Beard, Heredity and the epicycle of the germ-cells. 401 



by the corresponding letter of the other half of the alphabet 1 ). In this 

 way the phenomena of prepotency of a parent or ancestor become 

 somewhat more comprehensible. 



On p. 257 of the ,,Germplasni" Weisrnanu writes: ,,it is evi- 

 dently more than inaccurate to fix the limit of the hereditary power 

 - as is done by animal-breeders of a parent at '/?, of a grand- 

 parent at V*, 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 Gal ton. Owing to the nuclear duplication, referred to above, 

 and the evidences afforded by it and others factors as to the union of 

 two individualities and two complete lines of ancestry, it seems to the 

 writer, that Gal ton's formula should be represented by something 

 different. 



The total inheritance would be V* (V + V 4 + '/ 8 etc. + V + V* + J / 8 + etc.). 

 In the formula 2 ), as thus written, the results obtained by breeders find 

 their full recognition. 



Before leaving the subject let me briefly indicate, how the dia- 

 gram 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 gener- 

 ations 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 little or 

 nothing in common with previous ones. Underlying it is something 

 more than a mere morphological continuity of germ-cells. From its 

 nature it might be termed ,,the understudy-theory of heredity. ,,Given 

 in a certain life-history the period of formation of the primary germ- 

 cells. Of these let there be for simplicity but two ,A and A,. On 

 one of these falls the lot of developing into an embryo. To which of 

 the two this happens is not of consequence for the argument. In all 

 its essential characters the remaining primary germ-cell (whose im- 

 mediate destiny it is to become the founder of the ,,sexual products" 

 of the said embryo), is the exact counterpart of the developing one. 



1) A better simile would be two backs of cards, a red one and a blue 

 one. In the formation of the ,,embryo" only one pack can be employed, but 

 it may be made up of red or blue cards in any proportion. Prepotency is 

 the preponderance of one or more suits of either red or blue colour. 



2) 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. 



XXII. 20 



