REMARKS.-1. A pint of water weighs about 1 pound, Avoirdupois.

2. Potatoes and grains are usually sold to dealers and shippers by weight. 3. The beer gallon of 282 cubic inches is nearly obsolete.

EXAMPLES FOR PRACTICE.

403. 1. Reduce 21 bu. 6 qt. 1 pt., dry measure, to pints, liquid measure. 2. A grocer bought 12 bu. 3 pk. 3 qt. of chestnuts by dry measure, and when selling used a liquid pint measure. How many pints did he gain by the change?

3. A bushel of cherries, bought at 104 per quart, dry measure, was sold at the same price per quart, wine measure. How much was thereby gained? 4. A cask of cranberries, containing 5, bu., was bought for $15, and retailed at 10¢ per quart by wine measure. What was the gain?

6

5. A blundering clerk bought of a gardener 375 quarts of currants, measuring them by a liquid quart measure, and when selling used a dry quart measure. If he bought at 6¢ per quart and sold at 74, how much less did he receive than if he had measured by dry measure when buying and by liquid measure when selling?

MEASURES OF EXTENSION.

404. Extension is that which has one or more of the dimensions, length, breadth, and thickness; it may therefore be a line, a surface, or a solid.

405. A Line has only one dimension-length.

REMARKS.-1. The United States Standard of linear, surface, and solid measure, is the yard of 3 feet, or 36 inches.

2. The standard, prescribed at Washington, has been fixed with the greatest precision. It was determined by a brass rod, or pendulum, which vibrates seconds in a vacuum at the sea level, in the latitude of London, Eng., and in a temperature of 62° Fahrenheit. This pendulum is divided into 391393 equal parts, and 360000 of these parts constitute a yard.

406. A Surface or Area has two dimensions-length and breadth. 407. A Solid has three dimensions-length, breadth, and thickness.

LINEAR MEASURE.

408. Linear or Long Measure is used in measuring lengths and distances.

Scale, descending, 320, 53 3, 12; ascending, 12, 3, 5, 320.

1 Mile 320 rods, or 5280 feet, or 63360 inches.

Special Table.

of an inch = 1 Size, applied to shoes. | 3 geographic miles = 1 League, used for

6 feet 1 Fathom, used to measure 360 degrees Equatorial circumfer

=

depths at sea.

=

ence of the earth.

1.152 statute miles = 1 Geographic or 1 geographic mile 1 Knot, used to Nautical mile, used for measuring determine the speed of vessels.

distances at sea.

REMARKS.-1. In civil engineering, and at the Custom Houses, the foot and inch are divided into tenths, hundredths, and thousandths.

2. The yard is divided into halves, quarters, eighths, and sixteenths, for measuring goods sold by the yard.

3. The furlong of 40 rods is little used.

4. Degrees are of unequal length; those of latitude varying from 68.72 miles at the Equator to 69.34 miles in the polar regions. The average length, 69.16 miles, is the standard adopted by the United States Coast Survey.

5. A degree of longitude is 69.16 statute miles at the equator, but decreases gradually toward the poles, where it is 0.

EXAMPLES FOR PRACTICE.

REMARK.-For assistance refer to Rules under TROY WEIGHT.

409. 1. Reduce 2 mi. 1 rd. 7 ft. to inches.

2.

3.

Reduce 2501877 inches to higher denominations.
What part of a mile is of a foot?

4. Reduce of a mile to integers of lower denominations.

6.

7.

Reduce .542 of a mile to integers of lower denominations.
Reduce 285 rd. 7 ft. 4 in. to the decimal of a mile.

8. A wheelman ran 71 mi. 246 rd. 1 yd. 2 ft. 6 in. in the forenoon, and 20 mi. 10 rd. 8 in. less in the afternoon. What distance did he run in the entire day?

9. If a yacht makes an average of 227 mi. 227 rd. 2 yd. 2 ft. 2 in. per day, for the seven days of a week, what distance will be passed?

10. If the Servia steams 2905 mi. in six days, what is her average rate per day?

SQUARE MEASURE.

410. Square Measure is used for computing the surface of land, floors, boards, walls, roofs, etc.

411. The Area of a figure is the quantity of surface it contains.

ANGLE.

412. An Angle is the difference in the direction of two lines proceeding from a common point called the vertex.

D

413. A Right Angle is the angle formed when one straight line meets another so as to make the adjacent angles equal. The lines forming the angles are said to be perpendicular to each other. E and F are right angles, and the lines A B and C D are perpendicular to each other.

RECTANGLE.

3 inches.

414. A Rectangle is a plane or flat surface, having four straight sides and four square corners, or four right angles.

a

Contents

or

Six

square

Area.

inches.

6 sq. in.

d

415. The Contents or Area of any surface having a uniform length and a uniform breadth is found by multiplying the length by the breadth. In the accompanying diagram, in which the angles (a, b, c, d), are all right angles, and the corners all square corners, the area is 6 square inches, and is found by multiplying 2 inches by 3 inches.

3 X 2 in.

=

3 feet.

3X3 ft.9 sq. ft. 1 sq. yd.

416. A Square is a figure bounded by four equal lines, and having four right angles.

REMARK.-A square inch is a square, each side of which is 1 inch. A square foot is a square, each side of which is 1 foot. A square yard is a square, each side of which is 1 yard.

36 square miles (6 miles square), 1 township Scale, descending, 36, 640, 160, 304, 9, 144; ascending, 144, 9, 304, 160, 640, 36. REMARK.-All the units of square measure, except the acre, are derived by squaring the corresponding units of linear measure; as, a square foot is a surface one foot square; a square rod is a surface 1 rod or 16 feet square; a square mile is a surface 1 mile or 320 rods square.

417. The Unit of Land Measure 18 the acre, equal to 208.71 ft. X 208.71 ft.

REMARKS.-1. In sections of the United States where the original grants were from France, the arpent, a French unit of surface, equal to about of an acre, is still sometimes used. 2. The Rood, equal to 40 square rods, is but little used

418.

Dimension stuff is sold by board measure.

419. The Unit of Board Measure is a square foot surface, one inch thick, called a board foot.

420. To Find the Number of Roard Feet in a Board.

Rule.-Multiply the length in feet by the width in inches, and divide by 12; the quotient will be the number of square feet.

REMARK.-If the board tapers evenly, find the mean or average width, by adding the width of the two ends, and dividing by 2.

421. To Find the Number of Board Feet in Timbers or Planks.

Rule.-Multiply the length in feet by the product of the width and thickness in inches, and divide by 12.

422. To Find the Number of Squares in a Floor or Roof.

REMARK.-In flooring, roofing, slating, etc., the square, or 100 square feet, is used as a unit of measure.

Rule.-Point off two decimal places from the right of the number of surface feet.

423. To Find the Number of Yards of Carpeting that Would be Required to Cover a Floor.

Rule.-I. Divide one of the dimensions of the floor by 3, add the wastage, if any, and the result will be the length, in yards, of 1 strip of the carpet.

II. Divide the other dimension by the width of the carpet, and the quotient will be the number of strips it will take to cover the floor.

III. Multiply the length of each strip by the number of strips, and the product will be the number of yards required.

REMARK.—In carpeting and papering, it is usually necessary to allow for certain waste in matching the figures of patterns, and often carpets may be laid with less waste one way of the room than the other. Dealers charge for all goods furnished, regardless of the waste.

EXAMPLES FOR PRACTICE.

REMARK.-For assistance refer to rules under TROY WEIGHT.

424. 1. Reduce 5 A. 110 sq. rd. 7 sq. ft. to square inches.

2. Reduce 4 sq. mi. 527 A. 105 sq. rd. to square feet.

3. Reduce .1754 of a square mile to lower denominations.

4. Reduce of an acre to lower denominations.

5.

What fraction of a square mile is of a square foot?

6. What decimal part of an acre is 150 sq. rd. 3 sq. yd. 7 sq. ft. 100 sq. in.?

7. From .6375 of an acre take 14 of a square rod.

8.

9.

10.

To the sum of 3, %, and of an acre, add .0055 of a square mile.
How many squares in a roof, each side of which is 26 × C0 feet?

How many yards of carpet, 1 yard wide, will be required to cover a floor 10.5 yd. long by 6 yd. wide, if no allowance be made for matching?

11.

How many feet in 8 boards, each 15 ft. long, 9 in. wide, and 1 in. thick? How many feet in 15 boards, each 16 ft. long and 1 in. thick, the boards. being 13 in. wide at one end and 10 in. at the other?

12.

13. How many acres in a square field, each side of which is 64 rods in length?

14. What will be the cost of a tract of land 508 rd. long and 1350 rd. wide, at $25 per acre?

15.

acre.

A field 874 rd. wide and 240 rd. long, produced 27 bu. of wheat to the
What was the crop worth, at 904 per bushel?

16. A farm in the form of a rectangle is 75 rd. wide; if the area is 167.5 A., how long is the farm?

17. I wish to build a shed which will cover of an acre of land. If the width of the shed is 42 ft., what must be its length?

18. 17.75 bu. of timothy seed is sown on land, at the rate of 6 lb. per acre. What is the area thus seeded?

19.

21.

22.

23.

What is the difference between a square rod and a rod square?

What is the difference between two square rods and two rods square?
A square yard will make how many surfaces 5 in. by 9 in.?

How many acres of flooring in a six-story block 160 ft. by 220 ft.? A rectangular field containing 16 A. is 45 rd. wide. What is its length? 24. How many fields, each of 10 A. 56 sq. rd. 21 sq. yd. 5 sq. ft. and 28 sq. in., can be formed from a farm containing 124 A. 40 sq. rd. 16 sq. yd. 8 sq. ft. 48 sq. in. ?

25. How many acres in a road 17206 ft. long and 66 ft. wide?

26.

What will be the cost, at $3.50 per M, of the shingles for a roof 26 ft. wide and 110 ft. long, if the shingles are 6 in. wide and 4 inches of their length be exposed to the weather?

27.

sq. yd.

A hall 7 ft. wide and 193 ft. long is covered with oil cloth, at 65¢ per
How much did it cost?

28. If a farm of 106 A. 94 sq. rd. is divided equally into 11 fields, what will be the area of each field?

29.

Reduce 240689740 sq. in. to higher denominations.

30. How many rods of fence will enclose 100 A. of land lying in the form of a square?

31. How many additional rods will divide the farm into four fields of equal area ?