M. A. Lewenz and K. Pearson 
367 
(2) Dr J. Beddoe has recently taken up the relation of skull capacity to 
cranial circumferences and published* new formulae connecting the capacity with 
the product of three such circumferences. Dr Beddoe is a veteran who has done 
such good service in creating interest in anthropometric matters, that we should 
hardly have noticed his paper hostilely here, had he not (a) shown in it a complete 
ignorance of the nature of modern statistical theory, and (h) misinterpreted partly 
through misunderstanding and partly through faulty arithmetic Dr Lee's results. 
There is absolutely no reason why the product of three cranial circumferences 
should not be taken as a basis for estimating the capacity of the skull, but there 
is only one scientific way of reaching a suitable formula and that Dr Beddoe has 
not adopted. 
We will point out what considerations must guide us in the matter. Let us 
take first the following three circumferences of the Frankfurter Verstdndiguvg, 
U — horizontal circumference, S = sagittal circumference from nasion to opisthion, 
Q = transverse circumference from the top of one auricular passage to the top of 
the other in the vertical plane, i.e. the plane which is perpendicular to the 
" horizontal plane," and does not generally pass through the bregma. Let C be 
the capacity, and P = n'x S x Q, then we require to find a relation between G and P. 
In order to do this we must measure G and P for as many skulls of one sex and 
race as possible and then for as many races as possible to see how our formula 
changes with race. 
The process may be illustrated as follows. We take 164 Theban mummy skulls 
and pick out all those with G lying between 1380 and 1390 cubic centimetres. 
This is a group well within the probable error of capacity determination. 
We have 10 such skulls with the values for P in cubic centimetres given below. 
Now 10 cubic centimetres is about 1/11 of the standard deviation in capacity and 
we may take 500 cubic centimetres to be very roughly the same proportion of the 
variability of P. Picking out all the P's from 58,600 to 59,100 we have the 
following system : 
Capacities from 
P from 
1380—1390 
58,600 to 59,100 
63,407 
1310 
54,432 
1353 
1 54,568 
g 
1355 
^ 57,652 
1360 
58,892 
_g 
1.365 
=g 59,669 
1380 
g 60,194 
1426 
60,277 
1 
14.30 
> 60,596 
> 
1437 
62,390 
1470 
Mean 58,208 
Mean 
1389 
* " De I'Evaluation et de la Signification de la Capacity cranienne," L'Anthropologie, Vol. xiv. 
pp. 267—294, 1903. 
