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74 LOGARITHMS.
It is unnecessary to calculate the difference, as the average
difference between the logarithms in each line is given in the
column headed " i>" in the tables. The difference in this case
is given in the table as 119.
Example 2.
Find logarithm to 1892.5.
Solution :
The mantissa of the number 1892 is given in the table as
276921. The difference is given as 229. The index for a num-
ber consisting of four integers is 3. Thus:
Log. 1892 = 3.276921
0.5 X 0.000229 = 0.0001145 = 115
Log. 1892.5 = 3.277036
Example 3.
Find logarithm to 85673.
Solution:
The mantissa for the number 85670 is given in the table as
932829. The difference is given in the table as 51. The index
for a number consisting of five integers is 4.
When an increase- of 10 in the number increases the log-
arithm 0.000051 an increase of 3 must increase the correspond-
ing logarithm 0.3 times 0.000051. Thus:
Log. 85670 = 4.932829
0.3 X 0.000051 = 0.0000153 == 15
Log. 85673 = 4.932844
These calculations (or interpolations as they are usually
called) are based upon the principle that the difference between
the numbers and the difference between their corresponding
logarithms are directly proportional to each other.^ This, how-
ever, is not strictly true ; but within limits, as it is used here,
it is near enough for practical results.
To* Find the Number Corresponding to a Given
Logarithm.
Example 1.
Find the number corresponding to the logarithm 2.610979.
Solution:
Always remember when looking for the number not to
consider the index, but find the mantissa 610979 in the table.
In the same line as this mantissa, under the heading " N," is
408, and on the top of the table in the same column as this
mantissa is 3 ; thus, the number corresponding to this mantissa
is 4083 and the index of the logarithm is 2 ; consequently the
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