4. How many cubic feet of stone work are contained in 9 walls, each 30 ft. 6 in. long, 9 ft. 8 in. high and 2 ft. thick? Ans. 5307 ft.

5. How many cubic feet in a cellar 30 ft. 3 in. long, 27 ft. 6 in. broad, and 8 ft. deep? Ans. 6655 ft.

6. What is the content of a marble slab 6 ft. 7 in. long, 2 ft. broad, and 1 ft. 9 in. thick? Ans. 23 ft. 0 in. 6 s. 7. What is the superficial content of a stone 4 ft. 9 in. long, and 3 ft. 9 in. broad? Ans. 18 ft. 0 in. 1 s. 6 t.

MENSURATION.

IMPORTANT TO SHIP BUILDERS.

A concise Rule to find the length of Masts. RULE 1.-Multiply the length of the keel by 2, and divide the product by 3, and then to the quotient add the breadth of the beam, and the sum will be the length of the main mast.

1. Suppose a ship to be 84 feet by the keel, and 31 ft. by the beam, what is the length of her mast? Ans. 87 ft. 2. Suppose a ship to be 108 feet by the keel, and 40 feet by the beam, what is the length of her main mast? Ans. 112 feet.

ANOTHER METHOD.

When the length and thickness of Masts is required in

yards.

RULE. Add the breadth of the beam and the depth of the hold in feet together, and divide the sum by 1.5, and the quotient will be the length of the main mast in yards.

1. Admit a ship whose keel in length is 73 feet, and the breadth of the beam 28.5 feet, and the depth of the hold 12 feet, what is the length of her main mast?

Now to find the thickness, it is customary to allow of the length in feet for the thickness in inches; in that case, a main mast 81 feet long, must be 27 inches thick.

2. If a ship of 100 tons be 44 feet long at the keel, of what length must the keel of a ship be that carries 220 tons? tons. tons.

Say as 100 220 :: 443 = (85184) 187404.80, whose cube root is 57.226, the length of the keel sought.

To find Ship's Tonnage by Carpenter's Measure. RULE.-For single-decked vessels, multiply the length and breadth at the main beam, and depth of the hold together, and divide the product by 95.

For double-decked vessels, take half the breadth of the main beam, and work as above directed.

1. What is the tonnage of a single decked vessel, whose length is 60 feet, breadth 20, and depth 8 feet?

Ans. 101 tons. Operation.-60 x 20 x 8 101 tons.

95

2. What is the tonnage of a double-decked vessel, whose length is 65 feet, breadth 21 feet 6 inches, and depth 10 feet 9 inches? Ans. 158 tons.

TO FIND GOVERNMENT TONNAGE. GOVERNMENT RULE.-"If the vessel be double-deck-· ed, take the length thereof from the fore part of the main stem to the after part of the stern-post above the upper deck; the breadth thereof at the broadest part above the main wales, half of which breadth shall be accounted the depth of such vessel, and then deduct from the length

of the breadth; multiply the remainder by the breadth, and the product by the depth, and divide this last product by 95, the quotient whereof shall be deemed the true contents or tonnage of such ship or vessel; and if such ship or vessel be single-decked, take the length and

breadth, as above directed, deduct from the said length of the breadth, and take the depth from the under side of the deck-plank to the ceiling in the hold, and the multiply and divide as aforesaid, and the quotient shall be deemed the tonnage."

1. What is the government tonnage of a single-decked vessel, whose length is 69 feet 6 inches, breadth 22 feet 6 inches, and depth 8 feet 6 inches?

2. Required the tonnage of a single decked vessel, by

carpenter's measure, whose length is breadth 24 feet 8 inches, and depth 9

70 feet 6 inches, feet 10 inches?

Ans. 180 tons.

3. What is the Government tonnage of a double-decked vessel of the following dimensions: length 82 feet 3 inches, breadth 24 feet 3 inches, and depth 12 feet 11 inches? Ans. 2098 tons.

BOARD OR LUMBER MEASURE.

RULE.-Multiply the length in feet by its breadth in inches, and divide by 12 for the content.

1. What is the content of a board 24 feet long and 8 inches wide? Ans. 16 ft.

2. What is the content of a board 30 feet by 16 inches? Ans. 40.

3. What is the content of a board 14 feet by 15 inches? Ans. 17 ft.

4. What is the content of a board 18 feet by 15 inches? Ans. 22 ft.

TO MEASURE SCANTLING OR JOIST.

RULE.-Multiply the depth and width taken in inches by the length in feet, divide the product by 12, and the quotient is the content in feet.

1. How many feet are there in 3 joist, each of which are 15 feet long, 5 inches wide and 3 inches thick?

Ans. 561 feet. 2. How many feet in 20 joist 10 feet long 6 inches wide, and 2 inches thick? Ans. 200 feet.

CASE II.

When a Board is wider at one end than the other. GENERAL RULE.-Take the breadth in the middle, or add the measure of both ends together, and take the sum for a mean breadth which multiply by the length for the content.

1. Suppose a board be 10 feet long and 10 inches wide at one end, and 34 inches wide at the other end, what is its superficial content? Ans. 18 feet,

18 feet answer; or, if the length be

in feet and inches, reduce the length to inches, which being multiplied by the mean breadth in inches and divided by 144, we get the content in feet.

Q. Why do we divide by 144?

A. Because, when we multiply inches by inches, the product is square inches; therefore, we divide by 144, 144 square inches being to 1 square foot.

=

PAPERING ROOMS.

There is a room papered, the compass of which is 47 feet 3 inches, and the height 7 feet 6 inches, what is the content in square yards? Ans. 39 yds.

CARPENTER'S WORK.

Roofing, flooring, partitioning, and the principal carpentry in modern buildings, are measured by the square of 10 feet, that is 100 feet.

RULE FOR ROOFING.-Multiply the depth and half depth by the front, or, the front and half front by the depth, and you get the content. The dimensions are taken in feet and inches.

1. If a floor be 49 feet 6 inches long, and 26 feet 6 inches broad, how many square feet?

Operation. 49.5

26.5

2475

2970

990

1311(75 Ans. 13,11 ft. 9 in. or 13s. 11f. 9i.

12

9)00

BRICKLAYER'S WORK.

Bricklayers are generally paid by the day or perch.

1. Suppose a garden wall to be 254 feet round and 12 feet 7 inches high and 3 bricks thick, how many square rods does it contain?

F. F. I.

254+12.7 = 3196.2×2 = 6392.4

Ans. 23 sq. rods.

=231 sq. rods.

272