8 Proceedings of the Royal Society of Edinburgh. [Sess. 
measured by the standard deviation, the males, as judged by the first two, 
are more variable than the females, but are less so for height. 
A consideration of the indices shows that for the cephalic index the 
males are more variable than the females, but less so for the height and 
breadth-height index. 
The results arrived at for the unsexed skulls under all three indices 
give more variable values than for either sex, excepting for the height 
index, where the value is less variable. 
The coefficient of variation is a percentage measurement of the 
variability, and, according to Pearson (7), the true criterion for relative 
variability in both sex and race. On comparing the coefficient of variation 
for length and breadth, the males are seen to be more variable than the 
females, but less so for height, as is borne out in each case by the standard 
deviation, as can be seen from Table II. 
The test of homogeneity or purity of race is, as already shown, according 
to Pearson (11), a standard deviation of length for male skulls of 6*0, and 
a coefficient of variation of 3*0, and of about the same values for breadth. 
The standard deviation and coefficient of variation values for length of 
the male Australian skull are higher even than those given by Pearson, 
but the values for breadth fall within his range (Table II.). 
The evidence, therefore, from Pearson’s standpoint indicates, when the 
test is applied to length, that the Australian is an “ impure ” race, but a 
“ pure ” one when gauged by the values obtained for breadth. 
Turning now to the coefficient of correlation (Table IV.), a higher value 
of correlation is found for unsexed skulls than for either male or female 
skulls, and it is higher for males than for females. 
The most highly correlated pair of dimensions for unsexed and male 
skulls are length and height, and the least correlated pair are length and 
breadth ; while for female skulls breadth and height are the highest, and 
length and breadth the least. 
If we turn now to a comparison of the variability in length and breadth 
of skull as represented by Table III., which records, as far as I am aware, 
all the available data for comparison, it will be seen that the standard 
deviation for the length of the Australian male is higher than that for any 
other males in the series, while that for Australian females is the lowest, 
with one exception, viz. that for the Melanesians — positions also borne 
out by a reference to the coefficient of variation. 
The comparison of the standard deviation of breadth places the 
Australian male between the Aino, Naquada, Tasmanian, and Melanesian 
on the one hand, and the Bavarian, Whitechapel English, and Paris Cata- 
