The Area is four Acres, two Roods, and thirteen Poles.

To furvey a Field by going round it at feveral Stations.

Choose any Place for the first Station, as at O I, place theInftrument there, by the Needle, North and South, and fcrew it fast; then choose a B fecondStation, as at 2, and there set up a vifible Mark; turn the In

dex of your f

Inftrument about, till thro'

the Sights you

Ag

fee the Mark at O 2, and it will cut 10°. 30' N. E. for the Pofition of the Line you are about to measure, which enter in the middle Column of your Field-Book, as you fee below.

10°. 30

30

Offsets.

N. E.

ΟΙ

.52

3.51

.61

4.78

.46

279°.45'

N. W.

© 2

2.31

5.32

.35 .63

191°. 50

S. W.

Next lay the Chain from 1 in a right Line towards 2, the fecond Station; which being done, let it lie 'till you have entered the Obfervations in that Chain's Length, that is, measure the Distance from 1 to a, the Hedge or Ditch, fifty-two Links; which you muft enter in the outfide Column of your Field-Book, on the right Hand, the Hedge being on the right Hand of the Courfe; having entered O 1, for the firft Station, in the middle Column, against it put .52, the Offset, fignifying, that, at the Inftrument, the Hedge at the right Hand is fifty-two Links from the Chain: Then measuring on towards O 2, at the Distance 3.51 you come directly oppofite to the Angle F, and the Distance or Offset from the Chain to F is .61; therefore enter 3.51 in the middle Column of your FieldBook, and .61 in the right-hand Column: Then_measuring on to 2, you will find it to be 4.78, and the Offset .46; both which enter in your Field-Book, as before: So is your Work relating to the first Station finished.

O 3

5.21

Then bring your Inftrument to 2, place the Center directly over where the Staff ftood, and fend a Staff forward to

3; unscrew the Inftrument, lay the Index on 10°. 30 ́, the Angle cut from 1 to 2, and turn the Inftrument, with the Index in that Pofition, 'till thro' the back Sight you see the Staff left at ; fcrew the Inftrument faft, then turn the Index about 'till thro' the Sights you fee the Staff at O3, and it will cut 279°.45', which enter in your FieldBook: Then obferve, that at 2 the Offset to c is .35; and in measuring towards 3, at 2.31 Diftance from 2, the Offset is .63; and the whole Distance from 2 to 3 is 5.32, where the Offset is .46; all which enter in your FieldBook, as before.

In the fame Manner carry the Inftrument to proceed in all Refpects as at O 2, and the Angle to

be found 191°. 50': Then measure the Distance from 3 to 4, and alfo from O 4 to, together with the several Offsets; place them in the Field-Book, which will then stand as in the foregoing Page.

To protract the Work.

Draw any Line at Pleasure for the North and South Line, on which affume the first Station I, and with the Protractor lay down the Angle 10°. 30'; draw the Line

I, 1 to a; take 3.51 and Offset .61 from i to F; 2; take .46, the Offset at 2, and fet from 2 to b; the Offsets are to be set off perpendicular to the ftationary Line: Then, lay the Protractor on 2, with the Limb on the contrary Side of the Line; and, as the Degrees cut were 279°.45', take 279° 45′ from 360°, the Remainder is 80°. 15', thro' which Angle draw the Line 2, 3; then from the Scale lay 2.31 from

2, and fet the Offset .52 from fet from 1 to i, where fet off the take 4.78 and fet from 1 to

2 to k, where fet off .35 the Offset from k to D; then lay 5.32 from 2 to O 3, and fet off .46 from © 3 to d.

3 to 1,

Thro' 3 draw a Meridian-Line, as n s, parallel to the former Meridian-Line NS, by Prob. 6; lay the Center of the Protractor on 3, and, as the Degrees cut on the Inftrument were 191°. 50', mark off 11.50', the Excess above 180°, for the Angle that the Line 3, 4 is to make with the pricked Meridian-Line, and draw the Line 3,4, on which lay 2.78 from the Offset .95; and lay 5.21 from O 3 to 4, the Offset .54. From 4 draw a Line to fet 2.06 to m, and the Offsets as in the Table. ing down 5.44, it will reach from 4 to .42 from i to h; and draw Lines from the from F to b, c. which will be the true Representation of

the Field.

To find the Number of Acres,

where fet off where fet off 1, on which Lastly, laywhere fet off Offset a to F,

1,

At II obferve, I a is .52, and 1 h .42, which are Sides of the Parallelogram 1, a, G, h, for in this Cafe the Error is infenfible: Multiply the two Numbers together, and cut off five Places for Decimals in the Product, thefe will be the Decimals of an Acre; if there are not five Places of Figures in the Product, prefix a Cypher to make five Places: Then, for the Parallelogram 1, a, i, F, add .52, the

Width at one End, to .61 the Offset at i, the Width at the other End; the Half of that Sum is the mean Width, which, being multiplied into 3.51, the Length, gives the Area, remembering to cut off five Places for Decimals in the Product.

In the fame Manner may the Areas of all the Parallelograms be computed, remembering to fupply the Places with Cyphers where they are deficient.

Draw a Diagonal from 2 to 4, to divide the Part of the Field within the ftationary Lines into two Triangles; then set one Foot of the Compaffes in O 1, and extend the other to the Diagonal fo as not to pafs it; this being measured on the Scale will be 3.37 for the Perpendicular of the Triangle O 4, O 2, O 1; then fetting one Foot in 3, and extending the other to the Diagonal in the fame Manner, it gives 3.66 for the Perpendicular of the Triangle 4, 3,2; and the Diagonal is 7.48 for the Base of each Triangle.

Kk 2

7.48

The Area is four Acres and four Poles.

Surveying being by much the beft learned by Practice, I have been the fhorter in this Article: And, the Practice of Surveying requiring divers Inftruments, I would recommend my Readers, who may have Occafion to purchase any, to Meffrs. Heath and Wing, Mathematical Inftrument Makers, near Exeter-Change, in the Strand; where all Sorts of Mathematical and Philofophical Inftruments are made, to a great Degree of Exactnefs and Perfection.

The Conftruction of the Line of Chords, Sines, Tangents, and Secants.

E

Of the Line of Chords.

VERY Circle being divided into 360 Degrees, each Quadrant contains 90 Degrees: A Line of Chords, therefore, is the Chord of 90 Degrees, or a Quadrant to any Radius. The Way to project a Line of Chords is,

Draw