Thus :

00

62

84 70

98

57

91

66

4710

ac

r p

4710 Content o 2 2 by this method, which is 10 perches too little.

51810

4

7) 462 2.07240 And this method is always errone40 ous, except when the offsets stand at equal distances from one another.

2.89600

5. But in larger pieces, and whole eftates, confifting of many fields, it is the common practice to make a rough plan of the whole, and from it compute the contents quite independent of the measures of the lines and angles that were taken in furveying. For then new lines are drawn in the fields in the plan, fo as to divide them into trapeziums and triangles, the bafes and perpendiculars of which are measured on the plan by means of the fcale from which it was drawn, and fo multiplied together for the contents. In this way the work is very expeditioufly done, and fufficiently correct; for fuch dimenfions are taken, as afford the most easy method of calculation; and, among a number of parts, thus taken and applied to a fcale, it is likely that fome of the parts will be taken a small matter too little, and others too great; fo that they will, upon the whole, in all probability, very nearly balance one another. After all the fields, and particular parts, are thus computed feparately, and added all together into one fum, calculate the whole estate independent of the fields, by dividing it into large and arbitrary triangles and trapeziums, and add these alfo

Nn 2

548

alfo together. Then if this fum be equal to the former, or nearly fo, the work is right; but if the fums have any confiderable difference, it is wrong, and they must be examined, and recomputed, till they nearly agree.

A fpecimen of dividing into one triangle, or one trapezium, which will do for most single fields, may be feen in the examples to the laft problem; and a fpecimen of dividing a large tract into feveral fuch trapeziums and triangles, in prob. vi of chapter 11 of Surveying, page 524, where a piece is fo divided, and its dimenfions taken and fet down; and again at prob. vi of Menfuration of Surfaces, where the contents of the fame piece are computed.

6. But the chief fecret in cafting up, confifts in finding the contents of pieces bounded by curved, or very irregular lines, or in reducing fuch crooked fides of fields or boundaries to straight lines, that shall inclofe the fame or equal area with thofe crooked fides, and fo obtain the area of the curved figure by means of the right-lined one, which will commonly be a trapezium. Now this reducing the crooked fides to ftraight ones, is very eafily and accurately performed thus: Apply the ftraight edge of a thin, clear piece of lanthorn-horn to the crooked line, which is to be reduced, in fuch a manner, that the fmall parts cut off from the crooked figure by it, may be equal to those which are taken in which equality of the parts included and excluded, you will presently be able to judge of very nicely by a little practice: then with a pencil draw a line by the ftraight edge of the horn. Do the fame by the other fides of the field or figure. So fhall you have a ftraight fided figure equal to the curved one; the content of which, being computed 'as before directed, will be the content of the curved figure propofed.

Or, inftead of the ftraight edge of the horn, a horse

hair

hair may be applied across the crooked fides in the fame manner; and the eafieft way of ufing the hair, is to ftring a small flender bow with it, either of wire, or cane, or whale-bone, or fuch like flender fpringy matter; for, the bow keeping it always ftretched, it can be easily and neatly applied with one hand, while the other is at liberty to make two marks by the fide of it, to draw the straight line by.

EXAMPLE.

Thus, let it be required to find the contents of the fame figure as in prob. 1x of the laft chapter, page 530, to a fcale of 4 chains to an inch.

A

A

B

Draw the four dotted ftraight lines AB, BC, CD, DA, cutting off equal quantities on both fides of them, which they do as near as the eye can judge: fo is the crooked figure reduced to an equivalent right-lined one of four fides ABCD. Then draw the diagonal BD, which by applying a proper fcale to it, measures 1256. Alfo the perpendicular, or neareft diftance, from A to this diagonal, measures 456; and the distance of c from it, is 428.

And thus the content of the trapezium, and confequently of the irregular figure, to which it is equal, is cafily found to be 5 acres, 2 roods, 8 perches.

PROBLEM III.

To Transfer a Plan to another Paper, &c. After the rough plan is completed, and a fair one is wanted; this may be done, either on paper or vellum, by any of the following methods.

Lay the rough plan upon the clean paper, and keep them always preffed flat and clofe together, by weights laid upon them. Then, with the point of a fine pin or pricker, prick through all the corners of the plan to be copied. Take them afunder, and connect the

pricked

1

pricked points on the clean paper, with lines; and it is done. This method is only to be practifed in plans of fuch figures as are finall and tolerably regular, or bounded by right lines.

Rub the back of the rough plan over with black lead powder; and lay the faid black part upon the clean paper, upon which the plan is to be copied, and in the proper pofition. Then with the blunt point of fome hard fubftance, as brafs, or fuch like, trace over the lines of the whole plan; preffing the tracer fo much as that the black lead under the lines may be transferred to the clean paper; after which take off the rough plan, and trace over the leaden marks with common ink, or with Indian ink, &c.-Or, instead of blacking the rough plan, you may keep constantly a blacked paper to lay between the plans.

THIRD METHOD.

Another way of copying plans, is by means of fquares. This is performed by dividing both ends and fides of the plan, which is to be copied, into any convenient number of equal parts, and connecting the correfponding points of divifion with lines; which will divide the plan into a number of fmall fquares. Then divide the paper, upon which the plan is to be copied, into the fame number of fquares, each equal to the former when the plan is to be copied of the fame fize, but greater or less than the others, in the proportion in which the plan is to be increased or diminished, when of a different fize. Laftly, copy into the clean fquares, the parts contained in the correfponding fquares, of the old plan; and you will have the copy either of the fame fize, or greater or lefs in any proportion.