330 



THE AMERICAN NATURALIST [Vol. XL VI 



but have several pairs. Any one of these might be 

 wrong in its indication of the influence of ancestral en- 

 vironment because of uncontrollable factors making for 

 heterogeneity on the comparison tract, but as long as 

 these factors differ from series to series in a purely ran- 

 dom manner, we shall expect to get trustworthy values 

 by averaging the results for the several comparisons. 



This averaging may be done in one or both of two ways. 

 Most easily one may simply note the number of alterna- 

 tive cases, above zero and below zero, and calculate the 

 probable error of either class by the formula 



.67449 VN X.5X.5 



since, unless there be an influence of the treatment of 

 the ancestors, the probabilities of differences lying above 

 and below zero are equal. In the second case, the true 

 mean and standard deviation of the series of differences 

 may be obtained and the probable error of the mean 

 difference calculated by the familiar formula 



E =.67449^. 



VN 



It only remains to say that, except when specified, 

 Sheppard's modification was not applied in the calcula- 

 tion of the moments. 



III. Presentation of Data and Comparison of 

 Constants 



A. Number of Pods per Plant in Navy, White Flageolet 

 and Ne Plus Ultra Beans 

 The purpose of this section is to present the data for 

 number of pods per plant in three varieties, represented 

 by 40 series and over 21,000 individuals, and to draw the 

 comparisons which may profitably be based upon them. 

 The other characters for these varieties and all of the 

 data for still another variety are reserved for later treat- 

 ment. This character, which is the most easily deter- 



