K. Pearson 
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impossible also for a curve of the McAlister-Galtou type, for the simple reason 
that that cui've has high contact at both ends of the range. Now I contend that 
the anthropologist who either neglects such matters as human fertility, or confesses 
that he has no means of succinctly describing their distributions — and as long as 
he sticks to the Gaussian curve he certainly will not have — is simply putting on 
one side a fundamental factor in the science of man. Ranke lays great stress on 
homogeneity. He does not, however, clearly tlefine what he means by the term. 
Apparently any series which follows a Gaussian curve is to him homogeneous, any 
other series is not. I should be glad if he would then consider any craniological 
series, say, of adult crania. This will involve crania of adults from perhaps 25 or 30 
years of age to 50, and these are rather narrow limits considering our paucity of 
material. Now our data show that the correlation between head measurements and 
age may be of the order of about — "1 to — "2. After about 25 to 28 years of age 
in man, there is a continual shrinkage not only of stature but of skull capacity, 
brain- weight, circumferences and diameters of the skull. Under the circumstances, 
what right have we because the Gaussian curve is obtained to call this material 
" homogeneous " ? I will go further ; suppose we could, and we can, obtain the 
measurements on one or two thousand individuals of the same age ; are these to 
be considered as a homogeneous distribution ? My reply will be, in man the 
order of birth is an essential feature in determining the dimensions of the physical 
characters. My investigations show that physique and health are sensibl}' 
correlated with the position of a member in his own family. In mammals others 
have shown that the physique of an individual is sensibly correlated with the 
number of members born in that individual's litter. Now with these facts before 
us what stress can be laid on Ranke's conceptions of homogeneity ? The practical 
anthropologist requires curves which will successfully graduate his data. Only on 
the basis of such graduations can he allow for the influence of disturbing factors 
like age, order of birth, season or special position of production in the organism. 
I take this very case : How is it possible to allow for the influence of order of 
birth, unless you know the size of families or the distribution of births within the 
community ? It can only be achieved provided the distribution can be represented 
by a few simple constants which allow of definite mathematical handling. 
Ranke and Greiner say with considerable asperity that my method of 
determining the range from given data can be of no service. Yet take this very 
case of size of families. In the English middle classes for 4390 instances, I find 
that the observed limit is 17, but fitting a skew curve the range is determined as 
22 children running practically from just before 0 to over 21 births (Fig. 2). For 
Denmark by the same process in 34,000 cases the theoretical range is 26 and the 
observed range 22*. I then proceeded to take statistics for the Argentine 
Republic, and found for the town of Buenos Ayres, 27,510 births, that the range 
of the curve was from '25 to 36 61 births, or 37 possible births. The maximum 
observed in these 27,510 births was 23. But among the South- and Mid-American 
* The Chancer of Death, Vol. i. Reproduction Selection. 
Biometrika it 
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