DENOMINATE NUMBERS

DEFINITIONS.

330. A Denominate Number is a concrete number, and may be either simple or compound; as, 8 quarts, 5 feet 10 inches, etc.

331. A Simple Denominate Number consists of a unit or units of but one denomination; as, 16 cents, 24 hours, 30 barrels, etc.

332. A Compound Denominate Number consists of units of two or more denominations of the same nature; as, 10 pounds 6 ounces, 5 yards 2 feet 8 inches, etc.

333. In integral numbers, and in decimals, the law of increase and decrease is by the uniform scale of 10; but in Compound Numbers, the scale varies.

MEASURES.

334. A Measure is a standard unit established by law or custom, by which quantity, such as extent, dimension, capacity, amount, or value, is measured or estimated.

Thus, the standard unit of Measures of Extension is the yard; of Liquid Measure, the wine gallon; of Dry Measure, the Winchester bushel; of Weight, the Troy pound, etc. Hence the length of a piece of cloth is ascertained by applying the yard measure; the capacity of a cask, by the use of the gallon measure; of a bin, by the use of the bushel measure; the weight of a body, by the pound weight, etc.

MEASURES OF EXTENSION.

336. Extension is that which has one or more of the dimensions length, breadth, and thickness. It may be a line, a surface, or a solid.

337. The Standard Unit of measures of extension, whether linear, surface, or solid, is the yard.

LINEAR MEASURE.

338. Linear or Long Measure is used in measuring lines and distances.

339. A Line has only one dimension—length.

1. The Inch is generally divided into halves, quarters, eighths, sixteenths, and sometimes into tenths or twelfths.

2. Civil and mechanical engineers, and others, use decimal divisions of the foot and inch.

OTHER DENOMINATIONS.

3 Barley-corns, or sizes=1 Inch.

Used by shoemakers.

4 Inches

9 Inches

21.888 Inches

6 Feet

120 Fathoms

3 Feet

=1 Hand.

66

{to measure the height of

horses at the shoulder.

=1 Span. Among sailors, 8 spans

-1 Sacred Cubit.

1 fathom.

=1 Fathom. Used to measure depths at sea. -1 Cable's Length.

=1 Pace.

1.152 Common Miles =1 Geog. Mi. Used to meas. distances at sea.

1. A Knot is 1 geographical or nautical mile, used to measure the speed of vessels.

2. The geographic mile is

of ʊ, or

of the circumference of the earth. It is a little more than 1.15 common miles.

340. Cloth Measure is practically out of use. In measuring goods sold by the yard, the yard is divided into halves, fourths, eighths, and sixteenths.

At custom houses, in estimating duties, the yard is divided into tenths and hundredths.

341. Surveyors' Linear Measure is used by land surveyors in measuring roads and boundaries of land.

1. A Gunter's Chain is the unit of measure, and is 4 rods, or 66

feet long, and consists of 100 links.

2. Engineers commonly use a chain, or measuring tape, 100 feet long.

3. Measurements are recorded in chains and hundredths.

SURFACE OR SQUARE MEASURE.

342. Surface or Square Measure is used in computing areas or surfaces.

343. A Surface has two dimensions-length and breadth.

SQUARE INCH

1 inch.

1 inch.

344. The Area of a surface is expressed by the product of the numbers that represent these two dimensions.

345. A Square is a plane figure bounded by four equal sides, and having four right angles.

A Square Inch is a square each side of which is 1 inch in length.

TABLE.

144 Square Inches (sq. in.) = 1 Square Foot .

= 1 Square Yard.

= 1 Square Rod or Perch. sq rd., P. = 1 Acre.

sq. yd.

A.

1 640 102400

346. Surveyors' Square Measure is used by surveyors in computing the area or contents of land.

36 Square Miles (6 miles square) = 1 Township

1 Square Mile

sq. mi.

1. The Acre is the unit of land measure.

2. Measurements of land are commonly recorded in square miles, acres, and hundredths of an acre.

CUBIC OR SOLID MEASURE.

347. Cubic or Solid Measure is used in computing the contents or volume of solids.

348. A Solid or Body has three dimensionslength, breadth, and thickness.

349. The Volume of a body is expressed by the product of the numbers that represent these dimensions.

350. A Cube is a body bounded by six equal squares, called faces.

The sides of these squares are called the edges of the cube.

A Cubic Inch is a cube each side of which is 1 inch in length.

1 inch.

TABLE.

1 inch.

1728 Cubic In. (cu. in.) = 1 Cubic Ft. cu.ft.

cu. yd. cu. ft. cu. in. 1 =2746656

For Notes and Applications, see "Measurements" (474-477).