« ΠροηγούμενηΣυνέχεια »
I. TERMS.-Perch is from the French perche, a pole; acre was primarily an open plowed or sowed field.
II. UNIT. – The unit for land is the acre; for other surfaces it is usually the square yard.
III. The perch is a surface equal to a square rod. The rood is found now only in old title-deeds and surveys; it is equal to 40 perches.
IV. A square piece of land, measuring 209 feet, or about 70 paces on each side, equals very nearly one acre.
SURVEYORS SQUARE MEASURE. 383. Surveyors' Square Measure is used by surveyors in computing the area or contents of land.
TABLE. 10,000 square links (sq. li.) = 1 square chain, . sq. ch.
10 square chains . = 1 acre, . . A. 640 acres . . . = 1 square mile, . sq. mi.
36 sq. mi. (6 miles square) = 1 township, . . Tp. Tp. sq. mi. A. sq. ch. sq. li. 1 = 36 = 23040 = 230400 = 2304000000 1 = 640 = 6400 = 64000000
1 = 10 = 100000 SCALE.—Ascending, 10,000, 10, 640, 36; descending, 36, 640, 10, 10,000.
I. Also 625 sq. li.=1 perch; 16 perches=1 sq. chain; 10 sq. ch.=1 acre; or, 40 perches=1 rood ; 4 roods=1 acre. The perch and rood are not so much used as formerly, the contents of land being commonly estimated in square miles, acres, and hundredths.
EXAMPLES FOR PRACTICE. 1. How many square chains in 10 A. 150 P.?
Ans. 109.375 sq. ch. 2. Reduce 5 A. 120 P. to sq. in. Ans. 36067680 sq. in. 3. Reduce 89794172 sq. in. to acres.
Ans. 14 A. 50 P. 13 sq. yd. 1 sq. ft. 20 sq. in. 4. Reduce 78985432184 sq. li. to townships.
Ans. 34 Tp. 10 sq. mi. 94 A. 3 sq. ch. 2184 sq. li. 5. Required the value of a field containing 45 sq. chains at $120 an acre.
Ans. $540. 6. Bought 12 A. 100 P. of land at $160 an acre, and sold it for $161 a square chain; what did I gain? Ans. $63.12.
7. What is the difference in area between a garden bed 5 feet square and one containing 5 square feet?
Ans. 20 sq. ft.
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.
1728 cubic inches (cu. in.) = 1 cubic foot, cu. ft. 27 cubic feet . .
1 cubic yard, cu.yd. 16 cubic feet . . = 1 cord foot cd. ft. 8 cord feet, or )
1 cord of wood, cd. 128 cubic feets cd. cu. yd.
cu. in. 1 = 42. = 128 = 221184
27 = 46656 SCALE.—Ascending, 1728, 27; descending, 27, 1728. I. 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.
Ans. 4936 cd. 3. Reduce 8797 cu. ft. to cords. 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 determine 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.
4 gills (gi.) . . = 1 pint . . pt. 2 pints . . = 1 quart . . qt. 4 quarts . . . = 1 gallon. . gal. 312 gallons .'. = 1 barrel. . bar. 63 gallons or 2 bar. . = 1 hogshead : hod.
hhd. bar. gal. qt. pt. gi.
1 = 4 = 8 = 32 SCALE.— Ascending, 4, 2, 4, 313, 2; descending, 2, 313, 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 81 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. Ay, 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."
y. 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 measuring liquids in preparing medical prescriptions.
TABLE. 60 minims (m) . = 1 fluidrachm. f3.
8 fluidrachms . . = 1 fluidounce . . fz. 16 fluidounces . . = 1 pint .
. 0. 8 pints . . . = 1 gallon . . Cong.
SCALE.—Ascending, 60, 8, 16, 8; descending, 8, 16, 8, 60. I. TERMS.—Minim is from the Latin mirimus, 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 7 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.
TABLE. 2 pints (pt.) . . = 1 quart . i qt. 8 quarts . . . = 1 peck . . pk. 4 pecks . . . = 1 bushel . . bu. bu. pk. qt.
32 = 64 1 = 8 = 16 SCALE.- Ascending, 2, 8, 4; descending, 4, 8, 2.
I. TERMS.- Peck is supposed to be a corruption of pack, or to be derived from the French picotin, a peck.
II. UNIT.-The unit is the Winchester bushel, formerly used in England, and named from the place where the standard was preserved. In form it is a cylinder, 181 in. in diameter, and 8 inches deep. Its volume is 2150.42 cu.in., and contains 77.627113 lb. Av. of distilled water, at its maximum density. The New York bushel is nearly identical with the Imperial bushel of Great Britain, which contains 2218.192 cu. in.
III. The Cental of 100 lb. is a standard recently recommended by the Boards of Trade of New York, Cincinnati, Chicago, and other large cities for estimating grain, seeds, etc. Bushels are changed to centals, by multiplying by the number of pounds in 1 bushel, and dividing the product by 100. The remainder will be hundredths of a cental.
IV. The Chaldron, consisting in some places of 36 bu., and in others of 32 bu., is used in some parts of the United States for measuring coal and coke, but is being discontinued here, as it has been in England. The coal bushel contained 1 quart more than the Winchester bushel. Twenty-one chaldrons made a score. Foreign coal is imported by the chaldron, but American coal is generally bought and sold in large quantities by the ton, in small quantities by the bushel.
V. Where fruit and vegetables are sold by the basket or barrel, a peach basket should hold 2 pk., a potato basket 3 pk., and a barrel 3 potato baskets. Barrels made for measuring articles for market usually hold 100 quarts.
395. The Weight of a Bushel of the principal kinds of grain, seeds, and dried fruit has been fixed by statute in many of the States, as shown by the following
NOTE.-In Pennsylvania 80 lb. coarse, 70 lb. ground, or 62 lb. fine salt make 1 bushel, and in Illinois 50 lb. common, or 55 lb. fine salt make 1 bushel.
EXAMPLES FOR PRACTICE. 1. How many minims in 4 Cong. 2 0. 15fz. 7f3. ?
Ans. 268740 m. 2. How many Cong. in 8472347 m. ?
Ans. 137 Cong. 70. 2 fz. 5 f3. 47 m.