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For measuring dry goods, such as grain, fruit, &c., we have, further, the following denominations :

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In measuring liquids, the gallon is the largest measure recognised by legal enactment

however, besides the above, many denominations still used in trade, which are derived from the names of the casks themselves.

For instance, in measuring wine

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A farthing is indicated either as a fractional part of

a penny-thus, 1d.-or by the letter "q"-thus, 1 q.

The symbols £, s, d, q, are the initials of the Latin words Libra, solidus, denarius, quadrans.

These are the subdivisions of money in which accounts are always kept. Besides these, however, we have several coins representing other subdivisions, which are used to facilitate traffic. From this they are called current coins. The following is a list of our

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2-shilling piece, or Florin.

24-shilling piece, or Half-crown.

5-shilling piece, or Crown.

Half-Sovereign.

Gold...... Sovereign (the pound piece, equivalent
to 20 shillings).

Out

It has already been explained, under the head of Troy weight (Art. 13), that standard gold (that is, the gold of the coinage) is 1, or 22 carats fine. of a pound Troy are coined 4628 sovereigns; so that, dividing this by 12, we find the price of standard gold per ounce to be £3 178. 10d., no charge being made at the Mint for coining gold.

Standard silver is 37 fine, and out of a pound Troy 66 shillings are coined; so that the Mint price of standard silver is 5s. 6d. an ounce. The market price

of silver bullion is less than this-generally about 58. 1d. an ounce. The advantage which the Mint thus gains is called seignorage.

In the new bronze coinage 48 pence are coined out of a pound avoirdupois. The bronze consists of 95 parts copper, 4 tin, and 1 zinc.

The standard of our coinage is gold. By this is meant that any amount of gold coin can be legally paid in liquidation of a debt, the creditor being obliged

to take it. This is expressed by saying that gold to an unlimited amount is the only legal tender. No one is obliged to take more than 40s. worth of silver, or more than 12d. worth of copper.

Other coins besides the above were formerly in use. The guinea (218.), the half-guinea, the 7-shilling piece, the noble (6s. 8d.), mark (13s. 4d.), the pistole (16s. 1od.), moidore (278.).

ANGULAR MEASURE.

18. The circumference of a circle being divided into 360 equal parts, straight lines drawn to the centre will divide the four right angles at the centre into 360 equal angles. Each of these subdivisions, therefore, is equal to the goth part of a right angle. It is called a degree, and written thus: 1°. A degree is divided into 60 minutes, one of which is written thus, 1'; each minute into 60 seconds, one of which is written " (vide Art 3, "Division of Time"). The arcs of the circle which subtend at the centre an angle of 1°, 1′, 1′′ respectively, are also called a degree, a minute, and a second respectively. To know their actual magnitude, we must know the size of the circle (see Note on p. 105).

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116

CHAPTER XI.

COMPOUND REDUCTION, ADDITION, SUBTRACTION,
MULTIPLICATION, AND DIVISION.

1. FROM the preceding tables it is evident that any
compound quantity (Chap. X., Art. 1), could be ex-
pressed in a variety of ways, according as we use one
or other of the various units, or denominations, as they
are called, which are employed. Thus the compound
quantity, £2 38. 6d., could be indicated as here written,
or by 522 pence, or, again, by 43 shillings, &c. The
process of expressing a compound quantity given in
any one denomination in another, is called reducing
the quantity to a given denomination.
The process

is termed

REDUCTION.

2. EXAMPLE 1.-Reduce £5 28. 7 d. to farthings.

Since there are 20 shillings in a pound, in 5 pounds there are 5 × 20, or 100 shillings; and therefore, in £5 28., 100 + 2, or 102 shillings. Since there are 12 pence in a shilling, in 102 shillings there are 102 × 12, or 1224 pence; and therefore, in £5 28. 7d., 1224 + 7, or 1231 pence. Since there are 4 farthings in a penny, in 1231 pence there are 1231 × 4, or 4924 farthings; and therefore, in £5 28. 7 d. there are 4924 + 3, or 4927 farthings.

The process may be thus arranged

£5 28. 7 d.

20

100 + 2 = 1028.

12

1224 +7= 1231d.

4

4924 +34927 farthings.

EXAMPLE 2.-In 4927 farthings how many pounds,

shillings, pence, and farthings are there?

4927 divided by 4 gives a quotient 1231, and a remainder 3; hence 4927 farthings are 1231 pence and 3 farthings. 1231 divided by 12 gives a quotient 102 and a remainder 7; hence 1231 pence are 102 shillings and 7 pence. 102 divided by 20 gives a quotient 5 and a remainder 2; hence 102 shillings are 5 pounds and 2 shillings. Therefore 4927 farthings are 1231 pence, which is 1028. 7 d., which is £5 28. 7 d. The operation may be thus arranged—

4) 4927

12) 1231...3f.

20) 102...7d.

£5 28. 7 d.

In dividing by 20, note the remark, Chap. IV., Art. 7.

The same method would apply to compound quantities of any other kind.

Hence we get the following

Rule for the Reduction of Compound Quantities. (1.) To reduce quantities in given denominations to equivalent quantities of lower denominations.

Multiply the quantity of the highest denomination by that number which it takes of the next lower denomination to make one of the higher; and to the product add the number of quantities of that lower denomination, if there are any. Proceed in like manner with the quantity thus obtained, and those of each successive denomination, until the required denomination is arrived at.

(2.) To reduce quantities of given denominations to equivalent quantities of higher denominations.

Divide the number of quantities of the given denomination by that number which it takes of quantities of this denomination to make one of the next higher. Proceed in the same manner with this and each suc

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