Firft. Rub the back of the plan over with black lead powder, and then lay the black fide upon the sheet 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 fquares, 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 corresponding 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 glass, 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 glass, the other part is to be brought over the glass, and copied as before, and so on throughout the whole.

Then

and

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

Thus the finest plan may be copied without the least 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 prism is a folid body whose 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 prism; when pentagons, a pentagonal prism, &c.

3. A cube is a fquare 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.)

PROBLEM X.

TO FIND THE SUPERFICIAL CONTENT OF A BOARD OR

PLANK.

RULE. Multiply the length by the mean breadth.

Note. When the board is tapering, add the breadths of the two ends together, and take half the fum for the mean breadth.

EXAMPLE I. What is the fuperficial content of a board, whose length is 20 feet 3 inches, and mean breadth 10 inches?

When the board does not run regularly tapering, but is broader in fome parts than others; take feveral breadths and add them together, and divide the fum by the number of them, and the quotient will be the mean breadth.

PROBLEM XI.

TO FIND THE SOLID CONTENT OF SQUARE OR FOUR

SIDED TIMBER.

RULE. Multiply the mean breadth by the mean thickness, and that product by the length; and the last product will be the folid content.

Note. If the timber taper regularly from one end to the other, the mean breadth and thickness is found either by measuring

.VOL, I.

3 c

fures down from a scale, on the lines on the paper, taking offsets with the staff, to all bendings and windings in the ftreets, and to all remarkable objects; then take another flation in one of the foregoing lines, and repeat the process.

Thus, (fig. 6.) having chofen A for the first station, draw two lines in the direction of the two streets meeting there; and measure A B, marking the street on the left, and lay the fame measure down on the plan: let B be the second station, from which draw the directions of the streets meeting there; measure from B to C, noting the ends of the streets at n and o as you pass them; and lay the fame measure down on the plan. At C, the third ftation, take the direction of the streets meeting there, and measure from C to D. At D, the next station, do the fame, and measure D E, noting the cross street at p; and in the fame manner take the directions of all the principal streets, laying the measures down upon the plan. Then proceed to the next smaller streets; and lastly, to the lanes, alleys, courts, &c. ufing the fame process throughout the whole.

Note. In taking the furvey of a town there is no neceffity for having objects fixed up, as there are generally marks enough to serve as objects; such as the doors or windows of houses, &c.

OF PLANNING, CASTING UP, AND

DIVIDING.

PROBLEM I.

TO LAY DOWN THE PLAN OF A SURVEY.

When the furvey is taken by the plain table, a rough draft of the plan is already drawn on the paper; but where the furvey is taken with any other inftrument, the plan is to be drawn from the measures taken in the survey: first, a rough draft is to be drawn on paper, in which all the lines and angles must be laid down in the fame order in which they

were

were taken in the furvey; laying down first the angles, then the lengths of the lines, with the places of the offsets; then the offsets themselves. All these should be done with dry or obfcure lines; then a black line drawn through the extremities of all the lines, and the offsets will be the bounding line of the whole plan.

After the principal lines and bounds are laid down, proceed to mark the fmaller objects, till every thing be laid down that is neceffary.

The north fide of the map or plan is commonly placed uppermoft. And in fome vacant part a fcale of equal parts must be drawn. All hills must be shadowed, and all hedges coloured with different colours; all hilly grounds fhould be drawn like broken hills and valleys: foot-paths are reprefented by fingle dotted lines, and roads by double ones..

In taking large furveys, all oblique lines, fuch as are measured up and down hills, must be reduced to straight lines, by making a proper allowance; for which purpose there is generally a table engraved on fome of the inftruments.

PROBLEM II.

TO CAST UP THE CONTENTS OF A FIELD.

This is no more than what has been taught in the first fection of this chapter, for finding the contents of figures, whether they be triangular, fquare, four-fided, polygonal, or circular figures, by the proper rules there delivered; then, having found the area in links, after you have cut off five figures on the right hand, the remainder is acres. The five separated figures are to be multiplied by 4 for roods, and five figures cut off from this product are to be multiplied by 40 for perches.

In pieces of land bounded by winding hedges, in measuring the offsets, all the parts between the offsets are accurately measured feparately, like fmall triangles or trapezoids; but

fometimes