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THE AMERICAN NATURALIST [Vol. XLV 



and Tocher lias pointed out that as a test for significance 

 of divergence we may use either of the three ratios 



(a) {y," — y/)/Vnpq(N — n)/(N — I). 



(b) 100{.(y.V») — p)W100*pq{N — n)/n{N — 1). 



(c) 100{ - 1 }/100V q(N - n)/np(N - 1). 



The significance of these ratios can he judged from the 

 tables of the probability integral. 7 . 



III. Recapitulation 

 ^ Individual prepotency is here used to designate the 

 superior capacity of certain parents for producing off- 

 spring of any desired character. The conception is most 

 general, and does not imply a similarity in soma between 

 parent and offspring, but the prepotency of the parent is 

 judged entirely by the offspring it produces. The term 

 is used merely to describe a long-known phenomenon, 

 and no theoretical explanation is suggested. 



Various breeders have tried to obtain a measure of 

 individual prepotency in its present significance. The 

 purpose of the present note is to point out certain bio- 

 metric formulae, in use for other purposes for several 

 years, which seem well adapted for this purpose. They 

 at least obviate several of the objectional features of 

 some of the methods which have been employed. Their 

 applicability in practical work will probably be limited by 

 the arithmetical routine, but in experimental studies their 

 importance may be very considerable.' Illustration of 

 their application will be published soon. 



