4 on 



THE AMERICAN NATURALIST 



[Vol. XLIX 



neighboring small experimental plots, this heterogeneity 

 should become apparently less when expressed on a scale 

 of correlation between plots as the number of ultimate 

 plots combined increases. The reason for this condition 

 is quite simple. If the irregularities are very local in 

 nature they will influence in the same direction the yield 

 of only a very few neighboring plots. If too many ulti- 

 mate plots be combined the correlation will tend to vanish 

 because of the increased frequency of association of un- 

 like conditions due to the fact that the combination plots 

 have been made so large that they themselves have become 

 heterogeneous. 



That these conditions have been observed in actual ex- 

 perimentation is shown by the following constants based 

 on different groupings of the data used above. 



Consider first the Kothamsted wheat. For a 4 X 5 

 grouping of the plots the results were found to be 



For grain, r PlP2 = .186 ± .029, 



For straw, r PlP3 = .343 ± .027. 



If the plots be grouped by fives from east to west and 

 by twos from north to south, Table VIII is obtained. The 

 values S(p 2 ), p and <r P are the same as in the preceding 



m[»(»- 1)] =50 X 10 X 9= 4500. 

 For grain, S(C„ 2 ) = 78265.2822, r Pll > 2 = .214 ± .029. 



For straw, S(C,r) = 213939.8774, r PlP2 =.365 ± .026. 

 If the combination plots be made even smaller by group- 

 ing in a 2 X 2-fold manner for all but the last three north 

 and south rows, where a 2 X 3-fold combination must be 

 adopted, the results are. as illustrated above, 

 For grain, r PlP2 = .354 + .026, 



For straw, r PlP2 = .479 ± .023. 



For Montgomery's wheat data the results for a 4 X 4- 

 fold grouping (in as far as the nature of the records will 

 permit) have been shown to be 

 



