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WEIGHTS AND MEASURES.

197. Measure is that by which extension, capacity, force, duration, or value is estimated or determined.

198. Extension is that which has one or more of the dimensions of length, breadth, and hight or depth; as

199. A LINE, or that which has only length;
A SURFACE, or that which has only length and breadth;

A SOLID, Body, or Volume, or that which has length, breadth, and hight or depth.

The Faces of a solid or volume are its bounding surfaces.

200. Weight is the measure of the quantity of matter in a body, determined by the force by which it is naturally drawn toward the earth.

201. A Unit of Measure is some quantity used as a standard of comparison in measuring a quantity of the same kind.

COMMON WEIGHTS AND MEASURES.

202. Common Weights and Measures are those in general

use.

TROY WEIGHT.

203. Troy Weight is used for weighing gold, silver, and jewels.

Table.

24 grains (gr.)
20 pennyweights,

are 1 pennyweight, pwt.

1 ounce,
1 pound,

1b.

OZ.

12 ounces,

What is Measure? A Line? A Surface? A Solid, Body or Volume? Weight? A Unit of Measure? The Common Weights and Measures ? For what is Troy Weight used ? Repeat the Table.

OZ.

APOTHECARIES, in mixing medicines, use the pound, ounce (3), and grain, of this weight; but divide the ounce into 8 drams (3), each equal to three scruples ( ?), each scruple being equal to 20 grains.

A carat, for gold-weight, is 4 grains; for diamond-weight, is 3.2 grains. A pound Troy contains 240 pennyweights, or 5760 grains.

AVOIRDUPOIS WEIGHT. 204. Avoirdupois Weight is used for nearly all articles estimated by weight, except gold, silver, and jewels.

Table. 16 drams (dr.)

are 1 ounce, 16 ounces,

1 pound,

lb. 100 pounds,

1 hundred-weight, cwt. 20 hundred-weight,

1 ton,

T. Also, 25 pounds are 1 quarter (qr.).

The dram as a unit is used chiefly by manufacturers of silk, silktriinmings, etc.

Formerly, 112 pounds were reckoned a hundred-weight, and 2240 pounds a ton, now called the long ton. This is now seldom employed in this country, except at the mines for coal, or at the United States Custom-houses. · A pound Avoirdupois is equivalent to 7000 grains Troy, so that 144 pounds Avoirdupois are equal to 175 pounds Troy.

LINEAR MEASURE. 205. Linear or Long Measure is used in estimating distances and the length of articles.

Table.
12 inches (in.) are 1 foot,

ft.
3 feet,

1 yard, 51 yards, or 162 ft. 1 rod,

rd. 320 rods,

1 common mile, m. Also, 40 rods are 1 furlong (fur.); 8 furlongs 1 mile.

yd.

How do Apothecaries divide the ounce ? What is a carat? What does a pound Troy contain ? For what is Avoirdupois Weight used ? Repeat the Table? How was a hundred-weight formerly reckoned? Where is the long ton now used? To what is a pound Avoirdupois equal ? For what is Linear Measure used ? Repeat the Table.

In measuring cloth and other woven fabrics, the linear yard is divided into halves, quarters, eighths, and sixteenths. Formerly a sixteenth of a yard, or 24 inches, was called a nail.

An engineer's chain, or measuring tape, is usually 100 feet in length, with each foot divided into tenths. Surveyors, however, make frequent use of Gunter's chain, which is 4 rods, or 66 feet, in length, and divided into 100 links of 7.92 inches each. Links are usually expressed as hundredths of a chain.

4 inches equal 1 hand in measuring the hight of horses directly over the fore feet; 6 feet equal 1 fathom, in measuring deptbs at sea; and 3 common miles equal i league on the land.

A geographic or nautical mile is ab of the length of a degree of latitude.

The United States coast survey employ 6086.34 feet, or 1.15+ common miles, as the average length of a nautical mile, and 69.16 co miles as the length of a degree of longitude on the equator.

A mile is 320 rods 1760 yards 5280 feet 63360 inches.

SURFACE MEASURE.

206. Surface or Square Measure is used in estimating surfaces.

D

207. The Area of a figure is its quantity of stirface.

208. An Angle is the difference in direction of two straight lines, which meet at a point. Thus, ACD and DCB are angles.

А

с

B

209. A Square is a surface having four equal sides and four equal angles.

The area of a square, each of whose sides is 1 foot, is 1 square foot.

How is the yard divided in measuring cloth? What is an engineer's chain, or measuring tape ? Gunter's chain ? A geographic or nautical mile? The length of a nautical mile? A degree of longitude on the equator? To what is a mile equal ? For what is Surface Measure used ? What is the Area of a figure ? An Angle? A Square ?

210. A Rectangle is any surface having four sides and four equal angles.

In the large square are represented 3 rows of small squares, of 3 squares each. If each of these small squares is supposed to be one square foot, then in the large square there evidently are in one of the equal rows, 3 times 1 square foot, or 3 square feet; and in the three rows, 3 times 3 square feet, or 9 square feet, or as many as the product of the number expressing the length by that expressing the breadth. Hence,

The area of a rectangle is equal to the product of the length by the breadth.

Table.

sq. ft.

1 acre,

640 acres,

144 square inches (sq. in.)

are 1

square foot,
9
square feet,

1
square yard,

sq. yd. 304 square yards,

1
square rod or perch,

P. 160 square rods or perches,

A. 1 square mile,

M. In surveying by Gunter's chain, 1 square chain is 16 square rods, and square chains are 1 acre. In measurement of government lands, 640 acres, or 1 square mile, make 1 section of land.

A rood equals 40 square rods or perches, but this denomination in not now much used.

An acre is 4840 square yards=43560 square feet=6272640 square inches.

10

What is a Rectangle? To what is the area of a rectangle equal ? Repeat the Table. How much is 1 square chain? 10 square chains ? How many acres in one square mile or section of land ? What does a rood equal ?

An acre ?

SOLID MEASURE.

211. Solid or Cubic Measure is used in measuring bodies, or things having length, breadth, and hight or depth.

212. The Contents of a solid or volume are the number of times it contains a given unit of measure.

213. A Cube is a body bounded by six square and equal sides or faces.

If a cube has each of its equal faces 1 square foot, it is 1 solid or cubic foot.

214. A Rectangular Solid is a body bounded by rectangular faces.

In the large cube are represented 3 tiers of small cubes, of 3 rows each, and 3 in a row. If each of these small cubes is supposed to be one solid foot, then in the large cube there evidently are in one of the equal tiers 3 times three solid feet, or 9 solid feet, and in the 3 tiers, 3 times 9 solid feet, or 27 solid feet, or as many as the product of the numbers denoting the length, breadth, and hight or depth. Hence,

The contents of a rectangular solid are equal to the product of the length, breadth, and hight or depth.

Table.
1728 cubic inches (cu. in.) are 1 cubic foot,
27 cubic feet,

1 cubic yard, cu. yd.
128 cubic feet,

1 cord,

cu. ft.

C.

For what is Solid or Cubic Measure used? What is the Contents of : solid or volume ? What is a Cube ? A Rectangular Solid ? To what is the contents of a rectangular solid equal ? Repeat the Table.

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