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 sutile, and the remainder is the net weight. Examples 1. In 9 cwt. 2 qrs. 17 lb. gross, 2. In 342 cwt. 2 qrs. 14 lb. tare 37 lb. and trett as usual, how gross, tare 16 lb. per cwt. and much net? trett as usual, how inuch net ? cwt. qr. Ib. Ans. 282 cwt. 1 qr. 141b. 9 2 17 gross. 1 9 Tare. 3. In 7 casks of prunes, each weighing S cwt. 1 qr. 5 lb. gross, 26) 91 8 suttle. 1 11 trett. tare 17 Ib. per cwt. and trett as usual, how much net ? Ans. 8 3 25 net. Ans. 18 cwt. 2 qrs. 26 lb. QUESTIONS. 1. What are Tare and Trett ? 8. How do you proceed when the 2 What is gross weight? Tare is so much per box, &c. 3. What is Tare? 9. How, when Tare is so much per 4. What is Trett? hundred weight? 5. What is Cloff ? 10. How, when Trett is allowed with 6. What is Suttle? Tare ? 7. What is Net weight? 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.t-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 19 ' + 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. Examples. 1. A owes B 8750, to be paid 2. B owes C 8190, to be paid as follows, viz. $500 in 2 months, as follows, viz. 850 in 6 months, 8150 in 3 months, and 8100 in 860 in 7 months, and 880 in 10 41 months ; what is the equated | months; what is the equated time to pay the whole ? time to pay the whole ? 500 X2 : 1000 Ans. 8 months. 150 X3 450 100 X 4.5 450 3. Cowes D.a certain sum of money, which is to be paid è in 750 ) 1900 ( 24.8=215 2 months, 1 in 4 months, and the 1500 Ans. remainder in 10 months; what is the equated time to pay the 400 whole ? Ans. 4 months. mo. QUESTIONS: 1. What does the Equation of Payo ; 3. Is the rule perfectly correct? ments teach? 4. Why is it not ? 2. What is the rule? 5. Why then is it introduced ? 1. 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. che 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. 1. A and B made a joint stock 4. Divide 8160 among 4 men, of 8500, of which A put in $350, so that their shares shall be as 1, and B $150, they gain, 875; | 2, 3, and 4. what is each man's share of the 16 gain? 32 Ans. $ Ans. 48 S 350 : 52.50 A's share. 64 500: 75 :: 150 : 22.50 B's share. 160 proof. 75.00 proof. 2. A, B and C companied ; A 5. A person dying, bequeathed his estaie to his 3 sons; to the put in £480, B £680, C £840, eldest he gave 8560, to the next, and they gained £1010; what is 8500, and to the other 8450; each man's share? but when his debts were paid, £ 242 8 A's. there were only $950 left ; what 343 8 B's. was each son's share : Ans. 424 4 C's. 352.317 + 1st 3. Three persons make a joint 314.509 + 2d ŞAns. stock, of which each puts in an 283 112+ 3d equal share; A continues his stock in trade 4 months, B his 6 6. D and E companied ; D put months, and C bis 10 months, l.in $125, and took out of the and they gained 8480; what was i gain; what did E put in? each man's share ? Ans. 8375. 896 A's 144 B's 240 C's :} Ans. 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 weither the stocks por times are equal, the shares must be as their product. Examples. 1. Three farmers hired a pasture for 860.50. A put in 5 cows for 44 months, B put in 8 for 5 months, and C put in 9 for 68 months; how much must each pay of the rent ? 5x4.5=22.5 121:60.50::22.5 121: 60.50 :: 40 40 $ 242 0000 121 :60.50 ::58.5 58.5 30250 48400 302 30250 242 121)3539250(29.25 C's. 605 242 605 $11.25 A's. 1119 20.00 B's. Ans. 1089 29.25 C's. 2. Two merchants entered in 3. Three men hire a pasture to partnership for 18 months; A for 100 dollars; A puts in 40 at first put in £100, and at the oxen for 20 days, B 30 oxen for end of 8 months put in £50 more; | 40 days, and C 50 oxen for 10 B at first put in €275, and at days'; how much must each man the end of 4 months, took out pay? $ '£70; at the end of the 18 months they had gained £263 ; what is 48 B's. Ans. each man's share? 20 C's. 100 proof. 42 263 0 0 proof. QUESTIONS. 1. What is Fellowship? 5. What is Double Fellowship? 2. Of how many kinds is Fellowship? 6. What is the rule for Double Fel. 3. What is Single Fellowship? lowship? 4. What is the rule for Single Fel Iowship? 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. gave him Examples. 1. A has 350 yards of cloth at 2. A has 72 cwt. of sugar at 8d 1s. 4d. per yard, which he would per pound, for which B exchange with B for sugar at 258 | 12 cwt. ot four ; what was the 60 per cwt.; how much sugar i flour per pound? will the cloth come to ? Ans. 4 d. 350yds. at 1s. 4d.= 4669.-8d. $. How much tea at 9s. 4d. 5600d. and 25. 6d.=300d. d. cwt. d. per pound, must be given in bar ter for 156 gallons of wine, at Then 306 :1:: 5600 12s. 3 d. per gallon? Ans. 2051b. 13/ituz, Case II. 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 shoulè 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 2. I have 63 gal, of molasses at $3.927 per cwt. which he barters 62 cts. per gal. which I would with B for 9 pieces of broadcloth exchange for 5bushels of rye at at $12.50 per piece; which must. 75cts. per bushel ; must I pay or receive money, and how much? receive money, and how much ? Ans. B inust pay A 65.31. Ans. I must receive 37 Actes |