b. 10oz. of silk, at £4 5 9= £4·297 9lb. 10oz 9.625 21435 8574 25722 38583 41.262375 £41 5 3 Ans. Cases 6th, and 7th. may be wrought in this manner. VII. When the price is any odd number of shillings: If it be required to know what quantity of any thing may be bought for any sum of money, in pounds: Annex two cyphers to the money, and divide it by half the price. Note. As half a shilling (or 6 pence) is 5, therefore, to halve any odd number of shillings, is only to annex '5 to half of the greatest even number in the price. BILL OF PARCELS. Newburyport, January 1st, 1808. Bought of Samuel Merchant, Mr. Timothy Huckster 251 Bohea tea, at 3s. 6d. per Ib. 48 Cheese, at 9d. per . 15 Pair worsted hose, at 5s. 8d. per pair. 4 Dozen women's gloves, at 36s. 6d. per dożeń. 1. £34 3 3 Samuel Merchant. Received payment in full, TARE AND TRET. TARE and Tret are practical rules for deducting certain allow. ances, which are made by merchants and tradesmen in selling their goods by weight. 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 4b in every 104 for waste, dust, &c. Cloff is an allowance of 21 upon every 3cwt. Gross weight is the whole weight of any sort of goods, together with the box, barrel, or bag, &c. which contains them. Suttle is, when part of the allowance is deducted from the gross. Neat weight is what remains after all allowances are made. CASE 1.* When the tare is at so much per box, barrel or bag, &c. Multiply the number of boxes, barrels, &c. by the tare, and subtract the product from the gross, and the remainder will be the neat weight required. EXAMPLES. 1. In 6 hogsheads of sugar, each weighing 9cwt. 2qrs. 10lb. gross, tare 25lb, per hogshead; how much neat? *This, as well as every other case in this rulc, is only an application of the rules of Proportion and Practice, 2. In 5 bags of cotton, marked with the gross weight as follows, tare 231 per bag; what neat weight? Cwt. gr. 3. What is the neat weight of 15 hogsheads of tobacco, each 7cwt. 1qr. 13, tare 100 per hogshead? CASE II. Ans. 97cwt. Oqr. 11. When the tare is at so much per cot.: Divide the gross weight by the aliquot parts of a cwt. subtract the quotient from the gross, and the remainder will be the neat weight. EXAMPLES. 1. In 129cwt. 3qrs. 16lb. gross, tare 14lb. per cwt. what neat weight? | 14lb. | | Ans. Cwt. qr. lb. 16 0 113 2 2. In 97ewt. 1qr. 7lb. gross, tare 20lb. per cwt. what neat weight. 171 neat. 3. What is the neat weight of 9 barrels of potash, each weighing 305lb. gross, tare 12lb. per Ans. 79Cwt. 3qrs. 21lb. neat. cwt.? Ans. 2450 14oz. 44dr. 4. What is the value of the neat weight of 7hhds. of tobacco, at 51, 7s. 6d. per cwt. each weighing 8cwt. 3qrs. 10 gross, tare 21 per cwt.? Ans. £270 44 reckoning the odd ounces. CASE III. When tret is allowed with tare: Divide the suttle weight by 26, and the quotient will be the tret, which subtract from the suttle, and the remainder will be the neat.* * Tret is 4lb. in 104, which is And Cloff is lb. in 3Cwt, or 20 Z EXAMPLES. 1. In 247cwt. 2qrs. 15b gross, tare 28 per cwt. and tret 4 for every 104b what neat weight? | 28 || 247C.2qr.15 gross. 61 3 17 12 tare, subtract. Ans. 178 2. What is the neat weight of 4hhds oftobacco, weighing as follow: The 1st. 5cwt. 1qr. 12 gross, tare 65 per hhd.; the 2d. 3cwt Oqr 19th gross, tare 75: the 3d. 6cwt. 3qrs. gross, tare 49; and the 4th, 4cwt. 2qrs. 9b gross, tare 35, and allowing tret to each as usual? Ans. 17cwt. Oqr. 19+ CASE IV. When tare, tret, and cloff are allowed: Deduct the tare and tret as before, and divide the suttle by 168, and the quotient will be the cloff, which subtract from the suttle, and the remainder will be the neat. EXAMPLES. 1. What is the neat weight of 1hhd. of tobacco, weighing 16cwt. 2qrs. 20lb gross, tare 14 per 3cwt.? 14 is 1)16 2 per cwt. tret 4b per 104, and cloff 21k 20 O gross. 2 0 9 4b is)14 2 10 8 tare, subtract. 8 0 2 6 13 tret, subtract. 2. If 9hhds. of tobacco, contain 35cwt. Oqr. 2b, tare 30 per hhd. tret and cloff as usual, what will the neat weight come to at 61d. per ib after deducting for duties and other charges, 511. 11s. 8d? Aus. £187 18s. 5d. INVOLUTION TEACHES the method of finding the powers of numbers. A power is the product arising from multiplying any number into itself continually a certain number of times. Thus, any number is called the first power, as 3; if it be multiplied by itself, the product is called the second power or square, as 3×3; if the second power be multiplied by the first power, the product is called the third power, or cube, as 3×3×3; if the third power be multiplied by the first power, the product is the fourth power, or biquadrate, as 3×3×3×3, or 81 is the fourth power of 3, and so on. The power is often denoted by a figure placed at the right and a little above the number, which figure is called the index or exponent of that power. The index or exponent is always one more than the number of multiplications to produce the power, or is equal to the number of times the given number is used as a factor in producing the power. Thus the square of 3,3 x 3 = 32; and the cube of 3, = 3 × 3 × 3 = 33; and the 4th power of 3. = 3 × 3 × 3 × 3 = 3a ; and the 5th power of 3, = 3 × 3 × 3 × 3 × 335, and so on. In producing the square of 3, for instance, there is only one multiplication, or two factors; in producing the cube, there are two multiplications or three factors, and so on. Hence, Involution is performed by the following RULE, Multiply the given number, or first power continually by itself, till the number of multiplications be 1 less than the index of the power to be found, and the last product will be the power required. Note. Whence, because fractions are multiplied by taking the products of their numerators, and of their denominators, they will be involved by raising each of their terms to the power required, and if a mixed number be proposed, either reduce it to an improper fraction, or reduce the vulgar fraction to a decimal, and proceed by the rule. 2. What is the 5th power of ?? Ans. 243 3125 3. What is the fourth power of '045? Ans. 000004100625. Here we see, that in raising a fraction to a higher power, we decrease its value. |