ber last found be the value of all the numbers which were in the higher denominations, taken together.* EXAMPLE. 1. In 12347. 15s. 7d, how many farthings? £. 8. d. 1234 15 7 20 24695 Shillings. 12 296347 Pence. 4 Answer 1185388 Farthings. 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 pence. 3. Reduce 231. to farthings. 4. Reduce 337587 farthings to pounds, &c. 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 857.; 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. 52d.; also for rent, servants' wages, and other charges, 1271. 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. 6d. 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 arrears. The following Table shows the full pay and subsistence of each rank on the English establishment: |