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 



Number 



Vec 

 Fluted 



Dtiposal of Seed Produced 



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 p plots. The sum of the squares of p is subtracted 

 from the sum of the squares of C p and the result divided by m[n(n 1)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- p 2 . The quotient is the correlation between the 



