SECTION IV.

OF OFF-SETS.

IN taking surveys it is unnecessary and unusual to make a station at every angular point, because the field-work can be taken with much greater expedition, by using off-sets and intersections, and with equal certainty; especially where creeks, &c. bound the survey.

Off-sets are perpendicular lines drawn or measured from the angular points of the land, that lie on the right or left hand to the stationary distance, thus:

PL. 11. fig. 2.

Let the black lines represent the boundaries of a farm or township and let 1 be the first station; then if you have a good view to 2, omit the angular points between 1 and 2, and take the bearing and length of the stationary line 1, 2, and insert them in your field-book: but in chaining from 1 to 2, stop at d opposite the angular point a, and in your field-book insert the distance from 1 to d, which admit to be 4C. 25L. as well as the measure of the off-set ad, which admit to be 1C. 12L. thus: by the side of your fieldbook in a line with the first station, say at 4C. 25L. L. 1C. 12L. that is, at 4C. 25L. there is an off-set to the left hand of 1C. 12L.

This done, proceed on your distance line to e opposite to the angle b, and measure eb, supposing then I e to be 7C. 40L. and eb 3C. 40L. say (still in a line with the first station in your field-book) "at 7C. 40L. L. 3C. 40L." That is, at 7C. 40L. there is an offset to the left of 3C. 40L. proceed then with your distance line to f opposite to the angle c, and measure fc; suppose then 1 f to be 13C. and fc 1C. 25L. say in the same line as before, at 13C. L. 1C. 25L. Then proceed from ƒ to 2, and you will have the measure of the entire stationary line 1, 2, which insert in its proper column by the bearing.

In taking off-sets, it is necessary to have a perch chain, or a staff of half a perch, divided into links for measuring them; for by these means the chain in the stationary line is undisturbed, and the number of chains and links in that line from whence, or to which, thre off-sets are taken, may be readily known.

Having arrived at the second station, if you find your view will carry you to 3, take the bearing from 2 to S, and in measuring the

distance line, stop at opposite g; admit 21 to be 4C. 10L. and the off-set lg 1C. 20L. then in a line with the second station in your field-book, say at 4C. 10L. R. 1C. 20L. that is, the off-set is a right hand one of 1C. 20L. Again at m, which suppose to be 10C. 25L. from 2: take the off-set mh of 1C. 15L. and in a line with the second station, say at 10C. 25L. R. 1C. 15L. In the same line when you come to the boundary at i, insert the distance 2i, 13C. 10L. thus, at 13C. 10L. 0; that is, at 13C. 10L. there is no off-set. At n, which is 15C. from 2, take the off-set nk 45L. and still opposite to the second station say at 15C. L. 45L.

Let the line, 3, 6, represent the boundary, which by means of water, briers, or any other impediment, cannot be measured. In this case make one or more stations within or without the land, where the distances may be measured, and draw a line from the beginning of the first to the end of the last distance, thus: make stations at 3, 4, and 5, take the bearings, and measuring the dis tances as usual, which insert in your field-book, and draw a mark like one side of a parenthesis, from the third to the fifth station, to show that a line drawn from the third station to the farthest end of the fifth stationary line will express the boundary. Thus,

Suppose the point p of the boundary to be inaccessible by means of the lines 6p or p7, being overflowed, or that a quarry, furze, &c. might prevent your taking their lengths: in this case take the bearing of the line 6, 7, which insert opposite to the sixth station in your field-book with the other bearing; then direct the index to the point p, and insert its bearings on the left side of the field-book, opposite to the sixth station, annexing thereto the words Int. for boundary; and having measured and inserted the distance 6, 7, set the index in the direction of the line 7p, and insert its bearing on the left of the seventh station of the field-book, annexing thereto the words Int. for boundary: the crossing or intersection of these two bearings will determine the point p, and of course the boundary 6p7 is also determined.

If your view will then reach in the first station, take its bearing, stationary line, and off-sets as before, and you have the field-book completed. Thus,

If you would lay down a tower, house, or any other remarkable object in its proper place; from any two stations, take bearings to the object, and their intersection will determine the place where you are to insert it, in the manner that the tower is set out in the figure, from the intersection taken at the first and second stations of the above field-book.

A protraction of this will render all plain, on which lay off all your off-sets and intersections, and proceed to find the content by any of the methods in section the 4th.

The foregoing field-book may be otherwise kept, thus:

1, 2—1ƒ=2ƒ, 2ƒ—le=fe, le-1d=ed.

Then 1dxda=1da, by prob. 6, page 129, and ed×} (da+eb) =beda, (eb+fc) xfe=befc, and 2fxfc=cf9; the sum of all which will be 1abc21; the area contained between the stationary line, 1, 2, and the boundary, 1 abc 2.

In the same manner you may find the area of 2ihg2, of iksi, as well as what is without and withinside of the stationary line 7, 1.

If therefore the left hand off-sets exceed the right hand ones, it is plain, the excess must be added to the area within the stationary lines, but if the right hand off-sets exceed the left hand ones, the difference must be deducted from the said area; if the ground be kept on the right hand, as we have all along supposed; or in words, thus:

To find the contents of off-sets.

1. From the distance line, take the distance to the preceding offset, and from that the distance of the one preceding it, &c. in fourpole chains; so will you have the respective distances from off-set to off-set, but in a retrograde order.

2. Multiply the last of these remainders by the first off-set, the next by the sum of the first and second, the next by half the sum of the second and third, the next by half the sum of the third and fourth, &c. The sum of these will be the area produced by the off-sets.

Thus, in the foregoing field-book, the first stationary line is 22C. 12L. or 11C. 12L. of four-pole chains. See the figure.

ed=1.65×1C. 26L. the sum of the 1st and 2d 2.0790
ef 2.60 x 1C. 32L. the sum of 2d and 3d=

2f=4.62×37L. half the last off-set=

3.4320

1.7094

Content of left off-sets on the first dist. in square 7.9404

four-pole chains

In like manner the rest are performed,

The sum of the left hand off-sets will be

14.0856

And the sum of the right hand ones

3.6825

Excess of left hand off-sets in squ. 4-pole chains 10.4031

Acres 1.04031

.16124

Perches 6.4496

Excess of left hand off-sets above the right hand ones, 1A. OR. 6P. to be added to the area within the stationary lines.