A Coo2)erative Study 
331 
the general conclusion that except for very skew distributions, change in means 
does not involve change in correlation. Change in variability does usually denote 
change in correlation, but as we have indicated (p. 311) the changes in varia- 
bility are not significant except in the girths, and this may be the source of such 
modification as we find in the correlation of Length and Longitudinal Girth. To 
test this we note that if Longitudinal Girth only be changed the regression 
coefficient of the Length on the Longitudinal Girth ought not to be changed 
within the limits of random sampling. For 1914 this coefiicient of regression is 
•4501 + -0056 and for 1913 is •4215 + '0089. Hence the difference is "0286 ± -0105. 
Thus the difference in the regression coefficients is just as significant as it was in 
the correlation coefficients, or is not explicable on the basis of increased varia- 
bility in the Longitudinal Girth. If it is, which we doubt, to be considered 
significant it must depend on something else than a more variable Longitudinal 
Girth. 
We may consider in this place what changes have taken place in the formula 
connecting Longitudinal Girth with Length and Breadth. For 1914 we have : 
Gi = 1-1273 E -h 1-4840 L 1-9180, 
while for 1913 we had : 
= 1-2701 5 + 1-6415 X + -8224. 
The changes in the coefficients look more considerable than the changes that 
will be found in the values for Gi calculated from either formula for eggs which 
are not extrenie variants. At the same time the differences rather tend to 
emphasise the suggestion given by the correlation of Gi with L, that there may 
have been a seasonal change in the organic relationship between these chgiracters. 
(6) The Honiotypic Correlations. 
The results for the 1914 season are of a very startling character ; they demon- 
strate that while the organic correlations remain nearly constant the homotypic 
correlations can suffer a very considerable seasonable modification. In other 
words the birds laid eggs very much more alike in 1914 than in 1913. The 
reader will remember that 1913 was a bad season for the birds, many young 
perished and there were few nests. On the other hand 1914 was a good season ; 
there was plenty of food, numerous and possibly stronger birds. The eggs in the 
clutches were more alike in 1914 than in 1913. , . . 
We proceeded to investigate in the first place whether the greater intensity of 
homotyposis was due to there being a far larger proportion of three-egg clutches. 
Accordingly we took only the 1st and 2nd eggs in the clutches and obtained the 
homotypic correlation for Equatorial Girth. It was '7535, for 383 pairs of eggs. 
When we took all possible pairs out of all the clutches we had 796 pairs, and the 
correlation instead of rising, fell, but insignificantly to -7469. The difference 
between 1913 and 1914 cannot therefore be due to a far larger number of clutches 
providing three pairs in the latter than in the former year. 
22—2 
