ure, in square meters, the surface of a circular basin, the radius of the basin must be measured with the meter, the number obtained multiplied by itself, and this product by 22, and the result divided by 7.

My intention is not to demonstrate either these rules or others which Geometry prescribes for the measurement of surfaces. They are given in treatises on Geometry, to which it is necessary to refer for information. I wish only to designate the different surface-measures in use in the metric system. These measures are:

The square meter, or square whose side is one meter long.

The square decimeter, or square whose side is one decimeter long.

The square centimeter, or square whose side is one centimeter long.

The square millimeter, or square whose side is one millimeter long.

The meter contains ten decimeters; but the square meter contains one hundred square decimeters, as may be readily seen by the figure, in which each side is divided by ten equidistant points connected by lines with the corresponding points on the opposite side. By this process, the square meter is divided into one hundred equal squares which are one decimeter long on each side, and, consequently, are so many square decimeters.

So, also, a decimeter contains ten centimeters, and a centimeter contains ten millimeters; but a square

decimeter contains one hundred centimeters, and a square centimeter contains one hundred square millimeters.

Thus a square meter contains:

100 square decimeters. 10,000 square centimeters. 1,000,000 square millimeters.

m.

C.

In accordance with this principle, if we wish to represent decimally a surface composed of several square meters and several square decimeters, for example, 8 square meters and 6 square decimeters, we should write 8. 06; because the square decimeter is the hundredth part of a square meter. So, also, to represent decimally a surface composed of 48 square meters, 6 square decimeters, and 4 square centimeters, we should write 48. 0604, because the square centimeter is the ten thousandth part of a square meter.

m.

LAND MEASURE.

The square meter and its subdivisions suffice for every-day purposes. Larger measures than the square meter are seldom used, except for measuring land. They are then called Land Measures. They

are:

The Are, a square whose side is 1 dekameter long, thus containing 100 square meters, just as the square meter contains 100 square decimeters.

The Hectare, a square whose side is 1 hecto

meter long, thus containing 100 ares. Its surface is equal to 10,000 square meters.

The only subdivision of the are is the centiare, or square meter, the one hundredth part of the are.

For

The reader will perhaps ask why there is no deciare, or dekare (the tenth of an are, and ten ares). The answer is, that the decimal order has been applied to the length of the sides of the squares. example, the sides of the three squares-the centiare, the are, and the hectare — are in length, respectively, 1 meter, 1 dekameter, and 1 hectometer; and their surfaces are, respectively, 1 square meter, 100 square meters, and 10,000 square meters; and thus increase from a hundred to a hundred times greater. Therefore, in squares, we cannot have deciares and dekares, which would belong to the decimal order.

If, on the contrary, the decimal order had been applied to the surfaces, the sides of surfaces ten meters square and 1000 meters square could not have been expressed with precision in decimals; and in order to obtain them, it would have been necessary to extract the square root.

In fact, take ten small squares, and try to combine them in a single equivalent one, and you will fail; for if you place three of the small squares to serve as a side of the larger square, one will be excluded; if you place two, six will be excluded. You cannot, then, form a large square with ten small squares.

MEASURES OF VOLUME.

96

THE CUBIC METER,

SHOWING HOW IT IS COMPOSED OF CUBIC DECIMETERS, WHICH MAY BE DESCRIBED AS LYING IN THEIR SLICES, EACH CONSISTING OF 100 CUBIC DECIMETERS.

A

CUBE is a geometrical figure shaped like a die.
Its six faces are squares of the same size.

The cubic meter is a cube whose six faces are

each a square meter.

The cubic decimeter is a cube whose six faces are each a square decimeter

The cubic centimeter is a cube whose six faces are each a square centimeter.

The cubic millimeter is a cube whose six faces are each a square millimeter

A cubic meter contains 1,000 cubic decimeters. Recollect that the square meter contains 100 square decimeters. We can therefore divide a cubic meter into 100 narrow pieces, the base of each of which will be one square decimeter, and the height one meter, as may be seen by examining the figure at the head of this chapter. But if this height of one meter be divided into ten decimeters, we can make, with each of the narrow pieces, ten pieces, each of which will have a base of one square decimeter, and a height of one decimeter, and will consequently be cubic decimeters. Therefore there are 10 times 100, or 1,000 cubic decimeters in a cubic meter.

So, also, a cubic decimeter contains 1,000 cubic centimeters, and a cubic centimeter contains 1,000 cubic millimeters.

Therefore, a cubic meter contains:

1,000 cubic decimeters.

1,000,000 cubic centimeters.

1,000,000,000 cubic millimeters.

If it be desired to represent decimally a certain number of cubic meters and decimeters, one must remember that the cubic decimeter is the thousandth part of a cubic meter. Therefore, to represent 66 cubic meters and 3 cubic decimeters, we should write, 66. 003. So, also, to write, in cubic meters, 48

cubic meters