J. F. Tocher 
175 
Whether migrants from these counties partly account for the excess of medium 
eyes in Glasgow or not, excess of medium eyes is associated with densely populated 
centres and is accordingly dealt with in the section discussing the relationship 
between density of population and colour. It should be finally noted that the very 
sparsely populated regions, all of them having an excess of blue eyes, are inhabited 
by a people who have been undisturbed by any recent immigrations and who most 
probably are descendants of a race long resident in the country. 
The accompanying table (Table XXV.) gives a synopsis of the results respect- 
ing the relative divergency in eye colour, in the divisions, counties and districts 
respectively. 
(8) Glass Segregation. The Nature of the Distribution of Relative Local Differ- 
ences of each Glass considered collectively and interlocally, without reference 
as to where they occiir geographically, and the Degree of Segregation of each 
Glass determined. 
I. Interlocal Constants. It has been shown (Section 6) that, in each colour 
class, differences occur throughout the country in localities (specifically pointed 
out, in each case, in the section referred to), which are distinctly significant. 
Positive differences, much in excess of the expected, occur in contiguous areas, 
indicating a differentiation for each class more or less from the remaining 
population. That is, the existence of these individual local differences proves 
that the population is not an evenly distributed one with respect to the colour 
class or classes under consideration. It is true that many of the differences could 
quite well occur at random and therefore that many localities resemble the 
general population with respect to one or more classes. But those larger differ- 
ences, reckoned significant owing to the great odds against their occurring at 
random, quite upset the proposition that the distribution of the class over the 
whole country is a random one. Having indicated the localities where individual 
significant differences occur (thus proving segregation) and also those where non- 
significant differences occur, the differences for each class collectively will be 
considered without reference as to where they occur geographically in order to 
compare the degrees of segregation of the classes. It will then be seen which class 
has the greatest geographical separation. It is therefore necessary to provide a 
measure of local segregation, that is to say, one must have a single common 
measure, for each class, of the extent of the deviation from a uniform distribution 
of persons belonging to the class over the whole country. This measure is easily 
obtained when it is remembered that the relative local differences are all the local 
differences reduced to a common scale by dividing each difference by its standard 
deviation. Since this is the case, if the differences are such as would arise from 
a uniform distribution of the persons belonging to each class all over the country 
these differences as a series would of course form a normal distribution with a 
'67449 '67449 
mean value /t = 0 + — ; — , and a standard deviation s = 1 + —tt^s , where a is 
V9 V(2?) ^ 
the number of groups (either counties, districts, or units of area) considered. Thus 
