MEASURES OF VOLUME.

384. A Volume is that which has length, breadth, and thickness or height. A volume is also called a solid.

385. A Cube is a volume bounded by six equal squares.

386. A Rectangular Volume or Solid is a volume bounded by rectangles. Cellars, boxes, rooms, etc., are examples of rectangular volumes.

387. All Volumes are measured by ascertaining the number of times they contain a small cube regarded as a unit of measure.

Thus, in the cube in the margin, it will be seen that there are 3 times 3, or 9 cubes upon one surface, and since there are three such layers, there are 3 times 9, or 27 little cubes in all; and since these make up the entire volume, the measure of the cube, called its contents, is 27 cubic units.

CUBIC OR SOLID MEASURE.

388. Cubic or Solid Measure is used in measuring things which have length, breadth, and thickness.

SCALE.-Ascending, 1728, 27; descending, 27, 1728.

1. A cord of wood, so named from being originally measured by a cord, or string, is a pile 8 ft. long, 4 ft. wide, and 4 ft. high. A cord foot is a part of this pile 1 ft. long; it equals 16 cubic feet. See Art. 492.

II. The ton of 40 ft. for round, or 50 ft. for hewn timber is seldom used

EXAMPLES FOR PRACTICE.

1. Reduce 8 cd. 6 cd. ft. to cu. ft.

Ans. 1120 cu. ft.

2. Reduce 78976 cd. ft. to cords. 3. Reduce 8797 cu. ft. to cords.

Ans. 9872 cd.

Ans. 68 cd. 93 cu. ft.

4. In 798765432 cu. in. how many cubic yards?

Ans. 17120 cu. yd. 8 cu. ft. 888 cu. in.

5. What is the difference between a 4 inch cube and 4 cubic inches? Ans. 60 cu. in.

MEASURES OF CAPACITY

389. Measures of Capacity are volumes used to deter mine the quantity of fluids and many dry substances.

390. Measures of Capacity are, therefore, of two kinds, Measures of Liquids and Measures of Dry Substances. 391. Liquid Measures are of two kinds, Liquid or Wine Measure and Apothecaries' Fluid Measure.

LIQUID OR WINE MEASURE.

392. Liquid or Wine Measure is used for measuring all kinds of liquids.

1

=

31

=

126

= 252 = 1008

1 = 4 = 8= 32

SCALE.-Ascending, 4, 2, 4, 311⁄2, 2; descending, 2, 311⁄2, 4, 2, 4.

I. NAME. It is called Wine Measure because wine was measured by it, while beer was measured by another measure.

II. TERMS.-Gill is from Low Latin gilla, a drinking glass; pint is from the Anglo-Saxon pyndan, to shut in, to pen, or from the Greek pinto, to drink; quart is from the Latin quartus, a fourth. The derivation of gallon is not clear; in the French, a galon is a grocer's box.

II. UNIT. The standard unit of wine measure is the gallon, which contains 231 cubic inches, and will hold a little more than 83 lb. Av. of distilled water. This is called the Winchester gallon, from the standard having been formerly kept at Winchester, England. The Imperial gallon, now adopted by Great Britain, contains 277.274 cu. in., or 10 lb. Av. of distilled water, temperature 62° Fah., the barometer standing at 30 inches.

IV. Barrels and hogsheads are of variable capacity. The above values

are used in estimating the capacity of wells, cisterns, vats, etc. In Massachusetts, the barrel is estimated at 32 gallons. A pint of water weighs nearly one pound, hence the old adage, “A pint's a pound the world around."

V. Besides the above the following denominations are frequently given : 42 gal. = 1 tierce; 84 gal. 1 puncheon; 2 hhd., or 126 gal. 1 pipe or butt; 2 pipes = 1 tun. These are not measures, however, but vessels of no uniform capacity; they are usually gauged and have their capacities marked upon them.

VI. Ale, beer, and milk were formerly sold by a gallon of 282 cu. in., the subdivisions being quarts and pints. The measure was greater than wine measure, as beer was less costly than wine.

APOTHECARIES' FLUID MEASURE.

393. Apothecaries' Fluid Measure is used for meas uring liquids in preparing medical prescriptions.

SCALE. Ascending, 60, 8, 16, 8; descending, 8, 16, 8, 60.

I. TERMS.-Minim is from the Latin minimus, the least, the minim being the smallest fluid measure used. Several of the other terms are formed by prefixing fluid to the terms of Apothecaries' Weight.

II. SYMBOLS.-Cong. is the abbreviation of congius, the Latin for gallon, O. is the initial of octarius, the Latin for one-eighth, the pint being one-eighth of a gallon. Drops are indicated in a physician's prescription by gtt., for the Latin gutta.

III. In estimating the quantity of fluids, 45 drops equal about a fluidrachm; a common teaspoon holds about one fluidrachm; a common tablespoon, about a fluidounce; a wineglass, about 11 fluidounces; a common teacup, about 4 fluidounces. The minim is equivalent to a drop of water; but the drops of different liquids vary in size according to the tenacity of the liquid.

DRY MEASURE.

394. Dry Measure is used in measuring dry substances, such as grain, fruit, salt, coal, etc.

3. How many bushels in 78954 pints of timothy seed? Ans. 1233 bu. 2 pk. 5 qt.

4. What cost 8 gal. 3 qt. 1 pt. of kerosene at 3 cts. a pint? Ans. $2.13.

5. What cost 7 bu. 3 qt. 1 pt. of strawberries at 12 a Ans. $54.60.

pint?

CIRCULAR MEASURE.

396. Circular Measure is used to measure angles and directions, latitude and longitude, etc.

397. A Circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the centre.

398. The Circumference of a circle

B

is the bounding line; any part of the circumference, as BC. is an arc. An arc of one-fourth of the circumference is called a quadrant.

399. For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees; each degree into 60 equal parts, called minutes; each minute into 60 equal parts called seconds.

400. Any angle having its vertex at the centre, is measured by the arc included between its sides; thus, COB is measured by the arc BC. A right angle is measured by 90 degrees, or a quadrant; half a right angle, by 45 degrees,

Scale.-Ascending, 60, 60, 30, 12; descending, 12, 30, 60, 60.