July i, 1920 Universality of Field Heterogeneity 299 



fields, whereas the data provided by Smith are based on corn grown 

 without irrigation. 



Retaining the original division into quarter plots, we deduce for the 

 correlation between the subplots 



For 1915, r = 0.498 0.037, r/r=i3-4- 

 For 1916, r= -436 .040, r/E r = 10.8. 



The results for the two years can not, with due regard to their probable 

 errors, be considered to differ significantly. They indicate a degree of 

 heterogeneity in these Huntley plots quite comparable with that of 

 fields planted to various crops by other observers. 



If the quarter plots be combined by adjacent twos and the correlation 

 between the half plots be determined, we find 



For 1915, r = 0.494 0.053, 

 For 1916, r = .043i .057, 



The measure of heterogeneity has been only slightly lowered by divid 

 ing the plots into halves instead of into quarters. 



INFLUENCE OF SUBSTRATUM HETEROGENEITY ON YIELD OF OR 



CHARD CROPS 



In the preceding illustrations the crops considered have been her 

 baceous plants which are generally fairly superficial in their relation to 

 the soil and most of which complete their development in one or two 

 seasons. It seems of particular interest to extend the studies, as Batch- 

 elor and Reed (i) have done, to the yield of large individual plants, 

 such as orchard trees. 



For the purpose we employ the splendid series of data of Batchelor 

 and Reed. They say of their various groves (i, p. 251} : 



The fruit plantations herein discussed, to judge by the surface soil, size, and con 

 dition of the trees, as well as their apparent fruitfulness, appeal to the observer as 

 uncommonly uniform. All the orchards studied are situated in semiarid regions 

 and are artificially irrigated during the summer months. This fact is believed to be 

 a distinct advantage for the purpose of reducing the variability of one year s yield 

 compared with another, since it insures a fairly uniform water supply for the soil and 

 reduces one of the variants inevitable in nonirrigated localities. 



In the case of the Arlington navel oranges grouped in 8-tree plots as 

 the ultimate unit the authors (i, p. 264) report a correlation between 

 plots of r = 0.533 0.085 when the plots are combined by fours. 



It has seemed desirable to test the homogeneity of the soil in each of 

 the orchards studied by them. In determining the following coefficients 

 the individual tree has in each case been the ultimate unit. 1 



Consider first the relationship between the yields of adjacent trees of 

 two navel orange groves. 



1 Yields are reported in pounds per tree of ungraded product 



