STUDIES ON HYBRID DUCKS 253 



Fi certain characters are present in some females and absent in 

 others, and since in the males the same characters are always 

 present (or always absent according to the character in question) 

 it appears that these characters are sex limited. The following 

 generalized formula will show how the facts may be interpreted, 

 using Bateson's assumption of a sex homozygous male and sex- 

 heterozygous female. 



S, is a sex limited character; s, its absence, i. e. the presence of 

 another character. The Pi females are S ? s cf ; the males S cT 

 s cf . Coupling is assumed to occur between 9 and s. Or, if 

 prefered, a repulsion between 9 and S may be assumed, or a 

 coupling between cf and S. The Fi then, will be S c? So", S c? 

 s cf ; S cf s 9, s c?s 9. 



The Fi males, then, will be visibly alike, though of two gametic 

 constitutions; the females will be of two visible classes. 



Before going further, it may be well to point out that the data 

 at hand do not necessarily support Bateson's theory, for the 

 facts can also be represented thus; 



Females s 9 S 9 ; Males s 9 S d', giving females s 9 s 9, s 9 

 S 9 and males 80^89,8(^^89. 



Random matings of the Fi will give theoretical results in F2 

 agreeing sufficiently well with the observed results, which ever 

 formula is used, though according to the first method of formula- 

 tion, a few males should occur without the character in question 

 in F2. According to the second method all the F2 males should 

 have the character in question. The F2 black male lacks a ring 

 neck and white primaries, thus rather favoring the first mode of 

 representation. However, it will probably be necessary to estab- 

 lish suitable strains, before the bearing of the experiments on 

 the present theories of sex determination becomes perfectly clear, 

 but the experiments indicate unmistakably the existence of some 

 sort of sex limited inheritance with respect to several of the charac- 

 ters studied. 



In the formula given above I have assumed that both sexes of 

 the parent stock were heterozygous for certain characters. I 

 have made this assumption because of the variety of forms appear- 

 ing in Fi which ordinarily conforms to a single type. The unex- 



