3. A has 7 cwt. of sugar, at 12cts. per pound, for which B gave him 12 cwt. of flour-what was the flour rated at per pound? Ans. $.07,2. 4. How much wheat, at $1.25 per bushel, must be given in barter for 50 bushels of rye, at 70cts. per bushel? Ans. 28 bushels. 5. B delivered 189 gallons of brandy, at 80cts. per gallon, to C, for 126 yards of cloth-what was the cloth per yard? Ans. $1.20. CASE 2. When the quantities of two commodities are given, and the rate of selling them, to find, in case of inequality or difference, how much of some other commodity must be given. RULE. Find the separate values of the two given commodities; subtract the less from the greater, and the difference will be the amount of the third commodity, which divide by its price per yard, or bushel, &c. for the quantity. EXAMPLES. 1. A and B would barter; A has 150 bushels of wheat, at $1.25 per bushel, for which B gives 65 bushels of barley, worth 625 mills per bushel, and the balance in oats, at 375 mills per bushel-what quantity of oats must A receive from B? Ans. 391 bushels. 2. E has 5 pieces of muslin, each piece containing 95 yards, at 23cts. per yard, for which F is to give him 32 sheep, at $2.50 each, and the remainder in rye flour, at $1.50 per cwt.-how many hundred weight of flour must E receive? Ans. 19cwt. 2qrs. CASE 3. Having the ready money and bartering price of one commodity given, and the cash or ready money price and quantity of another commodity given, to find its bartering price, and the quantity of the other. RULE. As the ready money price of the one To the bartering price of the second. Then, the relative value of both commodities being given, and the quantity of one; the quantity of the other may be found by the Rule of Three. EXAMPLES. 1. A has muslin, at 22cts. per yard, ready money; but in barter he will have 25cts. B has cassinett, at 88cts. per yard, ready money-at what rate must B value his cassinett per yard, to be equivalent to A's bartering price, and how many yards of muslin, at 25cts. per yard, must A give for 30 yards of B's cassinett? Ans. { B's cassinett, at $1 per yard; A must give 120 yards of muslin. 2. A and B barter; A has 150 gallons of brandy, at $1.375 per gallon, ready money; but in barter he will have $1.50: B has whiskey at 44cts. per gallon, ready money—how must B sell his whiskey per gallon, in proportion to A's bartering price, and how many gallons are equal to A's brandy? Ans. B's whiskey 48cts. per gallon; and he must give 3. A has 200 yards of linen, at 1s. 6d. ready money, per yard, which he barters with B at 1s. 9d. per yard, taking buttons at 74d. per gross, which are worth but 6d.-how many gross of buttons will pay for the linen; who gets the best bargain, how much on the whole, and what per cent.? Ans. 560 gross of buttons B gains £1 on the whole, and £8 6s. 8d. per cent. CUSTOM-HOUSE ALLOWANCES. THE Only allowances which are made in the weight of goods, at the Custom-houses of the United States, are tare, and draft, or scalage. Tare is an allowance made for the weight of the box, bag, hogshead, cask, &c., which contains the goods, and is either at so much per cent., or so much per box, &c. or the real or actual tare. Draft or scalage is an allowance of per cent. on the whole gross weight of all goods, (except tea and sugar) which is to be deducted before casting the tare. On tea, no draft is allowed. On sugar there is a deduction to be made for draft or scalage, before casting the tare, of 7 pounds on every hogshead, 4 pounds on every tierce, 2 pounds on every barrel, and 4 pounds on every Havanna box. Gross weight is the whole weight of any kind of goods, together with the box or cask, &c., which contains them. Neat weight is the weight of the goods after all allowances have been deducted. CASE 1. To find the neat weight of goods, when the tare is at so much per cent., with the allowance for draft or scalage. RULE. 1. When the scalage is per cent., divide the whole gross weight by 200, and the quotient will be the scalage. 2. When the scalage is so much per hogshead, box, &c., multiply the scalage of one by the number of hogsheads, boxes, &c., and the product will be the whole scalage. 3. Subtract the scalage from the gross weight, then multiply the remainder by the tare per cent., and divide the product by 100, the quotient will be the whole tare, which subtract from what remained after the scalage was deducted, and the remainder will be the neat weight. NOTE. In casting tare and scalage, remainders which do not exceed half a pound, are not usually reckoned, but if they exceed half a pound, then another pound is reckoned. EXAMPLES. 1. A merchant bought 15 boxes of brown Havanna sugar, weighing 6740lbs. gross, tare 15 per cent., scalage 4 pounds per box; what was the neat weight of the sugar, and what was its value, at $10.25 per 100lb. Ans. S 5678lbs. and $581.99,5 value. 2. What is the neat weight of 4 bags of coffee, weighing 480lbs. gross, allowance 2 per cent. for tare, and per cent. for scalage; and what is the value of the neat weight, at 18 cents per pound? Ans. 468lbs. neat weight; $84.24 value. CASE 2. To find the neat weight of goods when the tare is so much per box, cask, chest, &c., either with or without the allowance for draft or scalage. RULE. 1. If draft or scalage be allowed, cast and deduct it as directed in Case 1. 2. Multiply the tare of one by the number of boxes, chests, &c., the product will be the whole tare, which subtract from what remained after the scalage was deducted, or from the whole gross weight when no scalage is allowed, and the remainder will be the neat weight. EXAMPLES. 1. What is the neat weight and value of 4 casks of raisins, weighing 520lbs. gròss, tare 12lbs. per cask, allowing per cent. for draft or scalage, at 75 mills per pound? Ans. 469lbs. neat weight; $35.175 value. 2. What is the neat weight and value of 150 chests of Hyson tea, weighing 11250lbs. gross, tare 20lbs. per chest, at 40cts. per lb. ? Ans. 8250lbs. neat weight; $3300. CASE 3. To find the neat weight of goods, when the real or actual tare is allowed. RULE. Subtract the whole amount of tare from the whole gross weight, and the remainder will be the neat weight. EXAMPLES. 1. What is the neat weight and value of 50 boxes of figs, weighing 1250lbs. gross, whole amount of tare 175lbs., with an allowance of per cent. for scalage, at 10cts. per lb.? Ans. 1069lbs. neat weight; $106.90 value. 2. What is the neat weight and value of 4 firkins of butter, weighing as follows: IN the first place, an inventory of the value of all the estates, both real and personal, and the number of polls for which each person is rateable, must be taken in separate columns. The most concise way is then to make the total value of the inventory the first term, the tax to be assessed the second, and $1 the third, and the quotient will show the value on the dollar. Secondly—make a table by multiplying the value on the dollar by 1, 2, 3, 4, &c. Thirdlyfrom the inventory take the real and personal estates of each man, and find them separately in the table, which will show you each man's proportional share of the tax for real and personal estates. NOTE.-If any part of the tax is averaged on the polls, or otherwise, before stating to find the value on the dollar, you must deduct the sum of the average tax from the whole sum to be assessed; for which average you must have a separate column, as well as for the real and personal estates. EXAMPLES. 1. Suppose the General Assembly should pass an act for raising $50000, of which the county of Gloucester is to pay $5312.50, and the polls being 1550, are to pay $1.25 each. The county's inventory amounts to $450000-what will it be on the dollar, and what is A's tax, whose estate (as by the inventory) is as follows, viz. real $1376, personal $1149, and he has 3 polls. pol. pol. First, As 1 1550 :: 125: 1937.50 the average part of the tax to be deducted from $5312.50, and there will remain $3375. Secondly, As $450000 : $3375 :: $1 : 7 mills on the dollar. Now to find what A's rate will be: his real estate being 1376 dollars, we find by this table, |