46 



STATISTICAL METHODS. 



The mantissa is always positive even when the characteristic 

 is negative. We may avoid the use of a negative characteristic 

 by arbitrarily adding 10, which may be neglected at the closf 

 of the calculation. By this rule we have 



Number. Logarithm. 



1.384 0.141136 



.1384 9.141136 



.01384 8.141136 



.001384 7.141136 

 etc, etc. 



No confusion need arise from this method in finding a number 

 from its logarithm; for although the logarithm 6.141136 repre- 

 sents either the number 1,384,000, or the decimal .0001384, yet 

 these are so diverse in their values that we can never be uncer- 

 tain in a given problem which to adopt. 



The table IX. contains the mantissas of logarithms, car- 

 ried to six places of decimals, for numbers between 1 and 9999, 

 inclusive. The first three figures of a number are given in the 

 first column, the fourth at the top of the other columns. The 

 first two figures of the mantissa are given only in the second 

 column, but these are understood to apply to the remaining 

 four figures in either column following, which are comprised 

 between the same horizontal lines with the two. 



If a number (after cutting off the ciphers at either end) con- 

 sists of not more than four figures, the mantissa may be taken 

 direct from the table ; but by interpolation the logarithm of a 

 number having six figures may be obtained. The last column 

 contains the average difference of consecutive logarithms on 

 the same line, but for a given case the difference needs to be 

 verified by actual subtraction, at least so far as the last figure 

 is concerned. The lower part of the page contains a complete 

 list of differences, with their multiples divided by 10. 



To find the logarithm of a number having six 

 figures : Take out the mantissa for the four superior places 

 directly from the table, and find the difference between this 

 mantissa and the next greater in the table. Add to the man- 

 tissa taken out the quantity found in the table of proportional 

 parts, opposite the difference, and in the column headed by the 

 fifth figure of the number; also add ^ the quantity in the col- 

 umn headed by the sixth figure. The sum is the mantissa 

 required, to which must be prefixed a decimal point and the 

 proper characteristic. 



