NOTE.-The Kilogram, in terms of which the weights of heavy articles are usually expressed, represents about 2 Avoirdupois pounds; a Kilogram containing 15,432 grains, whilst in 2 pounds (Avoir.) there are 15,400 grains.

metres.

It will be seen that, in the Metric System, there are no Compound Rules-the numbers employed to express lengths, surfaces, &c., being all simple numbers. Thus : 2 kilometres 4 hectometres dekametres and 8 metres 3 decigrams 5 centigrams and 7 milligrams

}

9 hectares 8 ares and 7 centi

ares

would be written 2468

grams.

357

ares.

908-07

It will also be seen that, in this system, Reduction is performed by the mere removal of the decimal point. Thus, for the reduction of kilometres to hectometres, dekametres, or metres, the point is simply removed to the right-one place, two places, or three places, as the case may be; whilst, for the reduction of litres to dekalitres, hectolitres, or kilolitres, the point is removed one, two, or three places—as the case may be—to the left :

67.89 kilometres=678.9 hectometres=6789 dekametres =67890 metres; 2345 litres=234'5 dekalitres=23'45 hectolitres=2345 kilolitres; &c.

Even the numbers which the French employ in expressing sums of money—that is, "money of account"are simple numbers: a smaller amount than a franc being

always written as so many "centimes," or hundredths of a franc. Thus, 234 francs and 56 centimes would be written 23456 francs.*

The following illustrations will enable the student to appreciate the advantages of the Metric System :

I.-A vintner sold 3 hectolitres 5 dekalitres 7 litres 9 decilitres of wine on Monday; 2 dekalitres 4 litres

and

* There is no special name for a sum of 10, or 100, or 1,000 francs; just as we have no special name for £10, or £100, or £1,000. The French have a coin called a "decime," equal in amount to 10 centimes, or to the tenth part of a franc, and of about the same value, therefore, as the British penny. The number of decimes is expressed by the figure in the first decimal place.

6 decilitres and 8 centilitres on Tuesday; 8 dekalitres 9 litres and 7 decilitres on Wednesday; 2 hectolitres 4 litres and 6 centilitres on Thursday; 7 dekalitres 6 litres decilitres and 4 centilitres on Friday; and 4 hectolitres 6 dekalitres 8 decilitres and 3 centilitres on Saturday: how much did he sell during the week?

By means of Simple Addition we find the answer to be: 1 kilolitre 2 hectolitres 1 dekalitre 3 litres 7 decilitres and 1 centilitre; in other words, 1,213 litres and 71 centilitres.

357'9

24.68

89'7 204'06

76.54

460.83

121371

II.—Off a piece of cloth, measuring 5 dekametres 6 decimetres and 7 centimetres, a draper cut a length of 8 metres and 9 centimetres: how much remained?

By means of Simple Subtraction we find the answer to be 4 dekametres 2 metres 5 decimetres and 8 centimetres; in other words, 42 metres and 58 centimetres.

50.67

8.09

42.58

III. A farm is divided into 4 fields, each containing 6 hectares 54 ares and 32 centiares: what is the area of the farm?

By means of Simple Multiplication we find the required area to be: 26 hectares 17 ares and 28 centiares; in other words, 2,617 ares and 28 centiares.

654.32

4

2617.28

IV. A quantity of silver, weighing 5 hectograms 9 dekagrams 2 grams 5 decigrams and 9 centigrams, was made into 6 spoons of equal weight: what did each spoon weigh?

By means of Simple Division we find the answer to be: 9 dekagrams 8 grams 7 decigrams 6 centigrams and 5 milligrams; in other words, 98

grams and 765 milligrams.

6)592.59

98.765

V. The price of a metre of cloth being 18 francs and 60 centimes, what would a length of 7 metres and 4 decimetres cost?

F

VI.—The rent of a farm containing 13 hectares 57 ares and 90 centiares is 3,394 francs and 75 centimes: what is the rent per are?

Dividing 3,394'75 by 1,357'9, we find the answer to be 2 francs and 50 centimes.

1357'9)3394*75

The Metric System of Weights and Measures has been introduced into most of the countries of Europe; and, except in the case of the Stere and its decimal multiples and submultiples, the adoption of the system has been rendered "permissive" (but not made compulsory) throughout the British Empire by an Act of Parliament passed in 1864. It is to be feared, however, that, in the absence of a decimal system of British MONEY, this Act, particularly so long as it is only permissive, will not be productive of much practical good,

The issuing of the florin or two-shilling piece was a step in the direction of a decimal system of money; but there are still required—(1) a coin, which it has been proposed to call a cent, equal in amount to one-tenth of a florin; and (2) a coin, which it has been proposed to call a mill, equal in amount to one-tenth of a cent. The cent would be a silver coin, not quite as large as the present threepenny piece; whilst the mill would be a bronze coin, a little less in size than the present farthing. The coins of account would then stand thus:

So that a pound being regarded as the standard3 pounds 5 florins 7 cents and 9 mills would be represented by the simple number £3*579.

CONVERSION OF SMALLER SUMS THAN I INTO DECIMALS OF £1, AND VICE VERSA.

A tenth of a pound being a florin (2 shillings), any number of tenths will represent the same number of florins :

£*1=28.; £*2=48.; £*3=68.; £*4=88.; £*5=108.;

&c.

As, when the unit is a pound, 5 in the first decimal place represents 5 florins or 10 shillings, 5 in the second decimal place—that is, 5 hundredths-must represent 10 times a smaller amount, or 1 shilling: £5=108.; £*05=18.

farthings thousandths

40)960 = 1,000

24= 25

A pound, which is worth 960 farthings, being divisible into 1,000 thousandths (or "mills"), we have 960 farthings 1,000 thousandths, and (dividing by 40) 24 farthings 25 thousandths. Accordingly, when writing farthings as thousandths, we add 1 for every 24; whilst, when writing thousandths as farthings, we reject 1 for every 25.

EXAMPLE I.—Express 148. 5d. as a decimal of £1.

In the given amount there are 7 florins, for which we write seven tenths of £1 (7). In the remainder of the amount (5d.) there are 22 farthings, for whichthe number being nearly 24-we write (22+1=) 23 thousandths. The required decimal is thus found to be £723.

EXAMPLE II.-Express 9s. 104d. as a decimal of £1.

In 9 shillings there are 4 florins and I shilling; for the florins we write 4 tenths, and for the I shilling 5 hundredths, of £1: 98.=£45. In the remainder of the amount (10d.) there are 43 farthings, for which—the number being nearly 48-we write (43+2=) 45 thousandths. The required decimal is thus found to be (*45+045=) £*495.

88. Rule for the Conversion of a smaller sum than I into a Decimal of £1: Set down as many tenths as there are florins (or two-shilling pieces); and if there be a shilling remaining, write 5 in the second decimal place. Reduce the remainder of the amount to farthings, for which write the same number of thousandths-adding 1 for every 24.

EXAMPLE III.-Convert 723 into shillings, &c.

For the 7 tenths (7) we take 7 florins, or 14 shil, lings. There then remain 23 thousandths, for whichthe number being nearly 25-we take (23-1=) 22 farthings, or 5d. The required amount is thus found to be 148. 54d.

EXAMPLE IV. Find the value of £495.

For the 4 tenths (4) we take 4 florins or 8 shillings, and for 5 of the 9 hundredths an additional shilling. There then remain (9—5=) 4 hundredths and 5 thousandths, or 45 thousandths, for which-the number being nearly 50-we take (45-2=) 43 farthings, or 10d. The required amount is thus found to be (8s.+18.+10d.=) 98. 10 d.

89. To find the Value of a Decimal of 1: Set down twice as many shillings as there are tenths, and an additional shilling when the number of hundredths is not less than 5. Express the remainder of the decimal as so many thousandths, for which write the same number of farthings-rejecting I for every 25.