374 Measurement of Internal Capacity of Skull 
hail already been published in a memoir which has been read by Dr Beddoe. We 
have in fact the following results : 
TABLE II. 
Correlation of Capacity and Cephalic Index. 
Eace 
Cephalic 
Index 
Number 
Correlation 
$ Thebans 
74-8 
187 
•15 
(J Naqadas 
73-2 
100 
•13 
^English 
74-3 
77 
•02* 
- ^15 
(J Aino 
76-5 
76 
•31 
$ Copts 
77-3 
56 
•14 
^ Etruscans 
78-5 
78 
+ 
•22 ^ 
^ French 
79-8 
56 
+ 
•14 
(J Malays 
81-9 
76 
+ 
•03 
- + •15 
(J Germans 
83-3 
100 
+ 
•20 . 
We see from this table (i) ttiat the relationship between cephalic index and 
capacity is slight and irregular, and (ii) that any formula like Dr Beddoe's which 
not only puts 70 zero but gives a value to 7.^ persistently constant in magnitude 
and sign must be erroneous. 
(5) Having shewn that Dr Beddoe's correction for cephalic index must be 
wrong for individual crania, when we pass from dolichocephalic to brachycephalic 
races, because in the former on the average the more dolichocephalic, in the latter 
the more brachycephalic individuals have the greater capacity, we turn to the 
main part of his expression (as it appears purely and simply in his first result B^, 
in which he takes the capacity solely proportional to the product p^ and ask 
whether this is reasonable. A little consideration will show how impossible it is 
that a formula of the type G = D^p^ can at all agree with a formula of the type 
G = A + D^pi to which the true theory of correlation leads us. In the accompanying 
figure the two lines are indicated. It will be seen at once that except near the 
actual mean values of p and C Dr Beddoe's formula cannot possibly give the mean 
or most probable value of any array. If, however, a small skull be taken with 
thick walls, or a large skull with thin walls, then Dr Beddoe's formula naturally 
gives a better result in extreme cases. This is the source of any advantage which 
may appear in its favour when he proceeds to select large crania, "decrits comme 
minces ou transparents," or small skulls, " decrits comme ^pais ou lourds," and 
points out that for certain such cases his rule gives a better result than Dr Lee's 
correlation formula. This he has actually done in Tables II and III of his paper f. 
The answer to such criticism is that he has obtained his advantage by causing his 
line to give bad results for the capacity of the average skull of a given product, 
i.e. he has swung it round till it makes an angle with the line of " probable values." 
Thus his guess-work formula is really only a line diverging very considerably from 
* Deduced from data provided by Dr Macdonell. The result sliows that there is sensibly no correla- 
tion between cephalic index and capacity iu the skulls here dealt with, 
t Loc. cit. pp. 275 and 276. 
