places c, d, e, &c, on the bafe line, can be very well determined by the eye, efpecially when affifted by laying down the offset-ftaff in a crofs or perpendicular direction. But when these perpendiculars are very large, find their pofitions by the crofs, or by the inftrument which you happen to be ufing, in this manner: As you measure along AB, when you come about c, where you judge a perpendicular will stand, plant your inftrument in the line, and turn the index till the marks A and B can be feen through both the fights, looking both backward and forward; then look along the cross fights, or the crofs line on the index; and if it point directly to the corner or bend h, the place of c is right. Otherwife, move the inftrument backward or forward on the line AB, till the crofs line points ftraight to h. This being found, fet down the diftance measured from A to c; then measure the offset ch, and fet it down oppofite the former, and on the left hand fide.

Then proceed forward in the line AB, till you arrive oppofite another corner, and determine the place d of the perpendicular as before. And fo on throughout the whole length.

Having fet up marks at the corners, which is to be done in all cafes where there are not marks naturally;

meafure

measure with the chain from A to P, where a perpendicular would fall from the angle c, and fet up a mark at P, noting down the diftance AP. Then complete the distance AB by measuring from P to B. Having fet down this measure, return to P, and measure the perpendicular PC. And thus, having the base and perpendicular, the area from them is eafily found. Or having the place P of the perpendicular, the triangle is eafily conftructed.

Or, measure all the three fides with the chain, and note them down. From which the content is easily found, or the figure conftructed.

2. By taking one or more of the Angles.

Measure two fides AB, AC, and the angle a between them. Or measure one fide AB, and the two adjacent angles A and B. From either of these From either of thefe ways the figure is cafily planned; then by meafuring the perpendicular CP on the plan, and multiplying it by half AB, you have the content.

Measure along either of the diagonals, as AC; and either the two perpendiculars DE, BF, as in the last problem; or else the fides AB, BC, CD, DA. From either of which the figure may be planned and computed as before directed.

Other

Measure on the longeft fide, the diftances AP, AQ, AB; and the perpendiculars PC, QD.

2. By taking one or more of the Angles.

Meafure the diagonal AC (fee the first fig. above), and the angles CAB, CAD, ACB, ACD.-Or measure the four fides, and any one of the angles as BAD.

To Survey any Field by the Chain only.

Having fet up marks at the corners, where neceffary, of the propofed field ABCDEFG. Walk over the ground, and confider how it can best be divided into triangles and trapeziums; and measure them feparately as in the last two problems. And in this way it will be proper to divide it into as few separate triangles, and as many trapeziums as may be, by drawing diagonals from corner to corner; and fo as that all the perpendiculars may fall within the figure, Thus, the following figure is divided into the two trapeziums ABCG, GDEF, and the triangle GCD. Then, in the firft, beginning at A, meafure the diagonal Ac,

and

and the two perpendiculars Gm, Bn.

Then the base

GC, and the perpendicular Dq. Laftly the diagonal DF, and the two perpendiculars pE, OG. All which measures write against the correfponding parts of a rough figure drawn to resemble the figure to be furveyed, or fet them down in any other form you choose.

Measure all the fides AB, BC, CD, DE, EF, FG, and GA; and the diagonals AC, CG, GD, DF.

Otherwife.

Many pieces of land may be very well furveyed, by measuring any bafe line, either within or without them, together with the perpendiculars let fall upon it from every corner of them. For they are by those means divided into feveral triangles and trapezoids, all whofe parallel fides are perpendicular to the base line; and the fum of thefe triangles and trapeziums will be equal to the figure propofed if the bafe line fall within it; if not, the fum of the parts which are without being taken from the fum of the whole which are both within and without, will leave the area of the figure proposed.

In pieces that are not very large, it will be fufficiently exact to find the points, in the bafe line, where

the

the several perpendiculars will fall, by means of the cross, and from thence measuring to the corners for the lengths of the perpendiculars.-And it will be most convenient to draw the line fo as that all the perpendiculars may fall within the figure.

Thus, in the following figure, beginning at A, and meafuring along the line AG the diftances and perpendiculars, on the right and left, are as below.

1. From one Station.

Plant the table at any angle, as c, from whence all the other angles, or marks fet up, can be feen; and turn the table about till the needle point to the flower-de-luce; and there fcrew it faft. Make a point for e on the paper on the table, and lay the edge of

E

the index to c, turning it about c till through the fights you fee the mark D; and by the edge of the index draw a dry or obfcure line: then measure the distance CD, and lay that distance down on the line

CD.

Then turn the index about the point c, till the

mark