To plot the fame proceed as in the last example; and for the area you have 4 triangles to find the content of.

1. Let fall a perpendicular from B to the diagonal A C, and measure it on your fcale, which multiply by AC and you have the content of that triangle.

2. Let fall a perpendicular from C to the diagonal A D, and meafure it on your fcale, which multiply by AD, and the product is the content of the fecond triangle.

3. Let fall a perpendicular from E on the diagonal A D, and meafure it on your fcale, which multiply by AD, and the product is the content of the third triangle.

4. Laftly let fall a perpendicular from F to the diagonal A E, and meafure it on your feale, which multiply by A E, and the product is the content of the fourth triangle.

5. Add the contents of thefe four triangles together, and the fum will be the content of the whole field.

PROBLEM V.

To take the plot and content of the former fix fided field at one station in any place thereof from whence you may fee all the angles, as in the following example.

Going into the field choose fome convenient place therein, as at O, and let marks be fet up at every angle; then take hold of one end of the chain and stand in O, and caufe an affiftant to take hold of the other end, let him go towards the angle A, and when you fee him exactly in a ftraight line with the angle A, bid him put down a peg at the end of the chain and leave it there at G; then cause your affiftant to go towards the angle B, and when you fee him in a straight line with the angle B, bid him put down another peg at the end of the chain and leave it there at H; then cause him to go towards the angle C, and put down a peg at the end of the chain at I; thus do for all the other angles. And when you are come to M and put down your laft peg, measure from it, to your first peg at G, which we will fuppofe 93

links;

links; then measure from your peg at G to your peg at H and fuppofe it to be 91 links; thus do for all the other pegs, and put them down as in the figure. Laftly, meafure the line OA and fuppofe it to be 4.30; then measure the line OB and fuppofe it 4.46, then the line and fuppofe it 4.48, and fo for the lines OD, O E, and OF, and then your work is done in the field; the next thing to be done is to plot it, or make a plan of it, which is done thus.

First take the length of 1 chain in your compaffes from any fcale of equal parts, and defcribe a circle; then from the same fcale take 91 links and lay it from G to H and take 1.07 from the fame fcale and lay it from H to Is and fo for I K 94 links, KL 1.20, LM .95, and MG .93. Then draw lines from at random O through thefe feveral points G, H, I, K, L, M ; and from the fame fcale of equal parts take 4.30 in your compaffes and lay it from to A; then take 4.46 and lay it from to B; do the fame for the other lines O C, O D, O E, OF; then draw the boundary lines A B, B C, D E, EF, FA, and thus you have the true figure of your field.

To find the content of this furvey, obferve the rules already laid down; viz. find the content of each fingle triangle (being here 6) and add their contents together into one fum, and that will be the content of the whole field..

PRO

1.64

PROBLEM VI.

To take the plan and content of a field at one ftation in any angle thereof from whence the other angles may be feen, without measuring the diagonals.

EXAMPLE. Let A, B, C, D, E, F, G, be the field, and F the angle at which you would take your obfervations.

1/53

275

3.65 H

1. Let an affiftant take the chain and go towards the angle G while you stand with the other end of the chain in the angle F; bid him put down a peg at the end of the chain at H, and leave it there.

2. Then

2. Then caufe him to go towards the angle A, and when you see him in a straight line with A, bid him put down another peg at I, and leave it there alfo.

3. Caufe him to go towards the angle B, and when you fee him in a straight line with B, bid him put down a peg at the end of the chain at K; proceed in this manner for the angles C, D, and E.

4. Then go to the peg at H and meafure to the peg at I which fuppofe 34 links. 5. Then meafure from H to K which fuppofe 68 links.

6. Measure from H to L which fuppofe 100 links, or I chain.

7. Meafure from H to M which is 125 links. 8. Meafure from H to N which is 153 links. 9. Measure round the field, putting down the measure of each particular fide, and your work is done in the field.

To plan thefe obfervations.

1. Draw the line G F at random, and from any fcale of equal parts take 100 links, or I chain, fet one foot in F and defcribe an arch; then take 34 from your fcale and lay it from H to I on the arch; and take 68 and lay it from H to K on the arch; alfo, take ico and lay it from H to L; and 125 and lay it from H to M; and take 153 and lay it from H to N; draw the lines FA, FB, FC, &c. thro' the points I, K, L, &c. at random.

2. From the fame fcale of equal parts take 3.65 and lay it from F to G; and take 1.64 in

your