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corner to the next "meander corner " upon the same or
another boundary of the same township, carefully noting
intersections with all the intermediate meander corners.
By the same method meander the opposite banks of the

The crossing distance between the meander corners on the
same line is to be ascertained by triangulation, in order that
the river may be protracted with entire accuracy. The
particulars are to be given in the field notes. The courses
and distances on meandered navigable streams are the bases
for the calculation of the true areas of the tracts of land
(sections, quarter-sections, etc.), known to the law as
fractional and bounding on such streams.

The surveyor is also to meander, in manner aforesaid, all
lakes and deep ponds of the area of twenty-five acres and
upwards, also navigable bayous.

As traverse tables are generally calculated to 15' angles,
it is advisable to make meander courses read to quarter
degrees instead of intermediate minutes, except in closing or
where the extreme length of a side of a lake or stream falls
in one course.

The precise relative position of islands in a township made
fractional by the river in which they are situated is to be
determined trigonometrically. To meander islands crossed
by government lines, meander corners are previously estab-
lished at opposite points on the shore of the island, and the
meanders run from one to the other. Should the island not
be crossed by a line, measure a special base line from the


meander corner nearest to the island, triangulating to and
establishing at any convenient point on the island a special
meander corner from and to which the meanders of the island
start and close.

1318. Marking Lines. All lines on which are to
be established the legal corner boundaries are to be marked
after this method, viz. : Those trees which may intercept
the line must have two chops or notches cut on each side of
them without any other marks whatever; these are called
sight trees or line trees. A sufficient number of other trees
standing nearest to the line on either side of it are to be
blazed QK. two sides diagonally or quartering towards the line,
in order to render the line conspicuous and readily traced,
the blazes to be opposite to each other, coinciding in direc-
tion with the line where the trees stand very near it, and
to approach nearer each other the further the line passes
from the blazed trees. Due care must ever be taken to have
the line so well marked as to be readily followed.

1319. Marking Corners. After a true coursing
and most exact measurements, the corner boundary is the
consummation of the work for which all the previous pains
and expenditure have been incurred. A boundary corner in
a timbered country is to be a tree, if one be found at the
precise spot; and if not, a. post is to be planted thereat, and
the position of the corner post is to be indicated by trees
adjacent (called bearing trees), the angular bearings and
distances of which from the corner are facts to be ascertained
and recorded by the surveyor. In a region where stones
abound, the corner boundary will be a small monument of
stones alongside of a single marked stone for a township
corner and a single stone for all other corners.

In a region where neither timber nor stone is available, >
the corner will be a mound of earth of prescribed size
varying to suit the case.

When posts are used, their length and size must be pro-
portional to the importance of the corner, whether township,
section, or quarter-section post.



Township corner posts are three inches square and set at
least twenty-four inches above ground.

Where a township post is at a corner, common to four
townships, it is to be set in the ground diagonally, as shown
in Fig. 311, and the cardinal points of the compass
indicated by lines cut or sawed out of its top at
least one-eighth of an inch deep, as shown in the
figure. On each face of the post is to be marked
FIG. 311. t he number and range of the particular township
which it faces. Thus, if the post be a common boundary
to four townships, viz., one and two south of the base line
and range two west, and also one and two. south of the
base line and range three west, the face markings will be as
follows :

From N to E

From N to W

E to S

From W to S

R. 2 W

T. 1 vS
S 31
3 W

1 S

2 W

2 S

3 W




T2S ' T2S

FIG. 312.

The position of the post which is here taken as an
example is shown in Fig. 312.

These marks are neatly chiseled into the wood, and are
also marked with red chalk. The number of the sections
which they respectively face will also be marked on the
township post.

Section or mile posts, being corners of sections, when
they are common to four sections, are to be set diagonally
in the earth (in the manner provided for township posts),
and with similar marks cut in the top to indicate the car-
dinal points of the compass, while on each side of the post is


cut the number of the particular section which the side
faces. Also, on one side is to be marked the number of its
township and range. To make such marks more conspicuous
and durable, red chalk is applied. A quarter-section or
half-mile post is to have no other mark than ^ S to indicate
what it stands for.

Township posts are to be notched with six notches on
each edge or angle corresponding to the cardinal points of
the compass. All mile posts on township lines must have
as many notches on opposite angles as they are miles dis-
tant from the corresponding township corners. Each ot
the posts at the corners of sections in the interior of a town-
ship must have on their four angles, corresponding to the
cardinal points, as many notches as they are miles distant
from the corresponding township corners. The four sides
of the post will indicate the numbers of the sections which
they respectively face. Should a tree be found at the place
of any corner it will be marked and notched in the manner
before described and will serve in place of a post; the kind
of tree and the diameter must be given in the field notes.

The position of all corner posts or corner trees of what-
ever description, which may be established, is to be perpet-
uated in the following manner, viz. : From such post or tree,
the courses shall be taken and the distances measured to two
or more adjacent trees in opposite directions as nearly as
may be, which are called bearing trees, and are to be blazed
near the ground with a large blaze facing the post and hav-
ing one notch in it, neatly and plainly made with an ax,
square across, and a little below the middle of the blaze.
"The kind of tree and the diameter of each are facts to be
clearly set forth in the field book.

On each bearing tree the letters B. T. must be distinctly
cut into the wood in the blaze a little above the notch or*
on the bark, with the number of the range, township, and

At all township corners and at all section' corners on
range or township lines four bearing trees are to be marked
in this manner, one in each of the adjoining sections.


At interior section corners four trees, one to stand
within each of the four sections to which such corner is com-
mon, are to be marked in the manner aforesaid if such be

From quarter-section and meander corners, two bear-
ing trees are to be marked, one within each of the adjoining
sections. Stones at township corners (a small monument of
stones being alongside thereof) must have six notches cut
with a pick or chisel on each edge or side towards the car-
dinal points; and where used as corners in the interior of a
township, they will also be notched with a pick or chisel to
correspond with the directions given for notching posts
similarly situated.

Stones when used as quarter-section corners will have
\ cut on them, on the west side in north and soutli lines, and
on the north side in east and west lines.

Wherever bearing trees are not found, mounds of earth
or stone are to be raised around posts on which the corners
are to be marked in the manner aforesaid. Wherever a
mound of earth is adopted, the same will present a pyra-
midal shape. At its base on the earth's surface a quadran-
gular trench will be dug; a spade deep of earth being thrown
up from the sides of the line outside the trench, so as to
form a continuous elevation along its outer edge. In mounds
of earth common to four townships or four sections, they
will present the angles of the quadrangular trench diagonally
to the cardinal points. In mounds common only to two
townships or two sections, the sides of the trench will face
the cardinal points. Prior to piling up the earth, in a
cavity, formed at the corner boundary point, is to be
deposited a stone, or a portion of charcoal; or a charred
stake is to be driven twelve inches down into such center
point to be a witness for the future. The surveyor is
further specially enjoined to plant midway between each
pit and the trench seeds of some tree, those of fruit trees
adapted to the climate being always to be preferred.

Double corners are to be found nowhere except on the
standard parallels or correction lines whereon are to appear


both the corners which mark the intersection of the lines
which close thereon and those from which the surveys start
in the opposite direction.

The corners which are established on the standard
parallel at the time of running it are to be known as
" standard corners" and in addition to all the ordinary
marks (before described) they will be marked with the
letters S. C. The closing corners will be marked C. C.

1320. Field Books. There are several field books,
viz. :

1. Field Books for the meridian and base lines, show-
ing the establishment of towns/rip, section, or mile, and
qiiarter-section, or half-mile boundary corners thereon ; with
the crossings of streams, ravines, hills, and mountains; the
character of the soil, timber, minerals, etc. These notes
will be arranged in series by mile stations consecutively
from number one to number .

2. Field Books for the standard parallels or correction
lines, showing the establishment of the township, section, and
quarter-section corners, besides exhibiting the topography of
the country on line as required on the base and meridian

3. Field Books for exterior lines of townships, showing the
establishment of the corners on line, and the topography as

4. Field. Books for the subdivision of townships into
sections and quarter-sections; at the close whereof will
follow the notes of the meanders of navigable streams.
Those notes will also show by ocular observation the estima-
ted rise and fall on the line. A description of the timber,
undergrowth, surface soil, and minerals upon each section
line is to follow the notes thereof, and not be intermixed
with them.

5. The Geodetic Field Book, comprising all triangulations,
angles of elevation and depression, leveling, etc.

1321. Retracing Old Lines. The original surveys
of lands in the older States of the American Union were



imperfectly made and full of errors. This was owing to two
principal causes; viz., the cheapness of the lands and the
lack of skill in the surveyors. Boundary lines described in
deeds and shown in maps as straight are found to be crooked
on the ground; tracts contain less or more land than
called for in descriptions. Records of adjoining tracts make
one to overlap another or leave an unclaimed gore between
them. These discrepancies and blunders often render the
work of the surveyor, when retracing old boundaries or
establishing corners, exceedingly difficult, and great tact and
judgment are often necessary in making amicable and satis-

factory adjustments of contending claims. In general, old
boundaries, such as line trees, stone monuments, and fences
are accepted as holding ; but, before retracing lines' the
surveyor should, if possible, secure the consent of adjacent
owners to abide by such monuments and boundaries, irre-
spective of the lines or quantities called for in contracts or
deeds. It must be borne in mind that the bearings of lines
are each year undergoing a slight change which, in a long
period, amounts to several degrees, and if the lines were re-
run according to original bearings as given in descriptions,
they would enclose a tract differing widely from that in-
cluded in the original survey. The surveyor must accord-



ingly determine the amount of magnetic variation or change
which has taken place between the time of the original
survey and the date of the survey about to be made, and
having determined such change or variation, he must make
the original bearings conform to the calculated variation
before commencing the survey.

Fig. 313 illustrates the effect of magnetic variation in
altering the direction of lines. The figured BCD gives
the outline of a tract according to the original survey, and
A B' C ' D' E' the relative directions of the boundaries when
resurveyed with the original bearings, there having been
during the intervening time a change in magnetic variation
of 3 west.

Let columns 1, 2, and 3 in the accompanying diagram
give the courses, original bearings, and distances, and col-
umn 4 the cor-
rected bearings
which the original
boundaries will
have, when allow-
ance has been
made for the mag-
netic variation.
When the north
end of the needle
has been moving westerly, i. e., when the variation or change
is west, the corrected or present bearings will be the sums of
the change and the old bearings which were nortlieastcrly or
southwesterly and the differences of the change and the old
bearings which were northwesterly or southeasterly ; when
the variation or change is easterly, the corrected or present
bearings will be the differences of the change and the old
bearings which were northeasterly or southwesterly and the*
sums of the change and the old bearings which were north-
westerly or southeasterly.

It will be seen, by reference to Arts. 1211 and 1212,
that declination is the reverse of variation, i. e. , a west decli-
nation results when the variation or movement of the N end











N 68 00' E


N 71 00' E


S 73 00' E


S 70 00' E


S 8 00' E


S 5 00' E


S 87 00' W


S 90 00' W


N 28 00' W


N 25 00' W


of the needle is to the east, and cast declination results when
the movement of the N end of the needle is to the west.
By this rule the bearings given in column 4 are obtained.
Before commencing the survey, the surveyor should cor-
rect all the bearings and write them out together with the
original bearings in their proper order.

1322. How to Determine Magnetic Variation.

If the date of the original survey is known, the amount of
variation may be determined from published tables giving
the yearly variation for different sections of the country, but
the date of the survey is often omitted. The date of the
deed must not be taken as the date of the survey.

If one of the original boundaries remains unchanged, the
magnetic variation can be determined at once by taking the
present bearing of the line. The difference between the
present bearing and that of the original survey is the re-
quired correction. The corrections are then to be made in
the original bearings and the resulting courses run out.
Where the measurements fall short of or overrun the
original measurements, corrections must be made, locating
the original corners if they can be found or establishing new
ones, and, if possible, to the mutual satisfaction of adjoining

1323. Establishing New Boundaries. Where the
description and map show a boundary to be a straight line
and the actual boundary is found to be crooked, it is a good
policy to establish a new and straight boundary by the prin-
ciple of "give and take," providing adjoining owners will
agree to the adjustment.

Fig. 314 illustrates the principle which is frequently em-
ployed in correcting such boundaries.

FIG. 314.

Let A and E be two corners and let the boundary line
joining them be described and shown in the map as a straight


line. Let the irregular line A B CD ^represent the actual
boundary. It is evident that the dotted straight line A E
may be substituted for the irregular line A B C D E, and
would equitably divide the adjoining properties. The prin-
ciple of give and take is applied, the adjoining owners ma-
king exchanges of equal areas.

The location of the new boundary is determined by ma-
king a careful survey of the old boundary and platting it to a
large scale; a fine thread is then stretched on the plat and a
line of division made as closely as may be estimated by the
eye. The areas of the equalizing triangles are then calcu-
lated by scaling their dimensions, and if they do not balance
the dividing line can readily be shifted until the desired
result is obtained. The line is then measured on the ground
and permanent corners established. Where the boundary
is in woodland, careful search must be made for line and
bearing trees. Blaze marks are very enduring, being easily
recognized on some varieties of trees after a lapse of a
quarter of a century.

1324. Lost and Obliterated Corners. Corner
monuments of perishable material, such as wooden posts,
decay and in time become obliterated. A pile of stones,
which is commonly used as a corner, may become scattered,
and, unless permanent witnesses remain, it may be a difficult
matter to restore the landmark. The most enduring wit-
nesses are live trees which are disposed as shown in Fig. 315.

Three trees facing the corner are chosen ; in each tree
three notches are cut in the side facing the corner, and the
bearing and distance from each to the corner are recorded in
the notes. A sketch is made in the note book giving the
relative positions of the corner and the witness trees. When
the corner is lost, but the witness trees still remain, the cor r
ner is restored by describing intersecting arcs from the wit-
ness trees as centers with radii equal to the given distances
from the original corner. Where both corner and witnesses
are gone, it is best to run from both directions towards the
missing corner, placing the corner at the intersection of the



lines. The surveyor need not expect to find his measure-
ments agree with those in original surveys, but he can save
his successor much annoyance and trouble by careful and
accurate work. He should always give both in map and in
description the exact date of the survey; the direction of

courses should also be given both in writing and figures, and
the corners should be fully described. A stone monument
is the best corner, and should always be used where the
material is available.


1325. The area of a surface is its superficial content.
In the surveying of public lands all measurements are made
with the surveyor's chain, commonly known as Gunter's
chain, from the name of the inventor. It is 60 feet in length
and contains 100 links, each 7.92 inches long. At each
interval of ten links a brass tag is attached with tally points
similar to those on the engineer's chain described in Art.
1 214, Tables of surveyor's linear and square measure are
given in Arts. 2O9 and 211. For land areas the unit of
measurement is the square foot = 144 square inches, though


areas of considerable extent are usually expressed in acres.
An acre contains 43, 500 square feet of surface. Rectangular
areas are determined by multiplying the length in feet by
the breadth in feet, and dividing the product by 43,500,
which gives the area in acres.

In surveys of farms or larger tracts, dimensions are given
in chains and links. The product of such dimensions is in
square chains, which, divided by 10 (the number of square
chains in an acre), gives the area in acres.

EXAMPLE. A rectangular piece of land is 1,060 feet in length by
820 feet in breadth ; required, the area.

SOLUTION. 1,060 X 820 = 869,200 sq. ft. 869,200 -=- 43,560 = 19.954
acres. Ans.


1326. By Dividing the Plat into Triangles.

Farms, especially in the older States of the Union, are com-
monly of irregular form. The readiest and where the
measurements have been accurately made a sufficiently
accurate method of determining areas is as follows : Make
an accurate plat of the tract to as large a scale as may be
conveniently used. Divide the resulting figure, an irregular
polygon, into triangles, making their sides of as nearly equal
length as possible. It is evident that the sum of the areas
of the several triangles into which the polygon is divided is
equivalent to the area of the polygon. This mode of calcu-
lating area is illustrated in Fig. 316.

Let the irregular polygon A B C D E F be the outline of
a tract of land the area of which is required. Draw the
diagonals B F, C F, and C F, dividing the figure into four
triangles, the combined area of which is equal to the area of
the polygon. From the vertexes A, B, D, and E drop th
perpendiculars A G, B //, D K, and F L upon the opposite
bases of the triangles. The lengths of the several bases and
altitudes are measured with the scale and the areas of the
several triangles calculated by the rule : the area of a trian-
gle is equal to one-half the product of its base and altitude.



The sum of the areas of the several triangles is equal to the
area of the polygon.

1327. By Dividing the Plat intoTrapezoids. A

plat of the area having been made, it may be resolved into


FIG. 318.

trapezoids by either of the methods shown in Figs. 317 and
318. In Fig. 317 the line A H is drawn parallel to B C, and
the lines B M, K H, and E L are drawn perpendicular to
A //, dividing the figure into trapezoids and the triangle
H D K. The area of each trapezoid is equal to one-half the
sum of its bases multiplied by its altitude, and the sum of
their areas together with the area of the triangle is equiva-
lent to the area of the polygon A B C D E F. In Fig. 318
a base line H P is drawn, and from each angle of the polygon
perpendiculars are drawn to it. The sum of the areas of the
three trapezoids A B K H, B C N K, C D PN is found, and



from that sum, the sum of the areas of the trapezoids
A G L H, G F M L, F E O M, and E D P O is subtracted.
The difference of these sums is the area of the polygon


1328. Definitions. The latitude of a point is its
distance north or south of some "parallel of latitude" or
line running east and zvcst. The longitude of a point is its
distance east or west of some meridian or line running north
and south.

The meridian from which the longitude of a point is
reckoned is the magnetic meridian.

The distance which one end of a line is
due north or south of the other end is called
the latitude of that line.

The distance which one end of a line is
due east or west of the other end is called
the departure of that line.

The latitude and departure of a line and
its determination are explained in Fig. 319.
Let A B be the given line whose length and
angle with the magnetic meridian N S is
known, and whose latitude and departure
are required. From B draw B C perpen-
dicular to N S, forming the right-angled triangle A C B, in
which the sides C A and C B about the right angle are, re-
spectively, the latitude and the departure of the line A B.

A C = A B X cos bearing, and
B C A B X sin bearing;

that is, the latitude is equal to the product of the cosine o
the bearing and the length of the course ; and the departure
is equal to the product of the sine of the bearing and the
length of the course.

Let A B = 400 feet and the bearing of A B, i. e., the
angle B A C = 30. Then, latitude A C = coj 30 X 400 =



.86603 X 400 = 340.412 ft., and departure B C = sin
30 X 400 = .50000 X400 = 200 ft.

If the course be northerly, the latitude will be north,
marked -f- , and be additive; if southerly, it will be marked
, and be subtractive. If the course be easterly the
departure will be east, marked -f, and be additive; if
westerly, the departure will be west, marked , and be

Online LibraryInternational Correspondence SchoolsThe elements of railroad engineering (Volume 2) → online text (page 8 of 35)