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fometimes fuch pieces are measured by finding a mean breadth, which is done by dividing the fum of the offsets by the number of them, accounting that for one where the boundary meets the station line, and the quotient is the mean breadth: but this last method is not very exact.

But in very large furveys, and where there are many fields, the best way of finding the contents of the whole is to make a rough plan of the whole, and divide it into feveral trapeziums and triangles, and find the area of each feparately, and add them together; then, to prove the work, divide the whole eftate into as few triangles or trapeziums as poffible, by drawing new lines in the plan: and if the contents found by this last method be equal to the contents found by the former method, the work is right; but if they differ, the work must be examined and recomputed till they nearly agree.

But the chief difficulty in cafting up the contents arises from the fides of the figure being curved, or of any other irregular shape; in which cafe fuch bounds of the figure muft be reduced to straight lines, in the following manner: make a fmall bow with a piece of horfehair, and whalebone, or cane, or any other elastic fubftance, which will keep the horsehair extended at full ftretch; then apply the horsehair to the crooked bounds of the figure, in fuch a manner, that those parts of the curve which are on one fide the hair may be equal to the parts of the curve on the other fide the hair ; then, by making two points, draw a straight line in the direction of the horfehair, which will be a straight fide to the figure, equal to the curve one. Do the fame by every curve fide of the figure; thus the figure may be reduced into a right-lined figure.

PROBLEM III.

TO TRANSFER A PLAN FROM ONE PAPER TO ANOTHER.

There are feveral methods of performing this; four of which I fhall mention:

First. Rub the back of the plan over with black lead powder, and then lay the black fide upon the fheet of paper on which the plan is to be copied, keeping it steady: then with a blunt point of a tracer, trace over all the lines in the plan, preffing the tracer fo that the black lead on the back of the paper may be transferred to the clean paper; then take off the plan, and you will fee all the marks on the clean paper in black lead, which must be traced over with a pen and ink, &c.

Secondly. The plan may also be transferred to another paper, by dividing both ends and fides of the plan into any convenient number of equal parts, connecting the correfponding points of divifion with lines; which will divide the whole plan into a number of squares, or parallelograms: then divide the paper upon which the plan is to be drawn into the fame number of fquares or parallelograms; next copy the parts contained in the fquares of the old plan, in the correfponding fquares of the new ones. (See figures 40 and 41.)

Thirdly. Another method is by the inftrument called a pentagraph, which will copy the plan in any fize required.

Fourthly. The best method of any is the following: fix the old plan on the front of a copying frame of glass, with the face uppermoft (which is a large fquare of the best window glafs, fet in a broad frame of wood, and constructed fo as to be raised up to any angle whatever), the clean paper on the face of the old plan being fixed to the frame by feveral pins; then the frame being raised up facing the window, by means of the light fhining through the paper, you will perceive every line of the plan through the clean paper, which is to be drawn thereon with a pencil: having copied that part which covers the glafs, the other part is to be brought over the glafs, and copied as before, and fo on throughout the whole.

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Then take them asunder, and trace the lines with pen and ink; and finish the piece, writing fuch names as are necesfary.

Thus the finest plan may be copied without the leaft injury..

The foregoing rules will be found fully fufficient to inftruct any ordinary capacity in all the practical parts of Menfuration and Surveying.I have avoided every thing that favours more of curiofity than real utility.

SECT. III.

OF SOLID MEASURE, MEASURING TIMBER, DIGGING, AND GAUGING.

Definitions.

1. Solids are fuch bodies as have length, breadth, and thickness.

2. A prifm is a folid body whofe ends are fimilar and equal plain figures, and its fides are parallelograms. It is called a triangular prifm when its ends are triangles (as fig. 1. in the folids); when its ends are fquares, a fquare prifm; when pentagons, a pentagonal prism, &c.

3. A cube is a square prism, having fix equal fquare fides perpendicular to each other. (Fig. 2.)

4. A parallelopipedon is a figure having fix rectangular fides; each two oppofite fides being equal, and parallel. (Fig. 3.)

5. A cylinder is a round prifm, having two equal circles for its ends. (Fig. 4.)

6. A pyramid is a figure that has a right-lined figure for its base, and each of its fides is a triangle, whose vertices meet in a point at the top, which is called the vertex of the pyramid, as A (fig. 5.) The pyramid takes its name from the figure of its bafe, like the prifm.

7. A cone is a round pyramid, having a circular bafe. (Fig. 6.)

8. A fphere is that folid body bounded by one continued convex surface, every part of which is equally distant from the centre. It may be supposed to be formed by the revolution of a femicircle about its diameter. (Fig. 7.)

9. The axis of any folid is a line drawn from the middle of one end to the middle of the oppofite end. Thus the axis of a pyramid is a line drawn from the top, or vertex, to the middle of the bafe; and the axis of a sphere is a line drawn through the centre. When the axis is perpendicular to the base, it is a right prifm, or pyramid; otherwise it is oblique.

10. The height or altitude of a folid is a line drawn from the vertex, or top, perpendicular to the bafe.

11. If the base of a prifm or pyramid be a regular figure, it is called a regular prifm or pyramid: but if the base be irregular, the prifm or pyramid is called irregular.

12. The segment of a pyramid is a part cut off the top by a plane, parallel to the base, as C E, (fig. 6.)

13. A fruftum, or trunk, is the part that remains after the segment is cut off, as E A, (fig. 6.)

14. A zone of a sphere is a part intercepted between two parallel lines.

15. The fegment of a sphere is a fegment lefs than a hemifphere, or half sphere; like a cone, whose base is the fame as the base of the fegment, and whofe vertex passes through the centre of the sphere.

16. A circular spindle is formed by the revolution of the fegment of a circle, about its chord, which remains fixed. (Fig. 8.)

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