Hence, the bearing and distance are both found.

OF SUPPLYING OMISSIONS IN THE FIELD NOTES.

36. The last problem affords an easy method of finding

when the bearings and lengths of all the others are known. It may be necessary to use this method when there are obstacles which prevent the measuring of a course, or when the bearing cannot be taken. Indeed, two omissions may in general be supplied by calculation. It is far better, however, if possible, to take all the notes on the field. For, when any of them are supplied by calculation, there are no tests by which the accuracy of the work can be ascertained, and all the errors of the notes affect also the parts which are supplied.

1. In a survey we have the following notes:

What is the bearing and distance from station 3 to 4?

Lost.

10.40

2. In a survey we have the following notes:

What is the bearing and distance from 3 to 4?

Ans.

Bearing, N 34° 47' E.

III. To determine the angle included between any two courses when their bearings are known.

REMARK. The above principles are determined, under the supposition that the two courses are both run from the

two courses run in the ordinary way, as we go around the field, the bearing of one of them must be reversed before the calculation for the angle is made.

1. The bearings of two courses, from the same point, are N 37° E, and S 85° W: what is the angle included between them?

Ans. 132°.

2. The bearings of two adjacent courses, in going round a piece of land, are N 39° W, and S 48° W: what is the angle included between them?

Ans. 87°.

3. The bearings of two adjacent courses, in going round a piece of land, are S 85° W, and N 69° W: what is the angle included between them?

Ans. 154°.

4. The bearings of two adjacent courses, in going round a piece of land, are N 55° 30' E, and S 69° 20′ E: what is the angle included between them?

OF DIVIDING LAND.

Ans. 124° 50'.

that it is difficult

It is by practice branch of survey

38. Fields are so variously shaped to give rules that will apply to all cases. alone that facility is obtained in that ing relating to the division of estates. We shall add only a few examples that may serve as general guides in the application of the principles of Plane Geometry to such cases as may arise.

I. To run a line from the vertex of a triangular field which shall divide it into two parts, having to each other the ratio of M to N.

39. Let ABC be any triangular field. Divide the side BC into two

parts, such that (Geom., Bk. IV.,

Prob. 1.)

BD : DC :: m : and draw the line AD:

n;

B

For, the two triangles ABD, ADC having the same altitude are to each other as their bases (Geom., Bk. IV., P. 6, C.): hence, the triangle is divided into parts having the ratio of m to n.

II. To run a line parallel to one side of a triangular field, that shall form with the parts of the two other sides a

m

triangle equivalent to the part of the field.

n

40. Let CBA represent a triangular field and CA the side parallel to which the dividing line is to be drawn.

At D, erect th› perpendicular DG to the diameter BC, and draw BG. Then, with B as a centre, and BG as a radius, describe the arc of a circle cutting BC at E. Through E draw EF parallel to CA, and it will divide the triangle in the required ratio.

But, since the triangles BEF, BCA are similar,

REMARK. The points E and F may easily be found

by computation.

For, since BE = BCX BD, and BD=

m =n

× BC,