210 Quantitative Analysis of Plant Growth 



ment; this may be taken as evidence that the probable error of the mean 

 values up to this stage was sufficiently small not to deprive the fluctua- 

 tions of significance. The curves A and B, Fig. 5, which are respectively 

 curves for plants selected as mean and for un selected plants of the same 

 variety grown in the same year, add further evidence of the same 

 nature that the results for about eight weeks at the beginning of the 

 life- cycle are comparatively reliable. After the first eight weeks there 

 is no agreement in the fluctuations in the case of the five varieties or in 

 the case of the selected and unselected plants. This lack of agreement 

 may be due in the case of the five different varieties to inherent dif- 

 ferences in the plants, and in the case of the selected and unselected 

 to earlier maturity of the unselected. The selected plants were harvested 

 "nacb Parcellen," and hence the plants grew in close proximity through- 

 out, whilst the selected ("nach Auswahl") were thinned out at each 

 succeeding harvest. 



The following considerations, however, incline us to the opinion that 

 the lack of agreement in the later stages is due partly to sampling error. 

 In the first place, the leaf -area ratio is constantly falling from about the 

 seventh week onwards. For the same coefficient of variation from week 

 to week of the dry-weight of the plants harvested, the probable error 

 of the Unit Leaf Rate will increase as the Leaf Area Ratio falls, provided 

 the Unit Leaf Rate remains roughly constant throughout. We should 

 expect therefore from about the seventh week onwards increasing ampli- 

 tude of the fluctuations for a given variety, and less agreement in the 

 results from different varieties, as is actually recorded. Secondly, 

 Kreusler's figures 1 show that whenever a decrease in mean dry-weight 

 is recorded a corresponding decrease in leaf-area accompanies it. It is 

 not likely, except at the end of the life-cycle, that either the dry-weight 

 or leaf-area ever decrease to any appreciable extent, still less that they 

 should decrease together. This is an indication that the larger fluctua- 

 tions in the later part of the life-cycle and the lack of agreement between 

 crops grown in the same year are due to sampling errors. 



In attempting to correlate the fluctuations of Unit Leaf Rate with 

 changes in environmental factors we think it advisable, except in the 

 case of the harvests "nach Auswahl," to neglect weeks subsequent to 

 the eighth. 



1 See tables in previous paper. 



