ners will thus be determined. When these are joined, the plat will be completed.

SECTION VII.

PROBLEMS IN COMPASS SURVEYING.

345. Problem 1.-GIVEN the bearing of one side, and the deflection of the next, to determine its bearing.

If the given bearing is northeasterly or southwesterly, add the deflection if it is to the right hand. If the sum exceeds 90°, take its supplement, and change north to south, or south to north.

If the deflection is to the left hand, subtract it from the bearing; but if it is greater than the bearing from which it is to be subtracted, take the difference, and change east to west, or west to east.

When the given bearing is northwesterly or southeasterly, add the left-hand and subtract the right-hand defections, applying the same rules as above.

EXAMPLES.

Ex. 1. Given AB (Fig. 148) N. 37° E., and the deflection of the next side 43° 15' to the right.

Fig. 148.

N

Ex. 2. Given AB N. 37° E., and the deflection of BC'

Ex. 3. Given the bearing of AB, N. 39° W., and BC deflects to the left 75° 26' required the bearing of BC. Ans. S. 65° 34' W.

Ex. 4. Given the bearing of a line S. 63° 29′ E., and the deflection of the next 29° 17' to the right: required its bearing.

Ans. S. 34° 12′ E.

Ex. 5. The bearing of one line being S. 34° 12′ E., and the deflection of the next 75° 32′ to the right: required its bearing.

Ans. S. 41° 20′ W.

346. Problem 2.- To determine the angle of deflection between two courses.

1. If the lines run between the same points of the compass, take the difference of their bearings.

2. If they run between points directly opposite, subtract the difference of the bearings from 180°.

3. If they run from the same point towards different points, add the bearings.

4. If they run from different points towards the same point, take the sum of the bearings from 180°.

EXAMPLES.

Ex. 1. AB (Fig. 149) runs S. 56° W., and BC S. 25° W.: required the de

flection.

B

56°
25°

Deflection 31° to the left.

14

*

Ex. 2. Given AB (Fig. 150) N. 46 W., and BC S. 79° E.: required the deflection.

Ex. 3. Given AB (Fig. 151) N. 39° E., and BC N. 63° W., to find the deflection.

Ex. 4. Given AB (Fig. 152) S. 82° E., and BC N. 67° E., to find the deflection.

B

S

DBC

=

31° deflection to the left.

Ex. 5. The bearing of a line is N. 46° 30′ E., and that of the next S. 63° 29′ W.: required the deflection.

Ans. 163° 1' to the left.

Ex. 6. What is the deflection in passing from a course

S. 63° W. to one N. 29° W.?

Ans. 88° to the right.

Ex. 7. What is the deflection in passing from a course N. 8210 W. to one N. 291° W.?

Ans. 531° to the right.

347. Angle between lines. If the angle between two

lines is required, reverse the first bearing, and apply the above rules.

EXAMPLES.

Ex. 1. Given AB N. 87° E., and BC S. 25° W., to find the angle ABC. Ans. ABC= 62°.

Ex. 2. Given AB S. 63° E., and BC N. 56° E.: required the angle ABC. Ans. ABC = 119°. Ex. 3. Given CD N. 15° W., and DE N. 56° W.: required the angle CDE. Ans. CDE = 139°.

Problem 3.-To change the bearings of the sides of a survey.

348. It is frequently useful to change the bearings of a survey so as to determine what they would be if one side were made a meridian. This change is made on the supposition that the whole plat is turned around without altering the relative positions of the sides. Every bearing will thus be altered by the same angle. The following rules take in all the possible cases.

The reason of these rules will be made apparent by drawing a figure to represent any particular case.

1. Deduct the bearing of the side that is to be made a meridian from all those bearings that are between the same points as it is, and also from those that are between points directly opposite to them. If it is greater than any of those bearings, take the difference, and change west to east,

or east to west.

2. Add the bearing of the side that is to be made a meridian to those bearings that are neither between the same points as it is, nor between points directly opposite. If either of the sums exceeds 90°, take the supplement, and change south to north, or north to south.

EXAMPLES.

Ex. 1. The bearings of a tract of land are,-1. N. 57° E.;

2. N. 89° E.; 3. S. 491° E.; 4. South; 5. S. 27° W.; 6. S. 5310 W.; 7. N. 89° W.; 8. N. 37° W.; 9. N. 43° E. to the place of beginning. Required to change the bearings, so that the ninth side may be a meridian.

Ex. 2. Change the bearings in the following notes, so that the second side may be a meridian:-1. N. 43° 25′ W.; 2. N. 29° 48′ E.; 3. S. 80° E.; 4. N. 89° 55′ E.; 5. S. 10° 13′ E.; 6. N. 63° 55′ W.; 7. S. 63° 45′ W.; 8. N. 57° 35′ W. Ans. 1. N. 73° 13′ W.; 2. North; 3. N. 70° 12′ E.; 4. N. 60° 7' E.; 5. S. 40° 1' E.; 6. S. 86° 17′ W.; 7. S. 33° 57' W.; 8. N. 87° 23′ W.

Ex. 3. Change the bearings in the following notes, so that the fourth side may be a meridian:-1. S. 63° E.; 2. S. 47° E.; 3. S. 591° W.; 4. N. 841° W.; 5. N. 12° W.; 6. N. 171° E., and 7. S. 29° W.

Ans. S. 2110 W.; 2. S. 371° W.; 3. N. 361° W.; 4. North; 5. N. 7210 E.; 6. S. 78° E.; 7. N. 65° W.