NOTE 1. The second may be supposed to be divided into 60 thirds, and these again into 60 fourths, &c.

NOTE 2. April, June, September, and November, have each 30 days; each of the other months has 31, except February, which has 28 in common years, and 29 in leap ' years.

I. When the reduction is from a greater name to a less.

Multiply the highest name or denomination by as many as one makes of the next less, adding to the product the parts of the second name; then multiply this sum by as many as one makes of the next less name, adding to the product the parts of the third name; and so on through all the denominations to the last.

II. When the reduction is from a less name to a greater.

RULE.

Divide the given number by as many as make one of the next superior denomination; and this quotient again by as many as make one of the next following; and so on through

The reason of this rule is exceedingly obvious; for pounds are Drought into shillings by multiplying them by 20; shillings into pence by multiplying them by 12; and pence into farthings by multiplying them by 4; and the contrary by division; and this will be true in the reduction of numbers, containing any denominations whatever.

all the denominations to the highest; and this last quotient, together with the several remainders, will be the answer required.

The method of proof is by reversing the question.

EXAMPLES.

1. In 1465l. 14s. 5d. how many farthings?

Ans. 81

6. In 2311. 16s. how many ducats at 4s. 9d. each?

Ans. 976.

7. In 274 marks, each 17s. 9d. and 87 nobles, each 8s. 11d. how many pounds? Ans. 2811. 19s. 3d. 8. In 1776 quarter guineas how many six pences?

Ans. 24864.

9. Reduce 1776 six and thirties to half-crowns sterling.

Ans. 25574.

10. In 50807 moidores how many pieces of coin, each

4s. 6d. ?

11. In 213210 grains how many lb. ?

Ans. 406456.

Ans. 37lb. 3dwt. 18gk 12. In 59lb. 13dwts. 5gr. how many grains?

13. In 8012131 grains how many lb. ?

Ans. 340157grs.

Ans. 1390lb. 11oz. 18dwts. 19grs.

14. In 35 tons, 17cwt. qr. 23lb. 7oz. 13dr. how many drams? Ans. 20571005dr. 15. In 37cwt. 2qr. 17lb. how many pounds Troy, a pound Avoirdupois being equal to 14oz. 11dwt. 15 grs. Troy? Ans. 5124lb. 5oz. 10dwt. 11grs. 16. How many barley corns will reach round the world, supposing it, according to the best calculations, to be 8340 leagues? Ans. 4755801600. 17. In 17 pieces of cloth, each 27 Flemish ells, how many yards? Ans. 344yds. 1qr. 18. How many minutes were there from the birth of CHRIST to the year 1776, allowing the year to consist of 365d. 5h. 48' 58"? Ans. 934085364′ 48′′.

COMPOUND ADDITION.

Compound Addition teaches to collect several numbers of different denominations into one sum.

RULE.*

1. Place the numbers so, that those of the same denomination may stand directly under each other, and draw a line under them.

2. Add the figures in the lowest denomination, and find how many ones of the next higher denomination are contained in their sum.

3. Write the remainder, and carry the ones to the next denomination; with which proceed as before; and so on

* The reason of this rule is evident from what has been said in simple addition; for, in addition of money, as 1 in the pence is epual to 4 in the farthings; 1 in the shillings, to 12 in the pence; and 1 in the pounds, to 20 in the shillings; therefore, carrying as directed, is nothing more than providing a method of digesting the money, arising from each column, properly in the scale of denominations; and this reasoning will hold good in the addition of compound numbers of any description whatever.

through all the denominations to the highest, whose sum must be all written; and this sum, together with the several remainders, is the whole sum required.

The method of proof is the same as in simple addition.

AVOIRDUPOIS WEIGHT.

cwt.qr. lb. oz. dr. T.cwt. qr. lb. oz. dr. T.cwt. qr. lb. oz.dr.

Compound Subtraction teaches to find the difference of any two numbers of different denominations.

RULE.*

1. Place the less number under the greater so, that those parts, which are of the same denomination, may stand directly under each other, and draw a line under them.

* The reason of this rule will readily appear from what has