Tables of Logarithms to Five Places of Decimals: With Auxiliary Tables

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Edwin Schofield Crawley
E. S. Crawley, University of Pennsylvania, 1899 - Logarithms - 76 pages
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Page x - The characteristic of the logarithm of a number less than 1 is negative, and is numerically one greater than the number of ciphers immediately following the decimal point.
Page x - ... decimal point. Characteristic of 1=0. 10 = 1. 100 = 2. 1000 = 3. etc. We have likewise observed that if a number is greater than .1 and less than 1, its log is between 0 and — 1; or, since we always use a positive mantissa, it is — 1 + the mantissa. Therefore, the characteristic is —1. Similarly, if the number is greater than .001 and less than .01, the log is between — 2 and — 3, which is written — 3 + the mantissa. Thus, the characteristic is — 3, etc. It is necessary to be especially...
Page xxix - AND T. I. When the angle a is between 0 and 2 : log sin a = log a" + S. log tan a = log a
Page x - ... than 2 and less than 3 its characteristic is 2, etc. We therefore derive the following rule: 1. The characteristic of the log of a number greater than 1 is one less than the number of figures preceding the decimal point. Characteristic of 1=0. 10 = 1. 100 = 2. 1000 = 3. etc. We have likewise observed that if a number is greater than .1 and less than 1, its log is between 0 and — 1; or, since we always use a positive mantissa, it is — 1 + the mantissa. Therefore, the characteristic is —1....
Page ix - The table gives only the mantissa; the characteristic, which may be positive, negative, or zero, must be supplied in every case by the computer.
Page x - Since the mantissa of the logarithm of a number depends only upon the sequence of figures, and not upon the position of the decimal point, only the mantissas of the logarithms of integers need be tabulated.
Page xii - As we have previously stated, the mantissa is always positive, and where the number is less than 1, the characteristics will always be negative, but as a rule negative characteristics are avoided by adding 10 to the characteristic and writing — 10 after the logarithm, which does not alter its true value. We can then change Rule No.
Page xxix - A, log sin A = log .4" + S log tan A = log A" + T To find an angle A, log A
Page xi - Go across the page, in the line containing the first three figures, until the column marked by the fourth figure is reached. The three figures found at this point are the last three figures of the mantissa.

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