Do SS eee oe a ad Le ed eee 
1913] EAST—CROSSES OF NICOTIANA 183 
recombination of cumulative unit factors that do not show the 
phenomenon of dominance. The frequency distribution of the 
F, generation in these cases is not (-+})", as it is where dominance 
is complete, but is ($-+4)*", because a factor in the heterozygous 
condition is to be regarded as producing one-half the effect that it 
produces when in the homozygous condition. 
Regarding this expression as proper for the moment, let us 
examine the F, frequency distribution for length of corolla with 
the idea of assigning a definite number for in the expression 
(5 a 1a 
If n is made equal to 3, (ies by the theory the F, distribution 
should have seven classes with the frequencies 
1-6-15-70-15~0-1 
per 64 individuals. For 828 individuals, the grandparental sizes 
should each be recovered (828-64) =13.0—) nearly thirteen times. 
This was not the case in the actual distribution. 
If m is made equal to 5, the F. distribution should have eleven 
classes with the frequencies 
I-I0-45-120-210-252-210-120-45-10-1 
per 1024 individuals. With 828 individuals the grandparental 
‘classes should each be recovered only 0.8 times; in fact, a majority 
of populations of this size would not show the grandparental classes 
at all. This also is not the condition that was actually found. 
There is left only the possibility of making equal to 4. When 
this is done the F: distribution for 256 individuals—the smallest 
number in which a representative of each class may be found— 
and for 828 individuals is as follows: 
1- 8- 2 56 7o 56- 28- & 1b 
3.2-25.9-90.6—-181 . 1-226. 4-181 . 1-90. 6-25 .9-3.2 
This calculation points to the recovery of each grandparent 
about 3 times in the F, population under observation. Reference 
to table I shows that the figures actually obtained agree rather 
closely with this observation. But table I also shows another 
important fact. The arbitrary classes used had a range of 5 mm., 
which makes 1 3 classes necessary to express the F, generation. 
