274 Journal of Agricultural Research voi. xii. No. s 



viously be satisfactory, provided there was no difference in the amount 

 of variation between the plants on different plots and that the soil varied 

 uniformly in one direction. 



The first method mentioned computes the ' ' normal ' ' (N) for the whole 

 area; the second, for a locus on that area. These normals may be com- 

 bined to represent the resultant of both general and local conditions. 

 Thus, the formula N=}4 (C+ ^Q + J^Cj) indicates that N is the mean of 

 the values for N computed by the two preceding formulas. This assumes 

 an equal value for the adjacent control plots and the mean of all control 

 plots. Its use as N brings up the calculated yields of plots on low- 

 yielding areas and reduces the same on high-yielding areas. In the case 

 of cereals there is usually small chance for difference in the yielding powers 

 of a plot and its nearest control on account of their proximity; but in 

 the case of orchard trees situated some distance apart there may be 

 greater soil changes between adjacent plots, and consequently a marked 

 difference in yield, aside from the effect of treatment, between a plot and 

 its nearest control plots. The introduction of the mean of all control 

 plots might be expected to introduce a stabilizing factor. In the formula 

 ^2 (C+^Ci + J4C2) the mean of all control plots has equal weight with the 

 normal derived from the nearest controls. Since the soil over any but 

 very small areas may not be uniformly variable, it might seem more 

 logical to weight the normal derived from the nearest controls more 

 heavily than that derived from the mean of all control plots, and to 

 combine the two. This has been done by Olmstead (1914) and others, 



making the formula ^^^ 1 L h — ^^ which p^ and p2 are constants 



Pl'p2 



arbitrarily chosen. Stockberger {1916) found satisfactory results by 

 assigning the values pi=i and p2=3- 



The method used by the Office of Cereal Investigations, of the Bureau 

 of Plant Industry, is K(c+Q). which employs half the sum of the mean 

 of all control plots and the yield of the nearest control plot as the normal 

 for any given plot. 



Stockberger {1916) compared the relative precision of these formulas 

 in computing the normal yields of plots of hops. Using the yields of 

 six years he obtained the greatest precision from the formula 



P, + P2 



though no formula maintained the same relative rank throughout the 

 six years. It would appear that there is no way of determining in 

 advance the formula best suited to any particular case, at least not 

 until more applications of the different formulas have been studied. 



The five formulas above stated have been tested on the Arlington 

 grove of navel oranges. The grove was parceled into linear plots of 

 10 trees each. Each alternate plot was designated as a guard row and 



