208. To find the difference of the time of day in two places, at the same absolute moment of time, when the longitude of each place is known.

Since the sun appears to go from east to west round the earth, 360° (Art. 109), in 24 hours, it appears to go of 360°, viz. 15° in 1 hour, and, consequently, 1° in of 1 hour, viz. 4 minutes, and 1' of distance in of 4 minutes, viz. 4 seconds. These facts give us the following

5

38. When it is 12 o'clock, noon, at Washington, what time is it at London, Washington being 77° 2' 48" west of London?

OPERATION.

77

2

48
4

5 h. 8 m. 1 11 sec. Ans.

=

60

Since 1" of longitude makes a difference of of a second of time, 48" of longitude give 192 33 sec. of time, and for a like reason 2 of longitude give 8 sec. of time, which added to the 33 sec. previously obtained, give 113 sec., and, finally, 77° of longitude give 4 times 77308 m. = 5 h. 8 m. of time; .. the difference in time between London and Washington is 5 h. 8 m. 113 sec., and as London is farther east than Washington, the hour of the day is later in London than in Washington, i. e. it is 8 m. 11 sec. past 5 o'clock in the afternoon at London when it is noon at Washington. Hence,

RULE. Multiply the difference of longitude, expressed in degrees, minutes, and seconds, by 4, and the product will be the difference in time, expressed in minutes, seconds, and 60ths of a second.

208. How far does the sun appear to move in one hour? Which way? Give the table of longitude and time. Rule for finding difference in time of two places when the Longitude of each is known?

NOTE 1. The place most easterly, has its hour of the day, at a given moment, latest; i. e. the day begins first, noon comes first, and the day closes first at the place most easterly.

39. The longitude of Boston is 71° 4' 9" west, and that of Washington is 77° 2' 48" west; what is the difference in the time of the two places, and what time is it in Washington, at 3 o'clock, P. M., in Boston?

By subtraction, the difference of longitude is found to be 5° 58′ 39′′,.. the difference in time is 23 m. 543 sec., and at 3 in Boston it is 36 m. and 53 sec. past 2 in Washington, Ans.

40. The longitude of Paris is 2° 20′ 15′′ east, and that of New York, 74° 0' 3" west from Greenwich; what is the difference in time in the two places? Ans. 5 h. 5 m. 21 sec.

NOTE 2. Since Paris is in east longitude, and New York in west, their difference in longitude is found by adding 2° 20′ 15′′ to 74° 0′ 3′′.

41. What is the difference in time between Philadelphia, 750 9' west longitude, and Chicago, 87° 35' west longitude? 42. What is the difference in time between New Orleans, 90° 7' west, and St. Petersburg, 29° 48′ east longitude? 43. What is the difference in time for 90° in longitude?

DIVISION.

209. Here, as in the three preceding sections, the principle is the same as in the corresponding operation in simple numbers. Hence,

To divide a compound by a simple number,

RULE. Divide the highest denomination of the dividend, and set down the quotient; if there is a remainder, reduce it to the next lower denomination; to the result add the given guantity of that denomination, and divide as before, setting down the quotient and reducing the remainder, etc.

208. Which has the hour of the day latest, the most easterly or most westerly place? How is the difference in longitude found when one place is in east and the other in west longitude? 209. Rule for dividing a Compound by a Simple Number? Principle?

Ex. 1. Divide 30£ 7 s. 1 d. 1 qr. by 7.

OPERATION.

£ S. d. qr. 7)30 7 1

1

3, Ans.

30£

7 give a quotient of 4£ and a remainder of 2£; 2£ reduced to shillings and added to 7 s. give 47 s., which, divided 1, Proof. by 7, give a quotient of 6 s. and a remainder of 5 s., etc.

7

2. Divide 1 fur. 9 rd. 2 yd. 0 ft. 9 in. 1 b. c. by 5.

Ans. 9 rd. 4 yd. 2 ft. 6 in. 2 b. c.

3. Divide 20 gal. 2 qt. O pt. 2 gi. by 7.

Ans. 2 gal. 3 qt. 1 pt. 2 gi.

4. Divide 18 lb. 1 oz. 15 dwt. 8 gr. by 4.
5. Divide 17 lb. 53 13 19 10 gr. by 6.
6. Divide 30 t. 5 cwt. 3 qr. 24 lb. 12 oz. by 8.
7. Divide 60 yd. 2 qr. 3 na. by 9.

8. Divide 3 wk. 6 d. 14 h. 17 m. 57 sec. by 3.

9. Divide 57 circ. 2 s. 25° 4' 10" by 10.

10. Divide 107 gal. 1 qt. by 12.

11. Divide 98 bush. 3 pk. 2 qt. 1 pt. by 11.

12. Divide 51 c. 7 c. ft. 15 cu. ft. 1716 cu. in. by 4.

13. Divide 16 a. 1 yd. 4 ft. 70 in. by 2.

14. Divide 37 t. 12 cwt. 3 qr. 5 lb. 10 oz. 4 dr. by 9.

15. Divide 71 a. 3 r. 14 rd. 8 yd. 1 ft. 72 in. by 6.

16. If 9 silver spoons weigh 1 lb. 4 oz. 17 dwt. 12 gr., what is the weight of each spoon? Ans. 1 oz. 17 dwt. 12 gr. 17. If a family use 29 gal. 3 qt. 2 gi. of molasses in 6 months, what is the average per month?

18. If 10 t. 18 cwt. 1 qr. of hay is harvested from 5 acres, what is the crop on one acre?

19. If 8 boxes of sugar weigh 2 t. 7 cwt. 2 qr. 10 lb., what is the weight per box? Ans. 5 cwt. 3 qr. 20 lb.

20. If 9 grain-bins contain 143 bush. 2 pk. 2 qt. 1 pt. of grain, what does 1 bin contain?

21. If a man travel 212 m. 1 fur. 26 rd. 2 yd. in 7 days, what distance does he travel per day?

22. Divide 96£ 5 s. 7 d. 2 qr. by 10.

210. To divide by a composite number, we may divide by its factors, as in division of simple numbers (Art. 79).

23. Divide 341 lb. 0 oz. 12 dwt. by 72.

24. Divide 396£ 2 s. 3 d. by 54.

25. Divide 725 bush. O pk. 6 qt. 1 pt. by 81.

26. Divide 397 113 73 19 4 gr. by 63.

27. Divide 958 m. 5 fur. 5 ch. 12 li. 518 in. by 48.

211. When the divisor is large and not composite, set down the work of dividing and reducing. There is no device for rendering the operation easier.

28. Divide 135 bush. 3 pk. 3 qt. 1 pt. by 47.

210. Rule for dividing by a composite number? 211. Method of dividing when the divisor is large and not composite? Is there no easier mode?

29. If 587 yards of cloth cost 662£ 4 s. 2 d. 1 qr., what is the price per yard?

30. Divide 1129 gal. 1 pt. 3 gi. by 73.

31. A farmer raised 35334 bush. 3 pk. 3 qt. 1 pt. of corn on 643 acres of land; how much was the yield per acre?

32. Suppose a man should travel 10599 m. O fur. 14 rd. 4 yd. 2 ft. 5 in. in 313 days, what distance would he travel per day? 33. In 127 days a ship sails 11 s. 9° 43' 30"; what is the distance per day? Ans. 2° 40' 30". 212. To find the difference in the longitude of two places, when the difference of time is known.

34. When it is 12 o'clock at Washington, it is 23 m. 543 sec. past 12 at Boston; what is the difference in the longitude of the two places?

OPERATION.

m.

sec.

4)23 543

5° 58' 39' Ans.

First divide the 23 m. by 4, because 4 m. of time make a difference of 1° of longitude. This gives 5° and a remainder of 3 m. The 3 m. and 548 sec.2343 sec. The 2343 sec. divided by 4, because 4 sec. of time make a difference of 1' of longitude, give 58′ and a remainder of 23 sec. Finally, reduce the 23 sec. to 60ths of a sec. and divide by 4, and the quotient is 39"; i. e. the difference in longitude between Boston and Washington, is 5° 58′ 39′′, Ans. Hence,

RULE. Divide the difference in time, expressed in minutes, seconds, and 60ths of a second, by 4, and the quotient is the dif ference in longitude, expressed in degrees, minutes, and seconds.

35. Paris is 2° 20′ 15′′ east of Greenwich; how many degrees west of Greenwich is New York, the difference in time between Paris and New York being 5 h. 5 m. 213 sec. Ans. 74° 0′ 3′′.

NOTE. The difference in longitude between Paris and New York is found to be 76° 20′ 18 and this diminished by 2° 20' 15", the east longitude of Paris, gives 74° 0′ 3′′ for the west longitude of New York.

212. Rule for finding the difference in the longitude of two places, when the difference in time is known?