Henry's is 14 years 6 mo. 19 days; can you tell me how much older William is than Henry ?

Circular Motion.

Ans. lyr. 9mo. 1da.

3. The whole circumference of the earth is 360 degrees. If a ship could circumnavigate the globe by a direct course, how much farther must she sail to complete her voyage, after sailing 248° 55′ 31′′? Ans. 111° 04′ 29′′.

EXERCISES IN COMPOUND ADDITION AND SUBTRACTION.

1. Borrowed £62 10s.; paid at one time £14 16s. 81d., and at another time £21 10s.; how much remains unpaid? Ans. £26 3s. 3 d.

2. Bought a hogshead of sugar, weighing 8cwt. 3qrs. 14lb.; sold at one time 3cwt. 1qr. 14lb. 5oz., and at another time 3qrs. 16lb. 12oz. How much remained unsold? Ans. 4cwt. 2qr. 10lb. 15oz. 3. From a piece of broadcloth, containing 56 yards 2 nails, a tailor made 3 suits, each 6 yards 3 qrs. ; how much remained in the piece? Ans. 35yds. 3qrs. 2na.

4. A merchant bought a hogshead of molasses, containing 65 gallons, and sold at one time 14 gallons 3 quarts, and at another time 9 gallons 2 quarts 1 pint; how much remained in the hogshead? Ans. 40gal. 2qt. 1pt.

5. A man owning a farm of 321 acres 2 quarters, sold one field containing 14 acres 3 roods 19 poles, and another containing 12 acres 1 rood; how much land had he left?

Ans. 294A. 1qr. 21 rods.

6. From a pile of wood, containing 25 cords, there was sold at one time 10 cords 84 feet, and at another time 6 cords 84 feet; how many cords were left? Ans. 7cds. 88ft.

7. The distance from Philadelphia to Washington is 138 miles; if a man travel 5 days from Philadelphia towards Washington, viz. the first day 18 miles 3fur. 25 rods; the

second, 23m. 2fur.; the third 20m. 1fur. 6 rods; the fourth 25m., and the fifth day, 22m. 3fur. 18 rods; how far will he then be from Washington? Ans. 28m. 5fur. 31 poles.

To find the length of Time from one date to another.

RULE.

Subtract the first date from the last date, reckoning the months according to their order; and in computing interest on Notes, &c., each month is reckoned 30 days.

EXAMPLES.

1. What is the difference in time from February 19th, 1827, to June 19th, 1833?

Operation.

yrs. mo. da. Last date 1833 5 19 First date 1827 1 19

Illustration. In reckoning from January 1st, to June 19th, inclusive, we find it to be 5 mo. 19 days, and from January 1st to Answer 6 4 0 February 19th, is 1 month 19 days; and the first date subtracted from the last date, leaves 6 years 4 months 0 days, the answer.

2. What is the difference of time from July 12, 1829, to January 27, 1834? Ans. 4yrs. 6mo. 15da. 3. A Note, bearing date July 15, 1830, was paid November 20, 1833; how long was the note at interest?

Ans. 3 years 4 months 5 days. 4. A Note, bearing date December 10, 1828, was paid January 5, 1834; how long was it at interest?

Ans. 5 years 0 months 25 days. 5. The war between England and America commenced April 19, 1775, and peace took place January 20, 1783; how long did the war continue ?

Ans. 7 years 9 months 1 day.

Questions.

What is a compound number?
What is Compound Addition?
How do you write numbers to be add-
ed?

How do you add the numbers?
What does Compound Subtraction

teach?

How do you place the numbers?
How do you subtract? (Repeat the
Rule.)

How do you find the length of time from one date to another?

COMPOUND MULTIPLICATION.

Compound Multiplication is when the multiplicand consists of diverse denominations.

I. When the Multiplier does not exceed 12.

RULE.

Write down the multiplicand and place the quantity under the least denomination for a multiplier. Multiply each denomination separately, and carry as in compound addition, setting down the whole product of the highest denomination.

EXAMPLES.

1. What will 6 yards of cloth cost at £1 5s. 72d. per yard?

Ans. 7 13 10 2=cost of six yards.

Illustration. 6 times 3qrs. are 18qrs., which we divide by 4 (as in compound addition,) and the remainder is 2qrs. which we set under the qrs., and the quotient is 4d. which we carry, saying 6 times 7d. are 42d. and 4 are 46d. which divided by 12 (the number of pence in a shilling,) the remainder is 10d. and the quotient 3s., then 6 times 5s. are 30s. and 3s. to carry make 33s., which divided by 20 the remainder is 13s. and the quotient is £1, and 6 times £1 is £6, and £1 to carry makes £7, which set down. 2. Multiply 11s. 4d. by 3. 3. Multiply £1 11s. 91d. by 5

4. Multiply £539 14s. 10d. 3qrs. by 5.

5. Multiply £50 18s. 10d. by 7. 6. What cost 9 yards of Irish per yard?

Ans. £2698 14s. 53d.

Ans. £356 11s. 10d. linen, at 7s. 9d. 2 grs. Ans. £3 10s. 11⁄2d.

7. What cost 11 pairsof shoes, at 10s. 6d. per pair? Ans. £5 15s. 6d.

dollar being 17 pwt. 8gr. ?

8. What is the weight of 9 dollars, the weight of one Ans. 7oz. 16pwt. 9. What is the whole weight of 12 hogsheads of sugar, each weighing 7cwt. 3qr. 161b.? Ans. 94cwt. 2qr. 24lb. 10. Multiply 3lb 13 63 20 14gr. by 6.

Ans. 18b 113 13 19 4gr. 11. How many yards of cloth are in 7 pieces, each containing 29 yards 2 quarters 3 nails? Ans. 207yd. 3qr. Ina. 12. How many bushels of corn are in 9 bags, containing each 3 bushels 1 peck 5 quarts? Ans. 30bu. 2pk. 5qts.

13. How much wine is there in six casks, each containing 49 gallons 2 quarts 1 pint? Ans. 297gal. 3qt.

14. Multiply 6 leagues 2 miles 5 furlongs 26 poles by 8. Ans. 55le. 5fur. 8rd.

15. How many acres in 5 fields, each containing 4 acres 1 rood 36 rods? Ans. 22 acres 1 rood 20 rod.

16. How much wood is there in 11 piles, ach containing 2 cords 32 feet 136 inches? Ans. 24 cords 96ft. 1496in. 17. Multiply 12 years 6 months 3 weeks 5 days by 10. Ans. 125yr. 9mo. 1w. 1da.

II. When the Multiplier is a Composite Number, and greater than 12.

RULE.

Multiply the multiplicand first by one of the component parts, and that product by another, and so on, and the last product will be the answer.

EXAMPLES.

1. What is the value of 24 yards of cloth at 6 shillings 10 pence per yard?

Illustration. 6×4=24, therefore we multiply the price of 1 yard first by one factor, and that product by the other, which gives the price of 24 yards.

2. What cost 54 yards of cloth at £1 3s. 6d. a yard? Ans. £63 11s. 3d.

3. Multiply 5cwt. 3qrs. 15lb. by 56. Ans. 329cwt. 2qrs. 4. How many yards of broadcloth are there in 35 pieces, each containing 36yds. 2qr. Ina.? Ans. 1279yds. 2qr. 3na. 5. How much cider is there in 45 barrels, each containing 31gal. 2qts. 1pt. ? Ans. 1423gal. 1pt.

6. Multiply 2° 58′ 10′′ by 56.
7. Multiply 24m. 3fur. 8rd. by 72.

Ans. 5S. 16° 17′ 20′′.

Ans. 1756m. 6fur. 16rd.

8. How many days in 25 years, the year containing 365d. 5h. 48m. 56s.? Ans. 9131ds. 1h. 23m. 20s.

9. How much wood is there in 32 loads, containing each 1 cord 16 feet 144 inches?

Ans. 36 cords 2 feet 1152 inches.

III. When the Multiplier is not a Composite Number.

RULE.

Multiply by those factors whose product will come the nearest to it, then multiply the upper line by what remained, which added to the last product gives the answer.

EXAMPLES.

1. What will 47 yards of cloth come to at 14s. 6d. per yard?

£ S. d.

32

12

1

5

6 price of 45 yards. 9 0=price of 2 yards. Ans. 34 1 6 price of 47 yards.

Illustration.—No two factors will exactly produce 47; but we multiply the price of 1 yard by 9, which gives the price of 9 yards; then multiply the price of 9 yards by 5, which gives the price of 45 yards; (9×5=45;) we then