5120 640 = 320 = 80 = 10 = 2 = 1 By this are measured all dry wares, as, Corn, Seeds, Roots, Fruit, Salt, Coals, Sand, Oysters, &c. The standard Gallon dry measure contains 2684 cubic or solid inches, and the Corn or Winchester bushel 2150 cubic inches; for the dimensions of the Winchester bushel, by the Statute, are 8 inches deep, and 18 inches wide or in diameter, but the Coal bushel must be 19 inches in diameter; and 36 bushels, heaped up, make a London chaldron of coals, the weight of which is 3156lb Avoirdupois. 54= 11 = 1 Butt 864 = 432 = 108 = 3 = 2 = 1 Note, The Ale Gallon contains 282 cubic or solid inches. Note, By this are measured all Wines, Spirits, Strong-waters, Cider, 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 Mo Da Hr Or 52 1 6 = 13 1 61 Julian Year Da Hr M Sec But 365 5 48 48 1 Solar Year. 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 as of the next lower 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 as of the next lower, 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 number last found be the value of all the numbers which were in the higher denominations, taken together.* *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 ⚫onsisting of any denominations whatever. II. When II. When the Numbers are to be reduced from a Lower Denomination to a Higher: DIVIDE the given number by as many as of that denomination make 1 of the next higher, and set down what remains, as well as the quotient. Divide the quotient by as many as of this denomination 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. 4)1185388 12) 296347 d 2,0) 2469,5 sid Answer 1234/ 15s 7d 3. Reduce 241 to farthings. Ans. 23040. Ans. 351 13s 03. 4. Reduce 337587 farthings to pounds, &c. 5. How many farthings are in 36 guineas? Ans. 36. 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 24877 miles? Ans. 4728620160. 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. COM. 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. |