July i, i 9 2o Universality of Field Heterogeneity 301 



fields which may be used for fertilizer tests, variety trials, or any other 

 experimental purpose involving plot yields. In the vast majority of 

 cases the heterogeneity is so great as to leave open to question conclu 

 sions drawn from experiments not carried out with all biological precau 

 tions and interpreted with due regard to probable errors. 



While the actual demonstration of differences in crop yields from one 

 portion of the field to another is the result of final importance from the 

 agronomic standpoint, and while it furnishes all but conclusive evidence 

 that this heterogeneity in yield is due to irregularities in the soil itself, it 

 seems desirable to show that such heterogeneity does actually obtain 

 in the physical and chemical properties of the soil which are determining 

 factors in plant growth. 



The desirability of determining the extent to which heterogeneity, in 

 the sense to which the term is used here, obtains in the physical and 

 chemical properties of the soil of experimental fields is emphasized by 

 the following sentences from one of the pioneer papers (21) on the 

 variability of soil samples. 



A number of papers have appeared dealing with the variation in the weight of 

 the crop produced over different parts of an apparently uniform field. Such varia 

 tions reflect the variability of the soil, serving simply as a substratum for the growth 

 of plants, but it is evident that the variations between such measurements as those 

 given do not depend upon the soil as the only variable factor. 



At the outset we must recognize that many factors may determine 

 differences in yield. Even if one could secure a tract initially uniform 

 in soil and exposure it is not always possible to be sure that it has all 

 been in the same crop in preceding years. Previous cultures may 

 influence tilth and soil composition by organic remains, by infection 

 with disease-producing organisms, or by differences in the demand of 

 various crops for certain of the plant foods. 1 Such sources of hetero 

 geneity are not readily detected by the eye or by physical or chemical 

 analysis. Even if the experimenter secures a field of sensibly uniform 

 texture, chemical composition, and previous cultural treatment, the 

 uniformity may be readily destroyed in planting or tillage. Rain may 

 interrupt the ploughing, thus exposing the soil of the different portions 

 of the field to air and light for different lengths of time and affecting the 

 physical condition very profoundly. Such sources of error are par 

 ticularly great in the planting of large experiments. Thus the sources 

 of field heterogeneity can never be fully determined in any case, although 

 individual factors may be demonstrated. 



To determine whether an experimental field is heterogeneous with 

 respect to physical or chemical factors, actual measurements of these 

 factors should be made over the field and the heterogeneity coefficient 

 applied. As a first illustration we take a series of soil-moisture 



1 These are factors of particular importance in rotation experiments. 



