No. 539] DISTRIBUTION OF PURE LINE MEANS 687 



paper. It is an exceedingly laborious Arbeit and appa- 

 rently done with scrupulous care. One who himself has 

 experienced the labor of calculating a few tables of con- 

 stants has sympathy for a worker who has industriously 

 filled pages with them. But the tenability of the geno- 

 type theory is one of the most pressing of current evolu- 

 tionary problems, and all available evidence must be 

 scrutinized. Eoemer's data are chosen for two very 

 excellent reasons, the first of which is that of all of the 

 men who have discussed the disposition of the means of 

 pure lines in a " Quetelet's Curve," he is, so far as I am 

 aware, the only one who has put on record sufficient data 

 for a critical test of his conclusions. If without over- 

 trying the case, as the lawyers have it, we can give the 

 second reason, it is that Eoemer's data and conclusions 

 have been accepted as perfectly valid by genotype 

 specialists. One of them, for example, says: 



The work is essentially a confirmation, with another plant, of 

 Johannsen's epoch-making investigations on beans, though it lacks any 

 extensive studies on the effect of selection within the pure line. The 

 essential objective point of Roemer's research is rather to determine 

 the biometric characteristics of pure lines as such in relation to the 

 general population. Among the more important general results are 

 the following: 



1. The different biotypes in a population arrange themselves in fre- 

 quency distributions in accord with Quetelet's Law. 



2. No relation was found to exist between the variability of the 

 biotypes (i. e., variation within the general population) and variation 

 within the pure lines. 



Our problem is twofold. First, we have to determine 

 whether Roemer is really justified in regarding his lines 

 as differentiated. Second, we have to inquire concerning 

 the critical value of his data as evidence in support of 

 the genotype theory of heredity. Incidently we shall 

 make the first of these problems serve as an illustration 

 of the use of a coefficient of individual prepotency recently 

 proposed in these pages. 3 



