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THE AMERICAN NATURALIST [Vol. XLIX 



S[n(n- 1)] = (110 X.4 X 3) + (10 X 6 X 5) =1620. 

 In the calculation of the weighted means and standard 

 deviations each entry, and the square of each entry, in the 

 first 22 rows must be weighted in an (n — 1) -fold = 3-fold 

 manner, while those for the last three rows must be 

 weighted in a 5-fold manner. 17 



The numerical values are : 



For grain, 



S[(n-l)p] =6378.72, S[(n — l)p 2 ] =25452.4154, 

 £=3.937, (V 2 = .207610, 

 S(Cp*)= 33129.7080, S(p 2 )= 7900.6790, 



whence 



r PlP2 = .354 + .026. 



Note that S(p 2 ) is constant for all groupings. 

 For straw, 



S[(n - l)p] = 10474.52, S[(n - l)p 2 ] = 69042.7194, 

 p = 6.466, <r„ 2 = . 813000, 

 S(C P 2 ) 89985.8976, S(p 2 ) = 21623.9802, 



whence 



r PlP2 = .479 + .023. 



Weighting has not materially changed the physical con- 

 stants from the values given under illustration 2 above. 

 The reasons for the conspicuous differences in the corre- 

 lations will be taken up presently. 



Montgomery's wheat data have been grouped into 2 X 2- 

 fold combination plots in the illustration above. If we 

 again combine the entries of Table III by twos, beginning 

 at the upper left-hand corner, we have 12 combination 

 plots each 4x4, or of 16 ultimate plots, and 4 combina- 



