C. D. Fawcett 
455 
heterogeneity, errors of sexing, and clustering due to family entombments to these 
factors, we find that cranial characters do not provide the same sound basis for 
investigation that is provided by a small series of long bones. Nevertheless this 
fact in itself — irregular and low correlation of cranial characters — is of great 
importance and well worth ample demonstration. If craniologists as a body would 
once realise it, many wide generalities which now pass muster as craniological laws 
would be tacitly dropped. We may more or less safely argue from one race to a 
second in a long bone result, but it is almost impossible from a minute study of 
the individual crania of one race to argue as to what will hold for the crania of a 
second race. These low correlations of cranial characters and their divergent values 
from race to race seem to indicate that if the skull has been the subject of 
extremely stringent and varied selection, then this selection has not tended in 
the direction of relative pi'oportioning of parts. 
In calculating the correlation of cranial characters a selection had to be made 
among the 47 characters, the means and vaiiabilities of which had been dealt 
with — otherwise we should have had 1081 possible pairs of characters to consider, 
and the arithmetic involved would have been interminable. Accordingly some 37 
pairs of characters were taken as being those of special interest, and their correla- 
tion coefficients calculated for both sexes. In all these cases since the series are 
small it was considered best not to group the measrirements into correlation tables 
but to proceed to the coefficient by calculating the sum of the products of the 
actual pairs of measurements. This involved considerably more labour, but it 
makes the results somewhat more reliable. It also frees us from the danger of 
drawing hasty conclusions from the graphical presentation of correlation results 
exhibiting the wide eccentricity due to the random character of small samples 
(see p. 425 footnote). 
TABLE XIII. 
Correlation of Naqada Cranial Characters. 
Pair of 
Characters 
No. 
No. 
? 
Pair of 
Characters 
No. 
No. 
? 
LkH ... 
L&lB ... 
B&R ... 
134 
139 
129 
•489 + -044 
■344 ±-050 
•273 ± •OSS 
163 
183 
163 
•283+^048 
•143 + ^049 
•1 19 ± •0.52 
HIL&NBINH ... 
HjL & 0.,IOi{L) ... 
i H/L & Oo'OiiR) ... 
HjL & G\|G.^ 
71 
70 
73 
59 
-•050 ±-080 
•175 + -078 
•170+^077 
•148f086 
107 
100 
102 
87 
-•132+ -064 
- ^002 + ^067 
-•016 + ^067 
-•041 ±^072 
G&H ... 
C&B ... 
C&L ... 
C&Q ... 
c&u ... 
U&Q ... 
86 
89 
89 
84 
84 
84 
•642 + ^043 
•434 + -058 
•501 + -054 
•656 + -042 
•681 + -040 
•512 ±-054 
114 
123 
123 
118 
115 
115 
108 
112 
116 
105 
101 
•519 + ^046 
•532 + ^044 
■599 +^039 
•603+ •0.39 
•723 + -030 
•454 ±^050 
BjL&NBjNH ... 
BIL&0.J0^(L) ... 
B/L & OJOiiR) .. 
\BIL&GJG^ 
75 
72 
74 
60 
- -148 + -076 
•106 + -079 
•165 + ^076 
•317 ±-078 
110 
102 
104 
88 
-•050 + ^064 
- -085 ± -066 
- ^036 + •oee 
•109f071 
NBjNH & (9„/0i (Z) 
NBjNFI & fX/Oi {R) 
NBjNH & a,/6r'i ... 
77 
76 
67 
-•276 + ^071 
- •323+^069 
-•194 ±-079 
111 
113 
97 
-•263 ±-060 
- ^279 + ^059 
•026±^068 
Oi & a, (Z) 
Oj & C»2 {R) 
NB & NH 
(?j & 6^2 
G'H& GB 
81 
82 
84 
73 
77 
•434 + ^061 
•405 + ^062 
•343+ 065 
•202 + -076 
•385 + •oes 
•477 + ^050 
•510 + ^047 
•125 + ^061 
•501 + -049 
•479 + •OSO 
G.^IG^ & a,/Oi (Z) 
(?2/(?i & OljO^ (R) 
62 
65 
•118 + ^085 
•177 ±-081 
93 
94 
■108 + ^069 
•216 ±-066 
