Note, The Ale Gallon contains 232 cubic or solid inches, Note. By this are measured all Wines, Spirits, Strong waters, Cyder, Mead, Perry, Vinegar, Oil, Honey, &c. The Wine Gallon contains 231 cubic or solid inches. And it is remarkable that the Wine and Ale Gallons have the same proportion to each other, as the Troy and Avoirdupois Pounds have; that is, as one Pound Troy is to one Pound Avoirdupois, so is one Wine Gallon to one Ale Gallon. Wk. Da. Hr. Or 52 1 6 Da. Hr. M. Mo. Da. Hr. = 13 1 6 = 1 Julian Year. 48 = 1 Solar Year. IMPERIAL MEASURES. By the late Act of Parliament for Uniformnity of Weights and Measures, which commenced its operation on the 1st of January, 1826, the chief part of the weights and measures are allowed to remain as they were; the Act simply prescribing scientific modes of determining them, in case they should be lost. The pound troy contains 5760 grains. The pound avoirdupois contains 7000 grains. The imperial gallon contains 277-274 cubic inches. The corn bushel eight times the above, or 2218·192 cubic inches. Hence with respect to Ale, Wine, and Corn, it will be expedient to possess a TABLE OF FACTORS, For converting old measures into new, and the contrary. N. B. For reducing the prices, these numbers must all be reversed, 59 RULES FOR REDUCTION. I. When the Numbers are to be reduced from a Higher Denomination to a Lower MULTIPLY the number in the highest denomination by as many of the next Jower as make an integer, or 1, in that higher; to this product add the number, if any, which was in this lower denomination before, and set down the amount. Reduce this amount in like manner, by multiplying it by as many of the next lower as make an integer of this, taking in the odd parts of this lower, as before. And so proceed through all the denominations to the lowest; so shall the uum ber last found be the value of all the numbers which were in the higher denominations, taken together.* II. When the Numbers are to be reduced from a Lower Denomination to a Higher, DIVIDE the given number by as many of that denomination as make 1 of the next higher, and set down what remains, as well as the quotient. Divide the quotient by as many of this denomination as make 1 of the next higher; setting down the new quotient, and remainder, as before. Proceed in the same manner through all the denominations, to the highest; and the quotient last found, together with the several remainders, if any, will be of the same value as the first number proposed. EXAMPLES. 2. Reduce 1185388 farthings, into pounds, shillings, and peece, 3. Reduce 231. to farthings. 4. Reduce 337587 farthings to pounds, &c. Ans. 22080. Ans. 351. 13s. 03d. Ans. 35280. Ans. 35. Ans. 340157. Ans. 1390 lb. 11 oz. 18 dwt. 19 gr. 9. In 35 ton. 17 cwt. 1 qr. 23 lb. 7 oz. 13 dr. how many drams? Ans. 20571005. 10. How many barley-corns will reach round the earth, supposing it, according to the best calculations, to be 25000 miles? Ans. 4752000000. * The reason of this rule is very evident; for pounds are brought into shillings by multiplying them by 20; shillings into pence, by multiplying them by 12; and pence into farthings, by multiplying by 4; and the reverse of this rule by Division.-And the same, it is evident, will be true in the reduction of numbers consisting of any denominations whatever. 11. How many seconds are in a solar year, or 365 days 5 hrs. 48 min. 48 sec. ? Ans. 31556928. 12. In a lunar month, or 29 ds. 12 hrs. 44 min. 3 sec. how many seconds? Ans. 2551443. COMPOUND ADDITION. COMPOUND ADDITION shows how to add or collect several numbers of different denominations into one sum. RULE. Place the numbers so that those of the same denomination may stand directly under each other, and draw a line below them.-Add up the figures in the lowest denomination, and find, by Reduction, how many units, or ones, of the next higher denomination are contained in their sum.-Set down the remainder below its proper column, and carry those units or ones to the next denomination, which, add up in the same manner as before.-Proceed thus through all the denominations, to the highest, whose sum, together with the several remainders, will give the answer sought. The method of proof is the same as in Simple Addition. 9. A nobleman, going out of town, is informed by his steward that his butcher's bill comes to 1977. 13s. 74d.; his baker's to 591. 5s. 23d.; his brewer's to 851.; his wine-merchant's to 1037. 13s.; to his corn-chandler is due 75l. 3d.; to his tallow-chandler and cheese-monger, 271. 15s. 114d; and to his tailor 557. 3s. 5d.; also for rent, servants' wages, and other charges, 1277. 3s.: now, supposing he would take 1007. with him, to defray his charges on the road, for what sum must he send to his banker? Ans. 8307. 14s. 64d. 10. The strength of a regiment of foot, of 10 companies, and the amount of their subsistence,* for a month of 30 days, according to the annexed Table, are required? * Subsistence Money, is the money paid to the soldiers weekly, short of their full pay; because their clothes, accoutrements, &c. are to be accounted for. It is likewise the money advanced to officers till their accounts are made up, which is commonly once a year, when they are paid their The following Table shows the full pay and subsistence of each rank on the English establislì arrears. ment: |
