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17. Multiply 112 feet, 3 inches, 5'' by 42 feet, 4 in., 6"! 112 ft. 3 in.

511
6x7=42

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a room

Ans. 4758 0

9 4 611 18. What is the freight of a bale of goods containing 65 feet 9 inches, at D15 per ton of 40 feet? 20 ft. }=15.00

Or, 65.75
5 ft.
= 7.50

15 x
6 in. To

1.87.5 2 in.) 18.7

40)986.25 9.3

D24.65.6 Ans. D24.65.5 19. What will be the expense of plastering the wall of 8 feet high, and each side 16 feet 3 inches long, at 50 cents per square yard ?

Ans. D30.69.4. 20. How many square feet in a board 17 feet 7 inches long, 1 foot 5 inches wide ?

Ans. 24 ft. 10', 11". 21. A load of wood is 4 feet 6 inches wide, 3 feet 10 inches high, and 7 feet 8 inches long; how many feet more than a cord does it contain ?

Ans. 41 feet. 22. What will the paving of a courtyard cost, which is 70 feet long, and 56 feet 4 inches wide, at 20c. per square foot ?

Ans. D788 667. 23. A man built a house consisting of 3 stories ; in the upper story there were 10 windows, each containing 12 panes of glass, each pane 14 by 12 inches; the first and second stories contained 14 windows, each 15 panes, and each pane 16 by 12; how many square feet of glass were there in the whole house?

Ans. 700 sq. ft.

REVIEW.

What are Duodecimals ? By whom, and how can those rules be applied ? What is the rule for addition ? subtraction ? mule tiplication ? &c

APPENDIX, Containing a variety of useful rules and examples in square and

cubical measure, mensuration, fc.

ARTIFICERS' WORK.

ARTIFICERS estimate or compute the value of their work by different measures ; but the best method of taking the dimensions of all sorts of work is by feet, tenths, and hundredths ; in other words, by decimals; glazing, and masons' flat work, &c., by the foot; painting, plastering, paving, by the yard ; flooring, partitioning, roofing, tiling, by the square of 100 feet; brickwork, by the rod of 161 feet, whose square is 272.25.

Note.-In calculating the square feet it is usual to omit the 25, but the more correct way is to use the perfect number (272.25).

The practice has formerly been to calculate the various prices of mechanical work, according to the rules and regulations of the several countries of Europe, particularly England and Germany, but the method has, in some respects, been departed from, which has rendered the calculations different in the several states of the Union. The general system of computation will de given, from which any others may easily be derived.

BRICKLAYERS' WORK. BRICKLAYERS compute their work at the rate of one brick and a half thick, and if the wall be more or less than this standard, it must be reduced to it as follows:

RULE.

Multiply the superficial content of the wall, in feet, by the number of half bricks in thickness, and of that product will be the content required.

It is generally the practice in this country, at the present time, to calculate bricks by the 1000. All windows, doors, &c., are to be deducted out of the content of the walls in which they are placed; but this deduction is made only with regard to materials; for the value of their workmanship is added to the bill at the rate agreed on.

1. How many square rods are there in a wall 52.5 feet long, 12.75 feet high, and 2.5 bricks thick ? Thus : 52.5 x 12.75= 272=2.4609 X 5 half bricks=12.3045-3=4.1015=4 rods. 27 feet, 7 inches. Ans.

2. How many square rods are there in a wall 621 feet Long, 14 feet 8 inches high, and 2} bricks thick ?

Ans. 5 rods, 167 feet, 9 inches, 4 pa. 3. How many bricks, 8 inches long, 4 inches wide, 24 inches thick, will build a wall in front of a garden, which is to be 240 feet long, 6 feet high, 1 foot 6 inches wide ? Ans. 51840 bricks.

4. How many bricks, 9 inches long, 5 inches wide, 2] thick, will it require to build a wall 90 feet long, 7 feet high, and 2 feet thick; and what will it cost at 90 cents per square foot ?

MASONS' WORK.

To masonry belong all sorts of stone-work; and the measure made use of is a solid perch, or a superficial, or a solid foot. Solid measure is generally used for materials, and the superficial for workmanship.

RULE.

In solid measure multiply the length, breadth, and thickness, continually together, and in superficial measure the length and breadth of every part of the projection must be taken.

1. Required the solid content of a wall, whose length is 48.5 feet, its height 10.75 feet, and thickness 2 feet.

48.5 X 10.75 X2=1042.75 feet. Ans. 2. What is the solid content of a wall whose length is 60.75 feet, its height, 10.25 feet, and its thickness 2 feet?

Ans. 1556.71875 feet. 3. What is a marble slab worth, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at 80 cents per foot ? Thus : 5 ft. 7 in.=5,5 ft.=i1 and 1 ft. 10 in.=la ft.= ft.

x==content of the slab in feet, 37 x 80c.=5886c. = 73,7c.=D8.18.8%. Ans.

4. How many solid perches of stone are contained in a cellar wall, the length being 45.5 ft. on a side, and the breadth 24 ft. at each end, 6.75 feet high, and 2 feet thick ? Ans. 113.72 perches.

5. Required the cost of making a stone wall under a building, whose length is 42 feet, breadth on the outside 26 feet, the height of the wall being 6.5 feet, and 2 feet thick, at 40 cents per solid perch.

Ans. D40.33.6+ 6. In a block of marble 5 st. long, 18 in. square, how many cubical, and how many square feet ? 18 in. x 18 x 60 in. 19440-1728=1lt cub. ft. ; 19440-144=135 sq. ft. Ans.

CARPENTERS AND JOINERS WORK.

CARPENTERS and joiners' work is that of flooring, partitioning, roofing, &c., and is measured by the square of 100 feet.

1. If a floor be 57.25 feet long, and 28.5 feet broad, how many squares will it contain? Thus, 57.25 X 28.5=1631.625 square feet, =16 squares, 31 feet, 7 inches, 6''. Ans.

2. A partition is 91.75 feet long, and 11.25 feet broad; how many squares does it contain ?

Ans. 10 squares, 32 feet. 3. A partition is 96.75 feet long, 11.5 feet broad; how many squares will it contain ?

Ans. 11.12625 squares. 4. What is the expense of flooring a building 45.5 feet long. 26.75 wide, 2 stories high, at D1.36 per square ? Ans. D49.65.87.

5. If a floor be 60 feet long, 28.75 broad, how many squares will it contain ?

Ans. 17.25 squares. 6. In a floor 46 by 24 feet, required the expense of flooring at 15 cents per square foot, and cost of boards at D7.50 per M.

Ans. Cost of flooring, D16.56; cost of boards D8.28.

SLATERS AND TILERS' WORK.

In these works, the content of a roof is found by multiplying the length of a side by the girth from eave to eave; and in slating, allowance must be made for the double row at the bottom. In taking the girth, the line is made to ply over the lowest row of slates, and returned up the under side till it meet with the wall or eaves-board; but in tiling, the line is stretched down only to the lowest part, without returning it up again. Double measure is generally allowed for hips, valleys, gutters, &c., but no deductions are made for chimneys. In all works of this kind, the content is computed either in yards of 9 square feet, or in squares of 100 feet, and the same allowance of hips and valleys is to be made as in roofing.

1. The length of a slated roof is 45.75 feet, and its girth 34.25 feet; required the content. Thus: 45.75 X 34.25= 1566.9375 square feet=174.104 yards. Ans.

2. The length of a slated roof is 48.5 feet, and its girth 36.25 feet; required the content. Ans. 1758.125 square feet.

3. What will the tiling of a barn cost at D3.40 per square, he length being 43 feet 10 inches, and the breadth 27 feet 5 inches on the fiat, the eave-board projecting 16 inches on each

493.5
12

side, allowing the roof to be a true pitch? Thus, 27 feet 5
inches=27=322, and 32+(2-2)=32 +1645
= true pitch. 16 X2=32 inches, 12 feet, to be added for pro-
jection; then, 413,5 +12=515=girt of roof; again, 43 feet
10 inches=438 feet=293, and 5255 x263 = 138296.5 feet=
1382,065 squares of roofing; hence 1887:965 D3.40:-
469952.1 cents =D65.26.4m., cost of roofing. Ans.

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PLASTERERS' work is of two kinds, namely, plastering upon laths, called ceiling; and plastering walls, called rendering; and these different kinds must be measured separately, and their content collected into one sum. Their work is measured by the square foot, or yard of 9 square feet, and moulding by running measure.

1. If a ceiling be 59.75 feet long, and 24.5 feet broad, how many yards does it contain? Thus : 59.75 X 24.5=1463.875 square feet=162.6528 square yards. Ans.

2. If the partitions between rooms are 141.5 feet about, and 11.25 feet high, how many yards do they contain ?

Ans. 176.87. 3. If a ceiling be 64.75 feet long, and 24.5 broad, how many square yards does it contain ?

Ans. 176.2639

PAINTERS AND GLAZERS' WORK.

PAINTERS' work is measured in the same manner as that of carpenters; and in taking the dimensions, the line must be forced into all the mouldings andаcorners. The work is estimated by the yard, except sashes, which are calculated per light. Glazers' work is calculated by the light. All work of this kind is done by the square yard of 9 feet.

1. If a room be painted, whose height is 16.5 feet, and its compass 97.75 feet, how many yards does it contain ?

Thus : 97.75 x 16.5=1612.875 square feet==179.208 square yards. Ans.

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