430 GENETICS IN RELATION TO AGRICULTURE 
faulty computation, unobserved variations in field treatment, sampling, 
etc.; (2) residual errors such as variations caused by soil heterogeneity due 
to natural conditions or to non-uniform treatment, uneven distribution of 
soil moisture, etc. The practical questions involved in reducing ac- 
cidental errors and the experimental determination of the probable 
error have received considerable attention particularly from English and 
American agronomists (see papers by Carleton, Farrell, Hall, Hall 
and Russell, Lyon, Mercer and Hall, Montgomery, Olmstead, Pritchard, 
Stockberger, Surface and Barber and Wood and Stratton). The need of 
some suitable mathematical criterion of soil heterogeneity has been 
pointed out by Harris. The criterion proposed is the coefficient of cor- 
relation between neighboring plots of the field. With the method of 
Plot Year : ; 
Number | Planted] Plant Seed Used Disposal of Seed Produeed 
Maine Agricultural Experiment Station PLOT INDEX 
Fig. 177.—Facsimile of plot index sheet used in all plant breeding work at the Maine 
Experiment Station. (After Surface and Barber.) 
treatment developed by Harris it has been shown that correlations 
between the yields of adjacent plots ranging from r=0.115+0.044 to 
0.603 + 0.029 can be deduced from the data of fields which have passed 
the trained eyes of agricultural experimenters as satisfactorily uniform. 
In three out of four cases tested the coefficient was more than 8 
times as large as the probable error indicating a relatively large degree of 
soil heterogeneity. Harris’ method in condensed form is as follows: 
Add together the yields of a chosen number of contiguous p plots to form a 
number m of combination C, plots. The sum of the squares of p is subtracted 
from the sum of the squares of C, and the result divided by m[n(n — 1)], where 
n is the number of ultimate plots in each of the m combination plots. The 
quotient is reduced by subtracting the square of the mean yields of the ultimate 
plots p, and the remainder divided by the square of the standard deviation 
of yields of ultimate plots, o,?. The quotient is the correlation between the 
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