E. Y. Thomson, J. Bell and K. Pearson 
11 
was of small importance, seems to receive further justification*. If we turn to the 
correlations of absolute sizes, these appear on the average to be slightly smaller for 
the autumn queens than for the spring queens. Now the effect of reducing 
variability, i.e. direct selection of variability, is to reduce correlation. Hence if 
the sole difference of the autumn and spring queens were a rather stringent 
selection round type of the former to provide the latter, we should have anticipated 
a reduced correlation for the spring queens. Instead of this we find a slightly 
larger correlation. The only reasonable assumption to make is that there has 
been a direct selection of correlation as well as a selection round type. In other 
words, the nature of the differential selection of queens to survive the winter 
depends not only on the wings of those queens differing not widely from type, but 
on the existence of a closer relationship between the dimensions of the parts of 
the wing. The selection that has taken place tends not only to approximate the 
wing closer to type, but to leave its parts more closely correlated. We have thus 
additional evidence that natural selection is really at work in causing sensible 
differences in the wings of spring and autumn queens. 
(7) Comparison of Correlations between Right and Left Wings in the three 
Series. (Table V.) 
We notice at once that the correlations of the spring and autumn queens are 
sensibly higher (28 °/ o to 29 °/ 0 ) than those of the nest queens; in fact in only one 
case — that of the anomalous cell h for the autumn queens — is the correlation less, 
and then not sensibly less, in the nest queens. This result is exactly what we 
should anticipate — as shewn in our second study (p. 62) — if we look upon the 
nest queens as a selection of decreased variability from the general population. 
But if we look upon the spring queens as a selection from the autumn queens 
— as a group somewhat stringently selected round type as we have shewn earlier 
in this paper — we should solely on this ground expect a reduced correlation in the 
spring queens. This expectation is, however, not fulfilled, but the left and right 
wings of the two series of queens are on the average equally correlated. We believe 
this result is due to a compensating principle, i.e. not only does natural selection 
acting between autumn and spring reduce wing variability by concentrating 
on type, but there is a direct selection of proportionality in wing characters. The 
former selection tends to lower, the latter to raise the correlations of the spring 
* It should be noted that there is nothing surprising about this result if we admit a high correlation 
of the absolute measurements. Let li — x\jy\ and i-i — x-Jijo be two indices, then their correlation is 
given by 
r . . _ ^1^2^x2 + v .'h v .v-2 r v\ y-i ~ Wi.v-2 ~ WVi ? >2.vi 
Jv Xl z + v y * - 2v Xl v yi r Xl!/1 Jv^ + v^-2v X2 v l/2 r x , m ' 
Now in our cases the coefficients of variation v for the absolute characters do not differ very widely 
from each other, and the coefficients of correlation differ from -6 by small quantities e say. Thus 
roughly : 
_ ei + € 2 - e 3 - e i _ e 1 + f 2 - £3 - ^ 4 
Hence if the e's are small this is a small quantity and we might anticipate small order correlations 
for the indices. 
2—2 
