694 



THE AMERICAN NATURALIST 



[Vol. XLV 



may be disregarded, since with such relatively low values 

 of n as those of Roemer 's data the first is practically 

 unity, while the second is generally insignificant and 

 may always be neglected, having a maximum value of 

 circa .010, and in the majority of the cases falling far 

 towards zero. The values of % 2 fN are given in Table 

 III. In practically every case the inclusion of % 2 /N in 



TABLE III 

 Values of 2>/N 



1. Weight of plant 0233 



2. Length of stem 1442 



3. Thickness of stem 0031 



5. Weight of pods 0100 



6. Number of seeds 0454 



7. Weight of seeds 0067 



formula would change the end result only insignifi- 

 cantly, and since we are working roughly it may be 

 omitted throughout. 



We have thus reduced the formula to the fundamental 

 term y/^/n. Fortunately for us, Roemer has not used the 

 correct formula for the probable error of the mean but 

 has given Johannsen's "Mittlerer Fehler," <r/Vw = 

 y/<r 2 /n. We now simply determine m — M 13 and 

 (m-M)/(<r/Vw) for each of his lines. Table IV gives 

 the ratios. 



Apparently there can be no question concerning the 

 reality of differentiation in Roemer 's lines. If the differ- 

 ences (m — M) were due purely to random sampling 

 from a homogeneous population, we should expect the 



13 This second test was carried out before the first, and so before the 

 actual population means and variabilities were available. The means used 



These would be the same as the population means^f all the lines had the 



cases only did I modify Roemer 's means— changing number of pods from 

 6.6 to 6.5 and weight of pods from 11.2 to 11.3, in the "Gelbe Viktoria 



