Draw the 4 dotted straight lines AB, BC, CD, DA, cutting off equal quantities on both sides of them, which they do as near as the eye can judge; so is the crooked figure reduced to an equivalent right-lined one of 4 sides, ABCD. Then draw the diagonal BD, which, by applying a proper scale to it, measures suppose 1256. Also the perpendicular, or nearest distance from A to this diagonal, measures 456; and the distance of C from it is 428.

Then, half the sum of 456 and 428, multiplied by the diagonal 1256, gives 555152 square links, or 5 acres, 2 roods, 8 perches, the content of the trapezium, or of the irregular crooked piece.

As a general example of this practice, let the contents be computed of all the fields separately in the foregoing plan facing page 448, and, by adding the contents altogether, the whole sum or content of the estate will be found nearly equal to 103 acres. Then, to prove the work, divide the whole plan into two parts, by a pencil-line drawn across it any way near the middle, as from the corner l on the right, to the corner nears on the left; then, by computing these two large parts separately, their sum must be nearly equal to the former sum, when the work is all right.

The content of irregular fields, farms, &c. when planned, may be readily and correctly found by the process of weighing. If the plan be not upon paper, or fine drawing pasteboard of uniform texture, let it be transferred upon such. Then cut the figure separately close upon its boundaries, and cut out from the same paper or pasteboard a square of known dimensions, according to the scale employed in drawing the plan. Weigh the two separately in an accurate balance, and the ratio of the weight will be the same as that of the superficial contents.

If great accuracy be required, cut the plan into four portions, called 1, 2, 3, 4. First, weigh 1 and 2 together, 3 and 4 together, and take their sum. Then weigh 1 and 3 together, 2 and 4 together, and take their sum. Lastly, weigh 1 and 4 together, 2 and 3 together, and take their sum. The mean of the three aggregate weights thus obtained, compared with the weight of the standard square, will give the ratio of their surfaces very nearly.

PROBLEM XVII.

To transfer a Plan to another Paper, &c.

AFTER the rough plan is completed, and a fair one is wanted; this may be done by any of the following methods.

First Method.-Lay the rough plan on the clean paper, keeping them always pressed flat and close together, by weights laid on them. Then with the point of a fine pin or pricker, prick through all the corners of the plan to be copied. Take them asunder, and connect the pricked points on the clean paper, with lines, and it is done. This method is only to be practised in plans of such figures as are small and tolerably regular, or bounded by right lines.

Second Method.—Rub the back of the rough plan over with black-lead powder, and lay this blacked part on the clean paper on which the plan is to be copied, and in the proper position. Then, with the blunt point of some hard substance, as brass, or such-like, trace over the lines of the whole plan, pressing the tracer so 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. Or, instead of blacking the rough plan, we may keep constantly a blacked paper to lay between the plans.

Third Method. This 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 on which the plan is to be copied into the same number of squares, each equal to the former when the plan is to be copied of the same size, but greater or less than the others, 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 old plan; and you will have the copy, either of the same size, or greater or less in any proportion.

Fourth Method. By the instrument called a pentagraph, which also copies the plan in any size required for this purpose, also, Professor Wallace's eido graph may be advantageously employed.

Fifth Method.-A very neat process, at least for copying from a fair plan, 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 up to any angle before you, facing a strong light; fix the old plan and clean paper together, with several pins quite around, to keep them together, the clean paper being laid uppermost, and over the face of the plan to be copied. Lay them, with the back of the old plan, on the glass; namely, that part which you intend to begin at 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. Then another part; and so on, till the whole is copied. Then take them asunder, 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.

OF ARTIFICERS' WORKS AND TIMBER MEASURING.

I. OF THE CARPENTER'S OR SLIDING RULE.

THE Carpenter's or Sliding Rule is an instrument much used in measuring of timber and artificers' works, both for taking the dimensions, and computing the contents.

The instrument consists of two equal pieces, each a foot in length, which are connected together by a folding joint.

One side or face of the rule is divided into inches, and eighths, or half-quarters. On the same face also are several plane scales divided into twelfth parts by diagonal lines; which are used in planning dimensions that are taken in feet and inches. The edge of the rule is commonly divided decimally, or into tenths; namely, each foot into ten equal parts, and each of these into ten parts again; so that by means of this last scale, dimensions are taken in feet, tenths, and hundredths, and multiplied as common decimal numbers, which is the best way.

On the one part of the other face are four lines, marked A, B, C, D; the two

middle ones B and C being on a slider, which runs in a groove made in the stock. The same numbers serve for both these two middle lines, the one being above the numbers, and the other below.

These four lines are logarithmic ones, and the three A, B, C, which are all equal to one another, are double lines, as they proceed twice over from 1 to 10. The other or lowest line, D, is a single one, proceeding from 4 to 40. It is also called the girt-line, from its use in computing the contents of trees and timber; and on it are marked WG at 17·15, and AG at 18.95, the wine and ale gage points, to make this instrument serve the purpose of a gaging rule.

On the other part of this face there is a table of the value of a load, or 50 cubic feet of timber, at all prices, from 6 pence to 2 shillings a foot.

When 1 at the beginning of any line is accounted 1, then the 1 in the middle will be 10, and the 10 at the end 100; but when 1 at the beginning is counted 10, then the 1 in the middle is 100, and the 10 at the end 1000; and so on. And all the smaller divisions are altered proportionally.

As,

II. ARTIFICERS' WORK.

ARTIFICERS Compute the contents of their works by several different measures.

Glazing and masonry, by the foot: Painting, plastering, paving, &c. by the yard, of 9 square feet: Flooring, partitioning, roofing, tiling, &c. by the square of 100 square feet:

And brickwork, either by the yard of 9 square feet, or by the perch, or square rod or pole, containing 272 square feet, or 301 square yards, being the square of the rod or pole of 16 feet or 5 yards long.

As this number 2724 is troublesome to divide by, the 4 is commonly omitted in practice, and the content in feet divided only by the 272.

All works, whether superficial or solid, are computed by the rules proper to the figure of them, whether it be a triangle, or rectangle, a parallelopiped, or any other figure.

III. BRICKLAYERS' WORK.

BRICKWORK is estimated at the rate of a brick and a half thick.

So that if a

wall be more or less than this standard thickness, it must be reduced to it, as follows:

Multiply the superficial content of the wall by the number of half-bricks in the thickness, and divide the product by 3.

:

The dimensions of a building may be taken by measuring half round on the outside and half round on the inside the sum of these two gives the compass of the wall, to be multiplied by the height, for the content of the materials. Chimneys are commonly measured as if they were solid, deducting only the vacuity from the hearth to the mantle, on account of the trouble of them. All windows, doors, &c. are to be deducted out of the contents of the walls in which they are placed.

The dimensions of a common bare brick are, 8 and 2 thick; but including the half-inch joint of

inches long, 4 inches broad, mortar, when laid in brick

work, every dimension is to be counted half an inch more, making its length 9

inches, its breadth 41⁄2, and thickness 3 inches. So that every 4 courses of proper brickwork measures just 1 foot or 12 inches in height.

450 stock bricks weigh about a ton.

The standard rod requires 4500 bricks of the usual size, including waste.

1 rod of brickwork requires 27 bushels of chalk lime, and 3 loads of road drift or sand.

2 hods of mortar make nearly a bushel.

EXAMPLES.

1. How many yards and rods of standard brickwork are in a wall whose length or compass is 57 feet 3 inches, and height 24 feet 6 inches; the wall being 2 bricks or 5 half bricks thick? Ans. 8 rods, 173 yards.

2. Required the content of a wall 62 feet 6 inches long, and 14 feet 8 inches high, and 2 bricks thick? Ans. 169-753 yards. 3. A triangular gable is raised 17 feet high, on an end wall whose length is 24 feet 9 inches, the thickness being 2 bricks: required the reduced content? Ans. 32-08 yards.

4. The end-wall of a house is 28 feet 10 inches long, and 55 feet 8 inches high, to the eaves; 20 feet high is 24 bricks thick, other 20 feet high is 2 bricks thick, and the remaining 15 feet 8 inches, is 11⁄2 brick thick; above which is a triangular gable, of 1 brick thick, which rises 42 courses of bricks, of which every courses make a foot. What is the whole content in standard measure? Ans. 253-626 yards.

REMARK.

Taking 4500 for the bricks employed, including waste, in a standard rod of 272 feet face, and a brick and a half thick, the following table will serve to determine the number of bricks required in any proposed case.

Area of the face of

the wall, in feet.

Number of bricks required for 1, 2, 3, 4, &c. feet at the
respective thicknesses.

1 brick. 1 brick. 2 bricks. 2 bricks.

3 bricks.

The left-hand column exhibiting the area of the face of a wall in feet, the numbers of bricks required for 1 brick thick, 11⁄2 bricks thick, &c. are shown in the corresponding horizontal column under the appropriate heading. For greater numbers, being 10 times, 100 times, 1000 times, &c. the number of square feet specified in any part of the left-hand column, take 10 times, 100 times, 1000 times, &c. the number given under the proper head.

EXAMPLE. Required the number of bricks necessary to build a wall of 2 bricks thick, the superficial area being 2346 feet.

Note. Tables may be constructed in a like manner for many other similar purposes.

IV. MASONS' WORK.

> To Masonry belong all sorts of stone-work; and the measure made use of is a foot, either superficial or solid.

Walls, columns, blocks of stone or marble, &c. are measured by the cubic foot; and pavements, slabs, chimney-pieces, &c. by the superficial or square foot.

Cubic or solid measure is used for the materials, and square measure for the workmanship.

In the solid measure, the true length, breadth, and thickness are taken and multiplied continually together. In the superficial, there must be taken the length and breadth of every part of the projection which is seen without the general upright face of the building.

A ton of Portland stone is about 16 cubic feet, of Bath stone 17, of granite 13, of marble, at a medium, 13 cubic feet

EXAMPLES.

1. Required the solid content of a wall, 53 feet 6 inches long, 12 feet 3 inches high, and 2 feet thick ? Ans. 1310 feet.

2. What is the solid content of a wall, the length being 24 feet 3 inches, height 10 feet 9 inches, and 2 feet thick? Ans. 521.375 feet.

3. Required the value of a marble slab, at 8s per foot; the length being 5 feet 7 inches, and breadth 1 foot 10 inches?

4. In a chimney-piece, suppose the

Ans. 47 ls 10 d.