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.

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 lower 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 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 consisting of any denominations whatever.

EXAMPLE.

1. In 1234 15s 7d, how many 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 241 to farthings.

4. Reduce 337587 farthings to pounds, &c.

Ans. 23040..

Ans. 351 13s 03.

5. How many farthings are in 36 guineas? Ans. 36288. Ans. 36. 6. In 36288 farthings how many guineas? 7. In 59 lb 13 dwts 5 gr. how many grains? Ans. 340157. 8. In 8012131 grains how many 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 Ans. 4752000000. miles? 11. How many seconds are in a solar year, or 365 days Ans. 31556925. 5 hrs 48 min. 451 sec? 12. In a lunar month, or 29 ds 12 hrs 44 min 3 sec, how Ans. 2551443. many seconds?

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 de. nomination 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

EXAM. 9. A nobleman, going out of town, is informed by his steward, that his butcher's bill comes to 1977 138 71d; his baker's to 591 5s 23d; his brewer's to 851; his winemerchant's to 1037 13s; to his corn chandler is due 751 3d ; to his tallow.chandler and cheesemonger, 271 15s 111d; and to his tailor 551 3s 53d; also for rent, servants' wages, and other charges, 1271 3s: Now, supposing he would take 100/ with him, to defray his charges on the road, for what sum must he send to his banker? Ans. 8301 14s 6}d,

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6

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; which is 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.