442 
Variation and Correlation of the Human Skull 
The curves we give in our diagrams are precisely similar to — showing neither 
greater nor less range than — those to which human, including cranial characters, 
closely approach in distribution, when we actually have the measurements on 
a large homogeneous population*. Hence we may fairly take them as representing 
cranial variation until more material is made available for comparison, especially 
in races of unquestionable purity. 
Adopting the notation of the memoir on skew variation j- we have the following 
system of constants for the 12 characters given in the first column, the second 
TABLE XII. 
Analytical Constants of Curves. 
Character 
No. 
Unit 
("2 
H 
Pi 
Criterion 
Mean 
Moae 
SkewnessJ 
141 
1 mm. 
34-2740 
13-5652 
3120-00 
-0046 
2-6560 
•7017 
184^91 
185-17 
- -0450 
L ? 
187 
1 mm. 
30-5756 
19-9421 
2903-14 
•0139 
3-1054 
- ^1691 
177^38 
177-07 
-0559 
B 6 
139 
1 mm. 
21-5419 
28-6959 
1561-16 
-0824 
3-3642 
- ^48 13 
134^77 
134-19 
•1247 
B ? 
181 
1 mm. 
20-8101 
1 -3987 
1125-26 
-0002 
2-5984 
•8038 
13r56 
131-51 
•0103 
H S 
134 
1 mm. 
28-9647 
32-8925 
2287-03 
-0445 
2-7260 
•6815 
135^21 
134-47 
■1385 
H ? 
169 
1 mm. 
22-5375 
21-5598 
1464-20 
-0406 
2-8826 
•.3565 
129^46 
128-91 
•1147 
OH S 
139 
1 mm. 
20-7052 
9-0319 
1449-16 
-0092 
3-3803 
- •7331 
115^57 
115-39 
•0398 
OH ? 
175 
1 mm. 
15-7281 
- 23-7639 
927-09 
-1451 
3-7477 
-ro60o 
112^57 
113-14 
-•1450 
U 
116 
3 mm. 
20-0378 
21-3658 
1120-35 
■0567 
2-7903 
•5896 
510^98 
508-97 
•0356 
u ? 
148 
3 mm. 
15-7876 
18-0031 
790-96 
-0824 
3-1734 
- ^0997 
493^92 
492-20 
•1390 
'S' s 
120 
3 mm. 
15-4-287 
6-3013 
761-12 
-0108 
3-1074 
- •,3623 
373^06 
372-51 
•0425 
s ? 
153 
3 mm. 
16-7380 
8-2974 
844-62 
-0147 
3-0156 
•0129 
364-31 
.363-57 
•0606 
Q 6 
115 
2 mm. 
25-8917 
50-4615 
1998-67 
-1467 
2-9814 
•4773 
304-29 
301-97 
•2279 
Q ? 
150 
2 mm. 
18-9225 
-2075 
1129-17 
•0000 
3-1536 
- ^3071 
296-49 
296-48 
•0011 
a'H s 
84 
1 mm. 
17-1063 
-17-9839 
788-55 
-0646 
2-6948 
•8043 
67-61 
68-35 
- ^0450 
G'H $ 
117 
1 mm. 
18-5722 
- 5-4600 
942-44 
•0047 
2-7323 
•5494 
65-05 
65^23 
- ^0422 
84 
1 mm. 
3-7738 
1-4915 
38-7783 
•0414 
2-7229 
•6783 
25-17 
24^91 
•1333 
NB $ 
116 
1 mm. 
3-0685 
1-0370 
28-1413 
•0372 
2-9888 
•1341 
24-28 
24-10 
•1010 
NH $ 
88 
1 mm. 
8-9208 
- 2-6028 
250-32 
•0095 
3-1455 
- ^2623 
49-04 
49-17 
- ^0450 
NH ? 
121 
1 mm. 
10-2777 
- 1-5166 
265-10 
-0021 
2-5097 
•9870 
46-69 
46-81 
- ^0359 
BiL S 
137 
1 point 
7-7552 
2-9348 
151-05 
-0185 
2-5114 
r0326 
72-97 
72-67 
•1087 
BIL ? 
181 
1 point 
9-4455 
4-6788 
261-60 
-0260 
2-9322 
•2136 
74-23 
73-96 
•0868 
HIL $ 
131 
1 point 
7-2499 
4-2003 
166-40 
-0463 
3-1658 
- ^1926 
73-47 
73-20 
•1013 
HjL ? 
159 
1 point 
8-6228 
5-5811 
219-76 
-0486 
2-9556 
•2345 
73-31 
72-96 
•1196 
column gives the number of skulls upon which the calculations were based ; these 
neither in total number, nor, if in total number, as individuals, are identical with 
those used for the results in Tables and V''. Thus the means and variabilities 
differ slightly, but always within the limits of probable error of random sampling. 
* See for example : Bavarian Skulls, Cephalic Index. Phil. Trans. Vol. 186, A, p. 388 and diagram ; 
Biomctrika, Vol. i. p. 158. Breadth and Height of Head in Criminals, Biometrika, Vol. i. pp. 183 — 5 
with diagrams. 
t Phil. Trans. Vol. 186, A, pp. 343—414. 
J Skewness = distance from mean to mode divided by the standard deviation. 
