432 THE AM ERIC AX NATURALIST [Vol. XLIX 



in an apparently uniform garden plot may be sufficient to 

 mask entirely the influence of the weight of the seed 

 {Phaseolus vulgaris) planted upon the size of the plant 

 (as measured by the number of pods) produced. It is 

 very probable that certain pure-line experiments and con- 

 clusions are entirely invalidated by the fact that the in- 

 fluence of irregularities in the substratum were not suffi- 

 ciently guarded against, 9 



Several authors have tried to obtain some measure of, 

 or some corrective term for, substratum heterogeneity. 

 For example, Mercer and Hall {loc. ext.) have plotted the 

 yields across the field in both directions. Such methods, 

 however, give but a very imperfect idea of irregularities 

 in the soil. Heterogeneity is perhaps more likely to occur 

 as a spotting of the field than as a relatively uniform 

 change from one side to the other. This is clearly indi- 

 cated in the diagrams published by Montgomery. The 

 mere plotting of yields in any line across the field can not 

 adequately take into account such irregularities. Fur- 

 thermore, some quantitative measure (and some probable 

 error of this measure) of the amount of irregularity, not 

 merely a demonstration of its existence, is required. 



Some generally applicable measure of the degree of 

 homogeneity of the soil of a field (as shown by actual ca- 

 pacity for crop production) seems highly desirable. Such 

 a criterion should be universally applicable, comparable 

 from species to species, character to character or experi- 

 ment to experiment, and easy to calculate. 



I believe we may proceed as follows. Suppose a field 

 divided into N small plots all planted to the same variety 

 of plants. Let p be the yield of an individual plot. The 

 variability of p may be due purely and simply to chance, 

 since the individuals of any variety are variable and the 

 size of the plots is small, or it may be due in part to differ- 

 entiation in the substratum. If the irregularities in the 

 experimental field are so large as to influence the yield of 



