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LESSON 29

Since the earth turns on its axis from west to east once in 24 hours, the sun appears to move from east to west around the earth in the same time. Therefore a circumference (360°) is described by the apparent revolution of the sun around the earth in 24 hours.

Since the sun appears to travel through 360° of longitude in 24 hours, in 1 hour it appears to travel through of 360°, or 15° of longitude; in 1 minute, through of 15°, or 15′ of longitude; and in 1 of 15', or 15" of longitude. Therefore we have the

second, through

following table:

15° of longitude correspond to 1 hour of time.
15' of longitude correspond to 1 minute of time.
15" of longitude correspond to 1 second of time.

All places east of a certain point have later time, all places west earlier time. Thus when it is 10 o'clock A.M. in Philadelphia, it is 11 o'clock A.M. at a point 15° east of Philadelphia; 12 o'clock M. 30° east; 1 o'clock P.M. 45° east, etc.

Again, when it is 10 o'clock A.M. in Philadelphia, it is 9 o'clock A.M. 15° west; 8 o'clock A.M. 30° west; 7 o'clock A.M. 45° west, etc.

1. In what direction does the earth rotate on its axis? 2. In what direction and in what time does the sun appear to move around the earth?

3. Through how many degrees of longitude does the earth rotate in 1 day, or 24 hours? In 12 hours? In 6 hours? In 1 hour?

4. How many degrees of longitude correspond to 1 hr. of time? 2 hr.? 3 hr.? 4 hr.?

5. Does the sun appear first to places east or west of us?

6. When it is sunrise at a place 15° east of us, how long will it be before it is sunrise with us?

LESSON 30

1. When it is noon with us, is it earlier or later east of us? West of us?

2. When it is noon at Philadelphia, what time is it at all other places lying on the same meridian?

3. At what places is it midnight when it is noon at Philadelphia?

4. When it is noon at any place, what time is it at a place 15° east? 30° east? 45° east? 90° east? 15° west? 30° west? 45° west?

5. Can you make a rule for finding the difference in time between two places when the difference in longitude is given?

6. The difference in longitude between A and B is 30°. What is the difference in time?

7. If A is west of B, when it is 10 o'clock A.M. at B, what time is it at A? When it is 2 o'clock P.M. at A,

what time is it at B?

What is the difference in time when the difference in longitude is :

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23. Since 15° of longitude equal 1 hour of time, what is the difference in longitude between two places, if the difference in time is 2 hr.? 3 hr.? 4 hr.? 3 hr.? 30 min.? 45 min.? 15 min. ? 2 hr. 20 min. ?

24. Can you make a rule for finding the difference in longitude between two places when the difference in time is given ?

What is the difference in longitude when the difference

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(See diagram, p. 35, for the following :)

37. When it is noon at E what time is it at I? At A? 38. When it is 10 A.M. at C what time is it at H?

39. What time is it at O when it is half past 10 o'clock A.M. at A?

40. What is the difference in time between L and N?

41. When it is 7 o'clock A.M. at N what time is it at L?

GENERAL ANALYSIS

LESSON 31

1. Find the cost of 12 bu. of corn at $3 a bushel. 2. How many bushels of corn can be bought for $12, at $ a bushel?

3. If 3 men can do of a piece of work in 6 da., how long will it take them to do the whole of it? How long will it take one man to do it? How long will it take two men to do it?

4. Find the cost of +++ 1 of a ton of coal, at $3.20 a ton.

5. How many pints in 371% of a bushel?

6. If 871% of a yard of silk cost $1.40, how much will 75% of a yard cost?

7. A wagon was sold for of its value, which was at a loss of $9. At what price was it sold?

8. Find 18% of $1680. 63% of $428.50.

9. What must be taken from 16§ to leave 7?

10. If a man spent and 3 of his money and had $9 left, how much money had he at first?

11. 331% of a day equals how many hours? 40% of an hour equals how many minutes?

12. If a man sold 10 out of a hundred turkeys, what per cent did he sell? If he had 250 at first, how many did he sell?

13. If a merchant buys an article for $1.25 and sells it at a gain of 100%, how much does he receive for it?

14. A certain number diminished by of itself equals 22. What is the number?

15. John has 36 marbles, and of John's number equals of of Henry's number. How many marbles has Henry? 124 16. At $5 a ton, how many pounds of coal can you buy for $3?

17. Find the cost of a dozen pairs of shoes, if 3 pairs cost $98.

of a farm and sold of his share What was the value of the whole farm?

18. A man owned for $3600.

LESSON 32

1. A man can do a piece of work in 163 days. What part of it can he do in 63 da.?

2. What part of 6 is 5?

3. What part of 21 is

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? 13 is ? is? 8 is ? 4. If of a dozen bananas cost 124, how much will 12 dozen cost?

5. of 100 equals 25% of what number?

6. How much will 34 bbl. of apples cost, if 14 bbl. cost $3.60 ?

7. How many barrels will be needed to hold 50 bu. of potatoes, if 1 bbl. holds 21⁄2 bu. ?

8. Find the interest of $800 for 2 yr. 3 mo. 10 da. at 6%.

9. .75 is what part of 3.25?

10. What part of a mile is 880 yd.? 830 yd.? 4500 ft.?

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