3d. By the cubic or solid measure, when it is estimated by the cubic foot, or the cubic yard. The work, however, is often estimated in square measure, and the materials for construction in cubic measure.

2. What proportion do the dimensions of a brick bear to

each other?

The dimensions of a brick generally bear the following proportions to each other, viz.:

Length twice the width, and

Width = twice the thickness, and

hence, the length is equal to four times the thickness.

3. What are the common dimensions of a brick? How many cubic inches does it contain?

The common length of a brick is 8 inches, in which case the width is 4 inches, and the thickness 2 inches. A brick of this size contains

8 × 4 × 2 = 64 cubic inches; and since a cubic foot contains 1728 cubic inches, we have

172864 27 the number of bricks in a cubic foot.

4. If a brick is 9 inches long, what will be its width and what its content?

If the brick is 9 inches long, then the width is 41 inches, and the thickness 21; and then each brick will contain 9 × 4 × 21 = 91 cubic inches in each brick; and 1728- 911 19 nearly, the number of bricks in a cubic foot. In the examples which follow, we shall suppose the brick to be 8 inches long.

5. How do you find the number of bricks required to build a wall of given dimensions?

1st. Find the content of the wall in cubic feet.

2d. Multiply the number of cubic feet by the number of bricks in a cubic foot, and the result will be the number of bricks required.

EXAMPLES.

1. How many bricks, of 8 inches in length, will be required to build a wall 30 feet long, a brick and a half thick, and 15 feet in height?

Ans. 12150.

2. How many bricks, of the usual size, will be required to build a wall 50 feet long, 2 bricks thick, and 36 feet in height? Ans. 64800.

6. What allowance is made for the thickness of the mortar? The thickness of mortar between the courses is nearly a quarter of an inch, so that four courses will give nearly 1 inch in height. The mortar, therefore, adds nearly one-eighth to the height; but as one-eighth is rather too large an allowance, we need not consider the mortar which goes to increase the length of the wall.

3. How many bricks would be required in the first and second examples, if we make the proper allowance for mortar?

7. How do bricklayers generally estimate their work? Bricklayers generally estimate their work at so much. per thousand bricks. To find the value of things estimated by the thousand, see Arithmetic, page 192.

4. What is the cost of a wall 60 feet long, 20 feet high, and two and a half bricks thick, at $7.50 per thousand, which price we suppose to include the cost of the mortar?

If we suppose the mortar to occupy a space equal to one-eighth the height of the wall, we must find the quantity of bricks under the supposition that the wall was 171⁄2 feet in height. Ans. $354.37.

8. In estimating the bricks for a house, what allowances are made?

In estimating the bricks for a house, allowance must be made for the windows and doors.

OF CISTERNS.

9. What are cisterns?

Cisterns are large reservoirs constructed to hold water, and to be permanent, should be made either of brick or masonry.

It frequently occurs that they are to be so constructed as to hold given quantities of water, and it then becomes a useful and practical problem to calculate their exact dimensions.

10. How many cubic inches in a hogshead?

It was remarked in Arithmetic, page 104, that a hogshead contains 63 gallons, and that a gallon contains 231 cubic inches. Hence, 231 × 63 = 14553, the number of cubic inches in a hogshead.

11. How do you find the number of hogsheads which a cistern of given dimensions will contain?

1st. Find the solid content of the cistern in cubic inches. 2d. Divide the content so found by 14553, and the quotient will be the number of hogsheads.

EXAMPLE.

The diameter of a cistern is 6 feet 6 inches, and height 10 feet: how many hogsheads does it contain?

The dimensions reduced to inches are 78 and 120. To find the solid content, see page 162. Then, the content in cubic inches, which is 573404.832, gives

573404.832

14553 39.40 hogsheads, nearly.

12. If the height of a cistern be given, how do you find the diameter, so that the cistern shall contain a given number of hogsheads?

1st. Reduce the height of the cistern to inches, and the content to cubic inches.

2d. Multiply the height by the decimal .7854.

3d. Divide the content by the last result, and extract the square root of the quotient, which will be the diameter of the cistern in inches.

EXAMPLE.

The height of a cistern is 10 feet: what must be its diameter, that it may contain 40 hogsheads?

Ans. 78.6 in. nearly.

13. If the diameter of a cistern be given, how do you find the height, so that the cistern shall contain a given number of hogsheads?

1st. Reduce the content to cubic inches.

2d. Reduce the diameter to inches, and then multiply its square by the decimal .7854.

3d. Divide the content by the last result, and the quotient will be the height in inches.

EXAMPLE.

The diameter of a cistern is 8 feet: what must be its height that it may contain 150 hogsheads?

Ans. 25 ft. 1 in. nearly.

SECTION IV.

MASONS' WORK.

1. What belongs to MASONRY, and what measures are used? All sorts of stone work. The measure made use of is either superficial or solid.

Walls, columns, blocks of stone or marble, are measured by the cubic foot; and pavements, slabs, chimney-pieces, &c., are measured by the square or superficial foot. Cubic or solid measure is always used for the materials, and the square measure is sometimes used for the workmanship.

EXAMPLES.

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

Ans. 13103 ft.

2. What is the solid content of a wall, the length of which is 24 feet 3 inches, height 10 feet 9 inches, and thickness 2 feet?

Ans. 521.375 ft.

following dimensions: feet 2 inches.