76 LINKAGE 



from one parent and aB from the other. In one 

 individual the line AB divides a certain number of 

 times more than aB, whereas in the other aB divides 

 just that many times more than AB. In other 

 words, the number of times a line of cells divides must 

 be assumed to be determined in some way by whether 

 or not, in its formation, certain factors separated 

 that had established a relation with each other by 

 being present together in the egg or sperm from which 

 the individual came. To explain this, Bateson and 

 Punnett have suggested that at the time of fertiliza- 

 tion there is established in the egg a "polarity" 

 which determines the planes of the segregating divi- 

 sions. But it seems impossible to imagine how this 

 or any other mechanism could bring about the above 

 result. On attempting to follow out in concrete 

 detail the events w r hich must be assumed to occur in 

 any case of reduplication, we find that, if the above 

 stated relation is to hold, then, on "polarity" or any 

 other hypothesis, the assumption of the most intricate 

 and improbable relations and processes is forced upon 

 us. 



This interpretation of linkage was originally based 

 largely upon the supposed fact that the "game tic 

 ratios" (ratio of parental combinations to new or 

 crossover combinations in the gametes) fell into the 

 series 1:1:1:1, 3:1:1:3, 7:1:1:7, 15:1:1 :15, 31:1:1 

 31, etc. The supposed connection between this 

 series and reduplication is too involved to explain 

 here, and gametic ratios which do not fall into it are 

 now definitely known. In fact, it seems probable that 



