Demonstration of the Proof-We first divide the nails by 4, because it takes 4 nails to make a quarter; and we next divide the quarters by 4, because it takes 4 quarters to make a yard. NOTE. In reduction it must be kept in mind, that we only change the name of our denominations, not altering their value or quantity. 2. In 1520 nails; how many yards? 3. In 800 quarters; how many yards? 4. In 340yds. 2qrs. 3na.; hów many nails? 5. In 4234 nails; how many ells English? Ans. 95yds. Ans. 200yds. Ans. 545 Ina. Ans. 211 ells 3qrs. 2na. 6. In 3464 yards; how many ells Flemish ? Ans. 4618 ells 2 qrs. 7. In 6846 ells French; how many ells English? Ans. 8215 E. E. 1qr. 8. In 60 ells French; how many yards? 9. In 60 ells English; how many yards? 10. In 60 ells Flemish; how many yards? 11. In 4 pieces of cloth, each 24 yards; how many nails? Ans. 1536na. 12. In 3 pieces of cloth, each containing 25 ells English; how many yards? Ans. 93yds. 3qrs. 13. In 1280 nails; how many pieces of cloth, each 20 yards? Ans. 4 pieces. 14. In 644 ells Flemish, how many ells French? Ans. 322 ells Fr. 15. In 84642 nails; how many ells Flemish? Ans. 7053 ells Fl. 1qr. 2na. This measure is used in measuring fruit, potatoes, apples, pears, &c. which are given in rounding measure. Grain, salt, &c. are mea sured by striked measure, unless sold by weight. NOTE.-In dry measure, a gallon contains 268 cubick inches. A Winchester bushel is 8 inches deep, and 18 inches in diameter, and contains 2150 cubick inches. This is the bushel in common use. 1. In 34 bushels; how many pecks, quarts, and pints? Proof 34bu. -136pks. 8 1088qts. 2 2)2176pts: Ang 34bu. Ans. 136pks. 1088qts. 2176pts. DEMWe first multiply by 4, because 4 pecks make a bushel; we next multiply by 8, because 8 quarts make a peck; and lastly, we multiply by 2, because 2 pints make a quart. NOTE. It is evident, that reduction descending may be proved by reduction ascending, because it is only reversing out work; that is, dividing by the same numbers, which we multiplied by. And in reduction ascending, it is plain that we must, in proving our work, multiply by the numbers which were our divisors in the first operation, making our last divisor our first multiplier, and so on. 2. In 1024 pints; how many bushels? 4. In 40 bushels; how many pints? Ans. 16bu. Ans. 1728pks. 5. How many pecks are there in 4 bins, each bin containing 25 bushels? 6. In 46321 pecks; how many chaldrons.?. Ans. 400pks. Ans. 321ch. 24bu. 1pk. 7. A man wishes to barrel 300 bushels of corn for ship ping, each barrel will hold 3 bushels and 3 pecks; how many barrels will it require? Ans. 80 barrels. LIQUID MEASURE.* (See top next page.) * All spiritous liquors are measured by this measure; Rum, Brandy, Gin, Whiskey, &c. NOTE.-The wine gallon contains 231 cubick or solid inches, and the ale gallon 282 cubick or solid inches. EXAMPLES. 1. In 44 barrels; how many gallons, quarts, and pints? Ans. 1386gal. 5544qts. 11088pts. 2. In 26 hogsheads; how many gallons, and quarts? 26 hhd. 63 78 150 1638 gal. 4 Ans. 1638gals. 6552qts. DEM.-Here, we multiply by 63, because we must have 63 times as many gallons as hogsheads to equal our hogsheads in quantity. We next multiply by 4, because we must have 4 times as many quarts as gallons to equal our gallons in quantity. 6552 qts. Ans. 4hhd. 16gal. 4. In 9 tuns of wine; how many gallons? Ans. 3hhd. Ans. 5292gal. 84hhd. 8. În 58 barrels of cider; how many gallons, quarts, and Ans. 1827 gal. 7308qts. 14616pts. pints? 9. In 2016 pints; how many barrels ? Ans. 8bl. Ans. 4hhd. 1 Degree on the earth, and 360 Degrees, the whole circumference of the earth. By this measure we find the distance of one place from another, where length is considered without regard to breadth or thickness.4 inches make a hand in measuring horses. NOTE.-66 Feet, or four rods, make a gunter's chain. 60 Geometrical miles make a degree. 5 Feet a geometrical pace. 6 Feet a fa thom, or one French toise. 6 points make 1 line; 12 lines an inch. A league is a denomination used to measure distance at sea. EXAMPLES. 1. In 3 feet; how many barley corns? 3 feet. 13 36 inches. 3 Ans. 108 b. c. Ans. 108 b. c. We first multiply by twelve, because every foot contains 12 inches we next multiply the inches by three, because every inch contains three bar. ley corns. 2. In 48 deg. 14 m. 7 fur. 30 rds. 5 yds. 2 ft. 3 in. and 1 b. c.; how many barley corns? Deg. m. fur. rd. yds. ft. in. b. c. 2 3350 miles in 48deg. 14m, 8 3 1 Ans. 636952762 b. c. DEM.We first multiply by 691, because 69 miles make a degree; we next multiply by 8, because 8 furlongs make a mile; we then multiply the fur longs by 40, be cause 40 rods make a furlong; we then multiply by 5 be 4 1072310 Brought up. 51 536155 5361555 5897710 yards in 48deg. 14m. 37fur. 30rds. 5yds 17693132 feet in 48deg, 14m. 7fur. 1230rds. 5yds. 2ft. 212317587 in. in 48deg. 14m. 7fuṛ. 330rds. 5yds. 2ft. 3in. 636952762 cause 5 yds. make a rod; we then multiply by 3, because 3 feet make a yard; we then multiply by 12, because 12 inches make a foot; and lastly, we multiply by 3, because every inch con3 barley tains Sb. c. in 48deg. 14m. 7fur. corns. 30rd. 5yd. 2ft. 3in. lb. c. 3. How many rods from Albany to 160 miles? New York, it being Ans. 51200rds. 4. In 3 miles; how many barley corns? Ans. 570240 b.c. 5. How many barley corns will reach round the globe, it being 360 degrees in circumference? 6. In 2640 yards; how many rods? yards. 522640 2 2 Half yards. 11) 5280 haf yds. Ans. 4755801600 b.c. Ans. 480rds. DEM.-We multiply by 2, to reduce our yards to half yards, we then multiply 51, the number of yards in a rod, by 2, to reduce the divisor to half yards; we then divide the number of half yards contained in our given number, by the number of half yards in a rod, and as often as our divisor is contained, it is evident, so many rods are in the given number, because our quotient shows how often our divisor may be subtracted from our given number. 7. How often will a carriage wheel, 16 feet and 6 inches in circumference, turn round in going from Watertown to Utica; the distance being 84 miles? Ans. 26880 times. 8. In 15840 yards; how many miles and leagues? Ans. 9 miles, 3 leagues. 9. In 9 leagues; how many yards and feet? Ans. 47520yds. 142560ft. 10. In 126720 feet; how many leagues? Ans. 8 leagues. |