11. Multiply 13 yr. 10 mo. 3 wk. 5 da. by 15, using the fac tors of the multiplier. Ans. 208 yr. 7 mo. 3 wk. 5 da. 12. If a man walk 17 mi. 300 rd. in each of 21 days, how far will he walk in all? Ans. 376 mi. 220 ra. 13. If a farmer raise 60 bu. 3 pk. 6 qt. 1 pt. of grain on on acre, how much can he raise at the same rate on 48 acres Ans. 2925 bu. 3pk

14. If a pipe discharges 11 hhd. 40 gal. 2 qt 1 pt. of wat in an hour, how much will it discharge in 56 hours? Ans. 652 hhd. 7 gal.

15. A had 1000 A. of land; he sold B 96 A. 150 P., and C 4 times as much; how much remained? Ans. 515 A. 50 P.

16. A farmer raised 4000 bu. of grain; he sold 50 bu. 3 pk. 7 qt. to A, 7 times as much to B, and to C 6 times as much as to A and B together; how much remained?

Ans. 1145 bu. 3 pk.

DIVISION OF COMPOUND NUMBERS.

309. Division of Compound Numbers is the process of finding the quotient when the dividend is a compound number.

310. There are two cases:—

1st. To divide a compound number into equal parts. 2d. To divide one compound number by a similar one.

CASE I.

311. To divide a compound number into a number of equal parts.

1. Divide £103 7 s. 6 d. into 5 equal parts, that is, take of it.

SOLUTION. We write the divisor at the left of the dividend, and begin at the highest denomination to divide. of £103 is £20 and £3 remaining; £3 equal 60 s., which added to 7 s. equals 67 s.; of 67 s. is 13 s. and 2 s. remaining; 2s. equal 24 d., which added to 6 d. equals 30 d.; of 30 d. is 6 d. Hence the following

OPERATION. £ s. d. 5,103 7 6

20 13 6

Rule.-I. Begin with the highest denomination of the dividend and divide each term in succession, as in simple numbers.

II. When there is a remainder, reduce it to the next lower denomination, add it to the term of that denomination, and divide the result as before.

III Proceed in the same manner until all the terms are divided.

Proof. The same as in division of simple numbers.

NOTE.-When the divisor is a large number and composite, the factors being not greater than 12, it is perhaps more convenient to divide by the factors. WRITTEN EXERCISES.

8. Five sons share 112 A. 144 P. 24 sq. yd. of land; how much does each receive? Ans. 22 A. 92 P. 29 sq. yd. 9. If 9 farmers raise 1137 bu. 3 pk. 4 qt. 1 pt. of grain, what is the average amount raised by each?

Ans. 126 bu. 1 pk. 5 qt. 13 pt. 10. A miner sends 37 lb. 10 oz. 17 pwt. 16 gr. of gold to his 8 sisters; how much does each receive?

1

Ans. 4 lb. 8 oz. 17 pwt. 5 gr.

11. A man walked 376 mi. 276 rd. in 22 days; what was the average distance each day? Ans. 17 mi. 41 rd.

12. If 26 casks contain 21 hhd. 11 gal. 2 qt. 1 pt., what is the capacity of each cask?

CASE II.

Ans. 51 gal. 1 qt. 17 pt.

312. To divide one compound number by a similar

one.

1. Divide £26 6 s. 2 d. by £4 15 s. 8 d.

SOLUTION.-£26 6 s. 2 d. equais 6314 pence; £4 15 s. 8 d. equals 1148 pence; and dividing 6314d. by 1148 d. we obtain a quotient of 5. From this solution we have the following

OPERATION. £26 6s. 2d.

6314d..

£4 15s. 8d.=1148 d.

1148)6314(5), Ans. 6314

Rule.-Reduce both dividend and divisor to the lowest denomination mentioned in either, and then divide as in simple numbers.

Proof. The same as in division of simple numbers.

NOTE.-The division may also be made without reducing to the lowest denomination, and this will be shorter when the quotient is integral.

WRITTEN EXERCISES.

2. Divide £48 7 s. 4 d. by £6 11 d.

3. 69 bu. 3 pk. 6 qt. by 6 bu. 3 pk. 6 qt. 4. If a man feeds his horse 1 pk. 6 qt. of long will 3 bu. 2 qt. last him?

Ans. 8. Ans. 10.

oats a day, how

Ans. 7 days.

5. How many demijohns, each containing 2 gal. 3 qt. 1 pt., can be filled from a tank holding 71 gal. 3 qt. 1 pt. of wine?

Ans. 25.

6. A drove of cattle ate 6 T. 15 cwt. 87 lb. of hay in a week; how long will 33 T. 19 cwt. 35 lb. last them?

Ans. 5 weeks.

DIFFERENCE BETWEEN DATES.

CASE I.

313. To find the difference of time between two dates.

1. Washington was born Feb. 22d, 1732, and died Dec. 14th, 1799; what was his age?

SOLUTION.-Dates are expressed in the number of the year, the month, and the day; hence the date of his birth is 1732 yr. 2 mo. 22 da., and the date of his death is 1799 yr. 12 mo. 14 da.; and the difference of these two dates will equal his age, which we find to be 67 yr. 9 mo. 22 da.

OPERATION.

yr. mo. da. 1799 12 14 1732 2 22

67 9 22

Rule. Write the number of the year, month, and day of the earlier date under the year, month, and day of the later date, and take the difference of the numbers.

NOTE. In this method we reckon 30 days to the month; when greater accuracy is required, we reckon the actual number of days in each month. The exact time between two dates is found by the table, Art. 296.

WRITTEN EXERCISES.

2. What is the difference in time from Dec. 12th, 1850, to Jan. 5th, 1860 ? Ans. 9 yr. 23 da.

3. Milton was born Dec. 9th, 1608, and died Nov. 8tu 1675; what was his age? Ans. 66 yr. 10 mo. 29 da. 4. Franklin was born Jan. 6th, 1706, and died April 17th, Ans. 84 yr. 3 mo. 11 da. 5. What is the exact time a note has to run, dated Dec 30th, 1862, and payable Jan. 16th, 1864? Ans. 1 yr. 17 da.

.

1790; required his age.

6. The Revolution was commenced the 19th of April, 1775, and terminated January 20th, 1783; how long did it continue? Ans. 7 yr. 9 mo. 1 da.

7. The Civil War began April 11, 1861, and closed April 9, 1865; how long did it last? Ans. 3 yr. 11 mo. 28 da. 8. How many years, months, and days, from your birthday to the present date?

SUPPLEMENTARY PROBLEMS,

To be omitted unless otherwise directed.

9. A man was born the 29th of Feb., 1824, and died the 3d of March, 1860; how many birthdays did he see, and what was his exact age? Ans. 10; Age, 36 yr. 4 da.

10. Two men were born on the first day of January, one in the year 1756, the other in 1822; both died 37 years after they were born, upon the 1st of January; required the difference of their ages?

Ans. 1 day.

11. What is the exact time from 45 min. and 25 sec. past 12 o'clock noon, May 20, 1874, to 24 min. 36 sec. past 4 o'clock P. M., July 4, 1876 ? Ans. 2 yr. 1 mo. 15 da. 3 h. 39 min. 11 sec.

CASE II.

314. To find the day of the week upon which any given day of the month will fall, the day of the week of some other date being given.

NOTE.-A common year ends on the same day it begins, hence each year begins one day later than the preceding year. A year following leap year begins two days later.

1. If the 3d of April, 1876, occur on Monday, on what day of the week will the next 29th of August be?

SOLUTION. By the table we find the difference of time to be 148 days: dividing by 7, the number of days in a week, we have 21 weeks and 1 day; the 29th of August must therefore be one day after Monday or Tuesday.

OPERATION.

148÷7-21,+1

Rule. Find the number of days between the two dates, reduce this number to weeks; the number of days remaining will be the number of days from the given day of the week to the required day.

NOTE. In solving the problems after the 2d, the date in a previous problem may be assumed as the starting-point.

WRITTEN EXERCISES.

2. If the year 1776 began on Monday, on what day of the week was the 4th of July following? Ans. Thursday. 3. What day of the week was the surrender of Burgoyne, Oct. 17, 1777? Ans. Friday. 4. On what day of the week was Daniel Webster born, Jan. 18, 1782? Ans. Friday. 5. On what day of the week was the battle of Waterloo fought, June 18, 1815? Ans. Sunday. 6. On what day of the week was President Lincoln assassinated, April 14, 1865? Ans. Friday. 7. On what day of the week was General Grant inaugurated the first time, March 4, 1869? Ans. Thursday."

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

8. The Centennial opened on Wednesday, May 10, 1876; on what day will the next open on the same date?

Ans. Monday.

9. Suppose a letter should be published purporting to have been written at New Orleans on the day of the battle, and dated Wednesday, Jan. 8, 1815; would it be genuine?

10. Let the pupils now determine, from the above principles, the day of the week upon which they were born.

LATITUDE AND LONGITUDE.

315. The Latitude of a place is its distance from the equator, north or south. It is reckoned in degrees, minutes, and seconds, and cannot exceed 90°, or a quadrant.

316. The Longitude of a place is its distance, east or west, from a given meridian. It is reckoned in degrees, minutes, and seconds, and cannot exceed 180°, or a semicircumference.