Feb.4,i9is Variability of Yields of Fruit Trees and Field Trials 251 



of individual trees and the average of surrounding trees. For example, 

 they found coefficients of correlation as high as 0.652 ±0.065 for the 

 Eureka lemons and 0.628 ±0.060 for the Arlington navels. According 

 to the formula given by Harris (1915), the correlation between individual 

 trees and eight adjacent trees in a plot of the Arlington navels is 

 0.576 ±0.04. In view of these results, the writers felt justified in using 

 this method of substituted values. 



The fruit plantations herein discussed, to judge by the surface soil, 

 size, and condition of the trees, as well as their apparent fruitfulness, 

 appeal to the observer as uncommonly uniform. All the orchards 

 studied are situated in semiarid regions and are artificially irrigated 

 during the summer months. This fact is believed to be a distinct advan- 

 tage for the purpose of reducing the variability of one year's yield com- 

 pared with another, since it insures a fairly uniform water supply for the 

 soil and reduces one of the variants inevitable in nonirrigated localities. 



All yields of the several fruit and nut plantations are given in pounds 

 per tree of the ungraded product. 



DESCRIPTION OP THE PLANTATIONS 



Navel orange (Arlington). — These records were of the 191 5-1 6 

 yields of one thousand 24-year-old navel-orange trees near Arlington 

 station, Riverside, Cal. The individual tree production is shown by 

 figure I. 



The grove consists of 20 rows of trees from north to south, with 50 

 trees in a row, planted 22 by 22 feet. A study of the records shows 

 certain distinct high- and low- yielding areas. The northeast comer and 

 the south end contain notably high-yielding trees. The north two-thirds 

 of the west side contains a large number of low-yielding trees. These 

 areas are apparently correlated with soil variation. Variations from 

 tree to tree also occur, the cause of which is not evident. These varia- 

 tions, which are present in every orchard, bring uncertainty into the 

 results of field experiments. 



In making their calculations this grove was divided by the writers into 

 imaginary plots of any size and shape desired. The yields of these plots 

 were then compared with one another and their variability ascertained. 

 The distribution of both the theoretical and actual yields of this grove 

 is shown in figure 10. The yields of the individual trees when plotted 

 according to their frequency give a skew curve of Pearson's Type I, since 

 the critical function 



4(4^2-3^x)(2i82-3/3i-6) °-^5- 



The distribution of the actual yields is shown on the figure by small 

 circles. The points for the theoretical curve were calculated by the 

 formula \ 1 / x 2 



