Thefe fix Triangles being measured severally, according to the direEtions before given, the Contents of all of them added together into one Sum, will give you the Content of the whole Piece in Acres, Roods, and Perches,

14

tent of

Which is the Content of the whole Field.

But for an Abbreviation of this Work, you need not to find the Conevery fingle Triangle, but of every Trapezia or Four-fided Figure, as is taught in the Fourth Problem next before going; for the Figure is as well divided into Trapezias as into Triangles, namely, into the Three Trapezias ABCD, A'DEF, and AFGH; and fo by this means you will abbreviate half your work; for if you measure the Three Trapezias feverally, you fhall find

SA DE

A. R. P.

2 3 28

The Trapezia ADEF Sto contain 4

AFGH

The Sum

I 13

4 I 13

II 2 14

Note, That of what Number of Sides your Figure confifts of, the Number of Triangles into which it will be reduced, will (always) be less by Two than the Number of Sides: As in this Figure; the Number of Sides are Eight, and the Triangles are but Six; two less.

And

And thus have I done with the Chain, as to the defcription of it, and how to caft up any Figure or Piece of Land, Regular or Irregular, meafured thereby, in Acres, Roods, and Perches: It refteth now, that I Thew you how to make use of it in the Field, in measuring of any Irregular Piece of Ground; and that shall be the Work of this next Paragraph..

VI. How to take the true Plot of any Irregular Field of many Sides and Angles, by the forementioned Chain only, without any Graduated Mathematical Inftrument; and to make a Plot of the fame upon Paper or Velum.

ET ABCDEFGHIK L, be an Irregular Field to be meafured as aforefaid.

When you first enter the Field, caufe Beacons or other Vifible Marks to be set up near the principal Angles or Corners of the Field, as those at M, N, O, and P.

Secondly, Confider the beft corner to begin at (tho any will serve) as I make choice of that Mark at O.

Thirdly, Take out your Chain, and holding one end at the Beacon at O, measure out 2 Chains (or more or lefs, as you fee occafion) from the Beacon at O towards the Beacon at N, and at the end of the 2 Chains fet up a small Bow or Stick at *. Then again, from your Beacon at O measure 2 Chains more in a right line towards P, and there up another small Bow or Mark as at *. And then measure with your Chain the diftance between your two Marks *and*, which here is 2 Chains 65 Links.

fet

Fourthly, Prepare a Book, or Sheet of Paper, Ruled as in the Margent, to fet down your Measures as you go along, but firft at the top of it make a Triangle anfwerable to that which you measured out in the Field, and fer fuch Numbers to it as you there measured, as 2 Chains from to both ways, and 2 Chains 65 Links from * to *.

G

This

This done, go into the Field to your Beacon at O, and mcafure the distance of it from the hedge on your left hand, finding it to be 20 Links of your Chain, which fet down on the left hand Column of against Ch. co L, because the Hedge was on your left hand.

2.65

A

2.00

your Book,

Then with your Chain meafure from the Beacon at O, towards that at P, in a right line, and as you go along, at the end of C. 40 L. you find a Break or Bend in the Hedge, diftant from your Chain 70 L. Set the 1 C. 40 Links in the middle Column, and the 70 L. by it; then going on farther, at the end of 3 C. 40 L. you come against another Break or Bow Sets off Ch. L. Sets off in the Hedge, diftant from your Chain

Line 50 Links, both which fet down in your Book: And going on farther towards P, at the end of 6 C. 50 Links, I find another Break or Bow diftant from my Chain-Line 90 Links, both which fet down, and measure on to your Beacon at P, which will terminate at 7 C. and 20 L. which fet down, and because the Beacon at P is 40 Links diftant from the Hedge, fet 40 Links by the 7 C. 20 L: and draw a Line cross your Book, to fig nify that you have done with that fide of the Field,

Then in your Book under Ch. L. write ooo; and because your Beacon at P is diftant. from the Hedge G H 70 L. fet that down against o co, and go on and measure towards the Beacon at M, and when you have measured 2 C. 70 L. you come to touch the Bow in the Hedge at F, wherefore fet down 2 C. 70 L. and against it write Touch. Then measuring on to your Beacon at M, you find the length to be 5 Ch. 50 L. which fer down, and by it 30 L. which is the diftance of the Beacon M from the Hedge. Thus having finished this fide of the Field, draw a Line crofs your Book, as before.

And in this manner muft you deal with the other two fides, i N and NO, till you come where you firft began, And this way for measuring of any irregular piece of Ground, is as exact as is poffible to be performed by the beft Graduated Inftrument that can be made.

And

And thus having fhewed you how to measure in the Field, and take account thereof in your Book, it refteth now to fhew you how to lay the Plot or Figure of this Field down upon Paper or Velum, in order to the finding of the Content or Quantity of it in Acres, Roods, and Perches.

VII. How to lay down upon Paper or Parchment any Piece of Ground taken by the Chain as before, in order to finding the Content or Quantity thereof.

FOR

OR the performance of this Work, you must provide for your use a Pair of very fine-pointed Compaffes, and alfo a Ruler with feveral Scales of Equal Parts, fuchas is mentioned in the next Chapter, with a figure thereof. This Plot here defcribed, is laid down by a Scale, that half an Inch is equal in length to one whole Chain of Four Pole; and the half Inch in the Scale is divided by Diagonals into 100 parts, anfwerable to the 100 Links into which your Chain is divided. Being thus provided of Scales and Compaffes, you may begin your Plot in this manner.

1. Upon a fheet of Paper draw a right line at pleasure, as the line PO; towards one end thereof, as at the Station or Beacon by O, make a Mark, as O.

2. With your Compaffes, out of your Scale take 2 Chains, (which in this Plot is one Inch) and fetting one foot of the Compaffes in O, the other will reach to the Point, upon the line OP, and one foot of the Compaffes ftill refting in the point , with the other describe the obfcure Arch x x. Then take out of your Scale 2 Ch. 65 L. (which was the distance you measured from *to*) and setting one foot of that diftance upon the Point *, in the Line OP, with the other defcribe another obfcute Arch z z, croffing the former in the Point *, which is upon the line ON; and through the Point draw another right line *N at length.

3. These two Lines being drawn, repair to your) Note-Book; and therein finding your Chain-Line OF to be 7 Chains 20 Links, take 7 C 20 L. from your Scale, and fet them from Oto P. Alfo finding by your Book, that the Chain-Line O N did contain & C. 90 L. take that alfo out of your Scale, and fet it upon the Line from Oto N; then the Chain-Line PM being 5 C. 50 L. take them out of your Scale, and fetting one foot of the Compaffes in P, with the other describe an obfcure Arch ss; and the Chain-Line M N being 6 C. 50 L. take them out of your Scale alfo, and fetting one foot of the Compaffes in N, with the other foot defcribe the obfcure Arch v v, croffing the former in the ftation point by M, through which Point draw the right lines P M and N M at length: And thus have you drawn upon Paper the Quadrilateral Figure MNOP, of the fame Length and with the fame Angles as you meafured them with your Chain in the Field.

I

4. Having gone thus far, lay your Note-Book before you; and feeing that at your beginning at O, your Beacon at O did ftand 20 L. diftant from the Hedge, take zo L. out of your Scale, and set them from Oto o; alfo at 1 C. 40 L. ata, the bow of the Hedge was distant from the Chain-Line 76 L. take first 1 C. 40 L. and fet them from O to a, and the 70 L. from a to B, and draw the line A B; Then take 3 C. 40 L. and set them from O to b, and 50 L. from b to C, and draw the line BC. Then take 6 C. 50 L. and fet them from O to c, and 90 L. from c to D, and draw the line CD. Then at 7 C. 20 L. which is at the

G 2

Beacon

Beacon P, fet 49 Links to the Hedge, and through that Point draw the Line DE: So is this fide of your Field finished.

5. Begin again at the Beacon by P, where you find by your Book, that the Beacon was diftant from the Hedge 70 L. fet 70 L. from to E. Then at 2 C. 70 L. you find that your Chain-Line did touch the Hedge; wherefore take 2 C. 70 L. from your Scale, and fet them from Pro F (or d) and draw the line E F; then your next length 5 C. 50 L. will reach from P to M, where the Beacon was 30 L. from the Hedge, fet 30 L from to the Hedge, and through that point draw the line F G. And thus have you finished your fecond fide: And in the fame manner you must deal with the other two fides; and in fo doing you fhall have compleated your Work, and have the exact Draught of your Field upon a fheet of Paper, which you may caft up into Acres, Roods, and Perches, by the Directions given in the preceding Third Paragraph.

And if you measure the fmall Triangles, and other four-fided Figures which are without the Chain-Lines, by themselves, and afterwards the Quadrilateral Figure M NOP, by it felf, (which is the better way) you will find this Field to contain 4 Acres, 2 Roods, and 35 Perches.

CHA P. V.

Wherein is fhewed how to take all manner of Heights and Distances; and to measure all manner of Land, of what kind foever, Inftrumentally.

N the foregoing Chapter you are taught how to take Heights and Diftances, and alfo to measure Land Mechanically, whereby any perfon may very well (with more labour) perform many Geometrical Conclufions by flight and common Tools ufed by Mechanick Artificers, as by Squares, Foynt-Rules, Rods, &c. But in this Chapter I fhall fhew more Artificially how to perform the forementioned by Graduated Instruments : And altho I have handled this Subject at large in my Compleat Surveyor, yet I will here give a fufficient and exact way to do the like by an Inftrument both portable and exact, not there mentioned; namely, a Semicircle, with its Appurtenances.

A

A. Defcription of the Semicircle.

Semicircle in Geometry is thus defined, A Semicircle is the one half of a Circle cut off by the Diameter, and is contained under a right Line, which is the Diameter; and an Arch or crooked Line, which is called fometimes the Circumference, Perifery, or Limb.

The Semicircle which we here intend to defcribe and fhew the use of, is usually made in Brafs, the Diameter whereof may contain in length about 10 Inches, the Semidiameter half as much; the Diameter and Limb are either of them about an Inch in breadth : The Limb of this Semicircle is divided into 180 equal parts, called Degrees, and every of thofe Degrees is ufually divided into fmaller equal parts, according to the bignefs of the Instrument, (ufually into four) fois every fmall divifion or part, 15 Minutes. It is fometimes divided by Diagonals, fo that you may (tho

the