691 


1796 


36 


846 


926 


1010 


1098 


1188 


1280 


1376 


1476 


1578 


1682 


1790 


1902 


38 


893 


978 


1066 


115C 


1254 


1351 


1453 


1558 


1665 


1776 


1890 


2007 


40 


940 


1030 


1122 


122C 


) 1320 


1422 


1530 


1640 


1752 


1870 


1990 


2112 


42 


987 


1081 


1178 


128] 


1386 


1493 


1606 


1722 


1840 


1963 


2089 


2218 


44 


1034 


1132 


1234 


134i 


I 1452 


1564 


1682 


1804 


1928 


2056 


2188 


2324 


46 


1081 


1184 


1291 


140c 


} 1518 


1636 


1759 


1886 


2016 


2150 


2288 


2430 


48 


1128 


1236 


1348 


1464 


t 1584 


1708 


1836 


1968 


2104 


2244 


2388 


2536 


60 


1175 


1287 


1404 


152c 


) 1650 


1779 


1912 


2050 


2191 


2337 


2487 


2641 



256 A MANUAL FOR NORTHERN WOODSMEN 

SPAULDING LOG RULE — continued 



o 


Diameter in Inches 


35 


36 


37 


38 


39 


40 


41 


42 


43 


44 


45 


46 


12 


673 


713 


755 


798 


843 


889 


936 


984 


1033 


1086 


1134 


1186 


14 


785 


831 


880 


931 


983 


1037 


1092 


1148 


1205 


1267 


1323 


1383 


16 


897 


950 


1006 


1064 


1124 


1185 


1248 


1312 


1377 


1448 


1512 


1581 


18 


1009 


1069 


1132 


1197 


1264 


1333 


1404 


1476 


1549 


1629 


1701 


1779 


20 


1121 


1188 


1258 


1330 


1405 


1481 


1560 


1640 


1721 


1810 


1890 


1976 


22 


1233 


1307 


1384 


1463 


1545 


1629 


1716 


1804 


1893 


1991 


2079 


2174 


24 


1346 


1426 


1510 


1596 


1686 


1778 


1872 


1968 


2066 


2172 


2268 


2372 


26 


1458 


1544 


1635 


1729 


1826 


1926 


2028 


2132 


2238 


2353 


2457 


2569 


28 


1570 


1662 


1760 


1862 


1966 


2074 


2184 


2296 


2410 


2534 


2646 


2766 


30 


1682 


1781 


1886 


1995 


2107 


2222 


2340 


2460 


2582 


2715 


2835 


2964 


32 


1794 


1900 


2012 


2128 


2248 


2370 


2496 


2624 


2754 


2896 


3024 


3162 


34 


1906 


2019 


2138 


2261 


2388 


2518 


2652 


2788 


2926 


3077 


3213 


3360 


36 


2018 


2138 


2264 


2394 


2528 


2666 


2808 


2952 


3098 


3258 


3402 


3558 


38 


2130 


2257 


2390 


2527 


2669 


2814 


2964 


3116 


3270 


3439 


3591 


3755 


40 


2242 


2376 


2516 


2660 


2810 


2962 


3120 


3280 


3442 


3620 


3780 


3952 


42 


2354 


2495 


2642 


2793 


2950 


3110 


3276 


3444 


3614 


3801 


3969 


4150 


44 


2466 


2614 


2768 


2926 


3090 


3258 


3432 


3608 


3786 


3982 


4158 


4348 


46 


2579 


2733 


2894 


3059 


3231 


3407 


3588 


3772 


3959 


4163 


4347 


4546 


48 


2692 


2852 


3020 


3192 


3372 


3556 


3744 


3936 


4132 


4344 


4536 


4744 


60 


2804 


2970 


3145 


3325 


3512 


3704 


3900 


4100 


4304 


4525 


4725 


4941 




47 


48 


49 


60 


51 


52 


53 


54 


55 


56 


67 58 


ft: 

12 


1239 


1293 


1348 


1404 


1461 


1519 


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 


2550 


2644 


2740 


2839 


20 


2065 


2155 


2246 


2340 


2435 


2531 


2630 


2730 


2833 


2938 


3045 


3155 


22 


2271 


2370 


2470 


2574 


2678 


2784 


2893 


3003 


3116 


3232 


3349 


3470 


24 


2478 


2586 


2696 


2808 


2922 


3038 


3156 


3276 


3400 


3526 


3654 


3786 


26 


2684 


2801 


2920 


3042 


3165 


3291 


3419 


3549 


3683 


3819 


3958 


4101 


28 


2890 


3016 


3144 


3276 


3408 


3544 


3682 


3822 


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 


4382 


4556 


4734 


4914 


5100 


5288 


5480 


5678 


38 


3923 


4094 


4268 


4446 


4626 


4809 


4997 


5187 


5383 


5582 


5785 


5994 


40 


4130 


4310 


4492 


4680 


4870 


5062 


5260 


5460 


5666 


5876 


6090 


6310 


42 


4336 


4525 


4716 


4914 


5113 


5315 


5523 


5733 


5949 


6170 


6394 


6625 


44 


4542 


4740 


4940 


5148 


5356 


5568 


5786 


6006 


6232 


6464 


6698 


6940 


46 


4749 


4956 


5166 


5382 


5600 


5822 


6049 


6279 


6516 


6758 


7003 


7256 


48 


4956 


5172 


5392 


5616 


5844 


6076 


6312 


6552 


6800 


7052 


7304 


7572 


60 


5162 


5387 


5616 


5850 


6087 


6329 


6575 


6825 


7083 


7345 


7612 


7887 
i 



TABLES RELATING TO PARTS III AND IV 257 



SPAULDING LOG RULE — continued 



w 

Eh 

o 

» 






Diameter 


IN Inches 




59 


60 


61 


62 


63 


64 


65 


66 


67 


68 


69 


70 


ftT 

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 


2892 


2988 


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 


9&i5 


9959 













258 



A MANUAL FOR NORTHERN WOODSMEN 



BRITISH COLUMBIA LOG SCALE 

Established by the government, and derived from the 
following rule: — Deduct \}/2 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. 





Diameter in Inches 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


fT 
1 


3 


4 


5 


6 


7 


9 


10 


11 


13 


15 


16 


18 


20 


22 


24 


26 


10 


34 


43 


53 


63 


74 


87 


100 


114 


130 


146 


163 


181 


200 


220 


241 


263 


12 


41 


52 


63 


76 


89 


104 


120 


137 


155 


175 


195 


217 


240 


264 


289 


315 


14 


48 


60 


73 


88 


104 


121 


140 


160 


181 


204 


228 


253 


280 


308 


337 


368 


16 


55 


69 


84 


101 


119 


139 


160 


183 


207 


233 


261 


290 


320 


352 


386 


421 


18 


62 


77 


94 


113 


134 


156 


180 


206 


233 


262 


293 


326 


360 


396 


434 


473 


20 


69 


86 


105 


126 


149 


173 


200 


229 


259 


292 


326 


362 


400 


440 


482 


526 


22 


76 


94 


115 


138 


164 


191 


220 


252 


285 


321 


358 


398 


440 


484 


530 


578 


24 


83 


103 


126 


151 


178 


208 


240 


274 


311 


350 


391 


434 


480 


528 


578 


631 


26 


89 


112 


136 


164 


193 


226 


260 


297 


337 


379 


424 


471 


520 


572 


626 


683 


28 


96 


120 


147 


176 


208 


243 


280 


320 


363 


408 


456 


507 


560 


616 


675 


736 


30 


103 


129 


157 


189 


223 


260 


300 


343 


389 


437 


489 


543 


600 


660 


723 


789 


32 


110 


137 


168 


201 


238 


278 


320 


366 


415 


466 


521 


579 


640 


704 


771 


841 


34 


117 


146 


178 


214 


253 


295 


340 


389 


441 


496 


554 


615 


680 


748 


819 


894 


36 


124 


155 


189 


227 


268 


312 


360 


412 


466 


525 


586 


652 


720 


792 


867 


946 


38 


131 


163 


199 


239 


283 


330 


380 


435 


492 


554 


619 


688 


760 


836 


916 


999 


40 


138 


172 


210 


252 


297 


347 


400 


457 


518 


583 


652 


724 


800 


880 


964 


1051 



TABLES RELATING TO PARTS III AND IV 259 



BRITISH COLUMBIA LOG SCALE — continued 



a 


Diameter in Inches 


26 


27 


28 


29 


30 


31 


32 


33 


34 


35 


36 37 


FT 
1 


29 


31 


33 


36 


39 


41 


44 


47 


50 


53 


57 


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 


696 


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 



X 
O 

z 


Diameter in Inches 


50 


51 


52 


53 


54 


55 


56 


57 


58 


59 


60 


61 


ftT 

1 


112 


117 


121 


126 


131 


136 


141 


147 


152 


157 


163 


168 


10 


1120 


1166 


1214 


1262 


1312 


1362 


1414 


1466 


1519 


1574 


1629 


1685 


12 


1343 


1399 


1457 


1515 


1574 


1635 


1696 


1759 


1823 


1888 


1955 


2022 


14 


1567 


1633 


1699 


1767 


1837 


1907 


1979 


2052 


2127 


2203 


2280 


2359 


16 


1791 


1866 


1942 


2020 


2099 


2180 


2262 


2346 


2431 


2518 


2606 


2696 


18 


2015 


2099 


2185 


2272 


2361 


2452 


2545 


2639 


2735 


2832 


2932 


3033 


20 


2239 


2332 


2428 


2525 


2624 


2725 


2827 


2932 


3039 


3147 


3258 


3370 


22 


2463 


2566 


2670 


2777 


2886 


2997 


3110 


3225 


3343 


3462 


3583 


3707 


24 


2687 


2799 


2913 


3030 


3148 


3269 


3393 


3519 


3646 


3777 


3909 


4044 


26 


2911 


3032 


3156 


3282 


3411 


3542 


3676 


3812 


3950 


4091 


4235 


4381 


28 


3135 


3265 


3399 


3535 


3673 


3814 


3958 


4105 


4254 


4406 


4561 


4718 


30 


3359 


3499 


3641 


3787 


3936 


4087 


4241 


4398 


4558 


4721 


4886 


5055 


32 


3583 


3732 


3884 


4039 


4198 


4359 


4524 


4691 


4862 


5036 


5212 


5392 


34 


3807 


3965 


4127 


4292 


4460 


4632 


4807 


4985 


5166 


5350 


5538 


5729 


36 


4030 


4198 


4370 


4544 


4723 


4904 


5089 


5278 


5470 


5665 


5864 


6066 


38 


4254 


4432 


4612 


4797 


4985 


5177 


5372 


5571 


5774 


5980 


6190 


6403 


40 


4478 


4665 


4855 


5049 


5247 


5449 


5655 


5864 


6077 


6294 


6515 


6740 




62 


63 


64 


65 


66 


67 


68 


69 


70 


71 


72 


73 


ft: 

1 


174 


180 


186 


192 


198 


204 


210 


217 


223 


230 


237 


243 


10 


1742 


1800 


1859 


1919 


1980 


2042 


2105 


2169 


2233 


2299 


2366 


2433 


12 


2091 


2160 


2231 


2303 


2376 


2450 


2526 


2602 


2689 


2759 


2839 


2920 


14 


2439 


2520 


2603 


2687 


2772 


2859 


2947 


3036 


3127 


3219 


3312 


3407 


16 


2787 


2880 


2975 


3071 


3168 


3267 


3368 


3470 


3573 


3678 


3785 


3893 


18 


3136 


3240 


3347 


3454 


3564 


3676 


3789 


3903 


4020 


4138 


4258 


4380 


20 


3484 


3600 


3718 


3838 


3960 


4084 


4210 


4337 


4467 


4598 


4731 


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 


6624 


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 


6272 


6481 


6693 


6909 


7128 


7351 


7577 


7807 


8040 


8276 


8516 


8760 


38 


6620 


6841 


7065 


7293 


7524 


7759 


7998 


8240 


8486 


8736 


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. 


Total Height of Tree — Feet 


, 










1 


Incha^ 


60 


70 { 


}0 90 


100 


110 


120 


130 


140 


160 


10 


60 


70 J 


50 95 






.... 








11 


75 


85 1( 


)0 115 


















12 


90 


100 1] 


5 135 


. . . 
















13 


100 


115 i: 


55 155 


180 
















14 


120 


135 U 


■)o 180 


210 
















15 


140 


160 1^ 


iO 200 


230 


'270 














16 


160 


185 2] 


LO 240 


270 


310 














17 


o • * 


210 2^ 


to 270 


310 


350 














18 






240 2" 


■0 310 


350 


390 


'446 












19 






270 3] 


LO 350 


390 


440 


490 












20 






... 3t 


)0 390 


440 


490 


550 












21 










3t 


)0 430 


480 


540 


600 


'680 


. . . . 








22 










4^ 


to 480 ] 540 


600 


670 


750 










23 










4c 


)0 540 600 


660 


740 


830 


"946 








24 










5- 


to 600 


860 


730 


810 


910 


1020 








25 












. 660 


720 


800 


890 


990 


1100 








26 












. 720 


790 


870 


970 


1070 


1190 


1320 


27 
















850 


940 


1040 


1150 


1280 


1420 


28 
















920 


1020 


1130 


1240 


1370 


1530 


29 
















990 


1100 


1210 


1330 


1470 


1640 


30 
















. . • 


1180 


1300 


1420 


1580 


1750 


31 




















1270 


1400 


1520 


1690 


1860 


32 




















1360 


1500 


1630 


1800 


1980 


33 




















1450 


1600 


1750 


1920 


2100 


34 




















1550 


1700 


1870 


2040 


2220 


35 




















1650 


1800 


1980 


2170 


2360 


36 




















1750 


1900 


2100 


2300 


2500 



Based oh 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 










Breast 




Total Height in 


Feet 




High 










Inches 


60 


70 


80 


90 


100 


7 


17 


24 








8 


29 


38 


50 




, , 


9 


44 


53 


68 


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 


i47 


• • • 


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 3 





40 


50 


60 


70 


80 


90 


100 


5 1 



















6 1 


5 


20 


30 












7 2 





30 


40 


50 


65 








8 2 


5 


35 


50 


65 


85 








9 3 





45 


60 


80 


105 


iis 






10 4 





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. 



'264 



A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLE No. 5. WHITE PINE IN CORDS 
CFrom State Forester of Massachusetts) 



Diameter 

Breast 

High 



Inches 



5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 



30 



.03 
.03 
.04 
.05 
.07 



Total Height of Tree — Feet 



40 


50 


60 


70 


80 


.04 


.05 








.05 


.07 


.09 






.07 


.09 


.11 


.13 




.09 


.11 


.13 


.16 




.11 


.13 


.16 


.19 


.22 


.13 


.16 


.19 


.23 


.26 


.15 


.19 


22 


.27 


.31 


.17 


.22 


.26 


.31 


.36 




.25 


.30 


.34 


.41 




.28 


.34 


.40 


.46 



90 



.30 
.35 
.40 
.45 
.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- 


Total Height of Tree — Feet 






eter 
















Inches 


40 


45 


50 


55 


60 


65 


70 


75 


80 9 





6 


4.9 


5.3 


5.8 


6.5 














7 


6.3 


6.9 


7.6 


8.5 


9.6 












8 


7.8 


8.6 


9.5 


10.6 


12.0 


14 










9 


9.8 


10.8 


12.0 


13.4 


15.0 


17 










10 1 


2.0 


13.5 


150 


16.5 


18.2 


20 


21 








11 




16.0 


18.0 


19.7 


22. 


23 


25 


27 






12 




18.5 


21. 


23. 


25. 


27 


29 


32 


34 . 




13 




22. 


24. 


27. 


29. 


31 


34 


36 


39 . 




14 








28. 


30. 


33. 


36 


38 


41 


44 . 




15 








31. 


34. 


37. 


40 


43 


46 


49 . 




16 












38. 


41. 


44 


47 


51 


55 ( 


53 


17 












43. 


46. 


49 


52 


56 


61 'i 





18 












47. 


50. 


54 


58 


62 


67 1 


'7 


19 












52. 


55. 


59 


64 


69 


74 S 


?5 


20 












56. 


60. 


65 


70 


76 


81 c 


)3 


21 














. . . 


72 


77 


82 


87 c 


)8 


22 












. . . 


. . . 


79 


84 


88 


93 1( 


)5 


23 












. . . 


. . . 


87 


92 


95 


100 11 


4 


24 
















96 


100 


104 


108 li 


23 



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 159-165 of this volume. Balsam fir, 
however, is believed to be pretty uniformly somewhat 
slimmer than spruce, having, as would appear from the 
results of a study on fir made by Mr. Zon of the United 
States Forest Service, 8 per cent less volume for the same 
breast diameter and height. 



VOLUME TABLE No. 7. SPRUCE IN FEET, BOARD 
MEASURE 



Breast 


















Diam- 


Total Height of Tree — Feet 






eter 


















Inches 4 





45 


50 


55 


60 


65 


70 


75 


80 e 





7 2 





20 


20 


25 


25 












8 2 





25 


30 


35 


40 


"45 




. . . 






9 3 





35 


40 


45 


50 


55 




. . . 






10 4 





45 


50 


60 


65 


70 


'so 








11 




55 


65 


70 


80 


90 


105 


iis 






12 




65 


75 


85 


100 


110 


120 


135 


150 ! 




13 




75 


90 


100 


115 


125 


140 


155 


170 . 




14 








105 


120 


135 


150 


165 


180 


195 . 




15 








120 


135 


155 


170 


IGO 


205 


220 . 




16 










155 


170 


185 


205 


225 


250 3] 


15 


17 












170 


190 


210 


230 


250 


275 31 


50 


18 












185 


210 


235 


255 


280 


310 3f 


iO 


19 












205 


235 


260 


290 


320 


350 4r 


50 


20 












235 


265 


295 


325 


355 


385 4- 


'0 


21 














300 


330 


360 


390 


425 5] 


LO 


22 














330 


360 


395 


430 


465 51 


)0 


23 














360 


400 


435 


470 


510 6( 


)0 


24 














400 


440 


480 


515 


555 6{ 


K) 



Based on 2500 trees scaled in 16-foot log lengths up to 
6 inches in diameter by the Maine rule and discounted 
from 5 to 10 per cent. Purports to give the yield in edged 
lumber of average spruce trees in economical woods and 
mill practice. 



266 



A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLE No. 8. SPRUCE IN CORDS 



Breast 
Diameter 




Total Height of Tree — Feet 






Inches < 


45 


50 


55 


60 


65 


70 


75 


80 


6 .( 


)4 .0^ 


) .05 


.06 












7 .( 


16 .oe 


) .07 


.08 


.09 










8 .( 


17 .OS 


i .09 


.10 


.12 


.13 








9 .( 


)9 .1( 


1 .12 


.13 


.14 


.16 








10 .] 


1 .V. 


I .14 


.16 


.17 


.19 


.20 


.22 




11 


.U 


> .17 


.19 


.20 


.22 


.24 


.26 


.28 


12 


.U 


? .20 


.22 


.24 


.26 


.28 


.30 


.32 


13 


.2 


L .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 lbs. 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- 




Total Height of Tree 


— Feet 




Diam- 
eter 


eter 
breast- 


























hark 


high 


30 




10 50 


60 


70 


80 


90 1 


00 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 




J7 53 


64 


76 


84 


93 


7 


13 




i. 


16 65 


78 


94 


100 


110 


7 


14 






^ 


S6 77 


95 


110 


130 


140 


7 


15 






\ 


55 90 


110 


130 


150 


160 


8 


16 








110 


130 


160 


180 


190 i 


200 8 


17 








120 


150 


180 


210 


220 i 


240 8 


18 








140 


180 


210 


240 


260 i 


280 8 


19 








160 


200 


240 


280 


300 ; 


J20 9 


20 








180 


230 


280 


310 


340 ; 


J60 9 


21 








200 


260 


310 


350 


380 '■ 


HO 9 


22 








220 


290 


350 


390 


430 


170 10 


23 










330 


380 


440 


480 i 


520 10 


24 










360 


420 


490 


540 


580 10 


25 










390 


460 


530 


600 ( 


550 10 


26 










430 


510 


580 


660 


r20 11 


27 










470 


550 


640 


720 / 


'90 11 


28 










500 


590 


690 


780 8 


570 11 


29 










540 


640 


750 


850 £ 


40 11 


30 










570 


680 


800 


920 1( 


)30 12 



Based on 534 trees cut in the Lake States and scaled 
from a 2-foot stump to diameter given in 16.3 foot log 
lengths. Crook, breakage, and defect not allowed for. 



268 A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLE No. 10. HEMLOCK IN BOARD FEET 
(From Report N. H. Forest Commission for 1906-7) 



Diameter 










Breast 




Total Height of Tree — Feet 




High 










Inches 


30 


40 


50 


60 


70 


6 


5 










7 


10 


20 


30 


42 


. . . 


8 


17 


28 


39 


50 


. . . 


9 


26 


36 


49 


60 




10 


36 


46 


59 


71 


86 


11 


47 


58. 


'72 


86 


103 


12 


60 


72 


86 


103 


123 


13 




88 


104 


124 


148 


14 




107 


125 


147 


173 


15 




126 


148 


172 


204 


16 




148 


171 


200 


240 


17 






197 


233 


281 



Based on 317 second growth trees grown in New Hamp- 
shire, cut with good economy (4§ to 6^ inches in the top) 
and sawed into edged boards and scantHng. 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 

/ 

8 
9 
10 
11 
12 
13 
14 
15 


.02 
.03 
.04 
.05 
.05 
.07 
.08 




04 
05 
07 
08 
10 
12 
14 
17 
19 
22 


.05 
.07 
.09 
.11 
.13 
.16 
.19 
.22 
.25 
.29 


.07 
.08 
.11 
.13 
.16 
.19 
.22 
.26 
.30 
.34 


.08 
.10 
.13 
.16 
.19 
.22 
.26 
.30 
.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 


'is 


■ • • 


• • • 




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 oO 
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 1|- 
inch plank. 

Table may be used for other second groTvi:h hard wood 
species when similarly cut and manufactured. 



270 A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLE No. 13. PEELED POPLAR IN CORDS 
(Adapted from Report of N. H. Forest Commission for 1906-7) 



Diameter 








Breast 




Total Height of Tree — Feet 




High 








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 46 


60 


56 


60 


66 


Number Trees per Cord 


3-5 
5-7 

7-9 


61 


47 


38 
24 


33 
20 


31 

17 
12 


is 
11 


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 







Total Height in Feet 


Diameter 
Breast High 


Basal 
Area 














40 


60 


60 


Inches 


Sq. Ft. 


Form Height Factors 


6 


.196 


.26 


.31 


.36 


7 


.267 


.26 


.31 


.37 


8 


.349 


.27 


.32 


.38 


9 


.442 




.33 


.38 


10 


.545 




.35 


.40 


11 


.660 


, 


.37 


.43 


12 


.785 




.39 


.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 ^ 


to 50 


60 


70 


80 


'90 


,100 110 


Inches 


Form Height Factors 


6 .J 


20 .23 


.28 












9 


l8 .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 .2 


4 


30 




.20 


.23 


.26 


.29 


.31 .S 


3 


36 






.22 


.25 


.28 


.31 .2 


13 


45 








.26 


.28 


.30 .2 


12 


If the ,co 


rd is 4' X 5 


' X 8', deduct % 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 
cord wood is in it? .545 (basal area) X .35 (form height 
factor) = .19 cord; or l-7-.19=5|, number of such 
trees required for a cord if closely utilized. 

Example 2. A bunch of chestnut averaging 80 feet 
tall and running 13 to 17 inches in diameter, to be cut 
into extract wood, proves after calipering to have a total 
basal area of 95 square feet. 95 X .29 (form height 
factor in second table above) = 27.55, number of cords 
in the stand. 



VOLUME TABLE No. 16. HARD WOODS. IN BOARD 
FEET, BY THE SCRIBNER RULE 

(From R. A. Brotherton, Negaunee, Mich.) 



Stump 




Number of Sixteen-Foot Logs 




Diameter 
Inches 








1 


2 


3 


4 


10 


30 


50 


90 




12 


55 


95 


130 


. . . 


14 


80 


140 


180 




16 


110 


180 


250 




18 


140 


250 


340 


390 


20 


190 


320 


440 


540 


22 


240 


400 


550 


650 


24 


300 


470 


640 


750 


26 


360 


560 


740 


900 


28 


420 


680 


900 


1100 


30 


500 


820 


1100 


1350 



Stumps average about 3 feet high. One and two log 
trees may either be short trees, or those that above a 
certain height are faulty or defective. 

Elm in the sizes above 18 inches yields about 10 per 
cent more than the above figures. 



TABLES RELATING TO PARTS III AND IV 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 
breast- 
high 



Inches 



9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 



Number of 16-foot Logs 



20 
20 
25 
25 
30 
30 



1 


u 


2 


2h 


3 


3i 


4 




Volume — Board Feet 







BO 45 










?5 50 


70 








10 60 


80 


100 




^ 


50 70 


95 


120 


140 




55 80 


110 


140 


170 


( 


35 95 


130 


160 


190 




rO 110 


140 


180 


220 


5 


50 120 


160 


210 


250 




140 


190 


240 


280 




160 


210 


270 


320 






240 


300 


360 






270 


340 


410 






300 


380 


460 






340 


430 


520 






380 


480 


580 






420 


530 


640 



230 
260 
290 
320 
380 
430 
490 
550 
620 
690 
770 



Diameter 

inside 

bark of 

top 



Inches 



6 

6 

6 

7 

7 

7 

8 

8 

9 

9 

10 

10 

11 

12 

12 

13 



Based on 800 trees cut in the Lake States scaled from 
taper measures in logs 16.3 feet long from a stump 1 foot 
high to top diameters found in actual logging: figures 
evened by curves. As no allowance was made for crook 
and defect, considerable discount is necessary in most 
timber. 

Note. Comparison between the values in this table and the preceding 
shows striking differences, and the text indicates how these arose, from dif- 
ferences in tree form and soundness, lumbering practice, and methods of re- 
cording and computing. The cruiser is under obligation before he applies 
either in practice to understand these points, and he will do well to check 
the table 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 
breast- 










eter 
















1 




inside 


high 


40 


50 


60 


70 


80 


90 


100 110 


120 ^^ark 
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 


230 


270 




510 .. 




7 


16 








175 


220 


260 


310 


c 


550 .. 




7 


17 










200 


250 


295 


350 


4 


too 45( 




7 


18 










225 


280 


330 


390 


4 


150 50( 




8 


19 










250 


310 


370 


440 


c 


)00 56C 


1 i 


)20 8 


20 














350 


420 


490 


c 


)60 63C 


1 ' 


'00 8 


21 














390 


470 


550 


e 


)20 70C 


1 7 


'80 8 


22 














440 


520 


610 


e 


)90 78C 


) S 


560 9 


23 














490 


580 


670 


7 


70 86C 


1 c 


(50 9 


24 


















640 


740 


8 


50 95C 


) IC 


)50 10 


25 


















710 


820 


c 


30 104C 


I 11 


40 10 


26 


















780 


890 


IC 


10 113C 


) 12 


!40 11 


27 


















840 


960 


IC 


90 122C 


) IS 


40 11 


28 




















1050 


11 


80 131C 


) 14 


40 12 


29 




















1140 


12 


80 141C 


) U 


50 12 


30 




















1230 


13 


80 152C 


) le 


70 13 


31 






















14 


80 163C 


> 17 


80 13 


32 






















IS 


80 174C 


ic 


00 14 


33 






















16 


90 186C 


2C 


30 15 


34 
























. . 198C 


21 


60 16 


35 
























.. 211C 


22 


00 17 


36 
























. . 223C 


23 


40 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 BulletLa No. 24, N. C. Geological and Economio Survey) 



Diam- 
eter 

breast- 
high 


Total Height of Tree — Feet 


Diam- 
eter 

inside 
bark 

at top 


40 


50 


60 


70 


80 


90 


100 


110 


120 130 140 


Inches 


Contents — Board Feet 


Inches 


8 


5 


13 


21 


27 














5 


9 
10 
11 
12 


12 
18 
25 
32 


22 

30 
40 
50 


32 

42 
54 
66 


42 
55 
68 
83 


52 
65 
81 
99 












6 
6 
6 

7 












93 
110 










130 


140 


150 ... 




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 1... 




9 


19 










300 


360 


410 


460 


500 53 


.... 


9 


20 










330 


410 


470 


520 


570 61 


.... 


9 


21 












460 


530 


590 


640 69 


.... 


10 


22 












510 


600 


660 


720 78 


.... 


10 


23 












570 


660 


740 


810 87 


.... 


10 


24 












620 


730 


820 


900 96 


1020 


11 


25 














810 


910 


990 106 


1130 


11 


26 














890 


990 


1090 117 


1240 


11 


27 














970 


1090 


1190 128 


1350 


12 


28 














1060 


1180 


1290 139 


1470 


12 


29 














1150 


1280 


1400 150 


1590 


; 13 


30 














1240 


1380 


1510 162 


1710 


! 13 


31 














• • • • 


1500 


1630 175 


1860 


13 


32 
















1610 


1750 188 


1980 


1 14 


33 
















1720 


1870 201 


2130 


14 


34 
















1840 


2000 214 


2250 


15 


35 


















2130 227 


2380 


15 


36 












::: 






2270 240 


2510 


15 



Based on measurement of about 3000 trees sealed 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 in that dimension ; it is habitual 
with others, however. The general reliability of tables 
of this kind was discussed on pages 170 and 171, and it 
is necessary here to add only a suggestion on the head of 
timber utiHzation. 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 w^hich 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 yeUow 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 
tabfe 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 
of Log 


Contents by 
Decimal 






Tree No. 


Outside 
Bark 


Inside 
Bark 




(32 Feet) 




Rule 


Inches 


\ Inches 


1 


2 


3 


4 


5 


Feet 


1 


27 


23 


19 


16 


13 


10 




1,110 


2 


38 


32 


26 


23 


20 


15 




2,590 


3 


53 


45 


36 


32 


27 


21 




5,030 


4 


84 


74 


62 


57 


51 


46 


36 


19,570 


5 




23 


18 


15 


11 






850 


6 




23 


20 


18 


16 


15 


i2 


1,750 


7 


26 


24 


20 


17 


14 


8 




1,290 


8 


39 


36 


31 


28 


24 


17 




2,760 


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 appHcation of these to standing 
timber somewhat the same diflBiCulties 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 heavj^ 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 case. The taper of the body of these trees is 
regular, however; the variation is in the butt and top 
log sections, the former being far more significant. Trees 
Nos. 15 and 16 show some real irregularity, though noth- 
ing extreme. Much wider departures from type than 
any of these could in fact be chosen. 

In conclusion, a contrast will be drawn between present 
commercial methods and the use of volume tables. In 
the construction of these it is customary to throw out 
swell butt and other abnormality of form, and, that 
done, the tables derive strength from the law of averages. 
Single trees may depart from the type and a certain 
amount of variation goes with age, but the table, based 
on a large number of trees and applied to large numbers, 
if that is done in the same way the measures behind the table 
were taken, gives results that are trustworthy within 
reasonable limits. Present-day commercial estimates may 
be equally correct, but that depends on a different thing 
— on the ability of the cruiser to size up each tree as 
seen, on the basis of his training of every description. 



TABLES RELATING TO 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- 


Number of Sixteen-Foot Logs 






eter 
breast- 










Basis 












1 




high 


2 


3 


4 


5 


6 7 


8 




9 10 




Inches 


Volimae 


— Board Feet 




Trees 


8 


40 


60 


85 


105 










7 


9 


45 


70 


95 


120 










40 


10 


55 


85 


110 


140 


ies '. '. '. 








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 


c 


)76 ; ; ; 


104 


18 










275 


350 


420 500 


570 


e 


)40 ... 


111 


19 










295 


380 


460 550 


630 


7 


'20 ... 


117 


20 










320 


410 


500 600 


690 


7 


'90 880 


115 


21 












430 


540 650 


760 


S 


!70 980 


103 


22 












460 


580 710 


830 


c 


(60 1080 


94 


23 


• 










480 


620 760 


910 


IC 


150 1190 


83 


24 












510 


660 820 


980 


11 


40 1300 


81 


25 














710 890 


1060 


12 


40 1410 


69 


26 














760 950 


1140 


12 


30 1520 


64 


27 














810 1010 


1220 


14 


30 1630 


65 


28 














. . . 1080 


1300 


IS 


30 1750 


40 


29 














. . . 1150 


1390 


16 


30 1870 


23 


30 














1220 


1470 


17 


30 1990 


28 


31 
















1550 


18 


30 2110 


14 


32 
















1630 


19 


30 2230 


9 


33 
















1710 


20 


30 2360 


14 


34 


















21 


40 2490 


6 


35 


















22 


50 2630 


6 


36 


















23 


60 2770 


4 










1791 



From timber grown in northern Idaho. 

Trees scaled to a top diameter inside bark of 6 to 8 
inches. Height of stump — 2 to 3 feet. All trees scaled 
as though sound. Loss by breakage was 4 per cent. 
Loss due to invisible rot was 5 per cent. 



282 



A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLE No, 21. WESTERN YELLOW PINE IN 
BOARD FEET, BY THE SCRIBNER RULE 

(From Bulletin No, 36, U. S. Forest Service) 



Diam- 














Diam- 




eter 




Height of Tree-Feet 






eter of 




breast- 














top in- 
side 
bark 


Basis 


high 
















10 50 


50 70 80 


90 


100 


110 


120 






Inches 














Inches 


Trees 


12 


50 60 


70 80 ... 










8.3 




13 


60 80 


90 100 ... 










8.5 


23 


14 


70 90 


110 120 140 


iso 








8.7 


48 


15 


90 110 


130 150 170 


180 


igo 






8.9 


91 


16 


110 130 


160 180 200 


220 


230 


240 




9.2 


117 


17 


130 160 


180 210 230 


260 


280 


290 


sio 


9.4 


142 


18 


160 180 i 


210 240 270 


300 


320 


350 


370 


9.6 


136 


19 


180 210 i 


250 280 310 


350 


380 


410 


430 


9.9 


135 


20 i 


210 250 i 


280 320 360 


400 


440 


470 


600 


10.1 


104 


21 i 


240 280 J 


J20 370 410 


460 


500 


540 


680 


10.4 


127 


22 i 


280 310 { 


?60 410 470 


520 


570 


620 


670 


10.6 


135 


23 


. . 350 ^ 


HO 470 520 


590 


640 


700 


760 


10.9 


103 


24 


. . 390 ^ 


150 520 590 


660 


720 


780 


850 


11.1 


105 


25 


. . 430 i 


500 580 650 


730 


800 


880 


950 


11.3 


85 


26 


. . 470 1 


550 630 720 


800 


890 


980 


1070 


11.6 


93 


27 


( 


510 690 790 


880 


980 


1080 


1190 


11.9 


83 


28 


( 


560 760 860 


960 


1080 


1190 


1310 


12.1 


63 


29 




. . 820 930 


1040 


1170 


1300 


1440 


12.4 


51 


30 




.. 880 1000 


1130 


1270 


1420 


1570 


12.7 


42 


31 




. . 940 1070 


1220 


1380 


1550 


1720 


12.9 


21 


32 




. . 1010 1150 


1310 


1490 


1680 


1870 


13.2 


28 


33 




1230 


1410 


1610 


1820 


2020 


13.5 


22 


34 




1310 


1510 


1740 


1960 


2180 


13.9 


22 


35 




1390 


1620 


1870 


2110 


2330 


14.3 


17 


36 




1470 


1720 


1990 


2260 


2500 


14.7 


13 


37 






1810 


2120 


2410 


2660 


15.2 


6 


38 






1900 


2250 


2550 


2820 


15.8 


4 


39 








2390 


2690 


2980 


16.4 


5 


40 








2530 


2840 


3150 


17.0 


1 


1822 



Measurements by T. S. Woolsey, Jr,, in Arizona. 

Trees scaled to 8-inch top inside bark — straight and 
sound. Allow 3 to 15 per cent for defects. The so-called 
" black jack " variety requires a further reduction of 
about 12 per cent, having a smaller volume than the older 
** yellow pine." 



TABLES RELATING TO PARTS III AND IV 283 



VOLUME TABLE No. 22. WESTERN YELLOW PINE, BY 
THE SCRIBNER RULE 

Same trees classified by 16-foot log lengths 



Diam- 




Number of 16-foot Logs 






f^tf^r 












breast- 














Basis 


high 1 






2 3 


4 


5 


6 




Inches 




Volume - 


— Board Feet 




Trees 


13 t 


)0 




80 








22 


14 ( 


)0 




100 140 


190 






47 


15 '> 


'0 




L20 160 


210 






93 


16 J 


iO 




140 180 


240 






119 


17 1( 


)0 




L60 210 


270 






142 


18 U 


JO 




L90 240 


310 


380 




140 


19 14 


m 




>20 270 


350 


430 




138 


20 1( 


)0 




>50 310 


400 


490 




108 


21 




^ 


J90 360 


450 


550 




128 


22 






530 410 


500 


610 




136 


23 






J80 460 


560 


680 




101 


24 




/ 


120 520 


630 


760 




108 


25 




< 


t70 580 


700 


840 




86 


26 




} 


530 640 


780 


920 ] 


mi 


) 95 


27 




, 


580 710 


860 


1010 ] 


L15( 


) 85 


28 




( 


530 790 


950 


1100 ] 


L25( 


) 65 


29 






870 


1040 


1200 ] 


136( 


) 54 


30 






960 


1130 


1300 ] 


147( 


) 43 


31 






1050 


1230 


1410 ] 


159( 


) 25 


32 






1140 


1340 


1530 ] 


L71( 


) 28 


33 






1240 


1460 


1660 ] 


183( 


) 21 


34 






1340 


1580 


1780 ] 


t96( 


) 21 


35 








1710 


1910 5 


J09( 


) 14 


36 








1830 


2040 i 


122( 


) 12 


37 








1950 


2160 i 


234( 


) 5 


38 








2060 


2280 i 


>45( 


) 3 


39 








2160 


2400 i 


256( 


) 3 


40 






.... 


2260 


2520 i 


267( 


) 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 


breast- 
high 












50 


60 


70 


80 


90 


100 


Trees 


Inches 
















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) 







Average Nimiber Obtained per Tree 




Diam- 
eter 






















breast- 




Hewn Ties 




Sawed Ties 




high 
Inches 












Tall 


Medium 


Short 


Tall 


Medium 


Short 




over SO' 


60-80' 


under 60' 


over 80' 


60-80' 


under 60' 


10 


1.7 


1.5 


1.1 








11 


3.0 


2.7 


1.8 


0.9 


0.8 


0.7 


12 


4.0 


3.5 


2.2 


1.9 


1.7 


1.2 


13 


4.9 


4.0 


2.5 


3.0 


2.6 


1.8 


14 


5.5 


4.4 


2.7 


3.9 


3.3 


2.2 


15 


6.0 


4.7 


2.9 


4.6 


3.8 


2.5 


16 


6.4 


5.0 




5.1 


4.2 




17 


6.7 


5.0 




5.5 


4.2 




18 


6.9 


5.0 




5.9 


4.2 




19 


7.1 






6.1 






20 


7.2 






6.3 







Results from 267 trees cut in eastern Oregon : Hewn ties 
from timber not less than 83^ 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- 










Diam- 




eter 


Nimaber of 16- Foot Logs 


eter 




breast- 










of top 
inside 


3 as is 


high 






























bark 




Inches 


3 


4 


5 


6 




7 8 


Inches 


Trees 


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 


.55 


205 


270 










7.6 


114 


16 


175 


230 


295 


380 








7.7 


119 


17 


195 


260 


325 


415 








7.8 


128 


18 i 


220 


285 


365 


455 








7.9 


100 


19 i 


240 


315 


400 


490 








8.0 


93 


20 5 


265 


345 


435 


535 




)45 ; 




8.1 


127 


21 




380 


475 


585 




^05 . 




8.1 


86 


22 






415 


520 


635 




'75 




8.1 


89 


23 






450 


560 


695 




540 1005 


8.2 


80 


24 






485 


605 


745 




)05 1085 


8.2 


79 


25 






525 


655 


805 




)75 1180 


8.2 


52 


26 






565 


700 


865 


1( 


)55 1275 


8.2 


32 


27 






605 


755 


930 


1] 


L30 1375 


8.3 


32 


28 






650 


805 


995 


U 


JIO 1470 


8.3 


35 


29 










855 


1060 


U 


J95 1565 


8.4 


17 


30 










910 


1130 


i: 


585 1670 


8.5 


21 


31 












1205 


14 


165 1770 


8.7 


12 


32 














1280 


11 


)60 1875 


8.8 


10 


33 














1360 


le 


)50 1975 


9.0 


4 


34 














1440 


17 


'45 2085 


9.2 


8 


35 














1525 


n 


545 2190 


9.4 


1 


36 














1600 


IE 


>45 2295 


9.6 


5 


37 














1685 


2C 


)40 2395 


9.8 


3 


38 














1770 


21 


45 2505 


10.0 


2 


39 














1850 


22 


40 2610 


10.2 




40 












1930 


23 


40 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 




Height of Tree — Feet 


eter 
of top 




breast- 














Basis 


high 
















bark 


Inches 





1 


)0 60 


70 


80 


90 


100 


110 120 _ , 

Inches 


Trees 


8 1 


5 




20 30 










6.2 


8 


9 1 


5 




25 35 


50 


70 






6.3 


19 


10 2 







30 45 


60 


80 






6.4 


19 


11 2 


5 




40 55 


70 


90 


iio 




6.5 


35 


12 3 







50 65 


85 


110 


135 




6.6 


45 


13 4 







60 80 


100 


130 


160 




6.7 


44 


14 5 







70 95 


120 


150 


185 


220 


6.8 


51 


15 6 







80 110 


140 


170 


210 


250 


6.9 


37 


16 7 







95 125 


160 


190 


240 


280 


340 ... 7.0 


61 


17 




] 


LIO 140 


180 


220 


270 


320 


380 ... 7.1 


57 


18 




] 


L25 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 

at Stump 

Outside 

Bark 



Inches 



18 
20 

22 
24 
26 

28 
30 

32 
34 
36 
38 
40 

42 

44 
46 
48 
50 

52 

54 
56 
58 
60 

62 
64 
66 
68 
70 

72 

74 
76 



Average 



40 
50 

62 

77 

91 

105 

125 

145 
169 
195 
228 
270 

312 
365 
425 
480 
535 

588 
645 
705 
765 
830 

900 

972 

1048 

1133 

1226 

1310 
1413 
1515 



Number of Thirty-two-Foot Logs 



2J 



3i 



5i 



Volume — Board Feet in Tens 



28 
32 


34 
39 

44 
49 
55 
61 
66 


41 

47 

53 
60 
68 
76 
84 

92 
100 
120 


50 
56 

66 
75 
84 
95 
106 

115 
125 
138 


58 
65 

78 

88 

98 

110 

124 

138 
149 
164 
183 


92 
102 
112 
124 
141 

162 
176 
192 
212 

228 

246 
268 
286 


122 
136 

157 

182 
203 
227 
253 
280 

306 
332 
358 
388 
420 

450 
480 


247 

278 
313 

342 
374 
403 
433 
468 

502 
530 


385 
420 
454 
487 
528 

566 
595 
630 
668 
711 

760 
808 
864 


437 
462 
494 
534 
581 

598 
654 
697 
744 
790 

838 

886 

953 

1030 

1118 

1198 
1285 
1364 


59'2 
644 

680 
722 
771 
821 
872 

926 

985 

1066 

1147 

1225 

1312 

1390 
1465 





























































































































































































































































































730 
774 
830 
888 
942 

1009 
1082 
1171 
1261 
1345 

1420 
1486 
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 


Total Height of Tree 


— Feet 


eter 




breast- 










of top 
inside 


Basis 


high — 










bark 




30 70 


80 


90 


100 1 


10 ^ , 




Inches 










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 


ioo 


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 ^ 


too 7.4 


64 


19 


190 240 


280 


330 


400 ^ 


t50 7.5 


57 


20 J 


210 270 


320 


370 


440 I 


)00 7.6 


55 


21 2 


230 300 


350 


410 


480 I 


)50 7.8 


57 


22 i 


250 330 


380 


450 


530 ( 


)00 7.9 


50 


23 


360 


420 


490 


580 i 


550 8.0 


45 


24 


390 


450 


540 


630 'i 


'10 8.2 


40 


25 


420 


490 


580 


690 7 


'70 8.3 


38 


26 


450 


530 


630 


750 J 


530 8.5 


31 


27 


480 


580 


680 


810 c 


)00 8.6 


22 


28 


520 


620 


730 


870 c 


)70 8.8 


12 


29 




670 


790 


940 1( 


)40 8.9 


9 



From timber cut in Wyoming and Idaho measured by 
Messr. Redington and Peters. 



TABLES RELATING TO PARTS III AND IV 289 



VOLUME TABLE No. 28. WASHINGTON HEMLOCK BY THE 

SCRIBNER DECIMAL RULE 

(By E. J. Hanzhk of U. S. Forest Service) 



Diameter 






Nimiber of Thirty-two-Foot Logs 


Breast; 
High 


Average 








1 




















Outside 




U 


2 


2i 


3 


3i 


4 


4i 


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 


39 


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 


140 






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 


288 




34 


245 








181 


204 


229 


263 


305 


353 


35 


264 








190 


213 


242 


278 


323 


376 


36 


284 










222 


253 


293 


343 


404 


37 


304 










231 


266 


310 


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 Httle over 80 per cent of above 
figures. 

The true firs are formed very neariy like hemlock. 



290 



A MANUAL FOR NORTHERN WOODSMEN 



VOLUME TABLES No. 29. WASHINGTON RED CEDAR 
BY THE SCRIBNER DECIMAL RULE 

TALL TIMBER 



Diameter 


First 32' 


Log 


Second 32 


' Log 


^ 


to 
o 


QQ 


Breast 














^S 


:js 


"3 o 
1^ 


High 














TJ.2 


-s 


^§ 


Outside 


Top 


Scale 


%of 


Top 


Scale 


%of 


;sQ 


Sq 




Bark 


Diam. 


Total 


JDiain. 


Total 


H 


^ 


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 


im 






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 
Breast 
High 
Outside 
Bark 


First 32' 


Log 


Second 32' 


Log 




Fourth Log 
Diam. 

51 Total 
» Volume 


Top 
Diam. 


Scale 


%of 
Total 


Top 
Diam. 


Scale 


%of 
Total 


:a5 


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(i) 


790 


34 


20 


560 


58 


15 


280 


32 


10 


960 


36 


22 


670 


57 


17 


370 


31 


11 


1180 


38 


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 ll(^) 1 1830 1 


44 


27 


1100 


52 


21 


610 


29 


16 ] 


L2(i) 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 






Diameter 
Breast- 






CO 00 
















high 


2 3 4 5 6 7 


8 


9 


10 


11 




12 Q§o 


l£ 


Inches 














t— ( 


«H 


Volume — Board Feet in Tens 


Inches 


12 


9 15 22 












8 




14 


10 17 24 












8 


*i 


16 


10 19 27 39 












8 


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 


122 










9 


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 


18C 








10 


53 


32 


. . . . 113 127 145 163 


192 


21J 








10 


50 


34 


. . . . 135 149 166 187 


217 


247 








10 


38 


36 


. . . . 160 173 191 213 


246 


27t 


) 31C 






11 


36 


38 


. . . . 183 200 220 245 


278 


31c 


5 346 






11 


40 


40 


. . . . 210 229 253 280 


313 


34c 


> 386 






11 


41 


42 


. . . . 240 261 288 319 


354 


39C 


) 427 


463 




11 


43 


44 


. . . . 271 295 325 359 


398 


43t 


) 473 


51£ 




12 


39 


46 


. . . . 303 330 365 401 


445 


482 


' 523 


567 




12 


31 


48 


. . . . 337 366 405 446 


493 


532 


575 


623 




12 


43 


50 


401 446 493 


544 


58€ 


630 


681 


1- 


'49 12 


41 


52 


438 489 544 


598 


642 


686 


74C 


J 


U8 12 


56 


54 


472 532 597 


653 


69S 


742 


801 


S 


!85 13 


36 


56 


575 652 


711 


75e 


800 


862 


c 


>53 13 


25 


58 


619 709 


769 


814 


860 


923 


IC 


)22 13 


25 


60 


660 764 


829 


872 


921 


987 


IC 


)90 14 


28 


62 


704 820 


886 


93C 


983 


1051 


1] 


59 14 


25 


64 


876 


943 


99C 


1046 


1116 


12 


!27 14 


27 


66 


. . . 933 


1000 


1053 


1109 


1181 


12 


97 14 


11 


68 


. . . 989 


1058 


1115 


1173 


1250 


12 


166 15 


9 


70 


. . • • 1048 


1117 


1177 


1239 


1319 


14 


34 15 


17 


73 




1176 


1240 


1305 


1388 


U 


02 15 


6 


74 




1235 


1303 


1370 


1456 


U 


70 16 


2 


76 




1296 


1368 


1435 


1523 


16 


39 16 


6 


78 




1358 


1431 


1500 


1590 


17 


07 16 


4 


80 




1420 


1497 


1565 


1659 


17 


78 16 


3 


910 




Average stump heights 1.3 to 3.1 feet. 








Logs scaled in commercial lengths as cu1 


t. 





SECTION III 
MISCELLANEOUS TABLES AND INFORMATION 

1. Rules for Area and Voltime of Different 

Figures ^^^ 

2. Weight of Materials ^^^ 

3. Handy Equivalents ^^^ 

4. Number of Plants per Acre with Different 

Spacing '^^' 

5. Compound Interest Table ^^^ 

6. Tevie 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. 



c d 



a I) 

Figure A 




Figure C 



Area of Parallelogram. (Figure A.) Multiply base a h 
by altitude h c, not hy h d. If b d and the angle at d are 
known, b c may be found by the formula 

bc= bdX sine of angle at d. 

Area of Triangle. (Figure B.) Multiply base a 6 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 

Vi s (i s — a) a s — b) (is— 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^ + AO = BC2, 



M 



01 



0+ N= M. 






^^\^ 


A 


N 



B 



Figure D 



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. 



Multiply the area 






Figure E 



Figure F 



Figure G 



Figure H 



Volume of Prism whether Right 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 62^ lbs. 

A cubic foot of cast iron weighs about 450 lbs. 

A cubic foot of wrought iron or steel weighs about .... 480 lbs. 

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 lbs. 

Red spruce, hemlock, poplar 30 lbs. 

Pitch pine, Norway pine, black spruce, white maple .... 31-35 lbs. 
White birch, red maple, tamarack, white ash, yellow birch, 

red oak 40-45 lbs. 

Beech, sugar maple about 48 lbs. 

White oak, black birch about 52 lbs. 

A cord of green spruce pulp wood weighs about 4500 lbs. ; 
fir and white pine a little more. A cord of dry spruce pulp 
wood weighs 3000 to 3500 lbs. 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 lbs. ; 
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 
lbs. are the usual limits of weight. Medium dry birch, 
beech, and maple, split, 66 per cent solid in the pile, weighs 
about 3000 lbs. to the cord. 

A thousand feet of old growth spruce logs, Andros- 
coggin scale, weighs about 6000 lbs., and this is probably 
the lower limit for green soft-wood lumber, while southern 
yellow pine at 8000 to 10,000 lbs. 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 rNFORMATION 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 lbs 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 Zl principal after any number of years and at 
given rates percent 



Yra. 
1 


2% 


2i% 


3% 


3i% 


4% 


4i% 


5% 


5i% 


6% 


1.020 


1.025 


1.030 


1.035 


1.040 


1.045 


1.050 


1.065 


1.060 


2 


1.040 


1.051 


1.061 


1.071 


1.082 


1.092 


1.103 


1.113 


1.124 


3 


1.061 


1.077 


1.093 


1.109 


1.126 


1.141 


1.158 


1.174 


1.191 


4 


1.082 


1.104 


1.126 


1.148 


1.170 


1.193 


1.216 


1.239 


1.262 


5 


1.104 


1.131 


1.159 


1.188 


1.217 


1.246 


1.276 


1.307 


1.338 


6 


1.126 


1.160 


1.194 


1.229 


1.266 


1.302 


1.340 


1.379 


1.419 


7 


1.149 


1.189 


1.230 


1.272 


1.316 


1.361 


1.407 


1.466 


1.604 


8 


1.172 


1.218 


1.267 


1.317 


1.369 


1.422 


1.478 


1.536 


1.594 


9 


1.195 


1.249 


1.305 


1.363 


1.423 


1.486 


1.661 


1.619 


1.690 


10 


1.219 


1.280 


1.344 


1.411 


1.480 


1.563 


1.629 


1.708 


1.791 


11 


1.243 


1.312 


1.384 


1.460 


1.640 


1.623 


1 710 


1.802 


1.898 


12 


1.268 


1.345 


1.426 


1.511 


1.601 


1.696 


1.796 


1.901 


2.012 


13 


1.294 


1.379 


1.469 


1.564 


1.665 


1.772 


1.886 


2.006 


2.133 


14 


1.320 


1.413 


1.513 


1.619 


1.732 


1.862 


1.980 


2.116 


2.261 


15 


1.346 


1.448 


1.558 


1.675 


1.801 


1.936 


2.079 


2.233 


2.397 


16 


1.373 


1.485 


1.605 


1.734 


1.873 


2.022 


2.183 


2.366 


2.540 


17 


1.400 


1.522 


1.653 


1.795 


1.948 


2.113 


2.292 


2.486 


2.693 


18 


1.428 


1.560 


1.702 


1.863 


2.026 


2.209 


2.407 


2.622 


2.864 


19 


1.457 


1.599 


1.754 


1.928 


2.107 


2.308 


2.627 


2.766 


3.026 


20 


1.486 


1.639 


1.806 


1.990 


2.191 


2.412 


2.653 


2.918 


3.207 


26 


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 


3.746 


4.322 


4.984 


5.744 


35 


2.000 


2.373 


2.814 


3.334 


3.946 


4.667 


6.616 


6.614 


7.686 


40 


2.208 


2.685 


3.262 


3.959 


4.801 


5.816 


7.040 


8.513 


10.286 


45 


2.438 


3.038 


3.782 


4.702 


5.841 


7.248 


8.985 


11.127 


13.766 


50 


2.692 


3.437 


4.384 


5.686 


7.107 


9.033 


11.467 


14.542 


18.420 



TIME IN WHICH A SUM WILL DOUBLE 



Rate 
Per cent 


Simple Interest 


Compound Interest 


2 

2i 
3 

3i 
4 

4i 
5 

5i 
6 


50 years 

40 years 

33 years 4 months 

28 years 7 months 

25 years 

22 years 2f months 

20 years 

18 years 7 months 

16 years 8 months 


36 years 

28 years 1 month 
23 years 6i months 
20 years 2^ months 
17 years 8 months 
15 years 9 months 
14 years 2^ months 
12 years 11^^ months 
11 years 111 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 



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 


15.04 


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 


3.69 


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 


7.69 


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 T\VENTY-SIX DAYS — continued 



D 


$29 


830 


$31 


$32 


$35 


$40 


$45 


1 


1.12 


1.15 


1.19 


1.23 


1.35 


1.54 


1.73 


2 


2.23 


2.30 


2.38 


2.46 


2.69 


3.08 


3.46 


3 


3.34 


3.46 


3.58 


3.69 


4.04 


4.62 


5.19 


4 


4.46 


4.62 


4.77 


4.92 


5.38 


6.15 


6.92 


5 


5.58 


5.77 


5.96 


6.15 


6.73 


7.69 


8.65 


6 


6.69 


6.92 


7.15 


7.38 


8.07 


9.23 


10.39 


7 


7.80 


8.08 


8.35 


8.61 


9.42 


10.77 


12.12 


8 


8.92 


9.23 


9.53 


9.85 


10.77 


12.31 


13.85 


9 


10.04 


10.38 


10.73 


11.08 


12.11 


13.84 


15.58 


10 


11.15 


11.54 


11.92 


12.31 


13.46 


15.38 


17.31 


11 


12.27 


12.69 


13.12 


13.54 


14.81 


16.92 


19.04 


12 


13.38 


13.85 


14.32 


14.77 


16.15 


18.46 


20.77 


13 


14.50 


15.00 


15.50 


16.00 


17.50 


20.00 


22.50 


14 


15.61 


16.15 


16.70 


17.23 


18.84 


21.54 


24.23 


15 


16.73 


17.31 


17.88 


18.46 


20.19 


23.07 


25.96 


16 


17.84 


18.46 


19.07 


19.69 


21.54 


24.61 


27.70 


17 


18.96 


19.62 


20.27 


20.92 


22.88 


26.15 


29.43 


18 


20.07 


20.77 


21.47 


22.15 


24.23 


27.69 


31.16 


19 


21.19 


21.92 


22.65 


23.38 


25.57 


29.23 


33.89 


20 


22.30 


23.08 


23.85 


24.62 


26.92 


30.77 


34.62 


21 


23.42 


24.23 


25.04 


25.85 


28.27 


32.31 


36.35 


22 


24.53 


25.38 


26.23 


27.08 


29.61 


33.84 


38.08 


23 


25.65 


26.54 


27.42 


28.31 


30.96 


35.38 


39.81 


24 


26.76 


27.69 


28.61 


29.54 


32.31 


36.92 


41.54 


25 


27.88 


28.85 


29.81 


30.77 


33.65 


38.46 


43.27 


26 


29.00 


30.00 


31.00 


32.00 


35.00 


40.00 


45.00 


D 


«50 


$60 


$70 


$75 


$80 


$90 


$100 


1 


1.92 


2.31 


2.69 


2.88 


3.08 


3.46 


3.85 


2 


3.85 


4.62 


5.38 


5.77 


6.15 


6.92 


7.69 


3 


5.77 


6.92 


8.08 


8.65 


9.23 


10.38 


11.54 


4 


7.69 


9.23 


10.77 


11.54 


12.31 


13.85 


15.38 


5 


9.61 


11.54 


13.46 


14.42 


15.38 


17.31 


19.23 


6 


11.54 


13.85 


16.15 


17.11 


18.46 


20.77 


23.08 


7 


13.46 


16.15 


18.84 


19.19 


21.54 


24.23 


26.92 


8 


15.38 


18.46 


21.54 


23.08 


24.62 


27.69 


30.77 


9 


17.31 


20.77 


24.23 


25.96 


27.69 


31.16 


34.61 


10 


19.23 


23.08 


26.92 


28.85 


30.77 


34.62 


38.46 


11 


21.15 


25.38 


29.61 


31.73 


33.84 


38.08 


42.31 


12 


23.08 


27.69 


32.31 


34.61 


36.92 


41.54 


46.15 


13 


25.00 


30.00 


35.00 


37.50 


40.00 


45.00 


50.00 


14 


26.92 


32.31 


37.69 


40.38 


43.08 


48.46 


53.85 


15 


28.85 


34.61 


40.38 


43.27 


46.15 


51.92 


57.69 


16 


30.77 


36.92 


43.08 


46.15 


49.23 


55.38 


61.54 


17 


32.69 


39.23 


45.77 


49.04 


52.31 


58.85 


65.38 


18 


34.61 


41.54 


48.46 


51.92 


55.38 


62.31 


69.23 


19 


36.54 


43.84 


51.15 


54.81 


58.46 


65.77 


73.08 


20 


38.46 


46.15 


53.85 


57.69 


61.54 


69.23 


76.92 


21 


40.38 


48.46 


56.54 


60.58 


64.61 


72.69 


80.77 


22 


42.31 


50.77 


59.23 


63.46 


67.69 


76.15 


84.61 


23 


44.23 


53.08 


61.92 


66.35 


70.77 


79.61 


88.46 


24 


46.15 


55.38 


64.62 


69.23 


73.85 


83.08 


92.31 


25 


48.08 


57.69 


67.31 


72.12 


76.92 


86.54 


96.15 


26 


50.00 


60.00 


70.00 


75.00 


80.00 


90.00 


100.00 



THE BILTMORE STICK 



301 



THE BILTMORE STICK 

This implement, employed to ascertain the diameter of 
standing timber when held at arm's length tangent to the 
trees to be measured, was briefly described on page 163. 
Relations between tree, stick, and eye when the stick is 
in use are made clear in the figure, the circle representing 
a section of a tree breast high, B X the Biltmore stick, 
A T the distance from the stick to the eye, and M a, 
radius vertical to the line of sight passing on one side of 
the tree. With this for a pattern it is clear how the woods- 
man, after having determined A T as a matter of practice, 
can plot circles of different diameters, draw tangents to 
them from A, and ascertain by measurement in each case 
B C, the proper stick graduation. 

The geometry of the matter is that of similar right- 
angled triangles, and consideration will show the soundness 
of the formula appended, from which may be derived 




BC= 



' ATxD 

AT{AT + D) 



the value oi 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 (25 + D) 



or, for Z) = 10 inches 



250 



250 



\/625 + 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 ^ 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 caliper; hence 
cross measures are the more desirable. 

(d) It is very easy in practice to vary the distance 
between the stick and the eye, and this introduces error 
that is material, though in continued work successive 
errors tend to balance. 

(e) Men of ordinary height have a constant tendency 
to measure tree diameter not breast high, but higher, near 
the eye level. 

To conclude, the Biltmore stick requires to be practi- 
cally tested before use and constant care in application. 
More liable to error than the caliper, in ordinary timber 
it works less rapidly as well. While serviceable in its 
field, its general use is not to be recommended. 

1 Bruce at previous reference. 



V.