62 
POPULAR SCIENCE REVIEW. 
has introduced_, in giving uniformity and stability in place of 
so many jarring scales and standards. Now let ns consider for 
one moment the amazing sim|)licity superinduced_, by making 
the number 10 the sole multiplier and divisor in the new 
system. The consequence is that the laborious process of 
compound multiplication and division, of reduction from higher 
to lower denominations, and vice versa, is virtually abrogated ; 
the arithmetical process is performed mechanically. A mere 
point, or comma, inserted in a number, suffices for multiplica- 
tion or division by a power of 10, and supersedes the necessity 
of any other arithmetical operation, except the simply mecha- 
nical one of advancing the comma forwards or backwards, as 
the case may be. We trust our readers are all well acquainted 
with this important principle in arithmetic ; but lest there 
should be any to whom this is new, we must be pardoned if 
we give an illustration. For example, let us consider a short 
number in the metric scale, such as the following : — 35 meters, 
6 decimeters, 3 centimeters. Now, as each order of units is 
equal in value to 10 units of the succeeding order (by defini- 
tion) it is evident the number supposed is equal to 35 meters 
6-tenths and 3-hundredths of a meter, or to 35 meters and 63- 
hundredths of a meter, and is therefore a decimal number and 
falls within the abstract decimal scale, although expressing a 
concrete quantity, as was before remarked ; for simplification, 
then, the given number is written 35m.,63, and the only re- 
duction consists in making the subordinate units fall into their 
proper column. 
Had we to multiply this number by 10, it is done by passing 
the comma one rank to the right ; thus, 356”^*, 3 ; (by 100, 
two ranks to the right, thus, 3563 m.). The reason of 
this is obvious, and arises from 10 being the basis of our 
system of numeration, so that a numeral (6) placed on the 
right of a number (35) in effect multiplies this number by 
10 : the fraction is itself multiplied by 10 in expunging its 
denominator, and the last fraction becomes now : hence 
the whole number (35™’,63) has been multiplied by 10, in 
multiplying each part of it by 10, and this has been effected 
by a simple displacement of the comma one rank to the right. 
Had we to divide the same number 35“*, 63 by 10, we move 
the comma one rank to the left : thus, 3'^‘,563 (3 meters, 5 
decimeters, 6 centimeters, 3 millimeters, or 3 meters, 563 milli- 
meters), and we see that each cipher in the proposed number 
remains unchanged, but with tenfold less value j the whole 
number has therefore been divided by 10 by the simple dis- 
placement of the comma one rank to the left. Had we to divide 
by 100, this is done by passing the comma two ranks to 
the left ,* or by any power of 10, and it is done by passing the 
