Case III.

When Treit is allowed with Tare.

RULE.*-Divide the suttle weight by 26, and the quotient is the trett; subtract the trett from the suttle, and the remainder is the net weight.

Examples.

3. Equation of Payments.

EQUATION OF PAYMENTS teaches to find the time for paying at once several debts due at different times, so that no loss shall be sustained by either party.

RULE.-Multiply each payment by the time at which it is due, and divide the sum of the products by the sum of the payment, and the quotient will be the time required.

* You divide by 26, because the trett is one twenty-sixth. When cloff is allowed, after deducting the tare and trett, divide the suttle by 168, and the quotient is the cloff which subtract from the suttle, and the remainder is the net weight. You divide by 168, because the cloff is 1 lb. in every 168 lb. or

+ This rule supposes that there is just as much gained by keeping some of the debts after they are due, as is lost by paying the others before they are due. But this is not exactly true: for by keeping a debt unpaid after it is due, there is gained the interest of it for that time; but by paying a debt before it is due, the payer loses only the discount, which is somewhat less than the interest, as has already been shown. The rule, however, is sufficiently correct for practical purposes.

1. What does the Equation of Pay- 3. Is the rule perfectly correct?

ments teach?

2. What is the rule?

4. Why is it not?

5. Why then is it introduced?

Fellowship.

FELLOWSHIP is a general rule, by which merchants and others, trading in company, with a joint stock, compute each person's particular share of the gain or loss.

Fellowship is of two kinds, Single and Double.

1. SINGLE FELLOWSHIP.

Single Fellowship is when the stocks or times are equal.

Rule.

If the stocks are equal, say, as the whole time is to the whole gain or loss, so is the time each man's stock is employed to his share of the gain or loss; and if the times are equal, say, as the sum of the stocks is to the whole gain or loss, so is each man's share in the stock to his share in the gain or loss.

Proof.

Add all the shares of the gain or loss together, and the sum will equal the whole gain or loss, if the work be right.

Double Fellowship is when unequal stocks are employed for unequal times.

RULE.-Multiply each man's stock by the time of its continuance in trade; then, as the sum of the products is to the whole gain or loss, so is each product to its share of the gain or loss.

*The shares of gain or loss are evidently as the stocks when the times are equal, so when the stocks are equal, the shares are evidently as the times; wherefore, when ueither the stocks nor times are equal, the shares must be as their product.

Examples.

1. Three farmers hired a pasture for $60.50. A put in 5 cows for 4 months, B put in 8 for 5 months, and C put in 9 for 64 months; how much must each pay of the rent?

5. Barter.

BARTER is the exchanging of one quantity for another, and teaches merchants so to proportion their quantities that neither shall sustain loss.

Case I.

When the quantity of one commodity is given, with its value, or the value of its integers, and also the value of the integer of some other commodity to be exchanged for it, to find the quantity of this commodity.

RULE.-Find the value of the given quantity, then find how much of the other, at the rate proposed, may be had for the same sum.

When the quantities of two commodities are given, and the rate of selling them, to find, in case of inequality, how much of some other commodity, or how much money should be given.

RULE. Find the separate values of the two given commodities and their difference will be the balance, or value of the other commodity.

Examples.

1. A has 30 cwt. of cheese at $3.927 per cwt. which he barters with B for 9 pieces of broadcloth at $12.50 per piece; which must receive money, and how much?

Ans. B inust pay A $5.31.

2. I have 63 gal, of molasses at 623 cts. per gal. which I would exchange for 52 bushels of rye at 75cts. per bushel; must I pay or receive money, and how much?

Ans. I must receive 37 cts.