128 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
I. Ratio of head-length to body-length. P= 0-13, 
or in only 13 cases in 100 would we expect to find as great 
a divergence between two samples of the one population. 
II. Ratio of position of centre of dorsal fin to body- 
Jeneth. P = <-000095, or in less than 95 cases in one million 
would we have as bad a fit. 
JIT. Ratio of position of centre of anal fin to body-length. 
P = -0003, or 3 cases in 10,000. 
IV. Ratio of position of pectoral fin to body-length. 
P = <-12, or less than 12 cases in 100. 
V. Ratio of length of dorsal fin to body-length. P = -024, 
or 24 cases in 1,000. 
VI. Ratio of length of anal fin to body-length. P = -44, 
or in 44 cases in every 100 we should expect as bad a result. 
This is a fair degree of probability. 
VII. Ratio of length of caudal fin to body-length. 
P = -096, or less than 1 in 10. 
Thus in only one of these characters have we any grounds 
for saying that there is any probability that the two groups 
of fish belong to the one population, while in most there is 
a very high degree of improbability. 
Thus we are justified, I think, in coming to the conclusion 
that, contrary to his own opinion, Matthews’ results give 
evidence of a racial distinction between the spring and winter 
herring of the Scottish coast. 
Heincke’s figures are, unfortunately, presented in such 
a form that it is difficult to get series for comparison. The 
most valuable characters for comparison are the number of 
keel-scales between ventral fin and anus (K,), and the number 
of vertebrae. Unfortunately, out of several tables dealing 
with fish from one locality we may find only two or three 
in which these are given, and it is difficult to find a fairly 
large series of autumn and spring fish from one district in 
which we can compare the characters. 
