In this survey 4 is the most easterly and 9 the most westerly station. The area is equal to 110A. 2R. 23P. It may vary a little, on account of the way in which the balancing is done.

7. What are the contents of a piece of land of which the following are the field notes?

In this survey 4 is the most westerly station and 9 the most easterly. The area is 110A. 2R. 23P. The result may, however, as in the other examples, be slightly varied by the balancing.

8. What is the area of a survey of which the following are the notes?

I. To determine the contents and boundary of a piece of land, by means of offsets from the principal lines.

33. An offset is a line measured perpendicular to a course, and may lie either on the right or left of it.

Let ABCDE be a piece of ground to be surveyed. Let us suppose it to be bounded on the west and north by a fence and road, and on the east and south by a creek or river.

Assume as stations the principal points A, B, C, D, and E. Take, with the compass, the bearings from A to B, from B to C from C to D, from D to E, and from E to A; and measure the distances AB, BC, CD, DE, and EA.

N

CD

10

S

At convenient points of the course AB, as a, c, and f, measure the offsets ab, cd, fg. Then, having measured

will be known to determine the area which lies without the station line AB. The points b, d and g, of the fence which runs from A to B, are also determined.

Erect, in a similar manner, offsets to the other courses, and determine the areas which lie without the station lines. These several areas being added to the area within the station lines, will give the entire area of the ground.

If the offsets fall within the station lines, the corresponding area must be subtracted from the area which is bounded by the station lines.

II. To determine the bearing and distance from one point to another, when the points are so situated that one cannot be seen from the other.

34. Let A and C be the two points, and AB a meridian passing through one of them. From either of them, as A, measure a course A2, of a convenient length in the direction towards C. and take the bearing with the com. pass. At 2, take the bearing of a second course, and measure the distance to 3. At 3, take a third bearing and measure to 4. At 4, take the bearing to C, and measure the distance from 4 to C.

3

B

1

Then, the difference between the sum of the northings and the sum of the southings will be represented by AB, and the difference between the sum of the eastings and the sum of the westings by BC. The base AB, and the perpendicular BC of the right-angled triangle ABC, are then known. The angle at the base, BAC, is the bearing from A to ; or the equal alternate angle at C is the bearing from C to A, and the hypothenuse AC is the distance.

35. Having measured the bearings and courses on the field, form a table, and find the base and perpendicular

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

Ans. {Bearing, S 38° 52' E.

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.