second and third, with points; as in the Rule of Three Direct. Then reduce the terms, if necessary, and work as directed in that rule.

Examples.

If I borrow of my friend £500 for 6 months, I demand to know, how long I ought to lend to him £75 to requite

his kindness ?

Suppose 36 men can build a boat in 12 days, in how many, can 27 build it ? A. 16 days.

How far can I have 4tons 2cwt. carried for the same money that I pay for 15 tons, carried 20 miles? A. How many yards of stuff, 3qrs. wide, will line 30 yards of cloth 5qrs. wide ? A. 50 yards.

If 30 men earn £25 in 25 days, how long will 15 men be in earning the same wages?

A.

What should a loaf weigh, when wheat is 3s. a bushel; if when at 5s. 3d. it weighs 2lbs. 8oz. ? A. 4lbs. 6oz.

If a loaf weighs 4lb. 6oz. when wheat is 4s. 6d. a bushel, what should it weigh when wheat is 5s. 3d. a bushel? A. 3lbs. 12oz.

wide, will cover a A. 40 yards. months, in what time

How many yards of carpet 3qrs. floor 18 feet long and 15 feet wide? Suppose £400 to gain £50 in 10 will £250 gain the same money ? A. 16 months.

FELLOWSHIP.

Fellowship is a rule used to calculate shares of gain and loss.

RULE. Add the given shares together, make as many statings as there are shares; saying

is to the whole

As the sum of the shares, or stocks gain or loss, :: so is each share, or stock, share of gain or loss.

to its

Proof.-Add all the shares of gain or loss together, and the sum will be equal to the given gain or loss; or invert the terms of the statings.

Examples.

Divide £140 among A. B. and C., so that A. shall have one share, B. two, and C. three.

A's stock is £70, B's £35, they gain £150, what is each man's share of gain? A. A £100, B £50.

B puts in £300, C £75, and D £150; they gain £260, what is each share of gain? A. B £150, C £37 10s., D £75.

E, F, and G lose in partnership £120; E' put in £140, F £300, and G £160, how much did each lose? A. E £28, F £60, C £32.

H, J, and K are joint ship owners; H gains £28, J £60, and K £32, the ship cost £600, what did each part cost?

Messieurs L, M, N, and O, engage in trade and lose £1000; L's stock is £400, M's £500, N's £900, and O's £1200, what is each merchant's loss? A. L £133 6s. 8d., M £166 13s. 4d., N £300, and O £400.

FELLOWSHIP WITH TIME.

RULE. Multiply each sum by its time, and add the products together; then state and say,—

As the sum of the products is to the whole gain or so is each product to its share of gain or loss.

loss,

Examples.

X puts £10 for 5 months, Y £8 for 10 months, and Z £6 for 5 months; they gain £60, what is each share?

The rent of a pasture is £30 10s. A puts in 12 sheep for 3 months; B puts in 8 for 8 months, and C 10 for 5 months; how much must each pay of the rent? A. A £8 Os. 11⁄2d., B £12 19s. 3d., and C £9 10s. 7 d.

E, F, and G lost £100 in partnership; E had £50 for 2 months, F £50 during 4 months, and G £60 for 5 months; what is each merchant's share of the loss? A. E's £16 13s. 4d., F's £33 6s. 8d., and G's £50.

BARTER.

Barter is the exchange of one commodity for another. RULE. Find the value of each commodity, and work by the Rule of Three, or otherwise, as the case may require.

Examples.

B delivers to C 49 yards at 3s. 4d. a yard, for 38 ells at 4s. 2d. an ell, what is the difference of value, and who must pay it? A. The difference is 5s. which C must pay.

How much tea at 10s. per lb. can I have in barter for lewt. 2qrs. 10lb. of chocolate, at 5s. per lb.? A. 89lbs. A had 41cwt. of hops at £1 10s. per cwt., for which gave £20 in money and the rest in prunes at 5d. per lb.; what weight of prunes did B give besides the £20 ? A. 17cwt. 3qr. 4lb.

B

X delivered to Y 189 gallons of wine at 6s. 8d. per gallon, for 126 yards of silk, what was the silk a yard ? A. 10s.

LOSS AND GAIN.

RULE 1.-Find the difference between the whole cost and the whole produce.

Examples.

Bought 18cwt. of sugar at 28s. per cwt. which I sell at 31d. per lb., what is the gain? A. £4 4s.

Bought butter at 20d. per lb. and sold at 17d., what is the loss on 1440lb. ? A. £18.

Bought 1371b. of tea at 4s. 11⁄2d. per lb. and sold at 4s. 9d., what was the gain?

RULE 2.-As the first cost is to the price sold at :: so is £100 to a fourth number.

If the 2nd. term be more than the first, subtract £100 from the fourth number, and the remainder will be the gain per cent. or on £100.

If the 2nd. terin be less than the first, subtract the fourth number from £100, and the remainder will be the loss per cent.

Examples.

Bought wine for £50 8s. and sold for £63, what is the gain per cent.? A. £25.

Tea, which cost me 12s. per lb. I sold at 16s. per lb., what was the gain per cent. ? A. £33 6s. 8d.

Sold for £1460, a ship which cost £1800, what was the loss per cent ? A.

ALLIGATION.

Alligation teaches how to mix quantities of different simples together, and to find the mean price of the mixture.

ALLIGATION MEDIAL

Is when the quantities and prices are given.

RULE.-Multiply each quantity by its rate or price, divide the sum of the products by the sum of the quantities, and the quotient will be the mean price. by Division.

Examples.

Proof

A farmer mixed 20 bushels of wheat, at 5s. per bushel, with 40 bushels of rye at 3s., what is the price of a bushel of this mixture?

A grocer mixed 4cwt. of an article at 56s. per cwt. with 7cwt. at 43s. and 5cwt. at 37s.; what is the price of lcwt. of the mixture? A. £2 4s. 41⁄2d.

Ten gallons of brandy at 18s. 6d. were mixed with 4gals. at 15s. and two gallons of water; what is the price of a gallon? A. 15s. 3 d.

Mixed one gallon of rum at 16s. with one at 15s., and another at 14s. with one gallon of water; what is the price of one gallon of the mixture? A. 11s. 3d.

ALLIGATION ALTERNATE

Is when the prices of several things are given, to find