QUANTITATIVE METHOD AND PRIMORDIA 33 



property tallness, which appears in F^ to the exclusion of the 

 opposite property, was called by MENDEL a dominant char- 

 acter ; dwarfness, which disappears in F^, he called recessive. 



The tall cross-bred F^ in its turn bore seeds by self-fertiHza- 

 tion. These are the next generation Fg (second filial genera- 

 tion). When grown up they proved to be mixed, many being 

 tall, some being short, like the tall and the short grandparents 

 respectively. Here the quantitative method was appUed. 

 Upon counting the members of this Fg generation it was dis- 

 covered that the proportion of tails to shorts exhibited a certain 

 constancy, averaging about three tails to one short, or, in other 

 words, 75 per cent, dominants to 25 per cent, recessives. 



These Fg plants were again allowed to fertilize themselves 

 and the offspring Fg of each specimen was separately sown. It 

 was then found that the offspring Fg of the recessives (Fg 

 dwarfs) consisted entirely of recessives. Further generations 

 bred from the recessives again produced recessives only, and 

 therefore the recessives which appeared in Fg are seen to be 

 pure to the recessive property (dwarfness). But the tall Fg 

 plants (dominants) when tested by the study of their offspring 

 Fg, instead of being all alike, proved to be of two kinds — viz. 



{a) Plants a which gave a mixed Fg consisting of both tails 

 and dwarfs, the proportion showing (just as in Fg) an average 

 of three tails to one dwarf (75 : 25) . 



(h) Plants h which gave tails only and are thus pure to tallness. 



The ratio of the impure plants a to the pure plants h was 

 as 2:1. The whole Fg generation therefore consists of three 

 kinds of plants, although, by external appearance (visible 

 properties), it seems to consist only of two kinds. There are, 

 in fact, in Fg two kinds of dominants {a and h) — viz. 



25^/0 h 5o7o ^ 25^'o 



pure dominants impure dominants recessives 



3 dominants i recessive 



The result is exactly what would be expected if both male 

 and female germ-cells of the cross-bred F^ were in equal number 

 bearers of either the dominant [D) or the recessive {R) property, 

 but not both. If this were so, and if the union of the male and 

 female germ-cells occurred at random, the result would be an Fg 

 family made up of (supposing 100 seeds to be taken) ^ 



25 DD + 2S DR + 2S RD + 2S RR 



^ In each pair of letters the first letter represents a S and the second a 9 

 germ cell. 



If the union occurred at random, the four possible combinations D cJ x 7) 9 , 

 D6 XR9, RS xD9 and 7^ <J xi^9 would occur in equal numbers, because 

 there exists no reason why one sort of combination would be more favoured 

 than any other. 



