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THE AMERICAN NATURALIST [Vol. XLIV 



calculation of S{xy) : (a) the writing down on the margin of the 

 correlation table of an assumed mean, V , of both the x and the 

 y characters, and (lie plus and minus deviations of the different 

 grades from these origins: ib) the entering in the body of the 

 table of the products of the deviations of the several classes of x 

 and y from their respective assumed means, care being taken to 

 regard sign, (Y) the summation of the products of the class fre- 

 quencies of x and y by the first two powers of their deviations 

 from their assumed means: (d) the multiplication of the fre- 

 quencies in the table by the products of the deviation of x and y, 

 and the summation of their products, with regard to signs. 

 This gives 



S(x'), Six'*), S(y'), S(y' 2 ), S{7/)/N=d,, 8(^)/N=^v/, 

 S(i/)/N=d y . S{y' 2 )=v.>, and S(*V), 

 from which we may obtain the moments and the products mo- 

 ments about their true means by the use of the formulae : 



Frequently there are several possible ways of carrying out the 

 arithmetic for a given formula, and the one chosen is largely de- 

 pendent on the mental and mechanical traits of the computer. 

 Personally I have found the process described rather cumber- 

 ants — have found slips coming into the work with unfortunate 



The chief difficulty lies in the fact that the products of the 

 deviations of x and y from their assumed means must be written 

 down as indices to the frequencies in the body of the table itself. 



there is no way of cheeking the results for blunders except to 

 go over the entire process again. After this has been done, all 



