300 Journal of Agricultural Research VOI.XIX.NO. 7 



Grouping the yield of the i ,000 trees at Arlington, shown in figure i 

 of Batchelor and Reed, in a 2 by 2 fold manner we find 



r = o.5i7o.oi6, r/ r =33.i. 



A navel orange grove of 495 trees at Antelope Heights, mapped as 

 figure 2 by Batchelor and Reed, when combined in a 3 by 3 fold manner 

 gives 



r = 0.375 0.026, r/E r = 14.4. 



Grouping the 240 Valencia orange trees of the grove shown in figure 3 

 of Batchelor and Reed in a 2 by 2 fold manner, we find for the correlation 

 between yields 



r = 0.306 0.039, r/E r = 7-75- 



For the yield in pounds per tree of Eureka lemons as shown in figure 

 4 of the authors cited, we find for a 2 by 2 fold grouping 



r = 0.448 0.02 8, r/E r = 15.8. 



This last result is of particular interest, since Batchelor and Reed say 

 of this plantation 



This grove presents the most uniform appearance of any under consideration. The 

 land is practically level, and the soil is apparently uniform in texture. The records 

 show a grouping of several low-yielding trees; yet a field observation gives one the 

 impression that the grove as a whole is remarkably uniform. 



Notwithstanding this apparent homogeneity there is a heterogeneity 

 coefficient of over 0.4. 



Taking the yields of seedling walnuts in pounds per tree as given in 

 figure 5 of Batchelor and Reed and grouping in a 2 by 2 fold manner, 

 we find 



r = 0.232 0.038, r/E r = 6.og. 



Finally, if the yields in pounds per tree of the Jonathan apple trees 

 mapped by Batchelor and Reed in their figure 6 be treated in a 2 by 2 

 fold grouping, the coefficient is 



r = 0.2 14 0.043, r /r = 4-97- 



Without exception these groves show material values of the hetero 

 geneity coefficients which are statistically significant in comparison with 

 their probable errors throughout. 



PHYSICAL AND CHEMICAL BASIS OF THE HETEROGENEITY OF 

 EXPERIMENTAL FIELDS 



In foregoing sections it has been shown that when tracts of land are 

 judged by their capacity for crop production the yields are such as to 

 indicate that heterogeneity is a practically universal characteristic of the 



