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1
6
RATIO AND PROPORTION.
In this example the dividend consists of only two decimals,
but the divisor has three, therefore we have to annex a cipher
to the dividend. This brings divisor and dividend to the same
denomination, and the quotient is a whole number.
Example 2.
43.62 -h 0.3 = 145.4
In this example the dividend has one decimal more than
the divisor, therefore the quotient has one decimal.
RATIO.
The word ratio causes considerable ambiguity in mechani-
cal books, as it is frequently used with different meaning by
different writers.
The common understanding seems to be that the ratio be-
tween two quantities is the quotient when the first quantity is
divided by the last quantity ; for instance, the ratio between 3
and 12 is %, but the ratio between 12 and 3 is 4. The ratio be-
tween the circumference of a circle and its diameter is tc or
3.1416, but the ratio between the diameter and the circumfer-
ence is \ or 0.3183, etc. This is the sense in which the word is
used in this book, as this seems to agree with the common cus-
tom with most mechanical writers.
The term ratio is also sometimes applied to the difference
of two quantities as well as to their quotient ; in which case the
former is called arithmetical ratio, and the latter geometrical
ratio. (See Progressions, page 68.)
PROPORTION.
In simple proportion there are three known quantities by
which we are able to find the fourth unknown quantity ; there-
fore proportion is also called "the rule of three", and it is either
direct or inverse proportion.
It is called direct proportion if the terms are in such ratio to
one another that if one is doubled then the other will also have
to be doubled, or if one is halved the other must also be halved.
For instance, if 50 pounds of steel cost $25, how much will 250
pounds cost?
9^0 V 9^
50 lbs. cost $25; 250 must cost
zou A zo
= $125.
50
This is direct proportion, because the more steel we buy,
the more money we have to pay.
In inverse proportion the terms are in such ratio that if one
is doubled the other is halved, or if one is halved the other is
doubled.
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