OBS. 1. The Avoirdupois Pound of the United States, is equal to 27-7015 cubic 10000 inches of distilled water, at the maximum density, and at 30 inches barometer. It is determined from the Troy pound, by the legal proportions of 5760 grains, which constitute the Troy pound, to 7000 grains Troy, which constitute the avoirdupois pound.* That is,

2. The British Imperial Pound Avoirdupois is defined to be the weight of 210000 7274 cubic inches of distilled water, at the temperature of 62° Fahrenheit, when the barometer stands at 30°.†

3. Formerly it was customary to allow 112 pounds for a hundred weight, and 28 pounds for a quarter; but this practice has become nearly or quite obsolete. The laws of most of the States, as well as general usage, call 100 lbs. a hundred weight, and 25 lbs. a quarter.

In estimating duties, and weighing a few coarse articles, as iron, dye-woods, and coal at the mines, 112 lbs. are still allowed for a hundred weight. Coal, however, is sold in cities, at 100 lbs. for a hundred weight.

4. Gross weight is the weight of goods with the boxes, casks, or bags which contain them, and allows 112 lbs. for a hundred weight.

Net weight is the weight of goods only, and allows 100 lbs. for a hundred weight.

Note. The term Avoirdupois, is thought by some to be derived from the French avoir du poids, a phrase signifying to have weight. Others think it is from avoirs, the ancient name of goods or chattels, and poids signifying weight in the Norman dialect.‡

APOTHECARIES' WEIGHT.

150. Apothecaries' Weight is used by apothecaries and physicians in mixing medicines. Its denominations are pounds, ounces, drams, scruples, and grains.

20 grains (gr.) make 1 scruple, marked sc., or .

QUEST.-Point to an object that weighs an ounce. A pound. Obs. How is the Avoirdupois pound of the United States determined? How many pounds were formerly allowed for a hundred weight? For a quarter? What is gross weight? Net weight? 150. In what is Apothecaries' Weight used? What are its denominations? Recite the Table.

* Reports of Secretary of Treasury, March 3d, 1832; June 20, 1832. Also, Congressional Documents of 1833.

+ Hind's Arithmetic, Art. 223.

Adams' Report on Weight and Measures; also, Hind's Arithmetic.

OBS. 1. The pound and ounce in this weight are the same as the Troy pound and ounce. The only difference between Apothecaries' and Troy weight, is in the divisions and subdivisions of the ounce.

2. Drugs and medicines are sold at wholesale by avoirdupois weight.

LONG MEASURE.

151. Long Measure is used in measuring length or distances only, without regard to breadth or depth. Its denominations are leagues, miles, furlongs, rods, yards, feet, and inches.

860 degrees make a great circle, or the circumference of the earth.

Note.-4 inches make 1 hand; 9 inches, 1 span; 18 inches, 1 cubit; 6 feet, Í fathom; 4 rods or 100 links, I chain; 25 links, 1 rod, 7-92 inches, 1 link.

100

The chain is commonly used in measuring roads and land, and is called Gunter's Chain, from the name of its inventor.

A knot, in sea phrase, answers to a nautical or geographical mile.

OBS. 1. The standard unit of Length adopted by the United States, is the Yard of 3 feet, or 36 inches, and is identical with the British Imperial Yard. It is made of brass, and is determined from the scale of Troughton,* at the temperature of 62° Fahrenheit. For the method of determining the standard unit of length adopted by Great Britain, France, and the State of New York, see Higher Arithmetic, Arts. 255, 273.

2. Long Measure is frequently called linear, or lineal measure. Formerly the inch was divided into 3 barleycorns; but the barleycorn, as a measure, has become obsolete.

The inch is commonly divided either into eighths or tenths; sometimes, however, it is divided into twelfths, which are called lines.

QUEST. Obs. To what are the apothecaries' ounce and pound equal? How are drugs and medicines bought and sold? 151. In what is Long Measure used? What are its denominations? Recite the Table. Draw a line an inch long upon the blackboard. Draw one a foot, and another a yard long. How long is your desk? Your teacher's table? How wide? How long is the school room? How wide? Obs. What is the standard unit of Length adopted by the United States ? What is Long Measuro froquently called?

• A celebrated English artist.

CLOTH MEASURE.

152. Cloth Measure is used in measuring cloth, lace, and all kinds of goods which are bought or sold by the yard. Its denominations are ells, yards, quarters, nails, and inches.

OBS. Cloth measure is a species of long measure. The yard is the same in both. Cloths, laces, &c., are bought and sold by the linear yard without regard to their width. Ells are seldom used.

SQUARE MEASURE.

153. Square Measure is used in measuring surfaces, or things whose length and breadth are considered without regard to heighth or depth; as land, flooring, plastering, &c. Its denominations are acres, roods, square rods, square yards, square feet, and square inches.

144 square inches (sq. in.) make 1 square foot,

1 square yard.

marked sq.ft.

square rod,
perch or pole,

1 rood,

1 acre

แ

1 square mile,

Note.-16 square rods make 1 square chain; 10 square chains, or 100,000 square links, make an acre. Flooring, roofing, plastering, &c., are frequently estimated by the "square" which contains 100 square feet.

OBS. 1. A square is a figure which has four equal sides, and all its angles right angles, as seen in the following diagram. Hence,

QUEST.-152. In what is Cloth Measure used? What are its denominations? Repeat the Table. Obs. Of what is cloth measure a species? What is the kind of yard by which cloths, laces, &c., are bought and sold? 153. To what use is Square Measure applied? What are its denominations? Recite the Table Obs. What is a square? Draw a square upon the blackboard.

2. A Square Inch is a square, whose sides are each a linear inch in length.

A Square Foot is a square, whose sides are each a linear foot in length, and is equal to 144 square inches, or the product of 12 in. x 12.

A Square Yard is a square, whose sides are each a linear yard, or three linear feet in length, and is equal to 9 square feet, or the product of 3 ft. x 3 as represented in the adjacent figure. Hence,

3 ft. x3=1 sq. yd.

3. The area of squares, and all right-angled parallelograms, is found by multiplying the length by the breadth.

CUBIC MEASURE.

154. Cubic Measure is used in measuring solid bodies, or things which have length, breadth, and thickness, such as timber, boxes of goods, the capacity of rooms, &c. Its denominations are tons, cords, cubic yards, cubic feet, and cubic inches.

1728 cubic inches (cu. in.) make 1 cubic foot,

27 cubic feet

40 feet of round, or
50 ft. of hewn timber S

42 cubic feet

16 cubic feet

8 cord feet, or

marked cu. ft.

66

1 cubic yard,

128 cubic feet

OBS. 1. A pile of wood 8 feet long, 4 feet wide, and 4 feet high, contains 1 cord. For, 8 x 4 x4=128. 2. A Cube is a solid body bounded by six equal quares. It is often called a hexaedron. Hence,

A Cubic Inch is a cube, each of whose sides is a quare inch, as represented by the adjoining figure. A Cubic Foot is a cube, each of whose sides is a 'quare foot.

A Cubic Yard is a cube, each of whose sides is a quare yard, and is equal to 27 cubic feet, or the product of 3 ft. x 3 x 3. Hence,

66 C.

3 ft. x 3 x3=1 cu. yd.

QUEST.-What is a square inch? A square foot? What is a square yard? Draw a square inch; a square foot; a square yard. 154. To what use is Cubic Measure applied? What are its denominations? Recite the Table. Obs. What is a cube? What is a cubic inch? A cubic foot? Draw a cubic inch upon the black board. What is meant by a ton of round timber?

3. The solidity of a cube, and all bodies having six sides perpendicular to eash other, is found by multiplying the length, breadth and thickness together.

4. The Cubic Ton is chiefly used for estimating the cartage and transportation of timber. By a ton of round timber is meant, such a quantity of timber in its rough or natural state, as when hewn, will make 40 cubic feet, and is supposed to be equal in weight to 50 feet of hewn timber.

The cubic ton, (formerly called load,) is by no means an accurate or uniform standard of estimating weight; for, different kinds of timber, are of very different degrees of density.

WINE MEASURE.

155. Wine Measure is used in measuring wine, alcohol, molasses, oil, and all other liquids except beer, ale, and milk. Its denominations are tuns, pipes, hogsheads, gallons, quarts, pints,

and gills.

4 gills (gi.)

339

OBS. The standard unit of Liquid Measure of the United States, is the Wine Gallon, which contains 231 cubic inches, and is equal to 8, pounds avoirdupois of distilled water, at the maximum density.

BEER MEASURE.

1000

156. Beer Measure is used in measuring beer, ale, and milk. Its denominations are hogsheads, barrels, gallons, quarts, pints.

1 hogshead,

66

hhd.

1 barrels, or 54 gals. OBS. The beer gallon contains 282 cubic inches. In many places milk is measured by wine measure.

QUEST.-155. In what is Wine Measure used? What are its denominations? Recite the Table. Obs. What is the standard unit of Liquid Measure of the United States? How many cubic inches in a wine gallon? 156. In what is Beer Measure used? What are its denominations? Recite the Table. Obs. How many cubic inches in a beer gallon?