EXPLANATION TO TABLE NO. 5.

The numbers in the first column are the sum of the two heights taken at the end of each division; the second column are the heights added together; the third column are the cube yards of the middle portion of the cutting, equal to the width of the base, taken in lengths of 66 feet and 1 foot in breadth. Note.-The decimal points for the middle part and slopes are taken from the table annexed.

Calculations to Fig. 7.

Provide a book in the following form: first enter the several heights in the first column, and the sum of them in the second column; then look for that number in the table, against which take out the quantities in the two next columns and enter them in their respective columns in the book.

Where any difference occurs in the two heights as first taken, enter that number in the fifth column, and the difference in cube yards in the sixth column.

Middle cube yards.

The length of each division is entered in the seventh column; the table thus far is dispensed with.

Now multiply the second, third, and fifth columns by the lengths, and enter the products in the three last columns; add them up; multiply the first total by the base, as shown; add the second and third totals together, which give the slopes of 1 to 1; if the slopes are more than 1 to 1, increase that ratio to the given ratio; bring all the totals together, the sum will be in cube yards.

TUNNELS.

Tunnels are avoided as much as possible, but when the ground rapidly increases in height, the open cutting is not continued beyond 50 feet in depth; and, although tunnelling is a very heavy and uncertain expense, it is in many instances the most economical method of continuing a line of railway. Where the tunnel is of great length, it is necessary to sink shafts into it, which answer, in the first place, for the working during the operations, and eventually as a ventilation.

The greatest possible care is required in setting out the line and taking the levels to form a correct section. In a straight tunnel there is no difficulty in setting out and proving the course of operations. It is otherwise when the tunnel is curved, being similar to that of mining.

The working shafts are generally 8 or 9 feet in diameter, and the air shafts about 3 feet in diameter.

Problem 16.

To find the quantity of earthwork, Fig. 1, Plate 34.

First. Calculate the rectilineal part by the rule. (Prob. 100, Mensuration of Solids.)

Second. The semicircular part by the rules of areas of circles and segments. (See Tables, Nos. 8 and 15.)

Required the content of a tunnel of the following dimen

EXPLANATION TO TABLE no. 5.

The numbers in the first column are the sum of the two heights taken at the end of each division; the second column are the heights added together; the third column are the cube yards of the middle portion of the cutting, equal to the width of the base, taken in lengths of 66 feet and 1 foot in breadth. Note.-The decimal points for the middle part and slopes are taken from the table annexed.

Calculations to Fig. 7.

Provide a book in the following form: first enter the several heights in the first column, and the sum of them in the second column; then look for that number in the table, against which take out the quantities in the two next columns and enter them in their respective columns in the book.

Where any difference occurs in the two heights as first taken, enter that number in the fifth column, and the difference in cube yards in the sixth column.

The length of each division is entered in the seventh column; the table thus far is dispensed with.

Now multiply the second, third, and fifth columns by the lengths, and enter the products in the three last columns; add them up; multiply the first total by the base, as shown; add the second and third totals together, which give the slopes of 1 to 1; if the slopes are more than 1 to 1, increase that ratio to the given ratio; bring all the totals together, the sum will be in cube yards.

TUNNELS.

Tunnels are avoided as much as possible, but when the ground rapidly increases in height, the open cutting is not continued beyond 50 feet in depth; and, although tunnelling is a very heavy and uncertain expense, it is in many instances the most economical method of continuing a line of railway. Where the tunnel is of great length, it is necessary to sink shafts into it, which answer, in the first place, for the working during the operations, and eventually as a ventilation.

The greatest possible care is required in setting out the line and taking the levels to form a correct section. In a straight tunnel there is no difficulty in setting out and proving the course of operations. It is otherwise when the tunnel is curved, being similar to that of mining.

The working shafts are generally 8 or 9 feet in diameter, and the air shafts about 3 feet in diameter.

Problem 16.

To find the quantity of earthwork, Fig. 1, Plate 34.

First. Calculate the rectilineal part by the rule. (Prob. 100, Mensuration of Solids.)

Second. The semicircular part by the rules of areas of circles and segments. (See Tables, Nos. 8 and 15.)

Required the content of a tunnel of the following dimen

sions: Length 10 chains, width 36 feet, and 15 feet to the springing of semi-arch, diameter of arch 36 feet.

362 x .7954 = 1017.88 ÷ 2 = 508.94

Then 508.94 × 660 = 335900.40 the area of semi

660 × 36 × 15 = 356400 + 335900 40 ÷ 27 = 25640 cube yards

To find the area of the semi-arch by the table, take the number opposite 36 1017.82508.9 the semi-arch.

=

=

Required the content of a shaft, diameter 8 feet, depth 15.

8 × .7854 × 15 = 753.98 27 = 28 cube yards

BRICKWORK.

Brickwork also forms another considerable item in the estimate of a railway, by the construction of tunnels, bridges, viaducts, retaining walls, culverts, drains, stations, lodges, &c.

In London and many other places, brickwork is calculated by the rod of 272 superficial feet (in practice the is not used). All thicknesses of work is reduced to 14 brick, and then it is reduced to rods by dividing the total by 272; 306 cube feet, or 114 cube yards, are equal to one rod of reduced brickwork to bring it to the standard thickness, multiply by 8 (the number of 14 inches to a foot) and divide by 9 (the number of 14 inches in a brick and a half, or 134 inches).

;

Engineers always calculate brickwork by the cube yard. According to the London practice there are numerous items allowed in the construction of works, for which consult the Builders' Price Book.

In abstracting quantities, care should be taken to separate every distinction of work, as each will have a different price per yard, such as bricks set in mortar, and other parts in cement. Table or weather bricks, being of a different quality, should also be separated; arches in particular, whether circular, segment, or groined.

The dimensions are entered into the measuring book and squared, therefore each product will either be in square feet or cube feet; they are then abstracted into separate columns under each particular work, and their totals reduced to square yards by dividing by 9, and to cube yards by dividing by 27.