PAINTERS' WORK.

Painters' work is computed in square yards. Every part is measured where the colour lies; and the measuring line is forced into all the mouldings and corners.

Windows are done at so much a piece; and it is usual to allow double measure for carved mouldings, &c.

EXAMPLES.

1. How many yards of painting contains the room which is 65 feet 6 inches in compass, and 12 feet 4 inches high?

Ans. 89 yards 6 feet 10'.

2. The length of a room being 20 feet, its breadth 14 feet 6 inches, and height 10 feet 4 inches; how many yards of painting are in it, deducting a fire-place of 4 feet by 4 feet 4 inches, and two windows each 6 feet by 3 feet 2 inches? Ans. 732 yds.

3. What cost the painting of a room at 6d. per yard; its length being 24 feet 6 inches, its breadth 16 feet 3 inches, and height 12 feet 9 inches; also the door is 7 feet by 3 feet 6, and the window shutters to two windows each 7 feet 9 by 3 feet 6, but the breaks of the windows themselves are 8 feet 6 inches high, and 1 foot 3 inches deep: deducting the fire-place of 5 feet by 5 feet 6? Ans. £3 38. 10d.

GLAZIERS' WORK.

Glaziers take their dimensions either in feet, inches, and parts, or feet, tenths and hundredths. And they compute their work in square feet.

In taking the length and breadth of a window, the cross bars between the squares are included. Also windows of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass.

EXAMPLES.

1. How many square feet contains the window which is 4.25 feet long, and 2.75 feet broad?

2. What will the glazing a triangular sky-light come to at 10d. foot; per the base being 12 feet 6 inches, and the perpendicular height 6 feet 9 inches? Ans. 1 15s. 1 d.

3. There is a house with three tier of windows, three windows in each tier, their common breadth 3 feet 11 inches;

now the height of the first tier is 7 feet 10 inches,

Required the expense of glazing at 14d. per foot.

8

4

Ans. £13 11s. 10d.

4. Required the expense of glazing the windows of a house at 13d. a foot; there being three stories, and three windows in each story: the height of the lower tier is 7 feet 9 inches,

The common breadth of all the windows being 3 feet 9 inches.

Ans. £12 5s. 6d.

PAVIORS' WORK.

Paviors' work is done by the square yard, and the content is found by multiplying the length by the breadth.

EXAMPLES.

1. What cost the paving a foot-path at 3s. 4d. per yard; the length being 35 feet 4 inches, and breadth 3 feet 3 inches? Cost £5 78. 111⁄2d.

Ans. Content 32 yards 3 feet 6'.

2. What will be the expense of paving a rectangular court yard, whose length is 63 feet, and breadth 45 feet; in which there is laid a foot path of 5 feet 3 inches broad, running the whole length, with broad stones, at 3s. a yard; the rest being paved with pebbles at 2s. 6d. a yard? Ans. £40 5s. 10d.

PLUMBERS' WORK.

Plumbers' work is rated at so much a pound, or else by the hundred weight of 112 pounds.

Sheet lead used in roofing, guttering, &c., is from 7 to 12tbs. to the square foot. And a pipe of an inch bore is commonly 13 or 14 tbs. to the yard in length.

EXAMPLES.

1. How much weighs the lead which is 39 feet 6 inches long, and 3 feet 3 inches broad, at 81 lbs. to the

Decimals.

square foot? Duodecimals. 39 6

39.5

31

118.5

2. What cost the covering and guttering a roof with lead, at 188. the cwt.; the length of the roof being 43 feet, and breadth or girt over it 32 feet; the guttering 57 feet long, and 2 feet wide the former 9.831 lbs., and the latter 7.373 lbs. to the square foot? Ans. £115 98. 1d.

:

ARCHED AND VAULTED ROOFS.

To find the concave surface of a circular, gothic, or elliptical vaulted roof.

RULE.-Multiply the length of the arch by the length of the vault for the required surface.

NOTE.--The length of the arch, for most practical purposes, is found by applying a small cord along its concavity, and then measuring its length.

EXAMPLE.

What is the concave surface of Caerfylly bridge, over the Taafe; which is a segment of a circle, span 140, height 35, and width 12 feet? Ans. 1944 4 square feet.

To find the content of a circular, gothic, or elliptical roof. RULE.-Multiply the area of the end by the length of the roof for the content of the vacuity.

To find the solid content of the materials.

From the solid content of the whole arch take that of the vacuity for the solid content of the materials.

EXAMPLE.

Required the solidity of the vacuity and of the materials of a

circular vault; span 36 feet, height 18 feet, thickness of walls at the spring 6 feet, thickness of crown 4 feet, and length of the vault 100 feet?

Ans.

{

1884.96 cubic yards solidity of vacuity. 2026 15 cubic yards solidity of materials. To find the surface and solidity of a dome, the height and dimensions of the base being given.

RULE. Take twice the area for the surface, and multiply the area of the base by 3rd of the height.

NOTE. Although these rules are only true when the domes are hemispherical, yet they are sufficiently near the truth for all practical purposes.

EXAMPLE.

Required the surface and solidity of a hemispherical dome, the diameter of its base being 60 feet.

Surface 314 16 square yards.

Ans. Solidity 2094-4 cubic yards.

NOTE 1. The surface of a saloon is found in the same manner as a vaulted roof.

NOTE 2. Rules might have been here given for the measurement of haystacks, coal-heaps, &c; but these may be readily resolved into two or more of those solids, the methods of finding the content of which are given in the Mensuration of Solids, Part IV. Moreover, haystacks are usually sold by weight, and seldom or never by measurement.

SPECIFIC GRAVITY.

The specific gravity of bodies are their weights when compared with an equal bulk of pure water, which, at the temperature of 40°, weighs 1000 ounces avoirdupois per cubic foot. The following table, therefore, contains the weights of a cubic foot of several bodies in ounces.

A TABLE OF THE SPECIFIC GRAVITY OF BODIES.

To find the weight of a body from its bulk.

RULE.-Multiply the content of the body, in cubic feet, by its tabular specific gravity for its weight in avoirdupois ounces.

EXAMPLES.

1. Required the weight of a block of marble, whose length is 63 feet, and breadth and thickness each 12 feet, being the dimensions of one of the stones in the walls of Balbec.

63 × 122 × 2700 16 x 112 x 20

=

683

tons, which is equal to the

burden of a second rate East India ship.

2. What is the weight of a block of dry oak, which measures Ans. 4336 lb. nearly.

10 feet long, and 3 feet by 2?

To find the magnitude of a body from its weight.

RULE.-Divide its weight in avoirdupois ounces by its tabular specific gravity for its content in cubic feet.

EXAMPLES.

1. Required the content of an irregular block of freestone, which weighs 1 cwt.

and

112 × 16
2520

112 x 16 x 1728

2520

= cubic feet,

=1228.8 cubic inches.

2. How many cubic feet are there in a ton of dry oak?

Ans. 3813 cubic feet. 3. A cast iron pipe is 6 inches diameter in the bore and 1 inch in thickness; required the weight of a running foot.

Ans. 67.45 lbs.

LAND SURVEYING.

DESCRIPTION OF INSTRUMENTS USED FOR MEASURING AND PLANNING SURVEYS.

THE CHAIN.

THE chain, usually called Gunter's chain, is almost generally used in the British dominions, for measuring the distances required in a survey. It is 66 feet, or 4 poles, in length, and is divided into 100 links, which are joined by rings. The length of each link, together with half the rings connecting it with the