492 FRETS, THE INDEX CEPHALICUS. 
cability of the normal curve, that FAWCETT, MACDONELL, PEARL 
a. o. (p. 485) found, is restricted to short series of distribution (p. 304). 
A further investigation of this question will have to consider, 
if the biological fact that brachycephaly is dominant over dolicho- 
cephaly may explain the skewness of the curve. 
There remains one irregularity in the Swedish material that may 
be due to faults of it. There are too many low indices (up to 
index 63), and also too many very high indices (higher than 85). 
The range of the material is 42, of the calculated one 26. In the 
Swedish material a few pathological forms have been inserted 
probably (see also RETZIUS and Fürst, p. 104). Yet we must think 
here of the warning of PEARSON (ELDERTON 1901, p. 157 cited 
from PEARSON) that a theoretical probability curve without limited 
range will never at the extreme tails exactly fit observation. 
According to Rerzius and Fürst the mean index is 75.855 (we 
found 76.122). With regard to this figure we must consider that 
Retzius and First have subtracted from the values for the head- 
index two units to get the values for the skullindex. Moreover 
they have rounded off the indices to wholes by omitting the figure 
bebind the decimal. In order to compare my results with those 
of RETZIUS and First my indices must be diminished with two 
or three units (see also p. 506). 
The standarddeviation of the Swedish material is + 3.08; of 
my material of men, it is + 3.22 and of adult men + 2.985 
(see p. 499). So the variability of the Swedish material is not 
smaller than of my material (PEARL 1905, p. 47, 48). 
Moreover table 2 contains the material of 900 Bavarian skulls, for 
which ELDERTON (1901) of the Biometrican School has calculated 
the normal distribution. We see, that my calculations according 
to YULE (also according to QUETELET) agree very well with those 
of ELDERTON. 
The result of the inquiry of the variability of our material is, that the 
headindex with men is 80.4 + 3.22 and with women 81.04 + 2.99, 
So these values with the standarddeviations show still more distinctly 
than those from the calculations of GALTON’s quart les, that the 
mean headindex of men is somewhat smaller than that of women 
and that the variability is larger in men than in women. 
