403 
1911-12.] Point Binomials and Mendelian Distributions. 
Table of the Moments of the Principal Forms discussed. 
(These, for any complex series, are sufficient by help of the preceding formulae.) 
Form. 
A 
a 
A 
(1 + 1)” 
chi 
T 
0 
3(*-2)q 
4 ( 4 ) 
(<?+!)” 
c 2 nq 
c B nq(q - 1) 
chi ) j 3n ~ 2q 
(2 + 1) 2 
(2 + 1) S 
(q+lf) (q+ l) 2 
1 +p + 1)” 
2 nc 2. 
0 
2 pn + kn(3n - 2) 4 
p + 2 
(j) + 2) 2 
Appendix on Special Cases of Blending. 
If a race with two elements denoted by (aa) be crossed with a race 
(bb) we have the stable population given by the proportions 
(aa) + 2(ab) + (bb). 
This gives twice as many organisms having the mean quality as either 
extreme. In like manner take another race of greater stature, say 
(cc) + 2 (cd) + (dd), and let them mate at random with the first population. 
The stable population will obviously consist of the proportions of 
(aa) + (bb) + (cc) + (dd) 
+ 2 (ab) + 2 (ac) + 2 (ad) 
+ 2 (be) + 2 (bd) 
+ 2(cd) . 
There is a great number of special cases, all, however, agreeing in that the 
range is between (aa) and (dd), taking these as the extreme types, and that 
each mixed element has properties equivalent to the arithmetical mean of 
the elements. 
(1) In the first case, let (bb) = (cc) in the quality examined. The grouping 
will then be as follows : — 
(aa) + 2 (ab) + (bb) 
(cc) + 2(cd) + (dd) 
2(ac) + 2(ad) + 2(bd) 
2 (be) , 
or 
1 + 4 + 6 + 4 + 1. 
In this case the permanent population is approximately normal, and only 
one mode appears. If the quality depend on two elements in each, if it is 
defined by 
aa j AA 
, etc. , 
aa 
AA 
bb 
BB 
