198. The earth rotates on its axis from west to east

equator passes under the

sun's rays in the same

time as a degree at any

latitude between the equator and the polar circle.

199. When the vertical rays of the sun are on the meridian of any place, it is noon, or 12 o'clock, at that place; and since the sun's rays pass over the earth's surface from east to west, it is after noon at all places east of this meridian, and before noon at all places west of it. When it is noon at Cincinnati, it is after noon at New York, and before noon at St. Louis.

apart), and also the hour of the day corresponding to noon on the meridian.

MENTAL PROBLEMS.

1. The earth rotates on its axis once every 24 hours:

what part of a rotation does it make in 1 hour?

2. How many degrees of the earth's surface pass under the sun's rays in 24 hours? In 1 hour?

3. How many degrees of longitude make a difference of 1 hour in time?

4. When it is noon at Washington, what is the hour of day 15° east of Washington? 15° west of Washington? 5. When it is 6 o'clock at Boston, what is the hour of day 30° east of Boston? 45° west of Boston?

6. If 15° of longitude give a difference of 1 hour in time, how much longitude will give a difference of 1 minute in time?

7. When it is 4 o'clock at Cincinnati, what is the time 15' east of Cincinnati? 45' west of Cincinnati ?

8. When it is 9 o'clock at Chicago, what is the time. 15° 15′ east of Chicago? 15° 45′ west of Chicago?

9. If 15′ difference in longitude gives a difference of 1 minute in time, what difference in longitude will give a difference of 1 second in time?

10. What difference in longitude gives a difference of 1 hour in time? 1 minute? 1 second?

11. The difference in time between two cities is 2 hours: what is the difference in their longitude? Which has the earlier time?

12. The difference in time between New York and St. Louis is 1 h. 2 min.: what is the difference in their longitude?

13. A gentleman left Boston and traveled until his watch was 1 h. 3 min. too slow: how far had he traveled, and in which direction?

14. Two captains observed an eclipse of the moon, one seeing it at 9 P. M. and the other at 111⁄2 P. M.: what was the difference in their longitude?

WRITTEN PROBLEMS.

15. The difference in longitude between two places is 31° 45' 30": what is the difference of time?

15) 31°

PROCESS.
45'

30"

2 h. 7 min. 2 sec.

Divide by 15 as in compound division.

16. The difference in longitude between two cities is 5° 31': what is the difference in time?

17. The longitude of Cincinnati is 84° 26' W., and San Francisco is 122° 26' 15" W.: when it is noon at Cincinnati what is the time at San Francisco?

18. Philadelphia is 75° 10′ W.: when it is noon at San Francisco what is the time at Philadelphia?

19. Boston is 71° 4' 9" W.: when it is 7 P. M. at Boston what is the time at Cincinnati? At San Francisco?

20. Berlin is 13° 23' 53" E.: when it is noon at Boston what is the time at Berlin?

21. The difference in time between two cities is 1 h. 35 min. 12 sec.: what is their difference in longitude?

PROCESS.

1 h. 35 min. 12 sec.

15

23° 48' O', Ans.

Multiply by 15 as in compound multiplication.

22. The difference in time in the observations of an eclipse, on two vessels at sea, is 2 h. 15 min. 10 sec.: what is their difference in longitude?

23. An eclipse was observed at New York, 74° W., at 9.30 P. M., and the time of its observation on a vessel in the Atlantic Ocean, was 11.45 P. M.: what was the longitude of the vessel?

24. The difference in time between the chronometers of two observatories is 45 min. 30 sec., and the longitude of the observatory having the earlier or faster time is 85° 40′ W.: what is the longitude of the other observatory?

25. The distance from Boston to Chicago is about 843 miles, and a degree of longitude at Boston contains about 51 miles: when it is noon at Boston what is the time at Chicago?

26. The distance from Washington to St. Louis is about 714 miles, and a degree of longitude at Washington contains about 54 miles: when it is 9 o'clock at St. Louis what is the time at Washington?

27. The difference in the longitude of two vessels, at the time of the observation of an eclipse, was 25° 30′: what was their difference in time?

28. How much earlier does the sun rise at Baltimore, which is 76° 37' W., than at Cincinnati, 84° 26' W.?

29. How much later does the sun set at Chicago, which is 87° 35′ W., than at Boston, 71° 4' 9" W.?

30. How much later does the sun set at San Francisco, which is 122° 26′ 15′′ W., than at Cincinnati ?

31. How much earlier does the sun rise at New York, which is 74° W., than at San Francisco?

32. How much later does the sun set at Boston than at Berlin, which is 13° 23′ 53′′ E.?

TABLE AND RULES.

200. TABLE: 15° difference in long. gives a difference of 1 h. in time.

15' difference in long. gives a difference of 1 m. in time.

15′′ difference in long. gives a difference of 1 sec. in time.

201. RULES.-1. To find the difference in time corresponding to any difference in longitude, Divide the difference in longitude, expressed in degrees, minutes, and seconds, by 15, and the respective quotients will be hours, minutes, and seconds of time.

2. To find the difference in longitude corresponding to any difference in time, Multiply the difference in time, expressed in hours, minutes, and seconds, by 15, and the respective products will be degrees, minutes, and seconds of longitude.

3. To find the time at one place when the time at another place and their difference of time are known, When the second place is EAST of the first, ADD their difference of time; when it is WEST of the first, SUBTRACT their difference of time.

SECTION XIV.

PERCENTAGE.

NOTATION AND DEFINITIONS.

202. One per cent. of a number is one hundredth of it, two per cent. is two hundredths; and, generally, any per cent. of a number is so many hundredths of it.

1. How many hundredths of a number is 4 per cent. of it? 7 per cent. of it? 15 per cent. of it?

2. How many hundredths of a number is 3 per cent. of it? 12 per cent.? 33 per cent.?

3. How many hundredths of a number is of one per cent. of it? of one per cent.? of one per cent.? 4. How many hundredths of a number is 115 per cent. of it? 135 per cent.? 180 per cent.?

5. What per cent. of a number is .05 of it? .09 of it? .15 of it? .35 of it?

6. What per cent. of a number is .03 of it? .331 of it? .00% of it? .00 of it?

40

7. What per cent. of a number is 115 of it? 148 of it? 1.25 of it? 1.65 of it?

8. How many hundredths of a number is 45% of it? 110%? 125%? 170%? 215 %?

NOTE. The character % is often used instead of the words "per cent." Thus, 15 % denotes 15 per cent.

9. What fractional part of a number is 10% of it? 20%? 25%? 50%?

SOLUTION.-50 % of a number is 1001 or of it.

10. What fractional part of a number is 12% of it? 16% 33%? 66% %?

?