(2) ABDC is a four-sided field; CP and DQ are perpendiculars on AB.

The following measurements

are taken in links:

P

AP=112, AQ=448, AB=626,

CP=223, DQ=295.

Hence we have PQ=336, QB=178.

The following will be the areas of the parts of the field in square links:

1

the triangle APC= × 112 × 223=12488,

1

the trapezoid PQDC= × 336 × 518=87024,

the triangle DQB=

1

× 178 × 295=26255.

The sum of these three numbers is 125767; so that the area of the field is 1.25767 acres, that is, about 1 acre 1 rood 1 pole.

J

XLVI. THE FIELD-BOOK.

The

408. Many fields may be conveniently surveyed by measuring a straight line from one corner to another, and also the perpendiculars on it from the other corners. first straight line is called a base-line, or a chain-line; and the perpendiculars are called offsets. It is often advantageous to take for the base-line the longest straight line which can be drawn in the field; and thus sometimes one of the sides of the field may be the base-line, as in the second example of Art. 407.

We will now explain the method in which the results of the measurements are usually recorded in the fieldbook.

409. The field-book. Each page of the field-book is divided into three columns; the surveyor begins at the bottom of the page and writes upwards.

In the middle column are entered lengths obtained in measuring along the base-line, in the right-hand column are entered the lengths of offsets to the right of the baseline, and in the left hand column the lengths of offsets to the left of the base-line. The offsets are entered against the corresponding distances of the points on the base-line at which they are measured.

The field-book is used to record not only measured lengths, but various particulars, which may be useful in drawing a plan of the estate surveyed. Thus a note is made in the margin of the point at which the chain-line crosses any fence, or foot-path, or ditch, or stream. The

positions of adjacent buildings, or of remarkable trees may also be indicated; and if the chain-line passes near a boundary which is rather irregular, the form of the boundary may be traced.

an offset bB to the left of 230 links; Ac is 625 links, and at c is an offset cC to the right of 250 links; Ad is 750 links, and at d is an offset dD to the left of 260 links; AE is 1125 links.

We can now calculate the areas of the parts; and we shall have the following results in square links:

Thus the whole area is 334125 square links, that is, 3:34125 acres, that is, 3 acres 1 rood 14'6 poles.

The measurements are

taken in links; and we shall

B

have the following results for the areas of the parts in square links:

the triangle AbB = × 315 × 350=55125,

1

2

Thus the whole area is 335075 square links, that is, 3-35075 acres, that is, 3 acres 1 rood 16·12 poles.

411. The ends of a chain-line are called stations; they are frequently denoted in the field-book thus: 0, 0, 0, ...

The situations of the chain-lines with respect to the points of the compass are often recorded. The record from Orange E, indicates that the chain-line commencing at the first station proceeds towards the East. So the record N. 50° W., indicates that the chain-line com

mencing at the second station proceeds in the direction which makes an angle of 50 degrees with the North direc tion reckoned towards the West.

Sometimes the situation of the successive chain-lines is sufficiently shewn by the words right and left. Thus the record from on L, indicates that on arriving at the second station, the surveyor turns to the left-hand of the direction in which he has been walking.

If 0 occurs in either offset column, it indicates that the chain-line meets at the corresponding point the boundary of the land which is being surveyed.

412. In order to provide themselves with a test of the accuracy of their work, surveyors always measure more lengths than would be theoretically sufficient. Thus, for example, suppose that a field bounded by four straight sides is to be surveyed; it would be theoretically sufficient to measure the four sides and one diagonal: for the area of each of the two triangles into which this diagonal divides the figure can then be calculated. But the surveyor will also measure the second diagonal. He will draw a plan of the figure from the measured lengths of the four sides and of the first diagonal, and draw the second diagonal on the plan: he will then examine if the length of the second diagonal as found from the plan by the known scale on which the plan was drawn corresponds with the measured length. If these two lengths do correspond, the surveyor gains confidence in the accuracy of the work: but if the two lengths do not correspond there is an error in the operations with the chain or in the drawing of the plan, and this error must be discovered and corrected.

If the field to be surveyed be in the form of a triangle, the sides will be measured, from which the area can be found, and a plan can be drawn. To test the accuracy of the work, either the perpendicular from an angle to the opposite side, or the straight line drawn from a definite point of one side to a definite point of another will be measured; and this measured length will be compared with the length obtained from the plan.

A length which is measured for the purpose of testing the accuracy of the work is called a proof-line, or a checkline, or a test-line.