253 
1910-11.] The Inheritance of Complex Growth Forms. 
should describe the result and not the normal curve. In the same way 
if n<. 2 we have a curve with the moment relationships of Type II. 
In the case considered n = 3 3, or the point binomial is represented 
by (3-f-10 + 3) p . To illustrate the manner in which this curve approxi- 
mates to the normal we may take p = 4<, i.e. there are eight pairs of 
allomorphs originally present in each parent. The distribution of this 
and the corresponding normal distribution are then : — 
Point binomial— 81, 1080, 5724, 15240, 21286, 15240, 5724, 1080, 81. 
Normal curve— 115*2, 1136, 5764, 15226, 21042, 15226, 5764, 1136, 115*2. 
It is to be noticed that the point binomial gives a “ leptokurtic ” dis- 
tribution, that is, one in which the radius of curvature at the apex is less 
than that of the normal curve ; in other words, one corresponding to that of 
Type IV., but not identical with it. On the numbers given by the total, 
namely, 66536, the difference between the two is most marked ; but on one- 
tenth of the numbers, namely, 6654, a number much in excess of that 
obtained in ordinary observations, the normal curve is an exceedingly good 
fit, giving by the test y 2 = 3*l or P = *91. It is interesting to observe that 
with only eight pairs of allomorphs a normal distribution of stature within 
the limits of error of observation is at once derived. 
Such a condition of dominance is, however, hardly likely to occur ; 
it is much more probable that there will be some blended inheritance as 
well, so that the resulting curve should be something between 
and 
(1 +4 + 6 + 4 + 1)* 
(3+10 + 3H 
With free mating and equal fertility the proportion of the mixed popula- 
tion is (3 + 10 + 3) p . The meaning of the value of n in the point binomial 
a+ n-{-l) v is therefore as follows: — If n is equal to 3*3 all matings are 
equally fertile, if n is >3*3 then the matings of hybrid with hybrid are 
most fertile and if n is <3*3, the matings of the purer races. 
The manner in which asymmetry arises may be seen by going back to 
the simple case. 
a, a 
b, b 
Let 
X 
and y 
c, c 
d , d 
mate at random ; 
after one generation we have a stable population composed of 
a, a 
a , b 
x 4 
2 
c, c 
c, c 
+ . . 
