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Here, 12 × 8 and 15 x 9 are the causes, and the distances travelled 100 and r are the effects: whence,

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Ex. 6. If 60 bushels of corn feed 6 horses for 50 days; in how many days will 15 horses consume 75 bushels?

The causes are 6 × 50 and 15 x x, and the effects are 60 and 75 bushels: and therefore

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In the former of these examples, the distances travelled are in the compound ratio of the numbers of days and their lengths: and in the latter, the numbers of bushels of corn have the same ratio as that which is compounded of the numbers of horses and days.

Ex. 7. If 25 labourers can dig a trench 220 yards long, 3ft. 4in. wide, and 2ft. 6in. deep, in 32 days of 9 hours each: how many would it require to dig a trench half a mile long, 2ft. 4in. deep, and 3 ft. 6in. wide, in 36 days of 8 hours each?

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In this example, both the causes and effects are compound quantities, consisting of their respective subordinate partial causes and effects.

131. In practice, when the partial causes and effects consist of compound quantities, it is most convenient to express them by vulgar fractions or decimals: and when the entire causes and effects are compound quantities, to proceed as in the third chapter, shortening the operations as much as possible by means of article (124),

(1)

Examples for Practice.

Find a number which shall have the same ratio to 7 that 27 has to 3: also, a magnitude to which 39 has the same ratio as 31 has to 2g.

Answers: 63 and 31}.

(2) Find the price of 39 cwt. 3 qrs. 26lbs. at £4. 17s. 10d. per cwt.

Answer: £195. 11s. 7 d.

(3) What quantity of cloth at 6s. 8d. a yard may be bought for 20 guineas?

Answer: 63 yards.

(4) If a piece of cloth measuring 9ells. 1 na. 1¦in., cost £3. 15s. 74d., what is its price per yard?

Answer: 6s. 8d.

(5) How much carpet 2ft. 3in. wide, will cover a floor 13 ft. 6in. long, and 10ft. wide?

Answer: 20 yards.

(6) What is the price of 19cwt. 2qrs. 23lbs., when 4 cwt. 1qr. cost £3. 14s. 61d.?

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(7) The rental of a parish is £5497. 13s. 4d., and £152. 10s. 6d. is to be raised by a rate; what is the rate in the pound?

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(8) If a person can perform a journey in 24 days of 10 hours each; what time will it take him to do the same when the days are 123 hours long?

Answer: 19 days.

(9) How much in length, that is 15 poles in breadth, will be equivalent to an acre of land, which is 40 poles in length and 4 poles in breadth?

Answer: 10po. 3 yds. 2ft.

(10) If £100. be sufficient to discharge a debt of £104. 17s. 6d. due a year hence; how much money will be sufficient to pay a debt of £1000. at the same date? Answer: £953. 10s. 3 d.375.

(11) If in 365 days. 5 hrs. 49 min., the Sun describe an arc of 360° in the heavens: what is his mean daily motion?

Answer: 59′. 8.328 &c."

(12) If 7 men earn £9. 10s. 6d. in 10 days; what sum will 28 men earn in 311⁄2 days?

Answer: £114. 6s.

(13) If with a capital of £500. a tradesman gain £100. in 14 months; in what time will he gain £60. 10s. with a capital of £770?

Answer: 5 months.

(14) If 400 soldiers consume 5 barrels of flour in 12 days; how many soldiers will consume 15 barrels in 2 days?

Answer: 7200 soldiers.

(15) If 20 men can perform a piece of work in 12 days; how many men will perform another piece of work three times as great, in a fifth part of the time?

Answer: 300 men.

(16) If 12 men can mow a field 300 yards square in 10 days: how many men can mow a field 600 yards long, and 10 yards wide, in 4 days?

Answer: 2 men.

(17) A bankrupt owes £1490. 5s. 10d., and has only £784. 17s. 4d.; how much will his creditors receive in the pound?

Answer: 10s. 61d.2099

(18) If 27 men can do a piece of work in 14 days, working 10 hours a day; how many hours a day must 24 boys work, in order to complete the same in 45 days, the work of a boy being half that of a man?

Answer: 8 hours.

(19) If 10 cannon, which fire 3 rounds in 5 minutes, kill 270 men in 11⁄2 hours; how many cannon, which fire 5 rounds in 6 minutes, will kill 500 men in 1 hour, at the same rate?

Answer: 20 cannon,

(20) If 120 men in 3 days of 12 hours each, can dig a trench 30 yds. long, 2 ft. broad, and 4 ft. deep; how many men would be required to dig a trench 50 yds. long, 6 ft. deep, and 14 yds. broad, in 9 days of 15 hours each? Answer: 180 men.

(21) A watch, which is 10 minutes too fast at twelve o'clock on Monday, gains 3 min. 10 sec. per day; what will be the time by the watch at a quarter past ten in the morning of the following Saturday?

Answer: 40 min. 36 sec. past 10.

1

20

(22) Find a fourth proportional to 35, and 33: also, to 125, .0145 and .35.

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(23) How much cloth

560

yard wide, will cover a room 12 ft. 6 in. long, and 2 ft. 9 in. wide; and what will it cost at 5s. 6d. a yard?

Answers: 7 yds. 2§ qrs., and £2. 2s. 0}d.

(24) If beer, which is brewed with 3 bushels of malt to the barrel, cost 1s. 3d. per gallon, when malt is at 62s. Sd. the quarter: how much will beer cost per gallon, which is brewed with 5 bushels of malt to the barrel, when a quarter of malt costs 50s.?

Answer: 1s. 73d. 37.

II. INTEREST, STOCKS, &c.

132. DEF. Interest is the payment made for the loan or use of money for any length of time, being generally estimated at so much for £100. during a year, and commonly expressed by so much per cent. per annum : the money lent is called the Principal, the interest of £100. for a year, the Rate per cent.: and the sum lent together with its interest is termed the Amount.

It is called simple interest, when the loan itself only pays interest for the whole time it is lent; and compound

interest, when, at the end of any assigned period, as a year for instance, the interest, which has accrued, is added to the principal, and the whole then bears interest at the same rate for another equal period, and so on.

Hence, it is evident that for one year, the sum lent may be regarded as the cause, and the interest produced as the effect.

Ex. Find the

Simple Interest.

simple interest and amount of £237. 10s. for 2 years, at 5 per cent. per annum.

From what has just been said, we have

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is the interest of 237. 10. for one year:

£. S. d.

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hence, 11. 17.6 × 21 29. 13. 9 is the interest of 237. 10 for 21 years: and therefore

£. 8. d. £. S. £. S. d.

29.13.9+ 237. 10

267.3.9

is the amount of the same sum for the same time.

In practice, we may work in the subsequent form, following up the same principles: thus,

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