No. 536] COEFFICIENT OF INDIVIDUAL PREPOTENCY 475 



The necessity of dealing with each generation inde- 

 pendently is also imposed by the possibility of a differen- 

 tiation between any two generations due to purely envi- 

 ronmental (meteorological or edaphic) influences. Taken 

 as a whole the entire offspring generation may be superior 

 or inferior to the parental generation ; and this because 

 of no hereditary influence of the parents at all, for all 

 families may be raised or lowered proportionally. This 

 fact vitiates at once any comparison between individual 

 parents and individual offspring unless the type and 

 variability of both parental and offspring generation are 

 taken into account. 



In the practical work of calculation two cases may be 

 conveniently recognized: in the first, the character is 

 capable of direct measurement on a quantitative scale, 

 in the second, the character is not capable of direct 

 measurement but the individuals may be grouped into 

 satisfactorily defined classes. In the first case the means 

 may be compared; in the second case the proportional 

 frequencies of one class must be used. 



(a) Case of Characters Measurable on a 

 Quantitative Scale 

 It is well known that the standard deviation of a mean 

 is a/y/N and its probable error is .67449 <r \'N. Given 



probable error is given by 



where a and 5 and n and N represent the standard devia- 

 tions and the numbers of individuals involved in the 

 series. Thus it is quite easy to test the significance of 



ilies in our case. But with a large number of families the 



What we need is some easily calculated criterion of the 

 biological significance of the deviation of the mean of an 



