July 1. 1920 Universality of Field Heterogeneity 309 



Kaserer s series of determinations (9) is not sufficiently large or prop 

 erly distributed over the field to make desirable an attempt to measure 

 heterogeneity. Fortunately Waynick and Sharp (22) have given four 

 excellent series, two for nitrogen and two for carbon, derived from two 

 California fields. 



Their samples were taken over a total area of a little more than i .3 acres 

 on two fields of very different character a silty clay loam at Davis and 

 a blow sand at Oakley. 



The fields were both selected for their apparent uniformity, both being nearly level 

 with no change in the soil mass from one part of the field to another great enough to be 

 detected by the usual field methods. Both fields were practically free from vegetation 

 when selected, and before the samplings were made in March, 1918, all extraneous 

 material had been carefully removed. 



Altogether they took 80 samples distributed at 30-foot intervals 

 over the entire area. These samples were arranged in an 8 by 10 fold 

 manner. The original data are given in their Tables 3 and 4. Arranging 

 these in the order of the map of the borings given in their figure i and 

 combining in a 2 by 2 fold manner, we derive the following heterogeneity 

 coefficients : 



For the silty clay loam at Davis 



For carbon, r = 0.417 0.063, r /Er 6.67. 



For nitrogen, r = .498 .057, r/E r = 8.75. 

 For the blow sand at Oakley 



For carbon, r = 0.317 0.068, r/E r = 4.65. 



For nitrogen, r .230 .072, r/E r = 3.20. 



All these values are statistically significant in comparison with their 

 probable errors. Although the total number of samples is rather small, 

 they indicate in each case a distinct heterogeneity for these important 

 constituents of the soil. Apparently the two fields differ in their hetero 

 geneity, the coefficients for both carbon and nitrogen being distinctly 

 lower on the blow sand at Oakley than on the silty clay loam at Davis- 

 The average carbon content at Oakley is only 0.444 as compared with 

 1.109 a t Davis, while the nitrogen at Oakley is 0.033 as compared with 

 o.ioi at Davis. Probably greater heterogeneity would be expected on 

 general physical considerations on the silt loam than on the blow sand. 



The analysis may profitably be carried one step farther. If these 

 fields are heterogeneous in respect to the soil constituents here under 

 consideration, one might anticipate a correlation between the carbon 

 and the nitrogen content of the samples distributed over these fields.. 

 The results are 



For the Davis loam, r nc = 0.785 0.029, 



For the Oakley blow sand, r nc = .744 .034, r/ r = 



