EXPLANATION OF TABLES. 45 



VI. Table of reduction from the common to 

 the metric system. This is given first for whole inches 

 from 1 to 99 excepting even tens, which may be got from the 

 first line of figures by shifting the decimal point one place 

 to the right. The table may be used for huudredths of an 

 inch by shifting the decimal point two places to the left. 

 Other fractious than decimals are given in the lower tables. 



VII. First to sixth powers of integers from 



1 to 3O. This table is useful in calculating moments. 



VIII. Squares, cubes, square roots, and re- 

 ciprocals of numbers from 1 to 1O54. The use 



of this table can be extended by using the principle that if auy 

 number be multiplied by n, its square is multiplied by ?i s , its 



cube by n 3 , and its reciprocal by . 



IX. Logarithms of numbers to six places. 



The following explanation of the use of the logarithmic tables 

 is taken from Seaiies' Field Engineering, pp. 257-263 [ed. 



1887]. 



APPENDIX IX. The logarithm of a number consists of 

 two parts, a whole number called the characteristic, and a deci- 

 mal called the mantissa. All numbers which consist of the 

 same figures standing in the same order have the same man- 

 tissa, regardless of the position of the decimal point in the 

 number, or of the number of ciphers which precede or follow 

 the significant figures of the number. The value of the char- 



o o 



acteristic depends entirely on the position of the decimal point 

 in 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 1.141136 



1.384 0.141136 



.1384 1.141136" 



.01384 2.141136 



.001384 3.141136 



etc. etc. 



