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Some Necessary Directions concerning Surveys in

general.

If you have a large quantity of ground to survey, which consists of many fields or holdings, and that it be required to map and give the respective contents of the same, it is best to make a survey of the whole first, and to be satisfied that it is truly taken, as well as to find its content; and as you go round the land, to make a note on the side of your field-book at every station where the boundary of any particular field or holding intersects or meets the surround; then proceed from any one of those stations, and in your field-book, say, “ proceed from such a station," and when you have gone round that field or division, insert the station you close at, and 'so through the whole : a little practice can only render this sufficiently familiar, and the method of protraction must be evident from the field-notes. When the whole is protracted, and you are satisfied of the close of the particular divisions, cast up each severally, and if the sum of their contents be equal to the content of the whole first found, you may safely conclude that all is right.

The protraction being thus finished and cast up, transfer it on clean paper, vellum, or parchment, as before; be careful to draw your lines with a fine pen, • write on it the names of the circumjacent lands, and set No. 1, 2, 3, 4, &c. in every particular field or division ; let every tenant's particular holding be dis

finely along the boundaries; let all the roads, rivulets, rivers, bogs, ponds, houses, castles, churches, beacons, (or whatever else may be remarkable) on the ground be distinguished on the map. Write the title of the map in a neat compartment either drawn, or done from a good copper-plate graving, with the gentleman's arms.

Prick off one of your parallels with the map, and on it make a mariner's compass, and draw a flower-de-luce to the north, and this will represent the magnetical north ; after which set off the variation, which express in figures, and through the centre of the compass, let a true meridian line be drawn of about 3 inches long, by which write True Meridian. Let a scale be drawn: or it is sufficient to express the number of perches to an inch, the map was laid down by. Draw a reference table of three, or if occasion be, of four or more columns : in the first insert the number of the field or holding: in the next its name, and by whom occupied : in the third the quantity of acres, roods, and perches it contains : - if you have unprofitable land, as bog or mountain, let the quantity be inserted in the fourth column; and if it be requird, you may make another column for statute measure, and then the map is completed.

OF THE DIVISION OF LAND.

SEC. VII.

The method of dividing land, or of taking off or in

closing any given quantity.

PROB. I.

Given the area, an angle, and a side, in any plane triangle; to find the other sides and angles.

Divide double the area by the given side; the quotient will be the perpendicular thereon, from the opposite angle; and by trigonometry the rest will be found.

[blocks in formation]

Suppose the area of the triangular field ABC to be 4A. 3R. 38P. the side AB. 57 perches, and the angle

A. R. P.

P. 4.3.38=798

2

57)1596(28=CD.

114

456 456

000

As Sine of zB: CD::R: BC=48.81
As Radius : BC : CS : B: BD=39.99
As AD: DC :: R: tang. 2 A=58° 43'
As Sine of LA: DC::R: AC-32.76

[blocks in formation]

Suppose AB 11. 50 chains; angle A 46°, and the

A.R.P. area 9.0.32; to find the sides.

Answer, AC=22.24. BC=16.48.

EXAMPLE III.

Given the area 10 acres, base AB 384 yards ; and the angle B, 63°; to find the sides and other angles.

Answer, BC=278 AC 8366.5; <C=710.36' and LA=43° 24'.

PROB. II.

To divide a triangle into any number of parts, hav. ing any assigned proportion to each other, by right lines drawn from one of its angles to the opposite side.

Divide the base in the same proportion with the assigned parts; from these divisions draw lines to the proposed angle; and the thing required is done.

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Given the area of the triangle ABC = 12 and the 'base AB 18 chains; to divide it into two parts, one of which shall be double the other by a line drawn

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