320 
On the Neitt and Eggs of the Common Tern 
respectively a green egg as the same in successive layings. The change of pigment 
in successive layings may be a physiological exhaustive process as a change from 
a melanin to a lipochrome. This hypothesis does not assume that any given bird 
may or may not lay a green or brown egg according to a given law of chance, 
but that physiologically there is a tendency with successive laying to alter the 
nature of the pigment in the glands or on the surface of the oviduct. For 
example the hen, as the incubation period approaches, may change the quantity 
or character of her food. 
It is probable, however, that the changes will not be the same for small and 
large layers, we shall therefore give generalitj^ to the problem by supposing the 
probability of laying a brown egg to vary not only with the number of eggs laid 
but with each egg. 
We have then the following system of notation: p^! , pg", ja/", .•• = chance of 
laying a brown egg in the 1st, 2nd, 3rd, ... laying of a hen who lays a clutch of 
s eggs. The corresponding chances of laying green eggs will be qg = 1 — pg, 
qj' = 1 — pj', qj ' = 1 — p.f"', — Let there be N^. s-clutch common tern hens. 
Then our data are to be provided by the equations: 
]S\p,' + N,q,' = 74 + 63 {N, = 137), 
- ^^p-Ip-" + N, {p:q:' + q:p.;') + N./i:q:' = 67 + 19 + 92 {n, = i78), • 
N,p^p.:'p.:" + N, ( p.; 'p;" q.; + p..;"p^q.; ' + p^p^'q"') 
+ ]S\,{p;q.;'q.!'' -\-p,!'q;''q.; +p.;''q.;q.^')-\r N.iq.iq"q"' 
= 62 + 8+14 + 119 {N,= 20Z). 
Dividing out by the totals in each case and equating corresponding terms we 
have the following system of equations to solve : 
^/ = -540,1460, = -459,8540 .....(i). 
pipl' = -376,4045, p;q.;' + /j./V/,' = -106,7416, q^q.!' = -516,8539 (ii), 
pi pi pi" = -305,4187, pl'pl'ql +p3"plql' + plpl'ql" = -039,4089, 
piqllql" + pl'ql"ql + pl"qlql' = -068,9655, qlqi'ql" = -586,2069 . . .(iii). 
(i) is solved as it stands. But it is clearly impossible to take ^.2' = g/ for this 
would involve ql' being greater than unity, an impossible value. Similarly 
ql and ql' cannot be equal to ql and q.!' respectively, or we should have ql" > 1. 
Thus it is needful that the probability of laying a green egg should increase 
with successive eggs or be a function of the fertility. Assuming this change of 
probability, we may write the first equations of (ii), the third is not independent : 
p^p^' = -376,4045, pi (1 -pl')+pl' (1 -pi) = -106,7416, 
which gives us pi + pi' = -859,5506, or p.^', pi' are roots of the quadratic 
p.f - -859,5506 p. + -376,4045 = 0. 
These roots are imaginary. 
