No. 583] ON SUBSTRATUM HOMOGENEITY 433 



areas larger than single plots 10 they will tend to bring 

 about a similarity of adjoining plots, some groups tend- 

 ing to yield higher than the average, others lower. 



Now let the yields of these units be grouped into m 

 larger plots, C P , each of n contiguous ultimate units, p. 

 The correlation between the p's of the same combination 

 plot, C P , will furnish a measure (on the scale of to 1) 

 of the differentiation of the substratum as expressed in 

 capacity for crop production. If tins correlation be sen- 

 sibly 0, the irregularities of the field are not so great as 

 to influence in the same direction the yields of neighboring 

 small plots. As substratum heterogeneity becomes greater, 

 the correlation will also increase. The size of the co- 

 efficient obtained will depend somewhat upon the nature 

 of the characters measured, somewhat upon the species 

 grown, and somewhat upon the size of the ultimate and 

 combination plots. A knowledge of the values of the cor- 

 relation to be expected must be determined empirically. 



Fortunately, very simple formulae are now available for 

 calculating such coefficients. 11 



Let S indicate a summation for all the ultimate or com- 

 bination plots of the field under consideration, as may be 

 indicated by the capital C,, or lower case />. Then in our 

 present notation which is as much simplified as possible 

 for the special purposes of this discussion 



where P is the average yield of the ultimate plots and <r p 

 their variability, and n is constant throughout the m com- 

 bination plots. 12 



