M. A. Lewenz and K. Pearson 
Thus taking the probable error for the inion-opisthion distance in the case of 
the superior inion we see that half the population will have inions less than 45 
or more than 50 mm., while half the female population will have inions less than 
43 or more than 51 mm. from the opisthion. In the face of such a variability 
what can be said of Dr Beddoe's round 50 mm. for both sexes in his formula for 
the inion-opisthion arc ? So far as English skulls are concerned he has not got 
even to the mean value of this arc. We can only protest strongly against a 
formula which involves such a rough approximation as this being used at all — as 
Dr Beddoe uses it — when dealing with the skull; it could only be used on the 
living head supposing there were a complete want of anything better ; and this is 
certainly not the case. 
We now turn to Dr Beddoe's transverse circumference, Q' in our notation ; we 
have already seen that it is not the Q of the German or of our measurements, which 
are taken from the top of one auricular passage to the top of the other. This 
measurement is made at University College with the skull "horizontal" on the 
craniophor from the top of one ear-plug to the top of tlie other. The same 
point is vital in the consideration of the auricular height. Dr Beddoe without in 
the least troubling about this point remarks : " Le rayon parietal de Barnard Davis 
^tait je pense identiciue a la hauteur auriculaire du Dr Lee*." The parietal 
radius of Barnard Davis differs sensibly from the auricular height of the 
Verstdndigimg, and this error affects all Dr Beddoe's applications of Dr Lee's 
formulae to Barnard Davis' measurements. We consider that we should be scarcely 
wrong in allowing even as much as a quarter inch for the difference between 
the auricular height as measured on a craniophor and Barnard Davis' parietal 
radius from the centre line of the auricular passages to the most prominent point 
of the parietal. 
This is probably the best that can be done, but it only shows how idle it is to 
attempt to use non-identical systems of measurements in any enquiry of this kind. 
We may take this opportunity of strongly protesting against the use of Barnard 
Davis' measurements at all for really scientific work. To begin with his capacities 
are certainly incorrect. Dr Beddoe reduces them to what he terras Flower's values 
by subtracting but we have strong reasons for believing that his errors in 
capacity measurement are not proportional, but to a considerable extent irregular. 
Further Barnard Davis tabulates his results only to of an inch and this is by no 
means sufficient for exactitude in craniological investigation. He appears also to 
have had curious views as to which tenth should be recorded ■[". In his tables of 
results for different races he gives in his first column the number of skulls used, 
but this number does not represent the number used in finding the mean of each 
character. Hence when the total number is small, as it usually is, no use ought 
to be made of Barnard Davis' mean results for calculating the mean capacity of 
* Loc. cit. p. 271. 
t For example, in finding means, where he also stops at the first decimal, he frequently (possibly 
invariably) records 4-29 as 4-2, and there is no evidence that his individual measurements are not treated 
in the same way. 
Biometrika iii 48 
