108 STATISTICAL METHODS. 



iii the number. It is always one less than the number of 

 figures in the number to the left of the decimal point. The 

 value is therefore diminished by one every time the decimal 

 point of the number is removed one place to the left, and vice 

 versa. Thus 



Number. Logarithm. 



13840. 4.141136 



1384.0 3.141136 



138.40 2.141136 



13.84 1.141138 



1.384 0.141136 



.1384 1.141136 



.01384 2.141136 



.001384 3.141136 



etc. etc. 



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 close 

 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. 



TABLE XI, 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 



