3. In 5 wk. 1 da. 1 h. 1 min. 1 sec. how many seconds? 4. In 3114061 seconds how many weeks? 5. How many times does a clock pendulum, 3 ft. 3 in. long, beating seconds, vibrate in one day? Ans. 86400. 6. If a man take 1 step a yard long in a second, in how long a time will he walk 10 miles? Ans. 4 h. 53 min. 20 sec. 7. In a lunar month of 29 da. many seconds? 12 h. 44 min, 3 sec. how Ans. 2551443. 8. How much time will a person gain in 40 years, by rising 45 minutes earlier every day? Ans. 456 da. 13 h. 30 min. CIRCULAR MEASURE. 20%. Circular Measure, or Circular Motion, is used principally in surveying, navigation, astronomy, and geography, for reckoning latitude and longitude, determining locations of places and vessels, and computing difference of time. Every circle, great or small, is divisible into the same number of equal parts, as quarters, called quadrants, twelfths, called signs, 360ths, called degrees, etc. Consequently tha parts of different circles, although having the same names, are of different lengths. 1= 60 = 3600 C. 1= 30 1800 = 108000 = 12 = 360 = 21600 = 1296000 SCALE-ascending, 60, 60, 30, 12; descending, 12, 30, 60, 60. 1. Minutes of the earth's circumference are called geographic or nautical miles. 2. The denomination, signs, is confined exclusively to Astronomy. Define circular measure. How are circles divided? Repeat the table. Give the scale. What is a geographic mile? What is a sign? 8. Degrees are not strictly divisions of a circle, but of the space about a point in any plane. 4. 90° make a quadrant, or right angle, and 60° a sextant, or of a circle. EXAMPLES FOR PRACTICE. 1. Reduce 10 S. 10° 10' 10" to seconds. 2. Reduce 1116610" to signs. 3. How many degrees in 11400 geographic or nautical miles? Ans. 190°. 4. If 1 degree of the earth's circumference is 694 statute miles, how many statue miles in 11400 geographic miles, or 190 degrees? Ans. 13148. 5. How many minutes, or nautical miles, in the circumference of the earth? Ans. 21600' or mi. 6. A ship during 4 days' storm at sea changed her longitude 397 geographic miles; how many degrees and minutes did she change? 208. IN COUNTING. 12 Units or Things....make....1 Dozen. Ans. 6° 37'. The terms folio, quarto, octavo, duodecimo, etc., indicate the number of leaves into which a sheet of paper is folded. A sheet folded in 2 leaves is called a Folio. A sheet folded in 4 leaves 66 a Quarto, or 4to. What is a degree? Repeat the table for counting. For reckoning paper. For indicating the size of books. EXAMPLES FOR PRACTICE. 1. If in Birmingham, England, 150 million Gillott pens are manufactured annually, how many great gross will they Ans. 86805 great gross 6 gross 8 dozen. make? 2. In 100000 sheets of paper, how many bales? Ans. 20 bales 4 bundles 6 quires 16 sheets. 3. What is the age of a man 4 score and 10 years old? 4. How many printed pages, 2 pages to each leaf, will there be in an octavo book, having 8 fully printed sheets? Ans. 128 sheets. 5. How large a book will ten 32mo sheets make, if every page be printed? Ans. 640 pages. PROMISCUOUS EXAMPLES IN REDUCTION. 1. How many suits of clothes, each containing 6 yd. 3o qr., can be cut from 333 yards of cloth? Ans. 48. 2. A man bought a gold chain, weighing 1 oz. 15 pwt., at seven dimes a pennyweight; what did it cost? Ans. $24.50. 3. A physician, having 2 b 3 3 5 3 10 10 gr. of medicine, dealt it out in prescriptions averaging 15 grains each; how many prescriptions did it make? Ans. 886. 4. A man bought 1 T. 11 cwt. 12 lbs. of hay, at 11 cents a pound; what did it cost? Ans. $38.90. 5. What will be the cost of a load of oats weighing 1456 pounds, at 37 cents per bushel? Ans. $17.0625. 6. If one bushel of wheat will make 45 pounds of flour, how barrels will 1000 bushels make? Ans. 229 bbl. 116 lb. 7. A load of wheat weighing 2430 pounds is worth how much, at $1.20 a bushel? Ans. $48.60. many 8. Paid $12.50 for a barrel of beef; how much was that per pound? Ans. 61 cents. 9. If a silver dollar measure one inch in diameter, how many dollars, laid side by side on the equator, would reach round the earth? Ans. 1577511936. 10. In 10 mi. 7 ch. 4 rd. 20 l., how many links? Ans. 80820 links. 11. What is the value of a city lot, 25 feet wide and 100 feet long, if every square inch is worth one cent? Ans. $3600. 12. How many cords of wood can be piled in a shed 50 ft. long, 25 ft. wide, and 10 ft. high? Ans. 97 Cd. 5 cd. ft. 4 cu. ft. 13. A cistern 10 feet square and 10 feet deep, will hold how many hogsheads of water? Ans. 118 hhd. 4649 gal. 14. A bin 8 feet long, 5 feet wide, and 4 feet high, will hold how many bushels of grain? 15. How many seconds less in every either Spring or Summer? Ans. 144 bu. Autumn than in Ans. 86400 sec. 16. If a person could travel at the rate of a second of distance in a second of time, how much time would he require to travel round the earth? Ans. 15 days. 17. How many yards of carpeting, 1 yd. wide, will be required to carpet a room 20 ft. long and 18 ft. wide? Ans. 40. 18. A printer calls for 4 reams 10 quires and 10 sheets of paper to print a book; how many sheets does he call for? Ans. 2170. 19. How many times will a wheel, 16 ft. 6 in. in circumference, turn round in running 42 miles? Ans. 13440. 20. How many days, working 10 hours a day, will it require for a person to count $10000, at the rate of one cent each second? Ans. 27 da. 7h. 46 min. 40 sec. 21. A town, 6 miles long and 4 miles wide, is equal to how many farms of 80 acres each? Ans. 216. 22. At $21.75 per rod, what will be the cost of grading 10 mi. 176 rds. of road? Ans. $73428. REDUCTION OF DENOMINATE FRACTIONS. CASE I. 211. To reduce a denominate fraction from a greater to a less unit. 1. Reduce of a bushel to the fraction of a pint. Case I is what? RULE. Multiply the fraction of the higher denomination by the numbers in the scale successively, between the given and the required denominations. Cancellation may be applied wherever practicable. EXAMPLES FOR PRACTICE. 2. Reduce of a £ to the fraction of a penny. Ans. d. 3. Reduce 1400 of a week to the fraction of a minute. 7. Reduce of of 2 pounds to the fraction of an ounce Troy. Ans. oz. 8. Reduce of a hogshead to the fraction of a pint. Ans. pt. Ans. rd. 9. Reduce of an acre to the fraction of a rod. CASE II. 212. To reduce a denominate fraction from a less to a greater unit. 1. Reduce of a pint to the fraction of a bushel. Give explanation. Rule. Case II is what? |