EXPLANATION OF TABLES. 107 



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 hundredths of an 

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

 Other fractious than decimals are given in the lower tables. 



VII. Table of minutes and seconds of arc in 

 decimals of a degree. This table will be found of use 

 in the fitting of curves of Type IV (p. 33). 



VIII. First to sixth powers of integers from 1 

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



IX. Table of the probable errors of the coeffi- 

 cient of correlation for various numbers of ob- 

 servations or variates (ri) and for various values 

 of r. The probable error of the coefficient of correlation 



, . 0.6745(1 -r 2 ) f 



being := -, a table for the varying values of n and r 



Vn 



is easily constructed, and for large values of n is accurate 

 with interpolation by inspection to two significant figures, 

 which are all that are required. 



X. Squares, cubes, square roots, and recip- 

 rocals of numbers from 1 to 1O54. The use of 

 this table can be extended by using the principle that if any 

 number be multiplied by n, its square is multiplied by n 2 , its 



cube by n 3 , and its reciprocal by . 



XI. Logarithms of numbers to six places. 



The following explanation of the use of the logarithmic tables 

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

 1887]. 



The logarithm of a number consists of two parts, 

 a whole number, called the characteristic, and a decimal, 

 called the mantissa. All numbers which consist of the 

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

 tiss"a, 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- 

 &cteristic depends entirely on the position of the decimal point 



