M. A. Lewenz and K. Pearson 
381 
to apply the formulae to it, shows in a sufficiently marked manner the superiority 
of the correlation formulae over Dr Beddoe's purely empirical guess-work. We 
propose to test this on two of Barnard Davis' series. We will first take a series 
of nine groups of skulls and predict their means by B^, P and L, and O.F., where 
O.F. stands for the general male formula (/) for circumferences given on p. 371 of 
this paper. In order to apply our results we have not taken Barnard Davis' 
mean values, which we have seen are unreliable, but have worked out afresh 
the means for all the </ crania in each series for which the entire system of 
characters needed are given. These characters are (i) the capacity G, (ii) the 
maximum length L, (iii) the maximum breadth B, (iv) the auricular height H, 
(v) the cephalic index /, (vi) the horizontal circumference U, (vii) the sagittal 
circumference S, (viii) the transverse circumference Q. We have obtained 
Dr Beddoe's S' from by deducting, as he asserts, 1-97 inches for the inion- 
opisthion arc, and his Q' from the intermastoid arc of Barnard Davis by sub- 
tracting 2'3 inches, as he does. We reach our auricular height from Barnard Davis' 
parietal radius by subtracting -25 inches, and our Q from his intermastoid arc 
by subtracting 2'5 inches. Only in the case of the Thais which number only 
four crania have we calculated the capacity of each individual skull and taken 
the mean result ; in all the other cases the formulae had been used on the mean 
values of the characters. The measurements are in inches except C and /. 
TABLE V. 
Mean Values of Characters in 9 Races. </ Crania. 
Eace 
No. 
C in ozs. 
L 
B 
H 
I 
V 
S 
Q 
Romans of Britain 
8 
73-3 
7-3 
5-7 
4-4 
77 
21-0 
14-8 
12-1 
Australians 
16 
67-6 
7-3 
5-3 
4-3 
72 
20'3 
14-7 
11-6 
New Hebridians . . . 
9 
72-1 
7-1 
5-1 
4-5 
73 
20-0 
14-8 
ir8 
Kanaltas 
66 
77-2 
7-0 
5-6 
4-8 
79 
20-3 
14-9 
12-8 
Marquesans 
17 
78-9 
7-1 
5-6 
4-7 
78 
20-5 
14-8 
12-5 
Netlierlanders 
16 
79-5 
7-2 
5-7 
4-5 
79 
20-7 
14-7 
12-5 
Finns 
7 
79-2 
7-0 
5-8 
4-6 
82 
20-6 
14-8 
12-7 
Russians 
11 
80-9 
7-4 
5-8 
4-5 
78 
21-2 
15-0 
12-4 
Thais 1 
1 
76-0 
6-6 
5-6 
4-85 
84 
19-8 
14-6 
13-3 
2 
1 
81-0 
7-4 
5-4 
4-75 
73 
20-5 
15-3 
12-6 
3 
1 
79-0 
6-6 
5-9 
4-75 
89 
20-2 
14-3 
13-4 
„ 4 
1 
78-0 
6-8 
5-5 
4-75 
80 
19-7 
14-9 
12-5 
Dr Beddoe's 8' and Q' are to be found from the above tabled values by 
subtracting 2 inches* from S and adding '2 inches to Q respectively. The reader 
may well ask what is the value of such an attempt to reach indirectly quantities 
directly measurable on the skull ? We should reply : Probably no value at all ! 
We have seen that the inion-opisthion arc is extremely variable and the same 
* 50 mm. — l"-97, but as Davis' values are given to inch only the yftr cannot be considered. 
