The signification of the remarks.

Mr. J. D.'s part of Grange bounds, or is adjacent to the surveyed 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 person's 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.

1

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 townland 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 parts sur

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 d; 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,

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 determine exactly that point in the arc where cd cuts it: but if the angle be taken in two parts, as ce and ed; such chords may with safety be laid on 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.

PROB. 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.

Let a mark be fixed at any point in the ground, as at H, from whence all the angles can be seen; let the measurers 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 radii: the measures of the respective lines of the mearing, viz. AB, BC, CD, DE, &c. being placed in the third column of distances, will complete the field-book. Thus,

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 side scale with

PROB. III.

To take a survey of the chain only, when all the angles cannot be seen from one point within it.

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 3 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 distances 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

3 sides of each; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter.

PROB. IV.

How to take any inaccessible distance by the chain only.

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. 2. theo. 3. sect. 1. and theo. 2. sect. 1.) the triangles EFD BFA, are mutually equi-angular.

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