222 Pigmentation Survey of School Childre7i in Scotland 
type is defined as meaning a population which has been isolated and has bred 
within itself in an environment unsuitable for the production of hair pigment for 
a sufficient length of time to ensure that every individual will be fair-haired, it is 
obvious none of the northern races are pure races of the blonde type. They have 
relatively large sections in their respective populations which are pigmented. 
Similarly if by a pure race of the dark-haired type is meant a population which has 
bred within itself in an environment suitable for the production of hair pigment 
for a sufficient length of time to ensure that every individual was uniformly 
pigmented dark, it is clear the southern Italian race is not a pure race of the 
dark-haired type. The Italian people are largely of the brown or intermediate 
type (about 60 per cent.); 31 per cent, or nearly one-third are dark; about 
S per cent, are fair. If all the races of mankind were uniformly pigmented or 
non-pigmented, hair colour would cease to be one of the tests of race. But this 
is not the case and the problem is : how far can one use colour as a test of race or 
of racial purity ? One must in the first place consider whether in conjugal unions 
between the fair and dark types blended or exclusive inheritance holds, or whether 
both exist. It is clear from observation that blended inheritance does exist for 
fair and dark hair colours, the shades of brown being the blend. What is wanted 
is a measure of the blended inheritance in this case. From observation it is 
possible that exclusive inheritance exists in the case of red hair. But the main 
point here is that, in hair colour, one has a problem in blended inheritance. 
Now granting equipotency of the two types, fair and dark, and random mating 
with respect to hair colour as well as other forms of mating as probable, and it is 
obvious that varying proportions of fair, dark and the shades of brown hair will 
occur in the population of a country according to the proportions of the fair and 
dark types originally settling in that country. Is anything known of an exact 
nature as to the distribution of colour in the offspring of fair and dark parents, i.e. 
of parents one dark and one fair? Insufficient data exist to show the exact nature 
of the distribution. A large number of carefully made observations are required. 
Individual cases can be cited. (A) Dark-haired, and (B) fair-haired, have a family 
of five. One is fair, one is dark, three are medium. All are children, but the 
oldest, classed medium, is getting darker and will probably be dark. To be 
accurate one must compare the colour of the parents when they luere children with 
the colour of the offspring as children ; or the colour of the parents with the colour 
of the offspring as adults. Can it be said that the most probable distribution of 
colour in the offspring of such parents, granting blended inheritance and equi- 
potency in determining pigment, is, in say a family of four, 1,2, 1 ; one fair-haired, 
two medium and one dark-haired ? The object of science is to give a shorthand 
description of the facts. In this case the expanded binomial + is put 
forward tentatively as the shorthand description. If true it is a problem like deter- 
mining the number of times two heads, one head and no heads, will turn up in 
spinning two coins together. The most probable distribution in this case is, 1, 2, 1. 
Can hair colour in Scotland be cited as an example of this simple binomial distri- 
bution, similar to the Mendelian example in the crossing of peas ? This has to 
