THIRD METHOD.

Another way of copying plans is by means of squares. This is performed by dividing both ends and sides of the plan, which is to be copied, into any convenient number of equal parts, and connecting the corresponding points of division with lines, which will divide the plan into a number of small squares. Then divide the paper, upon which the plan is to be copied, into the same number of squares, each equal to one of the former, when the plan is to be copied of the same size, but greater or less in the proportion, in which the plan is to be increased or diminished, when of a different size. Lastly, copy into the clean squares the parts contained in the corresponding squares of the other plan; and you will have the copy either of the same size, or greater or less in the required proportion.

FOURTH METHOD.

A fourth way is by the instrument, called a Pantograph, which also copies the plan in any size required.

FIFTH METHOD.

But the neatest method of any is this. Procure a copying frame or glass, made in this manner; namely, a large square of the best window glass, set in a broad frame of wood, which can be raised up to any angle, when the lower side of it rests on a table. Set this frame at any angle before you, facing a strong light; fix the plan and clean paper together with pins in the edges, to keep them together; the clean paper being laid uppermost, and on the face of the plan to be copied. Lay them with the back of the plan on the glass, namely, the part you inten 1 to copy first, and by means of the light shining through

the papers you will very distinctly perceive every line of the plan through the clean paper. In this state then trace all the lines on the paper with a pencil. Having drawn that part, which covers the glass, slide another part over the glass, and copy it in the same manner. And then another

part; and so on, till the whole be copied.

Then separate them, and trace all the pencil lines over with a fine pen and Indian ink, or with common ink.

And thus you may copy the finest plan, without injuring it in the least.

When the lines, &c. are copied on the clean paper or vellum, the next business is to write such names, remarks, or explanations, as may be judged necessary; drawing the scale for taking the lengths of any parts, a flower-de-luce to point out the direction, and the proper title, ornamented with a compartment; and illustrating or coloring every part in such manner, as shall seem most natural; as shading rivers or brooks with crooked lines, drawing the representation of trees, bushes, hills, woods, hedges, houses, gates, roads, &c. in their proper places; running a single dotted line for a foot path, and a double one for a carriage road; and representing either the bases or the elevations of buildings, &c.

PROBLEM IV.

To change a figure from one scale to another,

From one angle A draw lines AC, AD, AE, &c. to all the other angles of the given figure; then augment or diminish one side AB, till Ab be to AB in the given proportion of the scales; and, by means of a par

}

B

C

E

D

allel rule, draw be parallel to BC, and meeting AC in c, and in the same manner cd parallel to CD, de parallel to DE, ef parallel to EF; so shall AbcdefA be the figure required.

DIVISION OF LAND.

IN the division of commons, after the whole is surveyed and computed, and the proper quantities to be allowed for roads, &c. deducted, divide the net quantity remaining among the several proprietors by the rule of Fellowship, in proportion to the real value of their estates, and you will thereby obtain their proportional quantities of the land. But as this division supposes the land, which is to be divided, to be all of equal goodness, you must observe, that if the part, in which any one's share is to be marked off, be better or worse than the general incan quality of the land, then you must diminish or augment the quantity of his share in the same proportion.*

* Or, which comes to the same thing, divide the ground among the claimants in the direct ratio of the value of their claims, and the inverse ratio of the quality of the ground aliotted to each; that is, in proportion to the quotients arising from the division of the value of each person's estate by the number, which expresses the quality of the ground in his share.

But these regular methods cannot be always put in practice; so that, in the division of commons, the usual way is to measure separately all the land, that is of different values, and add into two sums the contents and the values; then, by the first part of

PROBLEM 1.

It is required to divide any given quantity of ground, or its value, into any given number or parts, and in proportion to any given numbers.

Divide the given piece, or its value, as in the rule of Fellowship, by dividing the whole content or value by the sum of the numbers expressing the proportions of the several shares, and multiplying the quotient severally by the said proportional numbers for the respective shares required, when the land is all of the same quality. But if the shares be of different qualities, then divide the numbers expressing the proportions of values of the shares by the numbers, which express the qualities of the land in each share; and use the quotients instead of the former proportional numbers.

EXAMPLES.

1. If the total value of a common be 25001. it is required to determine the values of the shares of the three claimants A, B, C, whose estates are respectively of these values, 10000, 15000, and 25000 pounds.

The estates being in proportion as the numbers 2, 3, 5, whose sum is 10, we shall have 2500÷10=250; which being severally multipled by 2, 3, 5, the products 500, 750, 1250, are the values of the shares required.

the following Problem I, the value of every claimant's share is computed by dividing the whole value among them in propor tion to their estates; and, lastly, by Problem II, a quantity is laid out for each person, that shall be of the value of his share before found.

2. It is required to divide 300 acres of land among A, B, C, D, E, F, G, and H, whose claims upon it are respectively in proportion as the numbers 1, 2, 3, 5, 8, 10, 15,

20.

The sum of these proportional numbers is 64, by which 300 being divided, the quotient is 4ac. 2r. 30p. which being multiplied by each of the nmubers 1, 2, 3, 5, &c. we have for the several shares as follow:

3. It is required to divide 780 acres among A, B, and C, whose estates are 1000, 3000, and 4000 pounds a year; the ground in their shares being worth 5, 8, and 10 shillings the acre respectively.

Here their claims are as 1, 3, 4; and the qualities of their land are as 5, 8, 10; therefore their quantities must be as,, or, by reduction, as 8, 15, 16. Now the sum of these numbers is 39; by which the 780 acres being divided, the quotient is 20; which being multiplied severally by the three numbers 8, 15, 16, the three products are 160, 300, 320, for the shares of A, B, C, respectively.