When the prices of quantities which have divers denominations are required, the principal difficulty seems to arise in finding the amount of the broken quantity, as it requires considerable practice to acquire the art of taking the best parts; various devices have been adopted to avoid this troublesome part of the operation, which if any have a desire to see at large, they can be amply gratified, by consulting Cox's, Deighan's, or M'Swiney's publications, particularly Cox's, which is the oldest of these works; but as some of those will be found in one, that are omitted in another, I here annex such of them as appear to me to be most useful, to which I have added some not noticed, that I know of, in any work but the present. Tons cwt. qrs. and lbs. are brought to the form of £ s. d. by making the pounds the fraction of a quarter, and multiplying this by 3 for pence; the tons and cwts. being taken as pounds and shillings. For as 20 shillings make a pound, and 20ct. make a ton at 20s. ton; cwt. costs 1 shilling, and a quarter of an cwt. 3 pence, whence the rule is manifest. Cwts. qrs. and lbs. by multiplying the quarters by 5 and lbs. by 24; for at 20s. p cwt. a quarter cost 5s. and a Ħ 24d. Pounds, oz. and drams avoirdupoise, by multiplying the oz. by 1 and subtracting from the drams thereof; for at 20s. every oz. cost 15d. or 14s. and á dram † of a penny. Pounds, oz. dwts. and grains troy, by making the grains the fraction of a penny-weight, and multiplying the oz. by 20d. adding thereto the penny-weights and fraction thereof counted as pence; for there are 240 penny weights in a pound troy and 240 pence in a pound, and at that price loz cost ls. 8d. or 1 shillings. Ounces, dwts. and grains troy, by counting the ounces and penny-weights as £ and s. and taking the grains as pence; because 20dwts, make an oz. and 24 grains a penny-weight therefore at 20s. oz. a penny-weight costs 1s. and a grain ] halfpenny. Yards, qrs. and nails, by multiplying the quarters by 5, and nails by 15; for at 20s. per yard a quarter costs 5s. Od. and a nail 15 pence. Ells English, qrs. and nails, by multiplying the quarters by 4 and counting every nail one shilling. Acres, roods and perches, are brought to the form of pounds shillings and pence, by multiplying the roods by 5, and perches by 1; because 14d. per perch and 5s. per rood, is just at the rate of 20s. per acre. Cwts. qrs. lbs. long weight are brought to like form by multiplying by 5 and 2; for there being 30tb in each quarter 1b costs 2d. and a quarter 5 shillings. The rule for common weight, before given, will answer for tons cwt. and qrs. long weight. An example or two in each particular case will I hope be sufficient to make these matters fully understood. Ton, Ct. qr. Ib. L 8 d Ct. qp. lb. £ s d 48 1 17 at 2 2 0 5 24 48 8 0 @20s ct 48 8 02/ 2s = 4 16 9 5 4 9 77 £201 14 63 lb. oz. £101 12 10 oz. dwt. £ s d 80 10 of silk at 365 17 5 14 at 3 6 9 24 12 6a41 8s 4d 12 10 16 12@51 12s 6d Let the pupil prove by the rules here explained, such of the examples in Case 14th as admit of their application, which will render these matters familiar to him. CASE 15th-When the quantity is of divers denominations and the price of one of the lower or lowest is given. By multiplication bring the compound quantity to the denomination of which the price is given, and find the amount by such of the foregoing rules as is best adapted for the purpose, adding thereto the amount of the odd parts, if any, at the given price. When the lowest denomination has a fraction in it or when the price of a mixed quantity is required. Find the price according to such of the preceding cases as is best adapted, adding thereto such proportional part or parts as are equal to the price of the fractional part, or else consider the given quantity as pounds or shillings, and annex thereto such part of a pound or shilling as the fraction was of the integer to which it belongs. |