A Cooperative Study 321 
Turning now to (iii) we find from the first three equations: 
J^sWW = '^05,4187, 
p-:'p-l" + p:"p: + = -955,6650, 
K +K' = 1"064,0394. 
These lead to the cubic for p^, 
p,s _ 1-064,0394 p.-' + -955,6650 p, - -305,4187 = 0. 
One root of this cubic is = -449,5251, which gives on dividing the factor 
— -449,5251 out 
- -GUJoUSp, + -679,4254 = 0. 
The roots of this quadratic are both imaginary. 
Accordingly neither the records for the nests with two eggs nor those for the 
nests with three eggs are consistent with a single gens the hens of which lay 
brown eggs with a tendency to lay green increasing with greater fertility. This 
hypothesis has therefore to be discarded. 
(iii) As a last hypothesis we will assume that there are two gentes or types 
of females, one of which lays brown eggs (p^) with a small chance of laying green 
(^1= 1 and the other of which lays green eggs (p.,) with a slight chance of 
laying brown (^'2=1 - P^)- Let NgV^,, iV, (1— v^) be the number of brown and 
green laying hens in the group JSfg which lays .9 eggs in the clutch. We suppose 
Pi and p.^ to be independent of the fertility of the hen, until this assumption is 
shown to be inadequate. 
Clutches of 1 egg. 
^iv^lh + (1 — Vi) q-z = number of brown eggs = iVje/, say, 
N-iV-^qi + (1 — i\) po number of green eggs - N^e.^, say. 
For our special case : 
v,p, + {l-v,)q.,^-UOMm, 
+ (I - = -459,8540. 
These equations are not, however, independent and only suffice to determine I'l 
from 
Vi = {€,' -q.)j{p, -q.^ (iv), 
or the proportions of brown and green egg layers in clutches of one, when pi 
and q., have been found. 
Clutches of 2 eggs. 
If the distribution of clutches be N.. (e/' + e^' + ej') 
P„p{' + ( 1 - I'.) (/,-' = fi", 
' v-zPiqi + ( 1 - r->)q-2P; = ie.,", 
-i'2?i^ +(1 -v^p-y' = e^"- 
