numbers, and write the remainder, 6 gal., under the column of gal. lons.

RULE. I. Write the subtrahend under the minuend, so that units of the same denomination shall stand under each other. II. Beginning at the right hand, subtract each denomination separately, as in simple numbers.

III. If the number of any denomination in the subtrahend exceed that of the same denomination in the minuend, add to the number in the minuend as many units as make one of the next higher denomination, and then subtract; in this case add 1 to the next higher denomination of the subtrahend before subtracting. Proceed in the same manner with each denomination.

6. A Boston merchant bought English goods to the amount of £4327 13s. 74d., and he paid £1374 10s. 11ąd ; how much did he then owe?

7. From 300 miles take 198 mi. 305 rd. 2 yd. 1 ft. 10 in. Ans. 101 mi. 14 rd. 2 yd. 2 ft. 8 in. 8. What is the difference in the longitude of two places, one 75° 20′ 30′′ west, and the other 71° 19′ 35′′ west?

Ans. 4° 55".

9. From 101 73 43 19 15 gr. take 3lb 8 3 23 20 18 gr. Ans. 6b 113 13 10 17 gr.

Give the Rule.

10. The apparent periodic revolution of the sun is made in 365 da. 6 h. 9 min. 9 sec., and that of the moon in 29 da. 12 h. 44 min. 3 sec.; what is the difference?

Ans. 335 da. 17 h. 25 min. 6 sec.

11. A man, having a hogshead of wine, drank, on an average, for five years, including two leap years, one gill of wine a day; how much remained? Ans. 5 gal. 3 qt. 1 pt. 1 gi.

12. A section of land containing 640 acres is owned by four men; the first owns 196 A. 961 P.; the second, 200 A. 60 P.; the third, 177 A. 36 P.; how much does the fourth own? Ans. 65 A. 127.75 P.

13. From a pile of wood containing 754 Cd. was sold at one time 16 Cd. 5 cd. ft.; at another, 24 Cd. 6 cd. ft. 12 cu. ft.; at another, 27 Cd. 112 cu. ft.; how much remained in the pile? Ans. 6 Cd. 3 cd. ft. 4 cu. ft.

14. If from a hogshead of molasses 10 gal. 1 qt. 1 pt. be drawn at one time, 15 gal. 1 pt. at another, and 14 gal. 3 qt. at another, how much will remain ?

220. To find the difference in dates.

1. What length of time elapsed from the discovery of America by Columbus, Oct. 14, 1492, to the Declaration of Independence, July 4, 1776?

FIRST OPERATION.

yr. mo. da. 1776 4 1492 10 14

283 8 20 first day of the month. and day, some use the

SECOND OPERATION.

ANALYSIS. Place the earlier date under the later, writing first on the left the number of the year from the Christian era, next the number of the month, counting January as the first month, and

next the number of the day from the Instead of the number of the year, month, number of years, months, and days that have

elapsed since the Christian era, thus: instead of saying July is the 7th month, we say 6 months and 3 days have elapsed, and instead of saying October is the 10th month, we say 9 months and 13 days have elapsed.

How is the difference of dates found?

Both methods will obtain the same result; the former is generally used.

1. When hours are to be obtained, we reckon from 12 at night, and if minutes and seconds, we write them still at the right of hours.

2. In finding the time between two dates, or in computing interest, 12 months are considered a year, and 30 days a month.

When the exact number of days is required for any period not exceeding one ordinary year, it may be readily found by the following

TABLE,

Showing the number of days from any day of one month to the same day of any other month within one year.

If the days of the different months are not the same, the number of days of difference should be added when the earlier day belongs to the month from which we reckon, and subtracted when it belongs to the month to which we find the time. If the 29th of February is to be included in the time computed, one day must be added to the result.

EXAMPLES FOR PRACTICE.

2. George Washington was born Feb. 22, 1732, and died Dec. 14, 1799; what was his age?

Ans. 67 yr. 9 mo. 22 da.

How can the number of days, if less than a year, be obtained?

3. How much time has elapsed since the declaration of independence of the United States?

4. How many years, months, and days from your birthday to this date; or what is your age?

5. How long from the battle of Bunker Hill, June 17, 1775, to the battle of Waterloo, June 18, 1815? Ans. 40 yr. 1 da. 6. What length of time will elapse from 20 minutes past 2 o'clock, P. M., June 24, 1856, to 10 minutes before 9 o'clock, A. M., January 3, 1861 ? Ans. 4 yr. 6 mo. 8 da. 18 h. 30 min. 7. How many days from any day of April to the same day of August? of December? of February?

8. How many days from the 6th of November to the 15th of April? Ans. 160 days.

9. How many days from the 20th of August to the 15th of the following June? Ans. 299 days.

221. To subtract denominate fractions.

1. From of an oz. take 3 of a pwt.

3. From £5 take of of a shilling.
4. From of a league take of a mile.

Ans. 1 mi. 193 rd. 11 ft. 7.9 in.

5. From 8 cwt. take 274 lb.

+

Ans. 8 cwt. 62 lb. 94 oz.

6. From of a week take of a day.

Ans. 1 da. 4 h. 48 min.

Give explanation of the process of subtracting denominate fractions,

7. Two persons, A and B, start from two places 120 miles apart, and travel toward each other; after A travels, and B, of the distance, how far are they apart?

Ans. 41 mi. 289 rd. 8 ft. 7 in.

8. From a cask of brandy containing 96 gallons, † leaked of the remainder was sold; how much still reAns. 25 gal. 2 qt. 33 gi.

out, and
mained in the cask?

MULTIPLICATION.

222. 1. A farmer has 8 fields, each containing 4 A. 107 P.; how much land in all?

OPERATION.

A.
4

P.

107

8

37

56

ANALYSIS. In 8 fields are 8 times as much land as in 1 field. We write the multiplier under the lowest denomination of the multiplicand, and proceed thus: 8 times 107 P. are 856 P., equal to 5 A. 56 P.; and we write the 56 P. under the number multiplied. Again, 8 times 4 A. are 32 A., and 5 A. added make 37 A., which we write under the same denomination in the multiplicand, and the work is done.

RULE. I. Write the multiplier under the lowest denomination of the multiplicand.

II. Multiply as in simple numbers, and carry as in addition of compound numbers.

Multiplication of compound numbers, how performed? Rule.