A Cooperative Studji 325 
the existing frequencies inconsistent with our observations and beyond the limits 
of random sampling ? Summing up our results we have : 
• 
B 
G 
£2 
BG 
G'-2 B» 
BHI 
Observed 
! 74 
63 
67 
19 
92 62 
8 
14 
119 
(Calculated 
74 
63 
68-92 
15-15 
93-93 1 59-13 
13-98 
9-72 
119-87 
From these we find x' = o'631, giving P = '688, or in 69 trials out of 100 the 
sample would be more discordant from the calculated than the actual observations. 
There is accordingly nothing to be said against the theory on the ground of its 
statistical improbability. 
Again of the two hypotheses involved, (i) the greater fertility of the green 
egg layers, (ii) the fixed small probability that a hen of one gens will lay occasion- 
ally an egg of the colour of the other gens, the first seems not unreasonable ; the 
second gives merely a quantitative measure of the assumption made by a number 
of ornithologists that birds can lay eggs of two colours. It assunu's, however, that 
as a rule they do not. Clearly we need to know more of the mechanism of egg 
coloration before we can settle how it happens that a bird usually staining its 
egg brown will stain it green on a few occasions. If it be a result of type of 
food, we have to assume that our two gente.-; feed as a rule differently, which is 
not easily to be admitted. Will this feeding habit then be hereditary and if so 
are the male birds also divided into two gentes and is the mating assortative i 
Granted on the other hand that it is not due to food, but to differences of pigmen- 
tation mechanism, we are compelled to ask whether this mechanism is inherited 
only through the female. If not, then are the matings within the gens, or what 
is the pigmentation mechanism of heterozygote hens ? If we could establish the 
existence of the two gentes each with its rule and its fixed exception to rule ; if 
further the pigmentation mechanism as one must decidedly expect from the eggs 
of many species is markedly hereditary, then it is possible that in these clutches 
of composite colour lies the .solvent of some difficulties which the Mendelian 
explanation meets with when the product of two protogene zygotes instead of 
being protogene is in rare cases found to be allogene. 
(5) The Organic Correlations. 
We devote this section to a consideration of the degree of relationship between 
size, shape and colour characters of the same egg, and their relative values in the 
seasons 1913 and 1914. 
(i) Mottling and Breadth, Length and Index of Egg. 
The value of the correlation of mottling and breadth in the 1913 census was 
■1803, but unfortunately the sign of it was possibly wrongly given, as may be seen 
from the Table p. 150 of the former paper (Bionietrika, Vol. x.). We have taken 
occasion already to refer to the difficulties in the mottling scale used, but after 
