2. They may also be surveyed by running straight lines connecting points on the bank, taking the bearings of these lines, the distances from the origin of these lines to the perpendicular offsets run from the lines to the bank of the river, and the length of the offsets, as exhibited in the following field notes and plot.

2.84

1.50

2.24

50

1.40

1.08

.40

The name of stations and the left-hand offsets are noted on the left of the parallels, the righthand offsets and bearings on the right, the distance from the station to the offsets, and the sign for station, between the parallels.

Station A A E

3. In surveying an existing winding road, keep in the road, run straight lines as far as possible, without running out of the road, note the bearing of these lines, the distances to the offsets at different points to the sides of the road, the lengths of these offsets, and make an accurate plot of the road.

B

C

4. To survey a new road, find the bearing of the middle line from the origin to the next angle or intersection with another road, measuring the distance

S. N. 24.

from the origin to the lines of farms, creeks, etc., which it intersects.

Set temporary stakes at the angles, and at convenient distances along the middle line, to guide in making the road, and plant monuments at a given distance and bearing from the angular points, so that they will not be disturbed in making or working the road. Take notes, and make a correct plot of the road.

281. Surveying Towns.

Commence at the intersection of principal streets, take their bearings, measure their lengths, noting the distances to the streets and alleys crossed, taking offsets to corners of streets and prominent objects, as public buildings, etc., till a prominent cross-street is reached, which survey in the same manner, changing the courses at such stations as will lead back to the original station.

Survey all the streets and alleys enclosed. Then survey an adjoining district, and so on, till the entire town or city has been surveyed.

Take notes, and make an accurate map of the town, on which locate not only the streets and alleys, but public buildings, parks, fountains, monuments, etc.

282. Reverse Bearing.

Let AB be a line run from A to B, AN and BS meridians, then will NAB be the bearing of AB, and SBA will be the reverse bearing.

Since the meridians AN and BS may be regarded as parallel, the bearing and reverse

bearing are equal. Thus, if the bearing of AB is N. 30° E., the reverse bearing is S. 30° W.

The bearing and reverse bearing agree in the value of the angle, and differ in both the letters which indicate the general direction of the line. In fact, the reverse bearing of a line is the bearing of the line if run in the opposite direction. Thus, SBA, the reverse bearing of the line AB, run from A to B, is the bearing of the line BA, run from B to A.

Of the letters used in bearings, we shall call N and S latitude letters, and E and W departure letters.

To guard against inaccurate observations, and the disturbance of the needle occasioned by local attraction, the reverse bearing should be taken at every station. If the bearing and reverse bearing agree in value, the bearing may be considered as correctly taken; if they differ materially, both should be taken again. If they still differ, the difference may be regarded as occasioned by local attraction.

To ascertain at which station the local attraction exists, place the instrument at a third station, at a considerable distance from each of the doubtful stations, and sight to each, then from these back to the third station. The local attraction may be considered to exist at the station where the bearing of the third station disagrees with its bearing taken at the third station.

If the error occurred in the foresight, correct it before entering the bearing in the field notes, and note the amount of disturbance; if the error occurred in the backsight, the next foresight will be affected, and should be corrected before entered.

PRELIMINARY CALCULATIONS.

283. Angles between Courses.

1. If the latitude letters are alike, also the departure letters, the included angle is equal to the difference of the bearings.

If AB bears N. 40° E., and AC N. 20° E., BAC BAN-CAN = 40°

=

N

2. If the latitude letters are alike, and the departure letters unlike, the included angle is equal to the sum of the bearings.

If AB bears N. 38° E., and AC N. 18° W., BAC=BAN÷NAC=38° +- 18° 56°.

If AD bears S. 38° W., and AE S. 18° E., DAE = 38°

DAS + SAE

+18°

=

56°.

E

3. If the latitude letters are unlike, and the departure letters alike, the included angle is equal to 180° minus the sum of the bearings.

If AB bears N. 45° E., and AE S. 30° E., BAE 180°- (NAB+SAE)

=

N. 30° W., DAC 180°-(DAS+CAN) = 180° 75° = 105°.

C N

B

4. If the latitude letters are unlike, also the departure letters, the included angle is equal to 180° minus the difference of the bearings.

If AB bears N. 45° E., and AC

NE

B

S. 15° W., BAC

=

180° = : 150°.

(NAB

If AD bears S. 45° W., and AE

N. 15° E., DAE
NAE) = 180° — 30°

=

180°

150°.

(SAD- D

Remark. These principles apply when both courses run from or toward the vertex; if one runs from the vertex, and the other toward it, reverse the bearing of one side before applying the principles.

284. Examples.

1. Find the angle A, if AB bears N. 78° E., and AC N. 24° E.

Ans. 54°.

2. Find the angle A, if BA bears S. 34° E., and AC S. 48° W.

Ans. 98°.

3. Find the angle A, if BA bears S. 70° W., and CA N. 25° E. Ans. 135°.

4. Find the angles of the polygon ABCDE, if AB bears N. 30° E.; BC, N. 60° E.; CD, S. 50° E.; DE, S. 40° W.; EA, N. 78° W.

A=72°, B=150°, C=110°, D=90°, E=118°.

285. Problem.

Given the bearings of the sides of a field, to find the bearings if the field be supposed to revolve, so as to cause one of the sides to become a meridian.