Size inheritance and the pure line tlieury. 231 



dominant and recessive elements, we shall ultimately recognise that the 

 discontinuity between these elements need not be universally absolute. 

 We may expect to find individuals, and perhaps breeds or strains, and 

 even individual gonads or groups of gonads, in which the discontinuity 

 is less sharp even in respect of these very characters; similarly, for 

 such units definite departures from statistical equality between D and R 

 germs may be expected. InPisum, for instance, we cannot be far out 

 in considering an average of 50 per cent. D and 50 per cent. R as 

 a close approximation to the truth for both male and female cells, but 

 there is nothing yet which proves even here that the discontinuity 

 must be always and absolutely complete." 



To show further that this idea was not an original part of Men- 

 delism Bateson says, p. 129: 



"Readers of Mendel's paper will be aware that he laid down no 

 universal rule as to the absolute purity of gametes, but merely pointed 

 out that his results were explicable on the hypothesis of such purity." 



Bateson also admits (p. 127) that there may be types of inherit- 

 ance not entirely Mendelian: 



"But besides the strictly alleloraorphic or Mendelian distribution 

 of characters among the gametes, we can imagine three other possible 

 arrangements. (1) There may be a substantial discontinuity, the two 

 types of gamete being connected by a certain proportion of intermediates, 

 such as are often met with in cases even of almost complete discontinuity 

 among zygotes. (2l There may be continuous variation among the ga- 

 metes, shading from gametes pure to the one type, to gametes pure to 

 the other type, the intermediates being the most frequent. (3) There 

 may be no differentiation among the gametes in respect of parental 

 characters at all, each representing the heterozygote characters unresolved. 

 By a sufficiently wide survey, illustrations of each of these systems and 

 of intermediates between them, will doubtless be found, and the classifi- 

 cation of gametic differentiation according to these several types, in 

 respect of various characters, in various species, will be a first step 

 towards the construction of a general scheme of heredity." 



The possibilities here outlined afford a sufficient basis for explaining 

 size inheritance without invoking the pure-line idea of Johannsen and 

 the multiple factor hypothesis of Nilsson-Ehle, on which the "Mendelian" 

 explanation of size inheritance rest. The facts which are supposed to 

 warrant that explanation are (1) the increased variability of F,. as 

 compared with Fi, and (2) the fact that the variability again decreases 

 in Fa if the Fj individuals are self fertilized. But these same facts 



