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and a Ruler or Index with Sights. The Table is fixed, by a Ball and Socket, to a three-legged Staff for a Stand, on which it may be turned round, or faftened by a Screw.

Of Chains there are two Sorts, each divided into one hundred Links, for the Conveniency of fetting down the Links as Decimals of the Chain: That called Gunter's Chain is four Poles, or fixty-fix Feet, in Length; the other is but one Pole, that is, fixteen Feet and an Half, but consists of one hundred Links as the other.

A Protractor is an Inftrument of Brafs, Silver, or the like, with a femicircular Limb, divided into one hundred and eighty Degrees, fubtended by a Diameter, in which is a little Notch called the Center: Its Ufe is to lay down the Angles in plotting a Field.

To take the Dimenfions of a Field at one Station.

Place the Inftrument in any Station, as at O, from whence all the Angles may be feen; turn the Table about 'till the Needle ftands over the North and South Points of the Compafs, then screw the Inftrument faft, and direct the Sights to the firft Angle, A, to the right Hand of the North and South Line; obferve the Degrees and Minutes contained between 360 of the Table and the Index, which is 56°. 20′ : Direct the Sights, in the fame Manner, to B, and obferve the Degrees and Minutes that the Index now cuts on the Table, which is 95.40': In the fame Manner, turn the Index to C, and fo on to D, E, and F, and the feveral Angles will be as under:

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Chains and thirty Links, or 7.30; the Distance B 8.45; and the reft as in the following Table, ufually called a Field-Book:

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To protract or lay down the Work.

Draw any right Line, as NS, for the North and South Line, any Point of which, as O, affume for the Station; lay the Center of the Protractor on this Point, turn it 'till the Diameter of the Pro

E

F

N

A

S

B

tractor falls upon the North U and South Line, and prick off the Angle 50°. 20', the Angle 95° 40', and fo of the reft; then draw the Lines OA, OB, O C, OD, OE, and OF: Now from the Diagonal take 7.30 for the feven Chains and thirty Links, and fet them from to A; do the fame for the eight Chains and forty-five Links, and fet it from O to B; and fo of the reft: Laftly, draw the Lines A B, BC, CD, DE, and E F, which is the Plot or Plan of the Field.

To find the Number of Acres it contains.

Draw the right Lines F B, F C, and F D, which divides the Figure into four Triangles: Take F B in the Compaffes, and apply it to the diagonal Scale, which measures 11.96 for the Bafe of the Triangle F A B; then fet one Foot of the Compaffes in A, and extend the other fo as just to reach the Line F B without paffing it, which, being measured on the diagonal Scale, is 3.48 for the Perpendicular of the fame Triangle. The other Bafes and Perpendiculars, being measured, will be as follows, for the feveral Triangles:

Bafe.

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Multiply each Bafe by its Perpendicular, and cut off five Figures for Decimals in the Products: Add thofe Products together, and divide their Sum by 2, and the Integers in the Quotient are Acres; multiply the Fraction by 4, and the Integers in the Product are Roods; and multiply this laft Fraction by 40, and the Integers in the Product are fquare Poles or Perches:

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By which the Area appears to be twelve Acres, three Roods, and thirty-nine fquare Poles or Perches.

The Reason of cutting off five Figures in the Products is, because, the Chain being four Poles in Length, every fquare Chain contains fixteen fquare Poles, which is the tenth Part of an Acre; and, as each of the Numbers has two Decimals, there must be four cut off, according to the Rule in Multiplication of Decimals, Art. 42; and then the Integers in the Product are Tenths of an Acre, therefore cutting off one Place more reduces them to Acres.

But then, as we multiplied the Bafes and Perpendiculars together, the Products are double the Area of the Triangles, for which Reafon we divide their Sum by 2.

To

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view all the feveral Angles, which will be as follows:

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H

N

Then choose another Station in the Field, from whence all the Angles may be feen, as at 2, at which fet up a Staff for a Mark; direct the Sights of the Inftrument to that Mark, and obferve the Angle cut by the Ruler, which is 97°.55'; then measure the Distance of the two Stations, which is two Chains and thirty-two Links, or 2.32.

Carry the Inftrument to the fecond Station, and leave a Staff, or fome other visible Mark, at the firft Station; fet the Center of the Inftrument over the Place where the Staff stood at 2, and put the Sights to the Angle they were at from O to 2, that is, to 97°. 55'; then unfcrew the Table, keep the Index and Sights fixed, turn the Inftrument and Index 'till thro' the back Sight you fee the Mark at O 1, and then fcrew the Inftrument, which will then ftand in the fame Pofition as at

1.

Direct the Sights to the Angle I, the Angle obferved first at the first Station, and obferve the Degrees and Minutes cut by the Index; then direct the Sights to K and L, and fo on to the other Angles, and the Degrees and Minutes cut from a Station will be as follows:

I 345°

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To protract or lay down the Work.

Draw a Line at Pleasure for the North and South Line, on which affume any Point, as 1, for the first Station; lay the Center of the Protractor on this Point, and the Diameter on the Line NS; prick off the Angles, and draw the Lines O II, O IK, &c. to a convenient Length: Then finding, by the Field-Book, that the Angle to O2 is 97°55', lay down that Angle, and draw the Line 1, 2; take from the diagonal Scale 2.32, the Distance from 1 to 2, and lay from 1 to 2, which is the fecond Station: Lay the Protractor to the Point 2, and turn it about 'till the right Line drawn from 1 to 2 cuts the Angle 97°. 55'; then lay down the feveral Angles at O2, beginning with that which was firft taken, and proceeding 'till you have taken down all the Angles; draw the Lines O 2 K, &c. 'till they interfect the former Lines in the Points K, L, M, G, H, and I, which Interfections will reprefent the feveral Angles of the Field: Then join the feveral Angles, by the Lines GH, HI, IK, KL, L M, and M G, and you have the Plot of the Field; which may be divided, by Diagonals drawn from any Angle, as G, into four Triangles, whofe Bafes and Perpendiculars, being measured on the diagonal Scale, as in the laft Example, will be as under:

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Multiply the Bafe and Perpendicular of each Triangle, and cut off five Figures; then add the feveral Products, and divide their Sum by 2, as in the other Example,

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