E. Y. Thomson, J. Bell and K. Pearson 
61 
general reduction of variability for the absolute characters as shown by Table II 
is about Now the effect of double selection on the variation of two characters 
is known to be given by the formula 
" Vl - r,/ (1 - /.r) V 1 - r,f ( 1 - /x^) ■ 
See Biometrika, Vol. vi. pp. Ill — 2. 
Putting /'la = "64 and /ij = = i, we find 
Turning to the last column of Table IV, headed Ratio P. Q.jN. Q., and omitting 
the pair A and D, we find the mean value of the ratio of the correlation coefficients 
of the remaining 12 pairs to be 2"68. This is sufficiently near to 2'77 for us to 
conclude that the decrease in correlation, when we pass from general population 
to a nest population, is quite compatible with the result which naturally flows 
when we look upon the nest as a selection of reduced variability made from the 
general population. It will indeed be noted that the three least correlation 
ratios involve A and D, the characters which correlated together give the 
exceptional case of a reduced variation when we pass from the general to a nest 
population. Can any explanation be offered of this anomalous case ? To begin 
with, the possibility of a stringent winter selection of these characters so that the 
correlation would be reduced below that of a nest is hardly tenable. Table II 
shows us that the variability ratios for the A and D characters are above the 
average. They ought therefore to show reduced correlation for the nest as com- 
pared with the general population. I would draw attention to the fact, however, that 
A, the total length of wing, and D, the breadth, are the two characters which are 
most likely to be affected by wear and tear of the wing. All damaged wings on 
which the measurement of J. or 7) was difficult or impossible were, of course, 
omitted. But it will be clear that the measurement of internal cells is less likely 
to be influenced by any action of the nature of weathering than these external 
measurements. The possibility is therefore before us — we do not lay much stress 
on it — that in the reduced correlation of the length and breadth of the wing, we 
have the one definite effect of the hibernation. At the same time, the fact that 
we do not find a reduced correlation in the case of right and left wings for either 
the characters of length or breadth (see Table V) is somewhat against this 
hypothesis. It would indicate that the action, whatever its character, is the same 
for the lengths of both wings or for the breadths of both wings, and can be nothing 
of the nature of local wear, affecting one wing here and another there. 
* Actually {Biometrika, Vol. vi. 112) /x should be found from 
2i2 = .riVi^ { 1 - rr/{l - m./)}/{1 - vy/ (1 - ^i^) (1 - ^2^) } 
by putting Si/tri = variability ratio for the characters taken weighted with the number of times they 
are taken. But the r-i^^ terms have little effect, e.g. if 2i/(ri=-5, /ti = ^.2="o3, and with this value 
iJi2/ri2 = 2-52 which is of the same order. In fact the observed mean value hes between the values 
of Jii2/ri2 for // = -50 and /i = -53. 
