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THE ELEMENTS



OF



RAILROAD ENGINEERING



PREPARED FOR STUDENTS OF

THE INTERNATIONAL CORRESPONDENCE SCHOOLS

SCRANTON, PA.



Volume II



SURVEYING RAILROAD LOCATION

LAND SURVEYING RAILROAD CONSTRUCTION
MAPPING TRACK WORK

RAILROAD STRUCTURES

WITH PRACTICAL QUESTIONS AND EXAMPLES



First Edition



SCRANTON

THE COLLIERY ENGINEER CO.
1897



Copyright, -1897, by THE COLLIERY ENGINEER COMPANY.



Surveying : Copyright, 1895, by THE COLLIERY ENGINEER COMPANY.
Land Surveying : Copyright, 1895, by THE COLLIERY ENGINEER COMPANY.
Mapping : Copyright, 1895, by THE COLLIERY ENGINEER COMPANY.
Railroad Location : Copyright, 1895, by THE COLLIERY ENGINEER COMPANY.
Railroad Construction : Copyright, 1895, by THE COLLIERY ENGINEER COMPANY.
Track Work : Copyright, 1896, by THE COLLIERY ENGINEER COMPANY.
Railroad Structures : Copyright, 1896, by THE COLLIERY ENGINEER COMPANY.



BURR PRINTING HOUSE,

FRANKFORT AND JACOB STREETS,

NEW YORK.



CONTENTS.



SURVEYING. PAGE

Geometrical Principles, - 001

Compass Surveying, .... g(>5

Transit Surveying, - . . 621

Triangulation, - 634

Curves, . 639

Leveling, . 655

Topographical Surveying, - - . - - 673

Indirect Leveling, 682

Hydrographic Surveying, - - - - 690

LAND SURVEYING.

United States System, - ... 693

Areas, - 714

Latitudes and Departures, - ... 717

Town Sites and Subdivisions, - - - 733

MAPPING.

Introduction, 741

Platting Angles, - 741 ) 743

Map of Railroad Location, .... 766

Topographical Drawing, 776

Contours and Slopes, ... ... 779

Conventional Signs, 789

Topographical Maps, -'792

Map of Village, - 799

RAILROAD LOCATION.

Introduction, 813

Reconnaissance, 815



i v CONTENTS.

RAILROAD LOCATION continued. PAGE
Field Work, -
Problems in Location, -

Specifications for Grading and Bridging, - 860

RAILROAD CONSTRUCTION.
The Engineer Corps, -

Cross-Sectioning, - 870

Culverts, - 8 ? 8

Retaining Walls, - 899

Excavation, - 912

Tunnel Work, 935

Protection Work, 966

Routine Work, 970

Bridge Work, - 978

Pile Work, - 1002

Estimates, 1017

TRACK WORK.

Track Laying, 1029

Track Joints, 1036

Rails, - 1038

Expansion and Contraction, - 1043

Spiking Rails, 1045

Surfacing Track, - - 1048

Drainage, 1052

Care and Maintenance of Track, - - - 1058

Curved Track, 1087

Frogs and Switches, 1102

Yards and Terminals, - 1145
General Instructions, - .... 1148

RAILROAD STRUCTURES.

Wooden Trestles, 1163

Framed Bents, 1177

Floor System, 1186

Bracing, 1195

Iron Details, - - 1198



CONTENTS. v

RAILROAD STRUCTURES continued.

Connection of Trestle with Embankment Pro- PAGE

tection Against Accidents, - 1207
Field Engineering and Erecting, - - - 1211

Specifications for Wooden Trestles, - - 1213
Bills of Materials, Records, and Maintenance, - 1224

Standard Trestle Plans, 1230

Simple Wooden Truss Bridges, 1246

Water Stations, - 1274

Coaling Stations, - 1281

Turntables, - 1285

QUESTIONS AND EXAMPLES.

Surveying, - Questions 014-705 1297

Land Surveying, Questions 706-755 1309

Railroad Location, - Questions 756-812 1315

Railroad Construction, Questions 813-872 1321

Railroad Construction, Questions 873-946 1327

Track Work, Questions 947-1016 1333
Railroad Structures, - Questions 1017-1082 1339



SURVEYING.




GEOMETRY.

1 ISO. If two triangles have two sides and the included
angle of the one equal to two sides and the included angle
of the other, the triangles are
equal in all their parts. Thus,
in the two triangles ABC
and DBF, Fig. 236, if the
side A B is equal to the side
D E ; the side B C to the side
EF, and the angle B to the
angle E, the triangles are equal in every respect.

1181. If a straight line, A B, Fig. 237, intersects two

parallel straight lines, C D and E F", it is called a secant

A with respect to them, and the eight

/ angles formed about the points of in-

G/ D tersection have different names applied

'/. to them with respect to each other, as

F follows:

First Interior angles on the
same side are those which lie on the
FIG. 237. same side of the secant and within the

other two lines. Thus, in Fig. 237, H G D and G H F are
interior angles on the same side.

'Second Exterior angles on the same side are those
which lie on the same side of the secant but without the,
other two lines. Thus, 'A G D and F H B are exterior
angles on the same side.

Third Alternate interior angles are those which lie
on opposite sides of the secant and within the other two
lines. Thus, C G //and G //Fare alternate interior angles.



a.1

/



602 SURVEYING.

Fourth Alternate exterior angles are those which
lie on opposite sides of the secant and without the other two
lines. Thus, A G C and F H B are alternate exterior angles.

Fifth Opposite exterior and interior angles are

those which lie on the same side of the secant, the one within
and the other without the other two lines. Thus, A G D
and G H F are opposite exterior and interior angles.

1182. If a straight line intersects two parallel lines,
the sum of the interior angles on the same side is equal to
two right angles, and the sum of the exterior angles on the
same side is also equal to two right angles. Thus, in Fig.
237, the 'interior angles D G H and F H G are together
equal to two right angles, and the exterior angles D G A
and F H B are together equal to two right angles.

1183. If a line intersects two parallel straight lines,
the alternate interior angles are equal to each other, and
the alternate exterior angles are also equal to each other.
Thus, in Fig. 237, the angle C G H is equal to F H G, and
angle C G A is equal to F H B.

1184. The complement of an angle is the difference
A between that angle and a right angle.

Thus, in Fig. 238, A B E is the comple-
ment of D B E.

c ~ j| D 1185. The supplement of an

FIG. 238. angle is the difference between that

angle and two right angles. Thus, C B E is the supplement
of D B E.

1 1 86. In any triangle, a line drawn
parallel to one of the sides divides the
other sides proportionally. Thus, in the
triangle A B C, Fig. 230, the line D E
drawn parallel to B C divides the sides
A B and A C proportionally ; that is,

A B : A D\: A C : A E

A D : DB:: A E : EC, and

A B : D B :: A C : E C.





SURVEYING. 603

1 1 87. Polygons are similar when they are mutually
equiangular and have their homologous sides proportional.

In similar polygons, any points, lines, or angles similarly
situated in each are called homologous. The ratio of a
side of one polygon to its homologous side in another is
called the ratio of similitude of the polygons.

1188. Triangles which are mutually equiangular are
similar, and their areas are to each other as the squares of
their homologous sides.

Thus, in the triangles
A B C and D E F, Fig. 240,
if the angle A is equal to the
angle D; the angle B to the
angle E, and the angle C to
the angle F, the triangles are FIG. 240.

similar, and their areas are to each other as the squares of
their homologous sides.

For example, if /?T=80 feet, EF=50 feet, and the
area of the triangle ABC 1,GOO sq. ft., then
80* : 50' :: 1,000 : area of DBF, or
6,400 : 2,500-:: 1,600 : 025 sq. ft.
Hence, area of D E F is 625^sq. ft.

1 1 89. The areas of similar polygons are to each other
as the squares of their homologous sides.

Thus, if the area of a regular hexagon with a side of 10
inches is 259.809 sq. in., the area of a similar hexagon whose
side is 15 inches may be found as follows:

10' : 15' :: 259.809 : area required, or
100 : 225 :: 259.809 : 584.57 sq. in.

1190. The circumferences of circles are to each other
as their diameters, and their areas are to each other as the
squares of their diameters.

Thus, if the circumference of a circle 12 inches in diam-
eter is 37.7 inches, the circumference of a circle of 18 inches
diameter may be found by proportion. Thus,

12 : 18 :: 37.7 : 56.55 in., the circumference required.



604



SURVEYING.




Again, if the area of a circle of 12 inches diameter is
113.098 sq. in., the area of a circle of 18 inches diameter
may be found as follows:

12' : 18" :: 113.098 : area required, or
144 : 324 :: 113.098 : 254.47 sq. in.

1191. An angle formed by a tangent and a chord

meeting at the point of contact is
measured by half the included arc.

Thus, in Fig. 241, the angle A C D
formed by the meeting of the tangent
A B and the chord C D is measured
by half the arc C E D. Similarly, the
c B angle B C D is measured by half the
FIG. 241. arc C D.

1192. Two tangents to a circle drawn from any point
are equal, and if a chord be drawn joining

these tangent points, the angles between
the chord and the tangents are equal.

Thus, in Fig. 242, the two tangents
A B and A C drawn to the circle from
the point A are equal, and the angles
ABC and A C B, formed by the chord
and tangents, are equal to each other.

1 1 93. In similar circles equal chords
subtend equal angles at the center and

also at the circumference. FIG. 242.

Thus, in Fig. 243, the angles A O B, B O C, and C O D'
subtended by the equal chords A B,
B C, and C D are equal to each
other.

Again, the angles BAG and
C A D are also equal to each
other.

1194. In Fig. 244, let A B C
be any triangle. If one of the
sides, as A C, is prolonged, the
angle BCD included between the





FIG. 243.




SURVEYING. 605

side thus prolonged and the other side B C of the triangle,
which meets A C at C, is called an
exterior angle. The two remain-
ing angles A and B of the triangle,
which are opposite to the angle C,
are called opposite interior
angles. In any triangle, an ex-
terior angle is equal to the sum of
the two opposite interior angles; that
is, in the above figure, the exterior angle B C D is equal to
the sum of the two opposite interior angles, A and B.

1 195. PROBLEM. Having given one of the angles of a
triangle, one of the including sides, and the difference of
A the other two sides, to construct

it.

Let C, Fig. 245, be the given
angle, A the given side, and B
the difference of the other sides.
Draw D E equal to the given
side A ; at D make the angle
E D F equal to the given angle C;
FIG. 245. on D F lay off D G equal to the

given difference B. Join E G. At the middle point H of
E G erect a perpendicular cutting D Fin K. Draw K E.
D E K is the required triangle.




COMPASS SURVEYING.

1196. The Compass. THe surveyor's compass

consists of the magnetic needle, the case in which it is en-
closed, and the support on which it is placed when ready for



1197. The Magnetic Needle. The magnetic
needle is a slender bar of steel, five or six inches in length,
strongly magnetized, and mounted upon a finely pointed
pivot on which it freely turns, always pointing in the same



606



SURVEYING.



^Platinum Wire.



direction, viz. : the north and south line, or, as it is called,
the magnetic meridan.

1198. North and South Ends of Needle. Owing
to the earth's attraction, the north end of the needle dips,
that is, it is drawn downward from a horizontal position,
while the south end is correspondingly raised. To prevent
this dipping, several coils of platinum wire are wound

around the south end
i v of the needle (see Fig.
,Pivot. 246), keeping it per-

fectly balanced upon
its pivot and permit-
ting entire freedom of movement. These coils of wire at
once indicate to the observer which is the north end and
which is the south end of the needle.

1199. The Sights. At either end of a line passing
through the needle pivot is a sight, which consists of an
upright bar of brass A and B. (See Fig. 247.) Narrow





vertical slits, with holes at their top and bottom, divide this
bar, as shown at C and D. These arrangements enable
the observer to train the line of sight upon any desired
object.



SURVEYING.



607



1 2OO. The Divided Circle. The compass box con-
tains a graduated circle divided to half degrees, at the
center of which is the pivot supporting the needle. The
degrees are numbered from to 90 both ways from the
points where a line drawn through the slits would cut the
circle.

1.2O1. Lettering. The lettering of the surveyor's
compass is at first confusing to those learning its use. A
person standing with his back to the south and facing the
north will have the east on his right hand and the west
on his left. These latter directions, viz., the east and
the west, are reversed in the lettering of the compass.
The reasons for this apparent error are explained in the
following figures:





Suppose the needle and compass are pointing due north
and south in the direction of the line A B, as shown in
Fig. 248, and the line of survey changes its direction 45 to
the right, or east. The magnetic needle will remain motion-
less, while the sights and the circle to which they are fast-
ened will move until the sights point in the direction C D,
Fig. 249, and, as the north end of the compass is ahead, the
needle will read N 45 E, which is the true direction being
run. If, however, the east and west points of the compass
were the actual magnetic directions, i. e., the right hand
east and the left hand west, the direction of the line C D



608 SURVEYING.

would have read N 45 W, which would be the reverse of
the actual direction.

1202. Levels. On the compass plate are two small
spirit levels F and G. (See Fig. 247.) They consist of
glass tubes, curved slightly upwards and nearly filled
with alcohol, leaving a small bubble of air in them. One
of these tubes, F, is in the line of sight, the other, G,
is at right angles to it. Their object is to enable the
observer to place the compass in a perfectly horizontal
position. This is done by so moving the compass as
to bring the air bubbles to the centers of the tubes. To
prove these bubbles to be in adjustment, proceed as fol-
lows: Having brought the bubbles to the centers of the
tubes, revolve the compass through 180 or one-half of
an entire revolution. If the bubbles remain in the cen-
ters of the tubes, they are in adjustment. If they do
not so remain, bring them half way back to the middle
of the tubes by means of small screws attached to the
tubes, and the remainder of the way by moving the plate
in the ordinary way, repeating the operation until the
bubbles remain in the center of the tubes in every position
of the compass.

1 2O3. The Tripod. The compass is usually supported
by a single standard, shod with steel, and called a Jacob's
Staff. A more perfect support, called a tripod, consists
of three legs shod with steel and connected at the top so as
to move freely. Both Jacob's Staff and tripod are connected
with the compass by means of a ball and socket joint, which
permits .free movement in all directions.

1204. Defects of the Compass. The compass is
not intended for work requiring great accuracy. The direc-
tion to which the needle points can not be read with pre-
cision, and the perfect freedom of movement of the needle
may be prevented by local attraction or by particles of dust
adhering to the pivot. An inaccuracy of one-quarter of a
degree in reading an angle, i. e., the amount of change in



SURVEYING. 609

the direction of two lines, will cause them to separate from
each other If feet in a distance of 400 feet.

Suppose the line A B, Fig. 250, is due east and west, and
the line B C, which is an actual boundary, has a true direc-
tion of N 85 E, and suppose the surveyor reads the
directions B C as N 84 45' E. Let B C = 400 feet, then,
the point C, when mapped, will take the position C', which is
If feet to the left of C where it should be. Another defect
of the compass lies in the fact that the magnetic needle does



not always point in the same direction. This direction some-
times changes between sunrise and noon to the amount of
one-quarter of a degree. Frequently its direction is changed
by local influence. A piece of iron on the surface of the
ground or a mass of iron ore beneath are frequent disturbing
influences.

12O5. Taking Bearings. The bearing of a line is
the angle which it makes with the direction of the magnetic
needle. By the course of a line we mean its length and its
bearing taken together. To take the bearing of a line, set
the compass directly over a point of it, at one extremity, if
possible. This may be done by means of a plumb bob sus-
pended from the compass, or, if the compass be mounted on
a Jacob's Staff, by firmly planting the staff directly on the
line. Then, by means of the air bubbles, bring the compass
to a perfectly level position. Let a flagman hold a rod care-
fully plumbed at another point of the line, preferably the
other extremity of it, if he can be distinctly seen. Direct
the sights upon this rod and as near the bottom of it as pos-
sible. Always keep the same end of the compass ahead;
the north end is preferable, as it is readily distinguished by
some conspicuous mark, usually a " fleur de Us" and always
read the same end of the needle, that is, the north end
of the needle if the north point of the compass is ahead,



010 SURVEYING.

and vice versa. Before reading the angle, see that the eye
is in the direct line of the needle so as to avoid error
which would otherwise result from parallax, or apparent
change of the position of the needle, due to looking at it
obliquely.

The angle is read and recorded by noting, first, whether
the N or 5 point of the compass is nearest the .end of the
needle being read; second, the
number of degrees to which it
points, and third, the letter E or
W nearest the end of the needle
being read.

Let A B, in Fig. 251, be the
direction of the magnetic needle,
B being at the north end. Let
the sights of the compass be
directed along the line C D. The
north point of the compass will be
seen to be nearest the north end
of the needle which is to be read. The needle which
has remained stationary while the sights were being
turned to C D, now points to 45 between the N and E
points, and the angle is read north forty-five degrees east
(N45 E).

1 2O6. Backsights. A sure test of the accuracy of a
bearing is to set up the compass at the other end of the line,
i. e. , the end first sighted to, and sight to a rod set up at the
starting point. This process is called backsighting. If
the second bearing is the same as the first, the reading is
correct. If it is not the same, it shows that there is some
disturbing influence at either one or the other end of the
line. To determine which of these two bearings is the true
one, the compass must be set up at 'one or more intermediate
points, when two or more similar bearings will prove the true
one. When a line can not be prolonged by magnetic bearings,
on account of local attraction, the true direction is maintained
by backsighting.




SURVEYING. Oil

1 2O7. Declination of the Needle. The magnetic
meridian is the direction of the magnetic needle. The true
meridian is a true north and south line, which,
if produced, would pass through the poles of the
earth. The declination of the needle is the
angle which the magnetic meridian and the true
meridian make with each other.

In Fig. 252, let 'N S be the true meridian for
any given place, and N 1 S 1 the magnetic meridian.
The angle N A N 1 is the declination of the needle
for that place.

1 2O8. The Polar Star. There is a star in
the northern hemisphere known as the North Star
or Polaris. It is the extreme star, in the row or
line of stars forming what is commonly called the ^,
handle of the "Little Dipper." This star very
nearly coincides with the true north point or FlG - 253 -
pole, being removed only 1 from it. It revolves about the
true pole, and twice in each revolution it is exactly in the true

O meridian ; that is, in a vertical plane passing
through the true pole P. See Fig. 253. One
may know when the North Star is in the true
meridian from the position of another star.
This other star is in the handle of the " Big
FIG. 253. Dipper, "or Ursa Major, the one nearest the
bowl of the dipper, and is called Alioth. When the North
Star is in the true meridian, Alioth will be found directly
below it.

TO DETERMINE A TRUE MERIDIAN.

1 2O9. By Observations of the North Star. The
time at which the North Star passes the meridian above the
pole for every tenth day of the year is given in published
tables, but those occurring in the day time are, of course,
of no value with ordinary instruments. The following
dates are available in almost every latitude of the United
States:



612



SURVEYING.



TIME OF NORTH STAR PASSING THE
MERIDIAN.



Months.


1st Day.


llth Day.


21st Day.


January
August . . .


6:30 P. M.
4-33 A. M.


5:51 P. M.
3-53 A. M.


5:11 P. M.
3-14 A. M.


September
October
November


2:31 A. M.
12:34 A. M.
10-28 P M


1 :52 A. M.
11:50 P. M.
9-48 P M


1:12 A.M.
11:11 P. M.
9-09 P M


December


8:30 P.M.


7:50 P. M.


7:11 P. M.



Note from the table the time of passing the meridian,
and, also, that it is the ujpper transit, i. e., above the pole.
Select a suitable spot for permanently establishing the
meridian line, and set up the transit and sight to Polaris,
following it by moving the cross-hairs with the tangent
screw. When it is exactly in line with Alioth, the line
of sight will be in the true meridian. Points should be fixed
immediately, a lamp being used to illuminate the cross-
hairs.

1210. Changes in Magnetic Declination. The

magnetic declination is not fixed for any place, but con-
stantly varies, its variations, however, being confined within
fixed limits.

1211. To Correct Magnetic Bearings. The dec-
lination at any place being known, the magnetic bearings
may readily be reduced to true bearings.

In the Northeastern States, the declination is west; in
the Western and Southern States, it is east ; hence, the true
bearing of a line in a Northeastern State, whose magnetic
bearing is N W or S E, will be the sum of the magnetic
bearing and the declination. If the magnetic bearing is
N E or S W, the true bearing will be the difference of
the magnetic bearing and the declination.



SURVEYING.



613



EXAMPLES FOR PRACTICE.



1212. Supposing the declination to be 7 west, what will be the



true bearings of the following lines :
Magnetic Bearing.

(1) N 12 10' W ?

(2) N 50 15' W ?

(3) S 11 15' E ?

(4) S 38 10' E ?

(5) N 50 20' E ?

(6) S 20 25' W ?

(7) N 87 30' W ?

(8) N 5 10' E ?

(9) S 89 20' E ?
(10) S 3 10' W?



Ans.



True Bearings.

(1) N 19 10' W.

(2) N 57 15' W.

(3) S 18 15' E.

(4) S 45 10' E.
(5). N 43 20' E.

(6) S 13 25' W.

(7) S 85 30' W.

(8) N 1 50' W.

(9) N 83' 40' E.
(10) S 3 3 50' E.



1213. By Equal Shadows of the Sun. On the
south side of any level surface set up a flag-pole and plumb
it with a plumb bob. Its horizontal
projection will be a point as 5 in Fig. .
254. Two or three hours before noon
mark the point A, which is the extremity
of the shadow cast by the flag-pole.
Then, describe an arc A B with a radius
equal to S A, the distance from 5 to the
extremity of the shadow. After noon,
note the moment when the shadow of the flag-pole touches
another point of the arc, as B. Bisect the arc A B at N.
The line 5 N is a true meridian.




FIELD WORK.

1214. The Engineer's Chain. The engineer's chain
is one hundred feet in length, and is composed of one hun-
dred links of steel wire, each one foot in length. Both ends
of the chain are fitted with brass handles with swivel move-
ments, and fitted with nuts for taking up any excess
in length resulting from continual stretching. At each
interval of ten feet is a brass tag with tally points to indi-
cate its distance from the nearest end of the chain. Each
tally point counts ten feet. At the middle point of the



614 SURVEYING

chain, the tag is of oval form to prevent confusion in reading
the chain.

1215. Danger of Error. There is much greater
danger of error in reading the chain than in reading bear-
ings. The danger arises from the fact that the compassman
is usually one of experience, who knows the liability of error,
and hence the .necessity for care, while chainmen are often
inexperienced, and, unfortunately, often careless.

1216. Keeping Chainmen in Line. When the
direction of a line has been given by setting up a flag, it be-
comes the business of the hind chainman or follower to keep
the measurement on a straight line. The head chainman
carries a flag which he moves to right or left, at the di-



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