Note. M. stands for the Latin mille, which signifies 1000, and C. for the Latin word centum, which signifies 100.

REDUCTION.

T33. We have seen, that, in the United States, money is reckoned in dollars, cents, and mills. In England, it is reckoned in pounds, shillings, pence, and farthings, called denominations of money. Time is reckoned in years, months, weeks, days, hours minutes, and seconds, called denominations of time. Distance is reckoned in miles, rods, feet, and inches, called denominations of measure, &c.

The relative value of these denominations is exhibited in tables, which the pupil must commit to memory.

ENGLISH MONEY.

The denominations are pounds, shillings, pence, and farthings.

Note. Farthings are often written as the fraction of a penny thus, I farthing is written d., 2 farthings, § d., 3 farthings,

things?

d.

How many farthings in 1 How many pence in 4 farpenny? in 2 pence? in 6 pence?

in 3 pence?

pence ?

in 8 pence?

in 1 shilling?

2 shillings?

in s farthings? in 12 farthings? 9 in 24 farthings?

in 32 in 36 - farin 48 qrs.?

?

in 12 pencetarthings?
in things?
How many shillings in 48 qrs.
in 96 qrs.?

in 2 shillings and 2 pence ?in 26 d. ?

in in 28 d. ?

in 2 s. 6 d. ?in 42 d.?

in 2 s. 3 d.?

2 s. 4 d. ?

in 3 s. 6 d. ?

4 s. 3 d.?

in 27 d.?

in 39 d.?

in 51 d.?

in

It has already been remarked, that the changing of one kind, or denomination, into another kind, or denomination, without altering their value, is called Reduction. ( 27.) Thus, when we change shillings into pounds, or pounds into shillings, we are said to reduce them. From the foregoing examples, it is evident, that, when we reduce a denomination of greater value into a denomination of less value, the reduction is performed by multiplication; and it is then called Reduction Descending. But when we reduce a denomination of less value into one of greater value, the reduction is performed by division; it is then called Reduction Ascending. Thus, to reduce pounds to shillings, it is plain, we must multiply by 20. And agam, to reduce shillings to pounds, we must divide by 20. It follows, therefore, that reduction descending and ascending reciprocally prove each other.

1. In 17 £. 13 s. 6 d. how] 2. In 16971 farthings, how many farthings? many pounds?

OPERATION.

£. s. d.
qrs.

17 13 6 3

20 s.

353 s. in 17£. 13 s.
12 d.

4242 d.

4 q.

Farthings will be reduced to 16971 qrs. the Ans. pence, if we divide them by 4 because every 4 farthings make 1 In the above example, because penny. Therefore, 16971 far20 shillings make 1 pound, there-things divided by 4, the quotient fore we multiply 17 £. by 20, in-is 4242 pence, and a remainder of creasing the product by the addi-3, which is farthings, of the same tion of the given shillings, (13,) name as the dividend. We then which, it is evident, must always divide the pence (4242) by 12, rebe done in like cases; then, be-ducing them to shillings; and the cause 12 pence make 1 shilling, shillings (353) by 20, reducing

we multiply the shillings (353) them to pounds. The last quoby 12, adding in the given pence, tient, 17 £., with the several re(6.) Lastly, because 4 farthings mainders, 13 s. 6 d. 3 qrs. constimake 1 penny, we multiply the tute the answer. pence (4242) by 4, adding in the given farthings, (3.) We then find, that in 17 £. 13 s. 64 d., are contained 16971 farthings.

Note. In dividing 353 s. by 20 we cut off the cipher, &c., as taught T 22.

T34. The process in the foregoing examples, if carefully examined, will be found to be as follows, viz.

To reduce high denominations To reduce low denominations to lower, Multiply the highest to higher-Divide the lowest dedenomination by that number nomination given by that number which it takes of the next less to which it takes of the same to make 1 of this higher, (increasing make 1 of the next higher. Prothe product by the number given, ceed in the same manner with if any, of that less denomination.) each succeeding denomination, Proceed in the same manner with until you have brought it to the each succeeding denomination, denomination required. until you have brought it to the

denomination required.

EXAMPLES FOR PRACTICE.

3. Reduce 32 £. 15 s. 8 d. tol 4. Reduce 31472 farthings to farthings.

5. In 29 guineas, at 28 s. each,| how many farthings?

7. Reduce $163, at 6 s. each, to

pence?

pounds.

6. In 38976 farthings, how many_guineas?

8. Reduce 11736 pence to dollars.

9. In 15 guineas, how many 10. Reduce 21 £. to guineas. pounds?

Note. We cannot reduce guineas directly to pounds, but we may reduce the guineas to shillings, and then the shillings to pounds.

TROY WEIGHT.

By Troy weight are weighed gold, silver, jewels, and all liquors. The denominations are pounds, ounces, pennyweights, and grains.

TABLE.

24 grains (grs.) make 1 pennyweight, marked pwt.
20 pennyweights.

12 ounces

1 ounce,

1 pound,

lb.

The fineness of gold is tried by fire, and is reckoned in carats, by which is understood the 24th part of any quantity; if it lose nothing in the trial, it is said to be 24 carats fine; if it lose 2 carats, it is then 22 carats fine, which is the standard for gold.

Silver which abides the fire without loss is said to be 12 ounces fine. The standard for silver coin is 11 oz. 2 pwts. of fine silver, and 18 pwts. of copper melted together.

11. Bought a silver tankard, 12. Paid $44'28 for a silver veighing 3 lb. 5 oz.. paying at tankard, at the rate of $1'08 an he rate of $1'08 an ounce; what ounce; what did it weigh? id it cost?

13. Reduce 210 lb. 8 oz. 12 14. In 50572 pwt. how many wt. to pennyweights.

15. In 7 lb. 11 oz. 3 pwt. 9 grs. 'silver, how many grains?

pounds?

16. Reduce 45681 grains to

pounds.

APOTHECARIES' WEIGHT.

Apothecaries' weight* is used by apothecaries and physicians, in compounding medicines. The denominations are pounds, ounces, drains, scruples, and grains.

By avoirdupois weight are weighed all things of a coarse and drossy nature, as tea, sugar, bread, flour, tallow, hay, leather, medicines, (in buying and selling,) and all kinds of metals, except gold and silver. The denominations are tons, hundred weights, quarters, pounds, ounces, and drams.

20 hundred weight.

1 ton,

T.

Note 1. In this kind of weight, the words gross and net are used. Gross is the weight of goods, together with the box, bale, bag, cask, &c. which contains them. Net weight is the weight of the goods only, after deducting the weight of the box, bale, bag, or cask, &c., and all other allowances.

Note 2. A hundred weight, it will be perceived, is 112 lb. Merchants at the present time, in our princípal seaports, buy and sell by the 100 pounds. The weight of hay and all heavy articles for

The pound and ounce apothecaries' weight, and the pound and ounce Troy, are the same, only differently divided, and subdivided.

† 175 oz. Troy 192 oz. avoirdupois, and 175 lb. Troy 144 lb. avoir dupois. 1 lb. Troy 5760 grains, and 1 lb avoirdupois 7000 grains Troy.

transportation, instead of being rendered in cwt. qrs. lbs. in conformity to the above table, is now usually rendered in pounds, and 2000 lbs. are considered a ton, whereas in the table the ton is 20 cwt. 2240 lbs.

19. What will 5 cwt. 3 qrs. [ 20. How much sugar, at 12 17 lb. of sugar come to, at 12 cents a pound, may be bought for cents a pound? $82,625?

21. A merchant would put 109 cwt. 0 qrs. 12 lb. of raisins into boxes, containing 26 lb. each; how many boxes will it require? 23. In 12 tons, 15 cwt. 1 qr. 19 lb. 6 oz. 12 dr. how many drams?

25. In 28 lb. avoirdupois, how many pounds Troy?

22. In 470 boxes of raisins, containing 26 lb. each, how many cwt.?

24. In 7323500 drams, how many tons?

26. In 34 lb. 0 oz. 6 pwt. 16 grs. Troy, how many pounds lavoirdupois?

*

CLOTH MEASURE..

Cloth measure is used in selling cloths and other goods, sold by the yard, or ell. The denominations are ells, yards, quarters, and nails.

Long measure is used in measuring distances, or other things, where length is considered without regard to breadth. The denominations are degrees, leagues, miles, furlongs, rods, yards, feet, inches, and barley-corns.