Plane trigonometry, by S.L. Loney.

LOGARITHMS.

149

140. Common system of logarithms. In the
system of logarithms which we practically use the base is
always 10, so that, if no base be expressed, the base 10
is always understood. The advantage of using 10 as the
base is seen in the three following articles.
141. Characteristic and Mantissa. Def. If the
logarithm of any number be partly integral and partly
fractional, the integral portion of the logarithm is called its
characteristic and the decimal portion is called its mantissa.
Thus, supposing that log 795 = 2-9003671, the number
2 is the characteristic and '9003671 is the mantissa.
Negative characteristics. Suppose we know that
log 2 = 30103.
Then
log = log 1 - log 2 = 0 - log2 =- 30103,
so that log I is negative.
Now it is found convenient, as will be seen in Art. 143,
that the mantissae of all logarithms should be kept positive.
We therefore instead of - -30103 write - [1 - '69897], so
that
log =- (1 - 69897)- + 69897.
For shortness this latter expression is written 1-69897.
The horizontal line over the 1 denotes that the integral
part is negative; the decimal part however is positive.
As another example 3'4771213 stands for
-3 + '4771213.
142. The characteristic of the logarithm of any number
can always be determined by inspection.