1911-12.] Point Binomials and Mendelian Distributions. 397 
each acting part of the combination can be read at a glance. This will take 
up a little more space in printing, but the greater clearness will more than 
compensate. 
So much for notation. There is, however, also a very easy use of 
symbolical multiplication which allows of the numbers of each special 
combination being immediately written down. As the F 2 generation is a 
complete picture of all possible combinations, this generation can always, 
be at once written down directly. 
If 
1 aa 
and 
AA 
bb 
BB 
are two races where a changes with A and b with B, we have the stable 
race, as far as (aa) and (AA) are concerned, represented by 
(eta) + 2 (a A) + (AA) ; 
likewise that of (bb) and (BB), represented by 
(6&) + 2(&B) + (BB). 
If these be multiplied symbolically together, the numbers of any com- 
bination can be at once seen. 
Thus those combinations containing the element (aa) are 
aa 
aa 
aa 
*2 
bb 
bB 
BB 
and likewise the same holds for the other two terms. 
In the same way symbolical multiplication may be applied to the mating 
of special cases. Thus, take the case given by Bateson on p. 193 of the 
current number of the Journal of Genetics, where the mating of (Ff P p I i 
ff P *p li) is discussed. Here, writing each gamete in columns, we have for 
the first eight possible gametes of the first parent 
/ 
P, 
F 
F 
F 
F 
f 
/ 
f 
P, 
P, 
P, 
P, 
V > 
V - 
V > 
I 
i 
I 
i 
I 
i 
I 
and for the four possible gametes of the second parent, each duplicate, 
/ 
P> 
i 
/ 
/ 
/ 
P» 
P> 
P, 
I 
I 
i 
