156 T. H. MONTGOMERY, JR. 



" Since the second and third of these are alike the result 

 would be expressed be the formula A A : 2Aa : aa which is the 

 same as that given for any character in a Mendelian case." 



But as a matter of fact this can be so only in a case where 

 there are only two chromosomes in the fertilized egg. For let 

 us take the case where the normal number of chromosomes is 

 four ; express by capital letters those chromosomes originally de- 

 rived from the spermatozoon, and by small letters those derived 

 from the ovotid ; and assume that A is homologous to a, and B 

 to b. Then the spermatogonium would have the chromosomes, 

 A, a, B, b, and the ovogonium have also A, a, B, b. By the 

 synapsis stage would be formed bivalent chromosomes Aa, Bb 

 in the spermatocyte, and Aa, Bb in the ovocyte. The reduction 

 division would separate A from a and B from b in both sperma- 

 togenesis and ovogenesis. The spermatids would contain then 

 either A, B, or a, b, or A, b, or a, B ; and the ovotids either A, 

 B or a, b, or A, b, or. a, B. In the fertilization of one of these 

 ovotids by one of the spermatozoa, 16 different combinations are 

 possible : A, B, A, B ; A, B, a, b ; A, B, A, b ; A, B, a, B a, 

 b, A. B ; a, b, a, b ; a, b, A, b; a, b, a, B ; A, b, A, B ; A, b, a, 

 b\ A, b, A, b \ A, b, a, B ; a, B, A, B\ a, B, a, b ; a, B, A, b ; 

 a, B, a, B. But only one of these combinations is of purely 

 paternal chromosomes, namely A, B, A, B ; and only one of 

 purely maternal, namely a, b, a, b. The other fourteen combi- 

 nations show paternal together with maternal chromosomes (six 

 cases where the paternal and maternal chromosomes are present 

 in equal number, four cases where there are three paternal chro- 

 mosomes to one maternal, and four cases where there are three 

 maternal chromosomes to one paternal). 



Hence the ratio is : \P : \j\PM : iM, where P stands for purely 

 paternal chromosomes, M for purely maternal, and PM for com- 

 binations of paternal and maternal chromosomes. This is clearly 

 not a Mendelian ratio of I : 2 : I. And obviously the disparity 

 would become greater with any increase in the number of chromo- 

 somes. According to Sutton's own computation, in forms which 

 have 24 chromosomes, the number of possible combinations of 

 these in the fertilized egg would be 16,777,216. That would 

 give the ratio of \P : i6,777,2i4/W : I M. 



