390 Measurement of Internal Capacity of Skull 
random* C. Fawoett's Naqada, T. Ranke's ' Altbaierisch ' and E. Schmidt's Theban 
mummy measurements. We have applied Dr Lee's mean formula for individual 
crania f. ^3 and the general formula were used as in the series of Table XI. It is 
impossible to print all the measurements and results for these 45 skulls but the 
general conclusions are given in the table below : 
TABLE XIV. 
Results of the Three Formulae for 4-5 j/" Crania. 
Series 
Quantity 
P and L 
G. F. 
Naqada Series 
Mean Error 
64 
50 
51 
Altbaieriscli Series ... 
Mean Error 
50 
62 
49 
Theban Series 
Mean Error 
49 
46 
42 
Wliole Series ... 
Mean Error 
Range of Error 
54 
+ 245 to - 169 
5.3 
+ 141 to - 164 
47 
+ 148 to - 165 
For a brachy cephalic race as we see from the table Dr Beddoe gains by his 
cephalic index correction and this is the source of his advantage over P and L for 
the Altbaierisch. But for a dolichocephalic race like the Naqada or Theban he 
loses ; thus his biggest negative error arises in the case of the largest Naqada skull 
where his correction for cephalic index still further reduces his underestimate. 
On the whole again we see that the advantage lies with the correlation formulae. 
Summing up our results we should say that for the skull : 
(i) Intra-racial and inter-racial formulae can be found for circumferential 
measurements which are superior, or at any rate equal to Dr Lee's diametral 
formulae. 
(ii) Such formulae give better results when their constants are found by 
statistical theory than by mere guesswork. 
(iii) The vagueness of the inion as a point of measurement renders it of the 
greatest importance that the sagittal arc should be measured from the opisthion 
and not from the inion. 
(iv) It is conceivable that a double regression formula would work better than 
a single regression formula like P and L or our present G. F. But it will hardly 
be obtained by taking as the second variable the product / x U x Q x 8. 
(v) Probably the best inter-racial results will be obtained by non-linear 
regression formulae based on a single product. 
* For the mummies every tenth skull starting with No. 489 of the Catalogue was taken ; for the 
Naqada every tenth skull so far as possible, allowing for the mixture of i and ? on the list ; for the 
Altbaierisch,' every fifth as far as the requisite data were provided, 
t C = -000337 Lx£xi? + 406-01. 
