mark E be feen through the fights, by which draw a line, and measure the distance to E, laying it on the line from c to E. In like manner determine the pofitions of CA and CB, by turning the fights fucceffively to A and B ; and lay the lengths of thofe lines down. Then connect the points with the boundaries of the field, by drawing the black lines CD, DE, EA, AB, BC.

2. From a Station within the Field.

D

C

B

When all the other parts cannot be feen from one angle, choofe fome place o within; or even without, if more conveni- Ex ent, from whence the other parts can be seen. Plant the table at o, then fix it with the needle north, and mark the point o on it. Apply the index fucceffively to o, turning it round with the fights to each angle A, B, C, D, E, drawing dry lines to them by the edge of the index, then measuring the diftances oA, OB, &c, and laying them down upon thofe lines. Laftly draw the boundaries AB, BC, CD, DE, EA.

A

3. By going round the Figure.

When the figure is a wood or water, or from fome other obftruction you cannot measure lines across it; begin at any point A, and measure round it, either within or without the figure, and draw the directions of all the fides thus: Plant the table at A, turn it with the needle to the north or flower-de-luce, fix it and mark the point A. Apply the index to A, turning it till you can fee the point E, there draw a line; and then the point B, and there draw a line: then measure thefe lines, and lay them down from A to E and B.

1

Next move the table to B, lay the index along the line AB, and turn the table about till you can fee the mark A, and fcrew faft the table; in which pofition alfo the needle will again point to the flower-de-luce, as it will do indeed at every station when the table is in the right pofition. Here turn the index about B till through the fights you fee the mark c; there draw a line, measure BC, and lay the distance upon that line after you have fet down the table at c. Turn it then again into its proper pofition, and in like manner find the next line CD. And fo on quite round by E to A again. Then the proof of the work will be the joining at A for if the work is all right, the laft direction EA on the ground, will pafs exactly through the point A on the paper; and the measured diftance will alfo reach exactly to a. If these do not coincide, or nearly fo, fome error has been committed, and the work must be examined over again.

PROBLEM VIII.

To Survey a Field with the Theodolite, &c.

1. From one Point or Station.

When all the angles can be feen from one point, as the angle E (firft fig. to laft prob.) place the inftrument at E, and turn it about till, through the fixed. fights, you fee the mark B, and there fix it. Then turn the moveable index about till the mark a is feen through the fights, and note the degrees cut on the instrument. Next turn the index fucceffively to E and D, noting the degrees cut off at each; which gives all the angles BCA, BCE, BCD. Laftly, measure the lines CB, CA, CE, CD; and enter the meafures in a fieldbook, or rather against the correfponding parts of a rough figure drawn by guefs to refemble the field.

2. From

2. From a Point within or without.

Plan the inftrument at o, (laft fig.) and turn it about till the fixed fights point to any object, as A; and there fcrew it faft. Then turn the moveable index round till the fights point fucceffively to the other points' E, D, C, B, noting the degrees cut off at each of them; which gives all the angles round the point o. Laftly, measure the distances OA, OB, oc, OD, OE, noting them down as before, and the work is done.

3. By going round the Field.

B.....

A

.....

E

D

By measuring round, either within or without the field, proceed thus. Having fet up marks at в, c, &c, near the corners as ufual, plant the inftrument at any point A, and turn it till the fixed index be in the direction AB, and there fcrew it faft: then turn the moveable index to the direction AF; and the degrees cut off will be the angle A. Measure the line AB, and plant the inftrument at B, and there in the fame manner obferve the angle A. Then measure BC, and obferve the angle Then measure the distance CD, and take the angle Then measure DE, and take the angle E. Then measure EF, and take the angle F. And lastly meafure the distance FA.

C.

D.

To prove the work; add all the inward angles A, B, C, &c, together, and when the work is right, their fum will be equal to twice as many right angles as the figure has fides, wanting 4 right angles. And when there is an angle, as F, that bends inwards, and you measure the external angle, which is lefs than two right angles, fubtract it from 4 right angles, or 360 degrees,

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degrees, to give the internal angle greater than a femicircle or 180 degrees.

Otherwife.

Inftead of obferving the internal angles, you may take the external angles, formed without the figure by producing the fides further out. And in this cafe, when the work is right, their fum altogether will be equal to 360 degrees, But when one of them, as F, runs inwards, fubtract it from the fum of the reft, to leave 360 degrees.

PROBLEM IX.

To Survey a Field with Crooked Hedges, &c.

With any of the inftruments measure the lengths and pofitions of imaginary lines running as near the fides of the field as you can; and in going along them measure the offsets in the manner before taught ; and you will have the plan on the paper in using the plain table, drawing the crooked hedges through the ends of the offsets; but in furveying with the theodolite, or other inftrument, fet down the measures properly in a field-book, or memorandum-book, and plan them after returning from the field, by laying down all the lines and angles.

So, in furveying the piece ABCDE, fet up marks a, b, c, d, dividing it into as few fides as may be. Then begin at any station a, and measure the lines ab, bc, cd, da, and take their pofitions, or the angles a, b, c, d; and in going along the lines meafure all the offsets, as at m, n, o, p, &c, along every station line. And this is done either within the field, or without, as may be moft convenient. When there are obftructions within, as wood, water, hills, &c; then measure without, as in the figure here below.

PROBLEM X.

To Survey a Field or any other Thing, by Two Stations.

This is performed by choofing two ftations, from whence all the marks and objects can be feen, then measuring the diftante between the stations, and at each station taking the angles formed by every object, from the ftation line or diftance.

The two stations may be taken either within the bounds, or in one of the fides, or in the direction of two of the objects, or quite at a diftance, and without the bounds of the objects, or part to be furveyed.

In this manner, not only grounds may be furveyed, without even entering them, but a map may be taken of the principal parts of a country, or the chief places

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