THE AMERICAN NATURALIST [Vol. XLIV 



To complete the calculation of the correlation r xy , we require 

 only A , A 8 , <r , a s . Taking the origin at for both of these char- 

 acters 10 and multiplying and summing at the same time, as 

 we did before, we get : 



S(x') - 109,818, S(x' 2 ) = 721,904, 

 S(y') -61,017, Stf*) -284,287, 

 S( x' ) / .V = 109, 818 / 16, 965 = 6. 4732 = A x , 

 8(y / )/N= 61,017/16,965 3.5966 = .4 y , 

 <r x = Vsjx'*)! N - A / = . 80629, 

 a v — V S{ ) jN— A y 2 = 1.95485, 

 ^S{xY)IN- A x Ay 2223> 



Now I think, nut withstanding these la rue numbers. 11 there has 

 been a material gain in facility of 4 calculation. The writing 

 down of the indices showing the products of deviation has been 

 entirely avoided. The direct calculation of the totals of arrays 

 is easy, and it is only one short step further to obtain the means 

 of arrays for testing linearity, either by the sensible agreement of 

 empirical and theoretical means, as shown by a graph or by the 

 application of Makeman's test to if — Note also that in the 

 conventional method of obtaining S(x'y') there is no way of 

 checking the work except to go over it independently. In the 

 method here described the larger part of the work of obtaining 

 8(x f y f ) is at once checked by the fact that the sum of the totals 

 of the y arrays = S(y'). The final multiplication and summa- 

 tion is very quickly verified. 



There are advantages in the method beyond these indicated by 

 this illustration. 



Suppose that one wishes to correlate between a first character 

 and a number of repeated characters and their sum. This some- 

 times happens in work on fertility. Take as an illustration a 

 table 12 showing the relationship between the length of the fruit 

 and the number of ovules on the two placenta 1 in the bloodroot, 



the method of calculating r suggested here, how the constants of the two 



series of observations with which we are dealing here is larger than is 

 generally available in biological work. 



