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How to take a survey by the CHAIN only.
PROBLEM I.

To survey a piece of ground by going round it, and the method of taking

the angles of the field by the chain only.
PL. 6, fig. 6.

Let ABCDEFG be a piece of ground to be surveyed: beginning at the point A, let one chain be laid in a direct line from A towards G, where let a peg be left, as at c ; and again the like distance from A in a direct line towards B, where another peg is also to be left, as at d'; let the distance from d to c be measured, and placed in the field-book in the second column under the denomination of angles, in a line with station No. 1; and in the same line, under the title of distances in the third column, let the measure of the line AB in chains and links be inserted. Being now arrived at B, let one chain be laid in a direct line from B towards A, where let a peg be left, as at f, and again the like distance from B in a direct line towards C, where let also another peg be left, as at e ; the distance from e to fis to be inserted in the field-book, in the second column, under angles, in a line with station No. 2; and in the same line, under the title of distances in the third column, let the measure of the line BC, in chains and links, be inserted : after the same manner we may proceed from C to D, and thence to E; but because the angle at E, viz. FED, is an external angle, after having laid one chain from E to h, and to g, the distance from g to h is measured and inserted in the column of angles, in a line with station No. 5, and on the side of the field-book against that station we make an asterisk, thus *, or any other mark, to signify that to be an external angle, or one measured out of the ground. Proceed we then as before from E to F, to G, and thence to A, measuring the angles and distances, and placing them as before in the field-book opposite to their respective stations: so will the field-book be completed in the manner following.

N. B.-After this manner the angles for inaccessible distances may be taken, and the method of constructing or laying them down, as well as the construction of the map, from the following field-notes, must be obvious from the method of taking them.

The form of the field-book, with the title. A Field-Book of part of the land of Grange, in the parish of Portmarnock, barony of Coolock, and county of Dublin;

being part of the estate of L. P., Esq., let to C. D., farmer. Surveyed January 30, 1782.

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Mr. J. D's part of Grange bounds or is adjacent to the sur-w veyed land from the first to the third station; Mr. L. P's part of Portmarnock bounds it from the third to the fourth station; the strand then is the boundary from thence to the sixth; , and from the sixth to the first station, the widow J. G.'s part of Grange is the boundary.

It is absolutely necessary to insert the persons' names, and town-lands, strands, rivers, bogs, rivulets, &c. which bound or circumscribe the land which is surveyed, for these must be expressed in the map.

In a survey of a town-land, or estate, it is sufficient to mention only the circumjacent town-lands, without the occupiers' names: but when a part only of a town-land is surveyed, then it is necessary to insert the person or persons' names who hold any particular parcel or parcels of such town-land as bound the part surveyed.

When an angle is very obtuse, as most in our present figure are, viz. the angles at A, B, C, E, and G, it will be best to lay a chain from the angular point, as at A, on each of the containing sides to c and to do; and any where nearly in the middle of the angle, as at e : measuring the distances ce and ed; and these may be placed for the angle in the field-book. Thus,

No. Sta. Angle.

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For when an angle is very obtuse, the chord line, as cd, will be nearly equal to the radii Ac and Ad ; so if the arc ced be swept, and the chord line cd be laid on it, it will be difficult to deter

mine exactly that point in the arc where cd cuts it: but if the angle be taken in two parts, as ce and ed, the arc, and the angle thence, may be truly determined and constructed.

After the same manner any piece of ground may be surveyed by a two-pole chain.

PROBLEM II.

To take a survey of a piece of ground from any point within it, from whence all the angles can be seen, by the chain only.

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Let a mark be fixed at any point in the ground, as at H, from whence all the angles can be seen; let the measures of the lines HA, HB, HC, &c. be taken to every angle of the field from the point H ; and let those be placed opposite to No. 1, 2, 3, 4, &c. in the second column of the radii: the measures of the respective lines of the mering, viz. AB, BC, CD, DE, &c. being placed in the third column of distances, will complete the field-book. Thus:

Radii. | Distance.

Remarks. No. ch. l. ch. l. 1 20. 00 17. 65

2 21. 72 18. 50

3 21. 74 28. 00

4 25. 34 20. 00

5 17. 20 14. 83

6 29. 62 19. 41

7 |, 21. 20 24. 53

Close at the first station.

If any line of the field be inaccessible, as suppose CD to be, then by way of proof that the distance CD is true, let the measure of the angle CHD be taken by the line oo, with the chain: if this angle corresponds with its containing sides, the length of the line DC is truly obtained, and the whole work is truly taken.

Note.—That in setting off an angle, it is necessary to use the largest scale of equal parts, viz. that of the inch, which is diagonally divided into 100 parts, in order that the angle should be accurately laid down; or if two inches were thus divided for angles, it would be the more exact; for it is by no means necessary that the angles should be laid from the said scale with the stationary distances.

PROBLEM III.

To take a survey by the chain only, when all the angles cannot be seen from one point within. PL. 6. fig. 7.

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Let the ground to be surveyed be represented by 1, 2, 3, 4, &c. Since all the angles cannot be seen from one point, let us assume three points, as A, B, C, from whence they may be seen; at each of which let a mark be put, and the respective sides of the triangle be measured and set down in the field-book; let the distance from A to 1, and from B to 1, be measured, and these will determine the point 1; let the other lines which flow from A, B, C, as well as the circuit of the ground, be then measured as the figure directs; and thence the map may be easily constructed.

There are other methods which may be used; as dividing the ground into triangles, and measuring the three sides of each; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter.

PROBLEM IV.
How to take any inaccessible distance by the chain only.
PL. 8. fig. 8.

Suppose AB to be the breadth of a river, or any other inaccessible distance, which may be required.

Let a staff or any other object be set at B, draw yourself backward to any convenient distance C, so that B may cover A ; from B, lay off any other distance by the river's side to E, and complete the parallelogram EBCD: stand at D, and cause a mark to be set at F, in the direction of A ; measure the distance in links from E to F, and FB will be also given. Wherefore EF: ED: ; FB : AB. Since it is plain (from part 1, theo. 3, sect. 4, and theo. 2, sect. 4) the triangles EFD and BFA are mutually equiangular.

If part of the chain be drawn from B to C, and the other part from B to E ; and if the ends at E and C be kept fast, it will be easy to turn the chain over to D, so as to complete a parallelogram; by reckoning off the same number of links you had in BC, from E to D, and pulling each part straight.

THE CIRCUMFERENTOR.

THIs instrument is composed of a brass circular box, about five or six inches in diameter; within which is a brass ring, divided on the top into 360 degrees, and numbered 10, 20, 30, &c. to 360; in the centre of the box is fixed a steel pin finely pointed, called a centre-pin, on which is placed a needle touched by a loadstone, which always retains the same situation; that is, it always points to the north and south points of the horizon nearly, when the instrument is horizontal, and the needle at rest. The box is covered with a glass lid in a brass rim, to prevent the needle being disturbed by wind or rain at the time of surveying: there is also a brass lid or cover, which is laid over the former to preserve the glass in carrying the instrument. This box is fixed by screws to a brass index or ruler of about 14 or 15 inches in length, to the ends whereof are fixed brass sights which are screwed to the index and stand perpendicular thereto : in each sight is a large and a small aperture or slit, one over the other; but these are changed, that is, if the large aperture be uppermost in the one sight, it will be lowest in the other, and so of the small ones: therefore the small aperture in one is opposite to the large one in the other, in the middle of which last there is placed a horse-hair or fine silk thread. The instrument is then fixed on a ball and socket, by the help of which and a screw you can readily fix it horizontally in any given direction, the socket being fixed on the head of a threelegged staff, whose legs, when extended, support the instrument while it is used.

To take field-notes by the Circumferentor.
PL. 6. fig. 6.

Let your instrument be fixed at any angle as A, your first station; and let a person stand at the next angle B, or cause a staff with a white sheet to be set there perpendicularly for an object to take your view to: then having placed your instrument horizontally (which is easily done by turning the box so that the ends of the needle may be equidistant from its bottom, and it traverses or plays freely) turn the flower-de-luce, or north part of the box, to your eye, and looking through the small aperture turn the index about till you cut the person or object in the next angle B with the horse-hair or thread of the opposite sight; the degrees o cut by the south end of the

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