ang, long, the length of a furrow; mile is from mille passuum, 1000 paces span is the space measured from the end of the thumb to the end of the little finger extended; cubit, from the elbow to the end of the middle finger; fathom, the length of the two arms extended. The ancient yard of England is said to have been determined by the length of the arm of King Henry I. II. UNIT.-The standard unit of length is the yard, from which all other measures of length, and also those of capacity, weight, etc., are derived. It is identical with the Imperial yard of Great Britain, which, under William IV., was declared to be fixed by dividing a pendulum, which vibrates seconds in a vacuum, at the level of the sea, at 620 Fah., in the latitude of London, 'nto 391393 equal parts, and taking 360000 of these parts for the yard. Subsequent scientific experiments have proved that such a standard is impracticable.-See Brooks's Philosophy of Arithmetic. III. THE MILE.-The geographic or nautical mile is equal to 1 minute of one of the great circles of the earth; hence it equals of 3 of the circumference of the earth, which equals about 1.15 statute miles. The English mile is the same as that of the United States. 3 statute miles make a land league; 3 nautical miles make a nautical league. IV. OTHER MEASURES.-The following denominations are frequently used in clock-making, 6 points=1 line, and 12 lines = 1 inch; in measuring the foot, 3 barleycorns or sizes=1 inch; in measuring the height of horses, 4 inches = 1 hand, the measure being taken directly over the foreshoulder; 1 span=9 inches; 1 common cubit 18 inches, and 1 sacred cubit=21.888 inches; 1 pace=3.3 feet; a knot is equal to a nautical mile. Formerly 40 rods made 1 furlong and 8 furlongs one mile, but these are seldom used. How many MENTAL EXERCISES. 1. Feet in 72 in.? 14 yd.? 2. Yards in 36 ft.? 10 rd.? 3. Rods in 22 yd.? 2 fur.? 4. Furlongs in 200 rd.? 7 mi.? 5. Miles in 320 fur.? 9 lea.? 6. Yards in 36 inches? 72 in.? 7. What part of 1 yard are 2 ft.; and what part of 2 furlongs are 5 yards? 8. How high is a horse which measures 15 hands in height? EXAMPLES FOR PRACTICE. Ans. 332 in. 1. Reduce 27 ft. 8 in. to inches. 2. 3 rods 4 yd. 2 ft. to feet. 5. 19870 ft. to miles. 6. 277 rd. 4 yd. to yards. 7. 70287 in. to miles. Ans. 63 ft. Ans. 2 rd. 4 yd. 2 ft. 3in Ans. 3 mi. 244 rd. 1 yd. 1 ft. Ans. 1 mi. 34 rd. 5 yd. 1 ft. 3 in. 8. 3 mi. 265 rd. 7 in. to inches. that, and how many steps, 3 feet long, would a person take to walk the distance? Ans. 5280000 steps. SURVEYORS' LINEAR MEASURE.. 269. Surveyors' Linear Measure is used by surveyors and engineers in measuring the dimensions of land, distances, etc. I. NAME. Gunter's Chain is named after the reputed inventor, Edmund Gunter, an English mathematician, born 1581. II. UNIT.-The unit is a chain called Gunter's Chain, which consists of 100 links, and is 4 rods, 66 feet, or 792 inches long. III. The denomination rods is seldom used by surveyors, distances being represented in chains and links. Since each link is of a chain, the num ber of links is generally expressed as a decimal; thus, 5 chains and 47 links are written 5.47 chains. Engineers generally use a chain 100 feet long. MARINERS' AND CLOTH MEASURES. 270. Mariners' Measure is used by seamen in measuring distances, the depth of the sea, etc. Cloth Measure is used for measuring cloth, ribbons, etc. I. The foot and yard of these two measures are the linear foot and yard The nail in Cloth Measure is obsolete. At the custom-houses the yard is divided into tenths, hundredths, etc. II. In the old table of Cloth Measure there were given 3 qrs. Flemish; 5 qrs. 1 Ell English; 6 qrs. Ell Scotch. 1 Ell French; 6 qrs. 1 MENTAL EXERCISES. How many 1. Inches in a chain? 2. Feet in a chain? a fathom? EXAMPLES FOR = 1 EL in. 3. Feet in 6 fathoms? MEASURES OF SURFACE. 271. A Surface is that which has length and breadth without thickness. 272. A Square is a plane surface which has four equal sides and four right angles. 273. All Surfaces are measured by ascertaining the number of times they contain a small square regarded as the nit of measure. Thus, in the surface in the margin there are three rows of squares, each row containing 4 squares; bence there are 3 times 4 or 12 squares in all; and since these make up the entire surface, the measure of the surface, called its area, is 12 square units. SURFACE OR SQUARE MEASURE. 274. Surface or Square Measure is used in measuring surfaces, as land, boards, amount of painting, papering, plastering, paving, etc. 1. 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. How many MENTAL EXERCISES. 1. Square inches in 3 sq. ft.? 5 sq. ft.? 5. Roods in 160 P.? 15 A.? 6. Acres in 84 R.? 3 sq. mi. 7. What is the difference between 3 feet square and 3 square feet? between 4 inches square and 4 square inches? EXAMPLES FOR PRACTICE. 1. Reduce 9870 P. to acres Ans. 61 A. 110 P. Ans. 94684 sq. yd. Ans. 1668894 sq. ft. Ans. 4295268 sq. in. Ans. 5 A. 77 P. 211 sq. ft. 108 sq. in. 6. 9876543 sq. in. to acres. Ans. 1 A. 91 P. 252 sq. ft. 51 sq. in. SURVEYORS' SQUARE MEASURE. 275. Surveyors' Square Measure is used by surveyrs in computing the area of land. = = = 1 square chain, sq. ch. 1 acre, 1 square mile, = 1 township, 1 perch; 16 perches : = A. 8q. mi. Tp. Also 625 sq. li. 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 esti mated in square miles, acres, and hundredths. How many MENTAL EXERCISES. 1. Square links in 4 sq. ch.? 6. Townships in 72 sq. mi.? 144 sq. mi.? EXAMPLES FOR PRACTICE, 1. Reduce 21 sq. mi. 65 A. 9 sq. ch. to sq. links. Ans. 1350590000 sq. li. 2. Reduce 1,000,000 sq. li. to acres. Ans. 10 A. 8. 2 Tp. 21 sq. mi. 47 A. to sq. ch. Ans. 595670 sq. ch 4. 8700 sq. chains to sq. miles. Ans. 1 sq. mi. 230 A. 5. 3 Tp. 250 A. 9 sq. ch. to sq. links. Ans. 6937090000. MEASURES OF VOLUME. 276. A Volume is that which has length, breadth and thickness, or height. A volume is also called a solid. 277. A Cube is a volume bounded by six equal squares. 278. 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. 279. Cubic, or Solid Measure is used in measuring things which have length, breadth, and thickness. 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. 358. II. The ton of 40 ft. for round, or 50 ft. for hewn timber, is seldom used. w many MENTAL EXERCISES. 1. Inches in 2 cu. ft.? 4 cu. ft.? 4. Feet in 6 cd.? in 4 cd.? 2. Feet in 3 cu. yd.? 5 cd ft.? 5. 3. Cubic yards in 81 cu. ft.? Cords in 256 cu. ft.? 72 cd. ft.? 6. Cubic yards in 135 cu. ft.? between a 2 inch cute and 2 cubic 7. What is the difference inches? between a 3 inch cube and 3 cubic inches? |