192 Pifimentation Survey of School Children in Scotland 
this with the number of births in each division. The value, r = '782, cannot be 
taken as the true measure unless the ratio of the number of possibly fertile wives 
to the number of families is quite approximately the same in each division. The 
correlation, however, between the number of births per family and density of 
population is so high as to warrant the conclusion that fertility is really greater 
among the inhabitants of densely populated areas. Since the more densely 
populated centres are occupied by the lower classes, this is tantamount to saying 
that the lower classes are more fertile than the remaining section of the population, 
a conclusion already reached by several observers. Let now the number of births 
per family, in each division, be compared with the pigmentation data. The 
following results were obtained : 
TABLE XXXIX. 
Correlation between Pigmentation and Births per Family. 
Colour 
r 
r 
■&'(r=0) 
Hair : 
Fair 
- -936 
-3^67 
Red 
-•043 
-o-n 
Medium 
•727 
2-85 
Dark 
- •059 
-0-23 
Jet Black ... 
-•504 
-1^98 
Eyes : 
Blue 
-•775 
-3^04 
Light 
•386 
Medium 
•671 
2^63 
Dark 
•292 
1^15 
These results show that the number of births per family is greater where there 
are excesses of medium hair and medium eyes and is much less in regions of excess 
of fair hair and blue eyes. Now these results are similar to those obtained in 
comparing density of population with pigmentation except that dark eyes are 
significantly associated with density, but not with the birth rate per family. Thus 
the lower class population is associated with a higher birth rate per family and 
with an excess of medium hair and medium eyes over the general population. Is 
one to say that the medium haired, medium eyed classes are as a whole more fertile 
over the whole country ; or are only those sections of them living in more densely 
populated parts (i.e. working class sections of these classes) the more fertile ? That 
question cannot be answered from the present data, but it can be said that the 
medium haired, medium eyed and populous lower classes are more fertile than the 
remaining population, and this factor is probably operating in favour of producing 
distinct excess of these classes in the more densely populated areas of Scotland 
where they are found. 
(C) The probability that excess of medium hair in dense centres is due to 
blending. Consider first a population consisting of more or less isolated groups of 
