THE AMERICAN NATURALIST [Vol. XLIX 



Map A represents the Kothamsted field of mangolds 

 grown by Mercer and Hall (loc. cit.). The upper entries 

 are for pounds of roots, the lower for pounds of leaves. 



I now reduce the 200 areas to 50 by combining the ad- 

 joining plots by fours, as indicated by the heavier lines on 

 the map. Thus for leaves the Southwest combination 

 plot, C P , is 67 + 52 + 56 + 51 = 226. Table I gives the 

 result. 



This gives for roots : 



S(p) =65715, S(p 2 ) = 21674871, # = 200, 

 2^ = 328.575, oy 2 = 412.824, 13 

 S(C P 2 ) = 86537439, m[n{n - 1)] = 50 X 4 X 3 = 600, 

 [S(Cp 2 ) — S(p*)]/m[n(n - 1)] = 108104.280, 



and 



108104.280 - (328.575)- 

 412.824 



.346 ± .042. 14 

 The results for yield of leaves are 



#(p)==9541, S(p 2 ) =45941, # = 200, 

 p= 47.705, <r P 2 = 23.938, 

 S(C,r) =1832095, wt[w(n-l)]=50x4x3=( 

 [S(C P *) -S(p 2 )]/m[n(n-l)] =2286.923, 



whence 



2286.923 - (47.705) 2 



2:;.i»:-;s 



.1)37. 



Illustration 2. Influence of Substratum Heterogeneity 

 upon the Yield of Straw and Grain in Experimental Plots 



