683 of engineering formulæ.
Involvtiom and Evolution of Fractions by Logarithm*.
In a logarithm the integer is called the characteristic, and
the decimal portion the mantissa.
Involution—The number carried from the mantissato
the characteristic being positive, must be deducted from the
negative characteristic.
Example.—Find the 5th power of -05, or the value of -05 .
Log. -05 = 5-69897 __
then 1X5 =10
and -69897X5= 3-49-185
Then log. -65’ = 7-49-485
* und 055— *0000003125.
Involution —Iftbe negative characteristic be not divisible
wiS a remainder by the index of the required root the
number of units sufficient to make it so divisible must bo
added to it, and the same number ot units must aUo be addt d
to the mantissa before division.
Example.—Find the value of £/' UG0UüU3L2a.
Log. •0000003125 = 7-49485
then 7+3=10, and 10-7-5 = 2
and 3 • 494«5 + 5 = -69897
Therefore log. ^uWOWOaTtia = 2-6989? = log. of -05.
Proportion by Logarithms.
Add together the logarithms of the 2nd and 3rd terms and
from their sum subtract the logarithm of the Ibt term, thin
the number corresponding to the logarithm uf the remainder
gives the required answer.
J'xample.—68’30 :13’70 :: ’tS'tO.
Log. 13-70 = 1-13672
Log. •»•40 = 1’89982
Sum 3’03654
Log. 68-30 = 1 •83442
Diff. 1-20212 = log. of 15-93.