100

100

100 Metres of France,

100 Canes of Marseilles and Montpelier,

100 Varas of Spain,

\ 109+

214

of Genoa, of 9 palms,

of Rome,

2454

227

93

100

of Portugal,

123

100 Cavidos of Portugal,

75

1 Dutch and Polish mile=31⁄2 American miles,

6160

1 Swedish and Danish mile=5 American miles, 9680

1 Spanish league-33 American miles,

6453

1 French league 2 American miles nearly.

1320

1 Russian verst of an American mile, 11 Irish miles 14 American miles.

30 Scotch miles 31 do.

121 Irish acres 196 American and English acres. 48 Scotch acres=61 do. nearly.

1 French are 119.6046+ American square yards. 607 French ares=15 American acres, nearly.

21. Ancient Measures, Weights, and Coins, mentioned in the Bible, and in the writings of Josephus.

The schaenus was the Egyptian line for land measure used to divide inheritances: they were of different lengths, but the shortest and most useful was 80 cubits.

1. When the given quantity consists of several denominations; multiply the number of the highest denomination by the number of units which it takes of the next lower denomination to make 1 of that higher; add to the product the given number, if any, of this lower denomination, and set down the amount. In like manner reduce this amount to the next lower denomination, adding in the given number, if any, of this denomination; and so proceed until the given quantity is reduced to the denomination required.

2. When the given quantity is of one denomination only; then it may be either reduced gradually from one denomination to another, as directed above; or, it may be reduced at once to the denomination required, by multiplying it by the number of units which 1 of the denomination given makes of that required. The multipliers to be used in working by the latter method, will be found in the Supplemental Tables.

*The reason of this rule is very evident: For instance, the reduction of Sterling Money, as 1 pound is equal to 20 shillings, 1 shilling to 12 pence, and 1 penny to 4 farthings; therefore, pounds are reduced to shillings by multiplying them by 20, shillings to pence by multiplying by 12; and pence to farthings by multiplying by 4; and the contrary by division and this reasoning will hold true in the reduction of numbers consisting of any denominations whatever. The rule for Reduction Ascending is simply the reverse of this, and equally evident.

EXAMPLES.

Money.

14 s. 6d. to farthings.

Explanation. Here, because 20 shil-" lings make 1 pound, I multiply the 27 pounds by 20, to bring them into shillings; and the product is 540 shillings, to which I add the 14 shillings of the given sum, and the amount is 554 shillings. Then, as 12 pence make 1 shilling, I multiply those 554 shillings by 12, to reduce them to pence, and the product is 6648 pence, to which I add the 6 pence of the given sum, and the amount is 6654 pence. Then, as 4 farthings make 1 penny, I multiply those 6654 pence by 4, to reduce them to farthings, and have 26616 farthings; and there being no farthings to add to these, the work is done. So the answer is 26616 farthings.

2. Reduce 498 l. to pence.

L. 498

240 d. 17.

19920

996

119520 d. Ans.

Here, the given quantity, or sum, is of one denomination only; and because 240 pence make 1 pound, I multiply the 498 pounds by 240, to reduce them to pence, and have 119520 pence for the answer.

N. B. The number of pence in a pound may be found in the Supplement to Table 2d.

Note. In reducing quantities which consist of several denominations; when the numbers of the lower denominations are small, they may be added in mentally, (i. e. in the mind,) in multiplying; as in the next example.

G2

3. Reduce 41. 17s. 4d. to pence.

L. S. d. 4.. 17.. 4

20

97 s.

12

Here, in multiplying the 4 pounds by 20, I add in the 17 shillings; and, in multiplying the 97 shillings by 12, I add in the 4 pence.

1168d. Ans.

4. Reduce 317. 11s. 10d. 1q. to farthings.

5. Reduce 64 7. 0 s. 7 d. to pence.

Ans. 30329 q.

Ans. 15367d.

6. In 183. 9 d. how many pence, and farthings?

Ans. 225 d., 900 q. 7. In 48 guineas, each 21 shillings, how many shillings and pence? Ans. 1008 s.,

12096 d.

Note. From the foregoing Rule, and the first Contraction in Simple Multiplication, it appears that Federal Money may be reduced from higher to lower denominations by annexing as many ciphers as there are places from the denomination given to that required; or, if the given sum be of different denominations, by annexing the several figures of all the denominations in their order, and continuing with ciphers, if necessary, to the denomination required; as in the following examples.

8. In 5 dollars how many cents?

Here, 5×100-500 cents, the Ans. Or, annexing two ciphers to the number of dollars, (which is the same as multiplying by 100,) gives 500, the number of cents, as before.

9. In 4 dollars, 8 dimes, how many dimes?

Annexing the 8 dimes to the 4 dollars (=40 dimes) gives 48 dimes for the answer.

10. Reduce 7 eagles and 5 dimes to cents.

11. Reduce 14 dollars, 2 dimes, to mills.

Ans. 7050 c.

Ans. 14200 m.

12. Reduce 8 dollars and 4 cents to cents. Ans. 804 c.