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NOTE. The true solar year is the time measured from the sun's leaving either equinox or solstice to its return to the same again. A periodical year is the time in which the earth revolves round the sun, and is 365d. 6h. 9m. 14 sec., and this is often called the sidereal year. The civil year is that which is in common use among the different nations of the world, and contains 365 days for three years in succession, but every fourth year it contains 366 days. When any year can be divided by four, without any remainder, it is leap year, and has 366 days, except the last year of those centuries which cannot be divided by 4; as the fifteenth, seventeenth, and nineteenth centuries. The days in each month are stated in the following lines:

"Thirty days hath September,
April, June, and November;
And all the rest have thirty-one,
Save February, which alone

Hath twenty-eight; and this, in fine,

One year in four hath twenty-nine.”

MENTAL EXERCISES.

1. In 3 minutes how many seconds? In 5 minutes? In 10 minutes?

2. In 2 hours how many minutes? In 4 hours? In 8 hours?

3. In 4 weeks how many days? In 6 weeks? In 12 weeks?

In 9 weeks?

4. In 2 days how many hours? In 3 days? In 7 days? In 11 days?

5. How many weeks in 21 days? In 30 days? In 50 days? In 84 days?

QUESTIONS.-What is a true solar year? What is a sidereal year? What is a civil year? How many days in a solar year? In a sidereal year? In a civil year? What is leap year? How often do we have leap year? Repeat the lines on the days of the month.

EXERCISES FOR THE SLATE.

1. How many seconds in 365da. 5h. 48m. 57sec., or one solar year?

OPERATION.

2. In 31556937 seconds how many days?

OPERATION.

3 6 5da. 5h. 48m. 57sec. 60) 3 1 5 5 6 9 3 7

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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 969407832 seconds how many solar years ?

7. How many weeks in 684592 minutes ?

8. In 67w. 6da. 9h. 52m. how many minutes?

CIRCULAR MEASURE OR MOTION.

ART. 99. Circular Measure is used in reckoning latitude and longitude, in computing the revolutions of the planets round the sun, and in the division of circles.

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QUESTIONS.-How do you reduce years to seconds? of the operation. How do you reduce seconds to days?

Give the reason To years? Give

the reason of the operation.-Art. 99. For what is circular measure used? Repeat the table.

MENTAL EXERCISES.

1. In 3 minutes how many seconds? In 5 In 8? In 10?

2. In 2 signs how many degrees? In 4 signs? In 6 signs? In 9 signs?

3. How many degrees in 120'? In 180' ? In 360'? 4. How many signs in 90°? In 120° ? In 600° ?

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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 of practical importance to the pupil, all of which are more or less used in business.

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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 of the operation. How many degrees in a circle? - Art. 100. What is embraced in the Miscellaneous Table? Recite the table.

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A sheet folded in two leaves is called a folio.

A sheet folded in four leaves is called a quarto, or 4to.
A sheet folded in eight leaves is called an octavo, or 8vo.
A sheet folded in twelve leaves is called a duodecimo, or 12mo.
A sheet folded in eighteen leaves is called an 18mo.

A sheet folded in twenty-four leaves is called a 24mo.

MISCELLANEOUS EXERCISES IN REDUCTION.

1. In $345.18 how many

mills?

2. How many dollars in 345180 mills?

3. In 46. 18s. 5d. how many farthings?
4. How many pounds in 45044 farthings?
5. Reduce 61lb. Ooz. 17dwt. 17gr. troy to grains.
6. In 351785 grains troy how many pounds?
7. How many scruples in 27tb 33 13 19?
8. In 7852 scruples how many pounds?
9. In 83T. 11cwt. 3qr. 18lb. how many ounces?
10. How many tons in 2996064 ounces?
11. How many nails in 97yd. 3qr. 3na. ?
12. In 1567 nails how many yards?
13. In 57 ells English how many yards?
14. How many ells English in 71yd. 1qr.?

15. How many inches in 15m. 7fur. 18rd.. 10ft. 6in. ?
16. In 1009530 inches how many miles?

17. In 95,000,000 of miles how many inches?
18. How many miles in 6,019,200,000,000 inches?
19. In 48deg. 18m. 7fur. 18rd. how many feet?
20. In 17714037 feet how many degrees?
21. How many square feet in TA. 3R. 16p. 218ft.?
22. In 342164 square feet how many acres?
23. How many square inches in 25 square miles?

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′′ 2

38. In 915497 how many signs?

39. What will be the cost of 13 gross of steel pens, at 21 cents per pen?

40. Bought 12 reams of paper, at 20 cents per quire; how much did it cost?

41. I wish to put 2 hogsheads of wine into bottles that will contain 3 quarts each, how many bottles are required ?

42. When $1480 are paid for 25 acres of land, what costs 1 acre? What costs 1 rood? What cost 37A. 2R. 18p.

43. John Webster bought 5cwt. 3qr. 18lb. of sugar at 9 cents per lb., for which he paid 25 barrels of apples at $ 1.75 per barrel; how much remains due ?

44. Bought a silver tankard weighing 2lb. 7oz. for $ 46.50; what did it cost per oz.? How much per lb. ?

45. Bought 3T. lcwt. 18lb. of leather at 12 cents per lb., and sold it at 9 cents per lb. ; what did I lose?

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.?

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.?

48. What is the value of a house-lot, containing 40 square rods and 200 square feet, at $1.50 per square foot?

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