J. F. Tocher 335 
TABLE XVII. 
Males 
Red 
Fair 
Medium 
Dark 
Totals 
Aberdeen 
8 
16 
78 
132 
234 
Remaining Po|)ulation ... 
58 
259 
2444 
1240 
4001 
Totals 
66 
275 
2522 
1372 
4235 
In a private communication* Professor Pearson gives the following eiiuivalent 
formula in terms of -^-j and thus obviates the necessity of determining each ')(^'-. 
If N = number in the general population and n = number in an}' locality : 
the measure of the divergence of the local group from the remaining population. 
Thus = ;!^'- (1 — «/iV), and Q, the divergency coefficient, is determined directly 
from ')(^^. The values of Q are given alongside those of log P in Tables XV. and 
XVI. Both sets of values are approximations, sufficiently correct to enable their 
significance to be seen on inspection. Their relationship is shown in Diagram XI. 
All values of logP > 3 (and thus, in this series, of Q > '055) are probably significant. 
A reference to the tables and to the colour divergency maps (where the values of 
Q and logP have been classed) will show that the south east of Scotland is like 
the general population in hair colour (</ and $ ) and eye colour ( $ ). Argyll, Ayr, 
Stirling and Fife, all contiguous, are least divergent among the males in eye colour. 
Generally speaking, the populous centres and environs are very like the general 
population, while in the spar.sely populated parts the divergencies are the greatest. 
Coming now to the cause of the divergencies (the excess frequencies of one or 
other of the various categories), the significance or non-significar)ce of the various 
frequencies was determined in the following manner. Let 3/5 = total number of 
inmates in Scotland possessing any particular hair or eye colour; A" = total number 
of inmates ; rn - number of inmates at any asylum, then m/]S^ y^, = ijs', the expected 
frequency. Let 3//'= the corresponding observed frequency ; y^jN = p; 1 — p = q 
then {ys' — ys)l^inpq{N — m)l{N - \) = difference between the observed and 
the expected fre(|uency relative to the standard deviation of v//' in the sample, 
m, of the population. The values of this rate for each category have been 
determined. 
It has been recently shown by Pearson f that, in a population of N individuals, 
Np of which possess a given character, and Nq do not, the distribution of frequency 
in the character for random samples of magnitude m (when m is commensurable 
* Since published. Biometrika, Vol. v. pp. 198 — 20.3. 
t Biometrila, Vol. v. pp. 172—175. 
43 ~2 
