284 Journal of Agricultural Research Voi. xrx, No. 7 



I . MANGOIvDS 



The yields of 200 plots of mangolds studied by Mercer and Hall (15) 

 may be grouped into combination plots in a 2 by 2 fold manner. When 

 this is done, the correlation between the yields of associated plots has 

 been shown * to be as follows : 



For weight of roots, r= 0.346 ±0.042,^ rjE^^ 8.24. 

 For weight of leaves, r= .466± .037, r/E,= i2.5. 



Thus, if one plot of a combination plot is higher or lower than the 

 general average by a given amount, an associated plot may be expected 

 to deviate from the general average by 35 to 40 per cent of this amount. 



2. — POTATOES 



Lyon {14) gives the yield in pounds for each of six sections of a series 

 of 34 rows of potatoes. This crop was harvested from " a piece of appar- 

 ently uniform land." Bach section was 72 feet 7 inches in length. The 

 distance between rows was 34 inches. 



Combining yields of rows and of sections of rows by twos, we reduce 

 the field from a 34 by 6 fold to a 17 by 3 fold combination. The correla- 

 tions between the sections of the rows is then found to be 



'■p^Pj = 0-31 1 ±0-043. r/Er=7.30. 



Yield of potatoes in this field is, therefore, markedly influenced by 

 irregularities of soil conditions. 



For data on a second test on the influence of field heterogeneity on the 

 yield of potatoes we may avail ourselves of the valuable records of yields 

 of individual hills reported by Stewart (jp). Since these are recorded 

 in quadruplets for the purpose of determining the influence of missing 

 hills upon yield, ^ it is not feasible to group them into plots. The influ- 

 ence of heterogeneity may be tested by determining the correlation 

 between the yields of the plants of a quadruplet.* 



1 For original data see Mercer and Hall (15, p. log); also Harris (5, p. 434-436). 



2 The probable errors have in all cases been computed on the basis of the actual, not of the weighted, 

 number of ultimate plots as A'. 



' The planting scheme adopted was 



ai a'l b'l bi aj a'2 b'2 b> as a'3 b'3 bs . . . , 



where a and a' are the two halves of the same tuber and b and b' are two halves of another tuber. Thus 

 halves a and b were grown adjoining missing hills and were subject to competition on one side only, whereas 

 halves a' and b' were subject to competition from two adjacent plants. 



* Since a and a' are halves of the same tuber and b and b' are halves of another, the correlations raa', rbb' 

 might be due to a specific physiological influence of the characters of the tuber upon both plants developing 

 from the corresponding half tubers rather than to an influence of differences in soil conditions. We have, 

 therefore, determined the correlations between the plants occupying the same relative position in the 

 quadruplet but derived from different parent tubers, that is rab, ra'b'. Hence rab represents the correla- 

 tion between the two outside tubers and ra'b' the correlation between the two inside tubers of the quad- 

 ruplet. As a control on the results the correlations between one outside and one inside plant have been 

 determined. These are rab' and rba'. 



