A Cooperative Study 
323 
using to obtain linearity = q., + v, where q.^ is the value given by the quadratic 
(ix) and t] is supposed a small quantity with negligible square. The values of 
Pi and qz found from (x) will be good, if not the best. Our system for 7'i, u^, Vs, 
jO], §2 will not be the optimum, possibile, but if our system is probable, that will be 
still more probable and the hypothesis of the two gentes of tern hens will not be 
contradicted by the data. 
Our system of e's is : 
e/ =-540,1460, e/' = -376,4045, e," =-106,7416, 
e/" = •305,4187, e,'" = -039,4089, e/" = -068,9655, 
leading to : 
/" =-429,7753, =-376,4045, 
//" = -354,6798, = -318,5550, /;" = -305,4187. 
(ix) now becomes : ' 
-192,7573^2- - -192,4337^, + -006,8485 = 0, 
giving the small value 5.= "036,9571 for the chance of a green gens hen laying a 
brown egg. 
We now return to (x) substituting the /'s and -036,9571 + 7) for q... Expanding 
and neglecting 77- we obtain, on extracting the root of jjj- in the third equation 
p, = -917,7816 + 1-242,3209 77, 
p, = -961,3638 + 1-909,4759 77, 
= -961,3638 + -991,441277. 
Solved by least squares these equations give for type equations : 
= -946,8364 + 1-381,0793 77, 
= -948,2960 + 1-489,7513 77, 
leading to : 
= -928,2876, r^, = -071,7124, 
_p, = -976,4736, 3., = -023,5264. 
Whence from (vii), the first of (v) and (iv), 
1;, = -366,0119, 1 - I', = -633,9881, 
1^2 = -449,0123, 1 - 1/2 = -550,9877, 
1/1 = -571.0011, 1 - = -428,9989. 
Thus about 7 of the eggs laid by hens of the brown-laying gens will be 
green, and only about 2 of the eggs laid by hens of the green-laying gens will 
be brown. Further the green-laying gens is far more fertile than the brown- 
faying gens, the proportion of brown to green layers falling from 57 to 43 in the 
single clutches to 37 to 63 in the triple clutches. The following is our analysis 
on this basis. 
