17. Add 49 bushels, 3 pecks, 4 quarts, 1 pint; 39bu. 1pk. 5qt. 1pt.; 59bu. 2pk. 3qt. Opt.; 40bu. 7pk. 2qt. 1pt.; 150bu. Opk. 6qt. 1pt.; 69bu. 1pk. 2qt. Opt.

18. Add 360 degrees, 15 miles, 6 furlongs, 16 poles, 13 feet, 6 inches; 240deg. 19m. 5fur. 29p. 11ft. 5in. 2b.; 159deg. 51m. 7fur. 32p. 14ft. 7in. 2b.; 201deg. 63m. 3fur. 15p. 12ft. 9in. 2b.

19. Add 971 miles, 6 furlongs, 11 poles, 3 yards, 1 foot; 239m. 5fur. 9p. 2yd. 2ft.; 269m. 7fur. 31p. lyd. 2ft.; 67m. 6fur. 9p. 2yd. 2ft.; 691m. 5fur. 8p. 2yd. 2ft.

20. Add 69 acres, 2 roods, 1 rod; 76acr. 3ro. 39rd.; 88acr. 1ro. 32rd.; 150acr. 3ro. 29rd.

21. Add 150 years, 221 days, 13 hours, 31 minutes, 29 seconds; 230yr. 300d. 23h. 49m. 59s.; 191yr. 149d. 21h. 39m. 23s.; 359yr. 75d. 23h. 59m. 19s.

COMPOUND SUBTRACTION.

1. If a picture book cost 4d., and a spelling-book 11d., how much more does one cost than the other?

2. James bought a book for 9d., and sold it for 1s. How much did he gain by the bargain?

3. From 2s. 6d., take 1s. 8d.

4. From 8s. 9d. 3qrs., take 6s. 8d. 2qrs.

5. From 4qts., take 3pts.

6. If a bushel of rye be worth 7s. 6d., and a bushel of corn 6s. 4d., how much more is the rye worth than the corn?

7. How much more is wheat worth at 9s. 8d. per bushel, than corn at 7s. 6d. per bushel ?

8. How much more is 2 bushels 2 pecks, than 1 bushel 3 pecks?

G

9. From £29, 9s. 6d. 3qrs., take £23 10s. 7d. 2qrs.

Operation.

£ s. d. qrs. 29 9 6 3 23 10 7 2

In this example, we write the difference between 2 and 3 farthings in the line of farthings, and proceed to the 5 18 11 1 column of pence; we carry none, because we borrowed none-but 7d. from 6d. cannot be obtained; we therefore borrow as many pence as make a shilling, and say 7 from 12-the remainder 5, we add to 6 in the upper line, and write eleven in the column of pence. We now carry one to the column of shillings, which is equal to the 12 pence we borrowed, and say 11 from 9, which cannot be obtained; again we must borrow as many of the denomination we have to subtract, as make one of the next higher, which is 20s., and say 11 from 20 and 9 remains, which added to 9 in the upper line is 18, which must be written in the column of shillings. Lastly, the 20s. which we borrowed, we pay by carrying one to the line of pounds, which must be subtracted as in simple subtraction. Hence

COMPOUND SUBTRACTION teaches to find the difference between two compound sums, or quantities.

RULE.

1. Write the less number under the greater, so that numbers of the same denomination may stand directly under each other.

2. Begin to subtract with the lowest denomination, and take the lower line from the one above it; proceed in this way with all the denominations.

3. Should the numbers in the upper line be less than the one standing under it, borrow as many units as make 1 in the next higher denomination.

4. From the units borrowed, subtract the lower number, and to the difference add the upper number; write their sum under the figures subtracted, observing to carry 1 to the next left hand column.

Proof-the same as Simple Subtraction.

QUESTIONS. 1. What does Compound Subtraction teach? 2. Rule? 3. If the numbers in the upper be less than the one above, how may you proceed?

11. From 31 tuns, 3hhd. 15gal., take 29 tuns, 2hhd. 26gal.

12. From 39yds. 3qr. 2na., take 27yds. 2qr. 3na.

13. From 127E. E. 3qr. 2na., take 121E. E. 4qr. 3na. 14. From 247E. Fl. Oqr. 2na., take 159E. Fl. 2qr. Ina. 15. From 671E. Fl. 4qr. 3na., take 582E. Fl. 5qr. 2na. 16. From 971 mi. 6 für. 11 p. 3 yds. 1ft., take 439 mi. 5 fur. 12 p. 4 yds. 2 ft.

17. From 69 acr. 2 ro. 31 rd., take 49 acr. 3 ro. 37 rd. 18. From 150 yrs. 221 d. 13 h. 31 m. 29 s., take 130 y yrs. 129 d. 14 h. 39 m. 41 s.

19. From 260deg. 15 mi. 5 fur. 16 p. 13 ft., take 159 deg. 17 m. 6 fur. 17 p. 12 ft.

20. From 240° 49′ 31'', take 159° 59′ 41′′.

21. From 9s. 21° 31′ 42′′, take 7s. 22° 36′ 37′′.

22. A note dated Feb. 3d, 1826, was paid March 12th, 1837; how long was it from the first date until it was paid? The time from one date to another may be found by subtracting the former date from the latter, observing to number the months in their order; thus, Jan. 1st month, Feb. 2d month, &c.

NOTE. The month, in casting interest, is reckoned 30 days. 23. What is the time from June 3d, 1835, to July 15th, 1837? Ans., 2 yrs. 1 m. 12 d. 24. The latitude of a certain place is 42° 50′ north, that of another place is 39° 37'-what is the difference of latitude? Answer, 3° 13'. 25. What is the difference of longitude between 39° 40′, and 29° 49' west? Answer, 9° 51'.

As every circle, whether greater or less, is divided into 360 equal parts, or degrees, consequently the circle, described by the revolution of the earth on its axis every 24 hours, contains 360 equal parts, or degrees-and as 360 degrees are described in 24 hours, it is plain, that, in 1 hour, 24 of 360, or 15 degrees, would be described; and, also, if 15 degrees be described in 1 hour, or 60 minutes, it is equally plain, that 1 degree would be described in of 60 m., or in 4 m., and I minute of a degree in 4 seconds. Hence, to reduce longitude to time, we have the following

RULE.

Multiply the longitude in degrees and minutes by 4, and we have the time in minutes and seconds.

EXAMPLE.

Reduce 14° 15' to time.

14° 15'

4

57' 0" Ans.

QUESTIONS. 4. How is the time from one date to another found? 5. How

many degrees in a circle? 6. How many degrees does the earth describe in one hour, in its revolution round the sun?

To find the difference of time between any two places, having the time of one place given, and their difference of longitude. Reduce the longitude to time, and add it to the given time, if the longitude of the place whose time is required, be east of the place whose time is given; and subtract it if the longitude be west.

NOTE. The reason of this is, because the farther east we go, the later is it in the day, and the farther west, the earlier in the day. That is, when it is 12 o'clock at noon, in London, 15 degrees east of London it would be 1 o'clock, P. M. and 15 degrees west of London it would be but 11 o'clock, A. M.

27. When it is 12 o'clock in London, what is the hour in Boston, 70 degrees west longitude from London? Ans. 7 o'clock 20 m. 28. When it is 12 o'clock in Boston, what is the time in London, lon. 70° east? Ans., 4 o'clock 40 m.

COMPOUND

ADDITION

and

SUBTRACTION.

1. A man bought a horse] 2. If a pair of oxen and a for £32 10s. and a pair of horse cost £57, 1s. 6d. 2qr. oxen for £24, 11s. 61d., how and the horse cost £32, 10s., much did both cost? what was the cost of the ox

3. If I purchase a farm for £1092, 4s. 8d., for how much

en?

4. If I sell a farm for £1150, must I sell it to gain £57 4s. 4d. and gain £57 19s. 8d. by the bargain, what did

19s. 8d.?

5. A pipe of wine sprang the farm cost?

a leak and leaked out 31 gal. 6. From a pipe of wine 1 qt. 1 pt. and there remain-containing 118 gallons, there ed 86 gal. 2 qt. 1 pt., how leaked out 31 gal. 1 qt. 1 pt., many gallons were there at how many remained?

first?

8. If the weight of a silver

7. There was a silver tank-tankard and lid be 4 lbs. 9 oz. ard which weighed 4 lbs. 34 pwt. 6 gr. and the lid alone oz.-the lid weighed 6 oz. weigh 6 oz. 4 pwt. 6 gr., what 4 pwt. 6 gr., how much did was the weight of the tankboth weigh? ard?

QUESTIONS. 7. In one minute? 8. In one second? 9. Rule for finding the difference of time between two places, the longitude being known?