TARE AND TRET. Tare and TreT are practical rules for deducting certain allowances, which are made by merchants and tradesmen in selling their goods by weight. Gross weight is the whole weight of any sort of goods, together with the box, barrel, or bag, &c. that contains them. Tare is an allowance made to the buyer for the weight of the box, barrel, or bag, &c. which contains the goods bought, and is either at so much per box, &c., at so much per cwt., or at so much in the gross weight. Tret is an allowance of 4. in every 104. for waste, dust, &c., or of the whole tare=suttle. Cloff is an allowance of 2. upon every 3cwt. or 336. Suttle is the weight when part of the allowance is deducted from the gross. Neat weight is what remains after all allowances are made. CASE I. When the tare is a certain weight per box, barrel, or bag, &c. RULE.-Multiply the number of boxes, or barrels, &c. by the tare, and subtract the product from the gross, and the remainder is the neat weight required. EXAMPLES. 1. In 10 casks of alum, each weighing 3cwt. 2qrs. 12. gross, tare 15. per cask, how much neat? 2. In 241 barrels of figs, each 3qrs. 19. gross, tare 10. per barrel, how many pounds neat? Ans. 22413. 3. What is the neat weight of 21 hogsheads of tobacco, each 5cwt. 2qrs. 17lb. gross, tare 100lb. per hogshead, at 25lb. to the qr.? Ans. 98cwt. 7lb. 4. What is the neat weight of 4 chests of hyson tea, weighing, gross 961b. 97lb. 101lb. and 103lb., tare 20lb. per chest? Ans. 317lb. CASE II. When the tare is a certain weight per cwt. RULE. Divide the gross weight by the aliquot* parts of an cwt. contained in the tare, and subtract the quotient from the gross, and the remainder is the neat weight. EXAMPLES. 1. Gross 372cwt. 3qrs. 17lb., tare 16lb. per cwt., how much neat? Cut. qrs. lb. 16lb. is )372 3 17 53 1 2 tare subtracted. 3. In 129cwt. 3qrs. 16lb. gross, tare 14lb. per cwt., what is the neat weight? Ans. 113cwt. 2qrs. 174lb. 4. In 25 barrels of figs, each 2cwt. 1qr. gross, tare 16lb. per cwt., how much neat? Ans. 48cwt. Oqrs. 24lb. CASE III. When tret is to be allowed with tare. RULE.-Divide the suttle weight by 26, and the quotient is the tret, which subtract from the suttle, and the remainder is the neat weight. EXAMPLES. 1. In 9cwt. 2qrs. 17lb. gross, tare 371b. and tret as usual, how much neat? 2. In 7 casks of prunes, each weighing 4cwt. gross, tare 174lb. per cwt. and tret as usual, how much neat, at 25lb. to the qr. ? Ans. 22cwt. 21lb. 3. What is the neat weight of 3hhds. of sugar weighing as follows; the first 4cwt. 5lb. gross, tare 73lb.; the second 3cwt. 2qrs. gross, tare 561b.; and the third 2cwt. 3qrs. 17lb. gross, tare 471b.; and allowing tret to each as usual; 25lb. a qr.? Ans. Scwt. 1qr. 124lb. 4. What is the neat weight of 10 casks of raisins, each weighing 3cwt. 2qrs., tare 14lb. per cwt. tret as usual; and what will be the amount at $15 per cwt.? Ans. 29cwt. 1qr. 22 lb. $441, 70cts. 6m.+ CASE IV. When tare, tret, and cloff, are all allowed. RULE.-Deduct the tare and tret, as before, and divide the suttle by 168, and the quotient is the cloff, which subtract from the suttle, and the remainder is the neat. EXAMPLES. 1. What is the neat weight of a hhd. of Tobacco, weighing 15cwt. 3qrs. 20lb. gross, tare 7lb. per cwt. tret and cloff as usual? Cwt. qrs. H. oz. 7lb. is)15 3 20 0 gross. 3 27 8 tare. NOTE.-Some say 2lb. for every 100lb. of tret-suttle ought to be allowed, to make the weight hold good when - sold by retail; instead of 2lb. on every 336lb. 2. What is the value, at 52d. per lb., neat weight, of 26 chests of sugar, each, 9cwt. 2qrs. 1515lb. gross, tare 13lb. per cwt., tret as usual, and cloff 2lb. on 300lb.; 25lb. a qr.? Ans. £499 15s. 5d. DOUBLE RULE OF THREE. THE DOUBLE RULE OF THREE teaches to solve such questions as require two or more statings in the Rule of Three. In these questions there is always given an odd number of terms as five, seven, or nine, &c. These are distinguished into terms of supposition, and terms of demand, the number of the former always exceeding that of the latter by one, which is of the same kind with the term or answer sought. RULE. Write the term of supposition, which is of the same kind with the answer, for the middle term. Take one of the other terms of supposition, and one of the demanding terms of the same kind with it; then place one of them for a first term, and the other for a third, according to the directions given in the Rule of Three. Do the same with another term of supposition, and its corresponding demanding term; and so on, if there be more terms of each kind, writing the terms under each other, which fall on the same side of the middle term. Multiply together all the terms in the first place, and also all the terms in the third place. Then multiply the latter product by the middle term, and divide the result by the former product; and the quotient will be the answer required. Or, take the two upper terms and the middle term, in the same order as they stand, for the first stating of a question in the Single Rule of Three; then take the fourth number resulting from the first stating, for the middle term of a new stating in the above Rule, and the two under terms of the Double Rule of Three stating, in the same order as they stand, for the extreme terms of the new stating; and the fourth term resulting from this new stating, will be the answer. NOTE 1.-The first and third terms of each line, if of different denominations, must be reduced to the same denomination. 2. After stating, and before commencing the operation, if one of the first terms, and either the middle term or one of the last terms will exactly divide by one and the same number, let them be divided, and the quotients used instead of them; which will much shorten the work. Make trial with the first Example. EXAMPLES. 1. How many men can complete a trench of 135 yards long in eight days, provided 16 men can dig 54 yards in 6 days? 54 yards : 16 men :: (135 yards |