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 which 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 “gametic. 
ratios” (ratio of parental combinations to new or 
crossover combinations in the gametes) fell into the 
series 1:1:1:1,3:1:1:8, 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 
nowdefinitely known. In fact,it seems probable that 
