By this measure, which is only a branch of long measure, cloth, tapes, ribbons, &c., are measured; the name expresses the use. SQUARE OR SUPERFICIAL MEASURE. 144 square inches make 9 square feet 1 square foot. 1 square yard. 100 square feet, or 10 feet sq. 1 sq. of mechanics' work. 2724 square feet, or 30 square yards 40 rods 4 roods 640 acres 1 sq. rod, pole, or perch. 1 rood. 1 acre. 1 square mile. All surfaces, as land, flooring, &c., are measured by this measure. The measure of boards, floors, &c., is generally expressed in square feet and inches; that of land in acres, roods, and poles. Dry measure is used for grain, fruit, salt, oysters, &c. NOTE. A Winchester bushel is 18 inches in diameter, and 8 inches deep. The standard gallon, dry measure, contains 2684 cubic inches. NOTE. The wine gallon contains 231 cubic inches: water, wine, and spirits are measured and sold by this measure. A barrel is to a hogshead. NOTE. The ale gallon contains 282 cubic inches: milk is sold by the beer gallon. Time is thus divided: 60 seconds, sec. make 60 minutes 24 hours 7 days 4 weeks TIME. 13 lunar months, 1 d. 6 h. or 365 days and 6 hours 12 calendar months 100 years 1 minute, min. 1 hour, h. 1 day, d. 1 lunar month or } 1 Julian year. 1 year, y. NOTE. The six hours in each year are not reckoned till they amount to one day; hence, a common year consists of 365 days, and every fourth year, called leap year, of 366 days. The following is a statement of the number of days in each of the twelve months, as they stand in the calendar or alma nac: Or, The fourth, eleventh, ninth, and sixth, Thirty days are in September, Which has but twenty-eight in fine, 1728 inches, in. make 27 feet SOLID MEASURE. 1 foot, ft. 1 yard, yd. 40 feet of round timber, or 50 feet of hewn timber, make a ton, 16 cubic feet make a foot of wood, and 8 feet of wood, or 128 cubic feet make a cord. The cubic contents of any thing which has 6 sides-its opposite sides being equal-is found in cubes, by multiplying together, the length, breadth, and depth. Reduction is the operation of changing the denomination of numbers, without altering their value. EXAMPLES. 1. In 15 lbs. Troy weight, how many ounces? Ans. 180 ounces. Why? Since 1 pound is equal to 12 ounces, there must be 12 times as many ounces as there are pounds. 2. In 350 lbs. Troy, how many ounces? Ans. 4200 oz. Why Ans. 3. In 76 pounds Avoirdupois, how many ounces? Ans. 1216 ounces. Why? Since 1 pound is equal to 16 ounces, there must be 16 times as many ounces as there are pounds. 4. In 56 pounds Avoirdupois, how many drams? 14336 drams. Why? Since 1 pound is equal to 16 ounces, there must be 16 times as many ounces as there are pounds, 16 times 56 is 896, and since 1 ounce is equal to 16 drams, there will be 16 times as many drams as there are ounces, and 56 lbs. is equal to 896 oz., and 16 times 896=14336 drs. NOTE. The learner should be required to give mental solutions to as great a number of such questions as the following, as possible, and in all cases to give the reason for the operation. EXAMPLES IN TROY WEIGHT. 5. In 95 pounds, how many ounces? Ans. 1140 oz. Why? 6. In 237 ounces, how many pennyweights? Ans. 4740 penny weights. Why? Since 1 ounce is equal to 20 penny weights, there will be 20 times as many pennyweights as there are ounces. 7. How many pennyweights in 174 ounces? Why? 8. In 145 penny weights, how many grains? Ans. 3480. Why? Since 1 pennyweight is equal to 24 grains, there will be 24 times as many grains as there are pennyweights. 9. In 15 pounds, how many pennyweights? Ans. 3600 pennyweights. Why? 10. In 75 pounds, how many grains? Ans. 432000 grs. Why? First change the pounds to ounces, then the ounces to pennyweights, and the penny weights to grains, and give the reason for each operation. 11. In 672 ounces, how many pounds? Ans. 56 pounds. Why? Since it takes 12 ounces to make one pound, as many times 12 as there are in 672, so many pounds 672 ounces will make. 12. In 6912 ounces how many pounds? Why? 13. In 34800 pennyweights, how many ounces? Ans. 1740 ounces. Why? 14. In 3480 grains how many pennyweights? Ans. 145 penny weights. Why? 15. In 3600 pennyweights, how many pounds? Ans. 15 pounds? Why? 16. In 432000 grains how many pounds? Ans. 75 lbs. Why? EXAMPLES IN AVOIRDUPOIS WEIGHT. 17. In 376 pounds, how many ounces? Ans. 6016 ounces. Why? 18. In 37 quarters, how many pounds? Ans. 1036 pounds. Why? Since 1 quarter is equal to 28 pounds, there will be 28 times as many pounds as there are quarters, the number of quarters in this question being 37, the number of pounds therefore will be 28 times 37. 19. In 3 cwt., how many lbs. ? 20. Change 7 cwt. to ounces. 21. Change 2 tons to drams. Why? Ans. 12544 oz. Ans. 1146880 drs. The following rule may serve as a guide to the pupil, though it were better that he should arrive at the proper result by a regular and simple process of reasoning. RULE FOR REDUCTION. When a greater denomination is to be changed to a smaller, multiply the greater denomination by that number which is required of the smaller, to make one of the greater; adding to the product so many of the smaller denomination as are expressed in the given sum. Perform a like operation on this product, and on each succeeding product. When a smaller denomination is to be changed to a greater, divide the smaller denomination by that number which is required of the smaller to make one of the next greater; the quotient will be of the greater denomination, and the remainder will be of the same denomination with the dividend. Perform a like operation on this quotient, and on each succeeding quotient. 22. Change 17 cwt. to drams. Here we reason thus,-since 1 cwt. is equal to 4 quarters, there will be 4 times as many quarters as there are hundred weight. Secondly, since 1 quarter is equal to 28 pounds, there will be 28 times as many pounds as quarters, then since 1 pound is equal to 16 ounces, there will be 16 times as many ounces as pounds, and lastly, since 1 ounce is equal to 16 drams, there will be 16 times as many drams as ounces. 17 cwt. 4 68 qrs. 28 544 136 1904 lbs. 16 30464 oz. 16 487424 drams. |