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railway communications. Without the latter there is small
excuse for a town. Where possible a main avenue should be
laid out, parallel with the railroad, leaving one tier of lots
between the street and track. This avenue may then be used
as a base from which to lay out the adjoining streets and
avenues, which may be parallel with and at right angles to
it if the surface be generally level, or at oblique angles if
the surface be rolling or hilly.

134O. Grades, Drainage, and Topography.

Grades and drainage should be so arranged that surface
water will tend to form main channels, i. e. , the surface
water of several streets will find its way into some particular
street where special provision can be made for its control
and discharge.

The streets in the residential portion of the town should,
so far as possible, conform to the existing topographical con-
ditions. This will greatly reduce the cost of grading the
streets, give easy grades, and so promote comfort of pedes-
trians and the efficiency of teams. There is no loss in front-
age from the employment of curves instead of straight lines,
and there is no question of the advantage of the former
from an artistic standpoint.

The accompanying plan, Fig. 326, is made to meet the
following conditions, viz., two lines of railroad, a main line
and branch, meet at the junction of two streams. The land



LAND SURVEYING.



735



bordering on the smaller stream, which is followed by the
branch road, rises rapidly from the stream, reaching a height
of 200 feet, and then falls gradually until an elevation of 50
feet above the stream is reached, when the surface remains
generally level. The land bordering the larger stream, which
is followed by the main line of the railroad, rises gradually
until a height of 50 feet above the stream is reached, beyond
which the surface is generally level.




FIG. 320.

That part of the given surface which is generally level
will be laid out in rectangular blocks. The unaided eye will
readily determine whether a town site is well adapted to
rectangular divisions. If it is so adapted the order of survey
will be as follows :

1341. General Directions for Preliminary Sur-
vey. Run a line enclosing the entire area, giving location
of prominent features, such as railroads, highways, streams,



736 LAND SURVEYING.

houses, etc., and accurately plat to a scale of 200 feet to the
inch. For cities, avenues are made 100 feet in width be-
tween building lines, and streets 60 feet, the avenues being
parallel to each other and the streets at right angles to the
avenues. City lots usually have fronts of 25 feet and depths
of 125 feet. Part of New York is laid out in blocks of 200
feet by 800 feet, the 200 feet facing the avenues. Lots are 100
feet in depth, each block containing 64 lots. Having deter-
mined the dimensions of the streets and blocks, lay out the
principal base line so that it will form the center line of a
street or avenue running parallel with the general direction
of the railroad, providing for overhead or sub-crossings
where practicable. If crossings must be at grade, the fewer
of them the better. Provide easy and safe access to railroad
stations and freight depots.

Lay out the plat in rectangular blocks, accurately scaling
all dimensions. Arrange the plan so as to interfere as little
as possible with existing lines of travel, at the same time
giving due regard to the future needs of an increasing popula-
tion. If the ground is wooded or sight obstructed by under-
brush, but one additional base line can be used. It should
be about midway between the extremities of the principal
base line and at right angles to it. If, however, the ground
is open with nothing to interfere with long sights, two base
lines should be laid out, one at either extremity of the main
base and at right angles to it.

1342. Measurements. All measurements should be
made with a standard steel tape and plumb-bob and care-
fully checked. The base lines especially should be measured
with great care, as the correctness of all the subsequent
measurements depends upon the degree of accuracy with
which these primary lines are measured.

1343. Base Lines and Subdivisions. The rect-
angular method of surveying town sites is illustrated in
Fig. 327, in which A B is the principal base, and the aux-
iliary bases A D and B C are laid off from the extremities
of A B. The avenues are at right angles to A B, and the



LAND SURVEYING. 737

streets parallel to A B. Avenue A is parallel to the railroad,
XM

& gj.



L



V W






25



A E 01 L y

FIG. 337.




60'



from which it is separated by a 25-foot alleyway and one
tier of lots 125 feet deep. Avenues are 100 feet in width,



738 LAND SURVEYING.

streets 60 ; blocks 250 feet by 600 feet, fronting 250 feet on
the avenues, and the lots are 25 feet by 125 feet.

The initial point A of the principal base A B is the center
of an avenue, and should be fixed by a plug 2" X 2* X 18*
driven flush with the surface of the ground and the center
marked by a tack, with a guard stake beside it, and num-
bered 0. Drive a temporary plug at X to be used as a fore-
sight in giving the direction of A B. Set up the instru-
ment at A and sight to X, frequently checking the foresight.
Measure from A on A B 50 feet, and drive a 12" plug, care-
fully centering the same. This point marks the north side
of Avenue B. Continue measuring on the line A B, driving
a stake at each hundred feet, marking the exact measure-
ment by a tack, and number in regular succession from A.
At 650 feet from A set a 12" plug with tack center, marking
the south side of Avenue C; 50 feet further, at Station 7,
set a 12" plug with center. This point will be in the center
of Avenue C; at 7 + 50 a plug with center is set, marking
the north side of Avenue C. In like manner locate the
center and sides of all avenues lying between A and X,
always checking the foresight before setting tack centers.
At B set a plug 2" X 2" X 18". At each station remeasure
the last 100 feet, so as to secure accurate results. The measure-
ment of the main base line A B being completed, take a
foresight on X and turn off an angle of 90, setting a tem-
porary plug at K Mark the center at Y with a pencil point
and repeat the angle five times, marking a center at Y for
each angular measurement. These points will vary slightly
in position, though two of them may fall at the same place.
Take the mean or average of these points, and mark the
point with a tack. Then, commencing at A measure the
line A F, setting stakes at each 100 feet, as in A B, and
set hubs on the side lines of Avenue A and at centers and
side lines of the streets parallel to it, checking the foresight
at F and the measurement of each station before setting
plug centers. On this line the measurements will be, first
50 feet, next 250, then 60, 250, 60, etc., the streets being
60 feet and the blocks 250 feet in width. At D set a plug



LAND SURVEYING. 739

2" X 2* X 18". In a similar manner locate the base line B C
and the street centers and side lines on B C. Then set up
at /?, which is a permanent point, and foresighting to C set
points on centers and sides of avenues on D C. Next set
up at E, foresighting to F. Provide a supply of plugs
1" X I" X 8" and measure from F, 50 feet in both directions
on the line E F, and mark the points with pins. These
pqints will be on the north and south lines of Avenue B.
On either side of these pins in the line E F, and about two
feet from them, set plugs, leaving two inches of their length
above the surface of the ground. Center these plugs, dri-
ving tacks half their length into each one. In the same
manner set plugs on both sides of each street line as indi-
cated by the small circles in the figure. In this example
B C is 2,800 feet distant from A D, too great a distance for
the accurate setting of plug centers; therefore, the measure-
ments from A D to B C should terminate on the south line
of Avenue D. In the same manner locate plugs on the lines
G //, / K, L M, etc. Having set all plugs between the
base A D and the south line of Avenue D, move the instru-
ment to F and, foresighting to E, set plugs on both sides of
all avenues between Avenue F and Avenue D, including the
north side of D. In like manner locate plugs on H G, K /,
ML, etc. Move the instrument to the point U; stretch
pieces of cord between the plugs on both sides of the line
X T; foresight to T, and at each intersection with the cord,
as at F, W, etc., drive a 12* plug, and center with a tack.
This method of locating street corners by intersections has
the advantage of bringing all corners on the same street in
perfect line, a result which it would be practically impossible
to obtain by direct measurement. The measurement of all
angles is referred to the base lines where special care is
taken in checking them.

1344. Permanent Monuments. The street and
avenue centers located on the base lines should always be
rendered permanent by setting stone monuments at those
points.



MAPPING.



INTRODUCTION.

1345. The object of this section is to furnish the stu-
dent thorough, practical instruction in mapping. Having
previously mastered the section on Geometrical Drawing,
he should by this time be familiar with the various instru-
ments employed in the drafting room, and be accustomed
to their use.

All the principles and methods here described are fully il-
lustrated by drawings, which comprise six plates, found at
the end of the volume on Mechanical Drawing. These plates
the student will be required to draw, and the degree of pro-
ficiency, as shown by his work, will determine his standing.
The examples given in the plates are similar to those met
with in practical field and office work.

1346. A map is a series of lines and angles so com-
bined as to represent the true outlines, proportions, and
character of any required surface.

1347. Lines are either boundaries or divisions of
the required surface. They have only the properties of
direction and length.

DRA WING THE PLATES.



PLATE, TITLE: PLATTING ANGLES I.

1348. This plate contains six angle lines, three of which
are comprised by Fig. 1 and three by Fig. 2. The three
lines a, b, and c, under Fig. 1, will be drawn to a scale of 200
feet to the inch, platting the angles with a protractor, the



742



MAPPING.



NOTES FOR LINE a.



Stations.


Angles.


25 + 84


End of Line.


21 + 94


L. 32 35'


15 + 53


R. 44 10'


11 + 72


L. 60 30'


5 + 25


L. 25 15'








use of which was fully explained in the section relating to
Geometrical Drawing.

The student will plat these lines according to the follow-
ing directions, being careful to give to each line approxi-
mately the same position it
occupies in the plate. This
statement also applies to all the
plates which are to be drawn
from the data given in this
section. In these examples,
distances are expressed in sta-
tions of 100 feet each, as in
the section on Surveying. The
direction of each line is referred
to that of the immediately pre-
ceding line, which line is pro-
duced and the angle recorded
as being to the right or left of
that line. In practical office work, the lines produced are
drawn lightly in pencil and erased as soon as the angles
are laid off. In the lines a and d, Fig. 1, the lines produced
are dotted and the angles written in dotted arcs, in order
that the student may clearly and fully understand the
method. The dimensions of the following plates and the di-
rections for drawing the border lines are the same as for the
plates on Geometrical Drawing. The notes for line a in
Fig. 1 are as shown.

1349. The starting point A of the line is numbered 0.
The first angle turned is at Sta. 5 + 25, which we denote by
B. Locating the starting point A about three-fourths of an
inch from the lower and left-hand border lines, we draw a
straight line, giving it the same direction as that given to it
in the engraving. Scale off from A, to a scale of 200 feet to
the inch, the first course, 525 feet in length, locating the
point B. Produce A B to C, being sure to make B C a
little greater than the diameter of the protractor. At Sta.
5 + 25, B, an angle of 25 15' is turned to the left. Now,



MAPPING. 743

placing the center of the protractor on the point B, with the
zero point on the line B C, lay off the angle 25 15' to the
left of B C, marking the point of angle measurement D with
a needle point. Through the points B and Z)draw a straight
line. The angle C B D is 25 15', and the line B D is the
direction of the next course. The second angle, 00 30', is
turned to the left at Sta. 11 -f 72. The length of the second
course is found by subtracting 525 from 1,172, giving a dif-
ference of 647 ft. Produce B D and scale off the second
course 647 ft., locating the point E at Sta. 11 + 72. Produce
B E to F, and lay off to the left of E F the angle 60 30', lo-
cating the point G. Join E and G. The angle PEG is
60 30', and the line E G is the direction of the next
course.

The third angle is R. 44 10', and is turned at Sta. 15 + 53.
The length of the third course is found by subtracting 1,172
from 1,553, giving a difference of 381 feet. Produce E G
and scale off from E the distance 381 ft., locating the point
H at Sta. 15 -f 53. Produce E H to K, and to the right of
H K lay off the given angle 44 10', locating the point L.
The line joining the points H and L forms with H~K an angle
of 44 10', and gives the direction of the next course.
The next angle is L. 32 35', and is turned at Sta. 21 + 94.
The length of the course is found by subtracting 1,553 from
2,194, giving a difference of 641 ft. Produce H L and scale
off from // the distance 641 ft., locating the point M at
Sta. 21 + 94. Produce H M to N, and to the left of M N
lay off the given angle 32 35', locating the point O.
Draw M O. The angle N M O is 32 35', and M O is
in the direction of the next and last course of line a,
whose length is found by subtracting 2,194 from 2,584.
The difference is 390 ft. We produce the line M O, and
from M scale off the last course of 390 ft., locating the'
point P at Sta. 25 -}- 84. At each angular point in the
line an arc is described, giving the measurement of the
angle.

The student will in a similar manner plat the following
notes for the lines b and c, Fig. 1, of the same plate:



744 MAPPING.

NOTES FOR LINE b. NOTES FOR LINE c.



Stations.


Angles.


Stations.


Angles.


23 + 10


End of Line


28 + 60


End of Line


16 + 35


R. 25 10'


21 + 46


R. 34 30'


12 + 82


L. 15 15'


17 + 09


R. 53 28'


8 + 50


L. 30 40'


11 + 96


L. 25 10'


4 + 40


R. 15 20'


5 + 33


R. 21 10'











c'




/ ^

J3XR - 400'?,



1 35O. To Lay Off an Angle by Chords. This is
done by means of a table of chords in which the lengths of

chords for all angles
from to 90 are
given in terms of a
radius 1. A radius
of any convenient
length may be as-
sumed, and the cor-
responding chord length obtained by multiplying the length
of the chord given in terms of radius 1 by the length of the
assumed radius. Thus, let it be required to lay off from a
given line an angle of 40 10' to the left. Let A B,
Fig. 328, be the given line. Produce A B to C, making
B C = 400 ft., the length of the assumed radius.

From a table of chords, we find that the chord of an
angle of 40 10' in terms of a radius 1 is .6868. Multiplying
this chord by 400 ft., the length of the assumed radius, we
have 274.72 ft., the length of the required chord. From B
as a center, with a radius B C = 400 ft,, describe to the left
of B C the indefinite arc C D, being sure that the length
of CD is slightly greater than the length of the required
chord, and from C as a center, with a radius of 274.72 ft.,
describe an arc intersecting the arc CD in C'. Through



MAPPING.



745



NOTES FOR LINE a.



B and C' draw a straight line. The angle C B C' is
40 10', the required angle. This method of platting angles
is more accurate, though less rapid, than platting with a
protractor.

NOTE. The table of chords used for the calculations given in this
Course may be found in Trautwine's Pocket Book, a very useful book
to all surveyors. If the student does not possess a copy, he may easily
find the required chord from his table of sines by multiplying the sine

of half the given angle by 2. Thus, the chord of 40 10' = 2 sin 4 2 10 =

2 sin 20 05' = 2 x. 34339 = .68678 = .6868, using but four places, the
same as given in the table.

1351. Fig. 2, same plate as above, contains three ex-
amples in the lines a, b, and c, in which the angles are laid
off by chords. The notes for example a are given in the
accompanying table.

The first course A B is 360 feet in length, which the stu-
dent will draw to a scale of 200 feet to the inch. The start-
ing point A is numbered 0,
and B, the end of the first
course, 3+60. At B an angle
of 30 30' is laid off to the
right. Produce A B 400 feet,
which we assume to be the
length of the radius in calcu-
lating chord lengths for lay-
ing off angles, and locate the
point C. Then, from B as a
center, with a radius of 400
feet, , describe the indefinite
arc C C' on the right side of
the radius B C, being sure that the arc shall contain at least
30 30'. We~find in a table of chords that the chord of
30 30' =.5261, which, multiplied by 400 ft., the length
of the assumed radius, .gives 210.44 ft., the length of the
required chord. From C as a center, with a radius of
210.44 ft., describe an arc intersecting the arc C C' in
the point E. A line joining B and E will form with the
radius B C an angle C B E 30 30', the required



Stations.


Angles.


25 + 80


End of Line


20 + 38


L. 37 20'


15+18


L. 31 08'


9 + 13


. R. 39 26'


3 + 60


R. 30 30'








746



MAPPING.



angle. The next angle R. 39 26' is turned at Sta. 9 + 13,
making the length of the second course 553 ft. Denote
Sta. 9+13 by F. Produce B F 400 ft. to G. From
F as a center, with a radius F G of 400 ft., describe to
the right of F G the indefinite arc G G', being sure
that the arc shall contain at least 39 26'. The chord of
39 26' to a radius 1 is .6747, which, multiplied by 400 ft.,
gives 269.88 ft., the length of the required chord. From F
as a center, with a radius of 269.88 ft., describe an arc in-
tersecting the arc G G' in H. A line joining F and H will
form with the radius F G the angle G F H 39 26', the
required angle. The next angle, viz., L. 31 08', is turned



NOTES FOR LINE b.



NOTES FOR LINE C.



Stations.


Angles.


22 + 40


End of Line.


16 + 50


L. 18 20'


8 + 60


R. 25 14'


3 + 25


R. 8 10'








Stations.


Angles.


25 + 34


End of Line.


19 + 94


L. 51 22'


14 + 81


R. 21 20'


10+38


R. 39 18'


4+13


L. 64 30'








at Sta. 15 + 18, making the length of the third course 605 ft.
Call Sta. 15 + 18, K. Produce F K 400 ft. to L. From K
as a center, with a radius K L of 400 ft., describe to the
left of K L the indefinite arc L M. The chord of 31 08' is
. 5367, which, multiplied by 400 ft. , gives 214. 68 ft. , the length
of the required chord. From L as a center, with a radius
of 214.68 ft., describe an arc intersecting the arc L -M in
the point N. Join K and TV, forming with K L the angle
L K N = 31 08'. The next angle, viz., L. 37 20', is turned
at Sta. 20 + 38, making the length of the fourth course
520 ft. Call Sta. 20 + 38, O. Produce K O 400 ft. to P.
From O as a center, with a radius O P, describe the indefi-



MAPPING.



747



nite arc P Q. The chord of 37 20' is .6401, which, multi-
plied by 400 ft., gives 256.04 ft., the length of the required
chord. From P as a center, with a radius of 256.04 ft.,
describe an arc intersecting the arc P Q in R. Join O and R,
forming with O P the angle P O R = 37 20'. The end of
the line 5 is at Sta. 25 + 80, making the length of the last
course 542 ft. In a similar manner, plat the notes for lines
b and c, which are given in Art. 1353.

1352. To Lay Off an Angle by its Bearing. By

this method of laying off angles, the direction of each line
is referred to the magnetic meridian, which maintains a con-
stant direction, being a north and south line. The bearing
of a line is the angle which the line makes with the magnetic
meridian. In platting a land or railroad survey, a pencil



a *




/ '



line giving the direction of the magnetic meridian is drawn
through each station at which a bearing is taken.

The direction of the meridian may be given by means qf
the ordinary T square and triangles, and the angles laid
off either by a protractor or by tangents. The use of T
square and triangles in laying off angles by bearings is illus-
trated in Fig. 329. A sheet of paper is fastened to a draw-
ing board. It is well known that if the head of the T square



748 MAPPING.

be kept firmly pressed against the side of the drawing board,
as shown in the figure, the lines drawn along the straight
edge will be parallel; hence, the lines drawn perpendicular
to this straight edge by means of the triangles, as shown in
the figure, will be parallel.

Either the parallels drawn along the straight edge of the
T square or of the triangle may be used as the magnetic
meridian, though the latter is preferable, as it brings the
north end of the meridian at the top of the map, which is
its proper position.

Let it be required to plat a line having a bearing of
N 60 E. As in Fig. 329, a point A is assumed as the station
at which the bearing is taken. Through the point A, a line
A B is drawn perpendicular to the straight edge of the T
square. This line will represent the direction of the mag-
netic meridian. As the bearing is east, the angle of 60 will
be to the right of A B. Place a protractor with its center
at A and its zero point in the line A B. Lay off the angle
60, and mark the point of measurement C with a needle
point. Draw a line joining the starting point A with the
point of angle measurement C. The line A C will then
form an angle of 60 with the meridian, and its course will
be N 60 E. From the notes find the length of the first
course, and measure on the line A C to some convenient
scale the length of that course, locating the point D, where
the next bearing N 30 E is taken. Slide the T square
upwards, and with the triangle draw through D another
meridian D E. From Z>as a center lay off from the right of
the meridian D E the bearing N 30 E. Let F mark the
measurement of this angle. The line joining D and F will
have a bearing of N 30 E.



PLATE, TITLE: PLATTING ANGLES II.
1353. This plate contains five angle lines, the angles of
the three lines given in Fig. 1 being platted by magnetic
bearings, and those in Fig. 2 by tangents. In Fig. 1, line ,
the distances are given in stations of 100 feet each ; in the
lines b and c, the distances are given in chains. The student



MAPPING.



749



NOTES FOR LINE a.



will draw line a to a scale of 200 feet to the inch, and lines b
and c to a scale of 2 chains to the inch. The notes of line
a are given below.

Let A be the starting point of the line, which we num-
ber Station 0. Let the arrow N S give the direction of the
magnetic meridian. Through
A draw a meridian A B parallel
to NS. The bearing of the
first course is N 10 15' E.
From the meridian passing
through A lay off this bearing
angle with a protractor, as
directed in Art. 1352. The
first course is 375 ft. Draw a
line through A having the
given bearing, and scale the
distance 375 ft. This will bring
us to Sta. 3 + 75, which we de-
note by the letter T, where a
bearing of N 60 E is taken.
-The end of this course is at
Sta. 6 + 90. The length of the
second course will, therefore, be the difference between
6 + 90 and 3 + 75, which is 315 feet. Through C draw a
meridian C D, from which lay off the bearing angle of 60
and draw a line marking the second course. Scaling the
distance 315 feet we reach Sta. 6 + 90, which we call E.
Here a bearing N 83 30' E is taken. Through E draw a
meridian E /% and from it lay off the bearing N 83 30' E.
The end of this course is at Sta. 10 + 40. Its length will,
therefore, be the difference between 10 + 40 and 6 + 90,
which is 350 ft.

Scale off this distance from , locating Sta. 10 + 4Q,
which we call G. The bearing at G is S 81 20' E.
Through G draw the meridian G H. As the bearing is
S E, the meridian will fall below the station, from which
lay off the bearing S 81 20' E, and draw a line in the
direction of this course. The next bearing is taken at



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