Jan. 1902.] BOTANICAL SOCIETY OF EDINBURGH 147 



total nuclear constituents, which together make up the 

 inherited characters of the two lines, one-half must be 

 suppressed, or remain latent, in the development. If these 

 characters be symbolised by the letters of the alphabet in 

 such a way that the first half of these represent the char- 

 acters of the one line, the second half those of the other, in 

 the development of the embryo only half of this total can 

 be made use of. Where one letter drops out, its place is 

 occupied by the corresponding letter of the other half of 

 the alphabet. In this way the phenomena of prepotency of 

 a parent or ancestor become somewhat more comprehensible. 



On p. 25 7 of the " Germplasm " "Weismann writes: "It 

 is evidently more than inaccurate to fix the limit of the 

 hereditary power, as is done by animal-breeders, of a parent 

 at h, of a grandparent at ^, etc." To the writer there- 

 would appear to be more correctness in doing this than in 

 limiting it to half this amount, as is done by Galton. 

 Owing to the nuclear duplication referred to above, and 

 the evidences afforded by it and other factors, as to the 

 union of two individualities and two complete lines of 

 ancestry, it seems to the writer that Galton's formula 

 should be represented by something different. 



The total inheritance would be — 



Ki + i + Hetc+^ + i + Hetc). 

 In the formula,^ as thus written, the results obtained by 

 breeders find their full recognition. 



Before leaving the subject, let me briefly indicate how 

 the diagram elucidates the phenomena of in-breeding. In 

 ordinary sexual reproduction in nature a set of primary 

 germ-cells, exactly like those of a given case, even those 

 of a given ancestor, can never reappear. This is clear 

 from the law of reduction, which in succeeding generations 

 is always leading further away from the particular 

 ancestor. But with in-breeding along two closely allied 

 lines, and by their final union, it may ultimately be possible 

 to approach the qualities of a given ancestor, though 

 probably mathematically an exact result is unobtainable. 



The theory of heredity, outlined in preceding pages, has 



1 Mathematically, dealing with abstract numbers only, this formula 

 is at the basis identical with that of Galton ; but, as the factors are 

 characters, not abstract numbers, this is not the case. 



