58 
POPULAR SCIENCE REVIEW. 
reckoned by millimeters ; tkus the thickness of a mirror is 
said to be 8^ millimeters_, which is written 8mm. 5. 
Surface. — The units of surface are the squares constructed 
on the units of length. The principal unity of surface is the 
square meter. Then we have the decameter square^ hecto- 
meter square_, kilometer square — and on the other side the 
decimeter square^ centimeter square. As this is square 
measure_, the units of surface are from hundred to hundred 
times greater^ by definition ; the value of each unit is one 
hundredfold that of the unit immediately inferior. Thus the 
square meter is equal to one hundred square decimeters, and 
so forth. For measuring land the principal unit employed is 
the square decameter, which then takes the name of are (from 
Latin area) ; the only units used in land measure are the 
hectare or 100 ares, the are, and the centiare or of the are. 
Thus an estate is said to consist of, 125 hectares and 47 ares ; 
a garden, of 23 ares and 50 centiares ; and these quantities are 
written : — 
125,47 hectares. 23,50 ares. 
The hectare is equal to 2J acres, nearly. The following 
tabular sketch will enable the reader to understand this very 
t/ 
simple scale at a glance — 
Hectometer square Hectare = 100 ares. 
Decameter square Are 
•Meter square Centiare = — o-o- 
Decimeter square 
Centimeter square 
Cubic Measure. — A cube is a solid terminated by six equal 
squares, such as a die. By definition the units of volume in 
the metric system are cubes, Vi^hich have for sides the units of 
length. The principal unit of volume is the cubic meter. On 
the one hand we have, in ascending order, the decameter cube, 
the hectometer cube, &c. ; and on the other, in descending" 
order, the decimeter cube, the centimeter cube, &c. Each 
unit is equal to one thousand times the unit immediately 
inferior in the scale. The whole series therefore forms a geo- 
metric progression — as do the foregoing — the ratio of which 
is 1000 : the ratio of the linear series being 10 ; that of super- 
ficies, likewise, being 100. To measure a volume is to ascer- 
tain how many cubic meters it contains, and what, if any, 
fraction of cubic meter ; or in other words, to ascertain how 
many cubic units of each order it contains, and it may contain 
999 units of each order. Thus the same scale suffices to 
express both abstract and concrete numbers, and it depends 
on choice how many concrete orders are to be considered. 
This constitutes one of the chief beauties of this elastic and 
wonderful system. The same feature is observable in the two 
