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That is an increase of one in the number here makes an increase of 26 in the mantissa. Then an increase of .32 of one (32 following the fourth place is .32 of 1 in the fourth place) in the number will make an increase of .32 of 26 in the mantissa = 8.32.

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NOTE 5.-The process employed in finding the logarithm of a number of more than four figures is called interpolation. 15. How to find the number corresponding to the logarithm. 1. To find the number corresponding to the logarithm 0.56514.

The mantissa increases constantly throughout the table. Follow the first column of mantissas till 56 is found, as the first two figures of the mantissa. Continuing 514 is easily found in the same horizontal line with 367 and in the column under 4.

Hence the number (placing the decimal point by Art. 6) = 3.674.

2. To find the number corresponding to the logarithm 8.26470

10.

This mantissa cannot be found in the table.

The nearest mantissa less than 26470 = 26458.

66

66

66

66

larger 26470 26482.

The number corresponding to mantissa 26458 (disregarding the decimal point) is 1839. For a mantissa 24 greater (26482) the corresponding number is 1840, that is, an increase of 24 in the mantissa, at this point in the table, means an increase of 1 in the number. Then an increase of 12, which is the amount the given mantissa, 26470, ex

ceeds the mantissa 26458, would mean an increase of 1

of 1, = .5.

Hence the number = .018395.

3. To find the number corresponding to the logarithm

1.71895.

The next smaller mantissa = 71892.

Then the given mantissa is 3 larger; and as the tabular difference is 8, 3 of 1 : = .375 must be added to 5235 the

number corresponding to mantissa 71892.

Hence the number = 52.3538.

NOTE 1.-Numbers corresponding to given logarithms should not be carried to more than five or six significant figures, in a five-place table.

NOTE 2.-Art. 4 makes it clear that the mantissa for 200 is the same as the mantissa for 2000; for 375, the same as for 3750, etc. So the mantissa for any number of three figures is found in the 0 column and in the same horizontal line with these three figures in the N column.

NOTE 3.-A negative quantity cannot be a power of a positive quantity, and hence a negative quantity, as such, has no logarithm. Hence when negative quantities occur in any example worked by logarithms, the negative sign is absolutely disregarded, except so far as it affects the sign of the result.

EXAMPLES.

16. Find by logarithms the values of the following:

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log

=

.. x 18465.4

(801.012) 2 × (.0315)*
(1.3907)

(.0315)(8.4983110) x 7.74747-10

colog (1.3907) (9.8567710) x

log x =

.*. x = 3358.2

3. 95.37 x .0313.

4. (93985) × 1.0484.

5. .0008601 × 1.28865.

3.52610

; find x.

2.90364 × 2 =

5.80728

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=

=

9.97135 - 10

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'(444) × (.00041007)3.7

(9.8563)

(15.434) × (3897.3) x .41984

(.000372)3 (784.96) × 5013.4 × (.003)

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