EXERCISES FOR THE SLATE. 1. How many seconds in 365da. 2. In 31556929 seconds 5h. 48m. 49sec., or one solar year? how many days? 3 6 5 da. 5h. 48m. 49sec. 60) 3 1556929 24 1465 730 87 6 5 hours. 60 525948 minutes. 60 Ans. 3155 69 29 seconds. 60) 525948 m. 49sec. 24) 8765 h. 48m. 365 da. 5h. Ans. 365da. 5h. 48m. 49sec. 3. Reduce 296da. 18h. 32m. to minutes. 4. In 427352 minutes how many days? 5. How many seconds in 30 solar years 262da. 17h. 28m. 42sec.? 6. In 969407592 seconds how many solar years ? 7. How many weeks in 684592 minutes? 8. In 67w. 6d. 9h. 52m. how many minutes? 9. How many days from June 5th to Dec. 11th? 10. How many days from March 17th, 1856, to May 16th, 1857 ? Ans. 425 days. 11. How many days from December 18th, 1856, to January 30th, 1857 ? 12. How many days from August 30th, 1857, to June 1st, 1858 ? 13. How many days from July 4th, 1859, to July 4th, 1860 ? 14. How many days from April 25th, 1855, to August 20th, 1858? Ans. 1213 days. NOTE. The last six examples are to be performed by aid of the table on page 103. QUESTIONS. How do you reduce years to seconds? Give the reason for the operation. How do you reduce seconds to days? To years? Give the reason for the operation. CIRCULAR MEASURE. ART. 99. Circular Measure is applied to the measurement of circles and angles, and is used in reckoning latitude and longitude, and the revolutions of the planets round the sun. 270 300 240 330 A 360 30 60 081 NOTE.-1. A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point called its centre. The Circumference of a circle is the line which bounds it, as shown by the diagram. An Arc of a circle is any part of its circumference; as AB. A Radius of a circle is a straight line drawn from its centre to its circumference; as CA, CB, or CD. Every circle, large or small, is supposed to be divided into 360 equal parts, called degrees. A Quadrant is one fourth of a circle, or an arc of 90°; as AB. An Angle, as ACB, is the inclination or opening of two lines which meet at a point, as C. The point is the vertex of the angle. If a circle be drawn around the vertex of an angle as a centre, the two sides of the angle, as radii of the circle, will include an arc, which is the measure of the angle; as the arc AD 120° is the measure of the angle ACD, and AB=90°, the measure of the angle ACB; hence the one is called an angle of 120°, and the other an angle of 90°. NOTE.-2. As the earth turns on its axis from west to east every 24 hours, the sun appears to pass from east to west 24 of 360° of longitude every hour, or over 15° of longitude in 1 hour's time, or 1° in 4 minutes of time, and 1' in 4 seconds of time; so that, for instance, at any place, when it is noon, it is 1 hour earlier for every 15° of longitude westward, or 1 hour later for every 15° of longitude eastward. Thus, Boston being 71° 4' west of Greenwich, and San Francisco 51° 17' west of Boston, when it is noon at Boston, it is 4h. 44m. 16sec. past noon at Greenwich, and wanting 3h. 25m. 8sec. of noon at San Francisco. QUESTIONS. Art. 99. To what is circular measure applied? Recite the table. What is a circle? What is an angle? 3. In 27S. 19° 51′ 28′′ how many seconds? 4. How many signs in 2987488 seconds? MISCELLANEOUS TABLE. ART. 100. This table embraces a variety of things in business important to be known. QUESTIONS.-How do you reduce signs to seconds? Give the reason of the operation. How do you reduce seconds to degrees? To signs? Give the reason for the operation. How many degrees in a circle?— Art. 100. What is embraced in the miscellaneous table? MISCELLANEOUS EXERCISES IN REDUCTION. 1. In $345.18 how many mills? 9. In 83T. 11cwt. 3qr. 18lb. how many ounces? 15. How many inches in 15m. 7fur. 18rd. 10ft. 6in. ? 17. In 95,000,000 of miles how many inches? QUESTION. What gives name to the size or form of books? 24. In 100362240000 square inches how many square miles? 25. How many cubic inches in 15 tons of timber? 26. In 1036800 cubic inches how many tons? 27. How many gills of wine in 5hhd. 17gal. 3qt. ? 28. In 10648 gills how many hogsheads of wine? 29. How many quarts of beer in 29hhd. 30gal. 3qt.? 30. In 6387 quarts of beer how many hogsheads? 31. How many pints in 15ch. 16bu. 3pk. of wheat? 32. In 35632 pints of wheat how many chaldrons ? 33. How many seconds of time in 365 days 6 hours? 34. In 31557600 seconds how many days? 35. How many hours in 1842 years (of 365da. 6h. each)? 36. In 16146972 hours how many years? 37. How many seconds in 8S. 14° 18′ 17′′? 38. In 915497" how many signs? 39. What will be the cost of 13 gross of steel pens, at 21 cents per pen ? Ans. $46.80. 40. Bought 12 reams of paper at 20 cents per quire; how much did it cost? Ans. $48. 41. I wish to put 2 hogsheads of wine into bottles that will contain 3 quarts each; how many bottles are required? Ans. 168 bottles. 42. When $1480 are paid for 25 acres of land, what costs 1 acre? What costs 1 rood? What cost 37A. 2R. 18p.? Ans. $2226.66. 43. John Webster bought 5cwt. 3qr. 181b. of sugar at 9 cents per lb., for which he paid 25 barrels of apples at $1.75 per barrel; how much remains due? Ans. $9.62. 44. Bought a silver tankard weighing 2lb. 7oz. for $46.50; what did it cost per oz.? How much per lb. ? Ans. $18. 45. Bought 3T. lcwt. 18lb. of leather at 12 cents per lb., and sold it at 9 cents per lb. ; what did I lose? Ans. $183.54. 46. Phineas Bailey has agreed to grade a certain railroad at $5.75 per rod; what will he receive for grading a road between two cities, whose distance from each other is 37m. 7fur. 29rd.? Ans. $69856.75. 47. If it cost $17.29 per rod to grade a certain piece of railroad, what will be the expense of grading 15m. 6fur. 37rd.? Ans. $87,781.33. 48. What is the value of a house-lot, containing 40 square rods and 200 square feet, at $1.50 per square foot? Ans. $16635. |