This done proceed on your distance line to e, opposite to the angle b, and measure eb, supposing then 1 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 fe; suppose then 1 f to be 13C. and fe 1C. 251. say in the same line as before, at 13C. L. 1C. 25L. Then proceed from f 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 perchchain, 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, the 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 3, and in measuring the distance line, stop at / opposite g admit 2l 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 1€. 20L. Again at m, which suppose to be 10C. 25L. from 2; take the offset 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 ; 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, taking the bearings, and measuring the distances as usual, which insert in your fieldbook, and draw a mark like one side of a parentheses, from the third to the fifth station, to show that a line drawn from the third station to the furthest 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 of a quary, 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 bearings; then direct the index to the point p, and insert its bearing 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 fieldbook, 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 to 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 intersections taken at the first and second stations of the above field-book.

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

B

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

How to cast up off-sets by the pen.

1, 2—1ƒ,=2ƒ, lf,-le-fe, le-1d=ed.

Then 1dxda=lda, by prob. 6. page 183, and ed xda+eb-adeb by the doctrine of trapezia; also fex eb+fc-befc, and 2fxfc=cf2; the sum of all which will be 1 abc. 21; 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 ik3i as well as what is without and with-inside 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 off-set, and from that the distance of the one preceding it, &c. in four-pole 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