212 Table of the Gaussian ''Tail" Functions 
the Table. We take out from his Tables, pp. 244 — 248, the diameter of head of 
femur for 174 male bones. 
Diametei- of Head in mm. . . . 
45 
46' 
47 
4S 
Jf9 
50 
51 
52 
53 
54 
55 
Frequency 
9 
10 
33 
17 

38 
20 
18 
12 
6 
8 
3 
The constants of this distribution are 
Mean = 49-14, cr = 2-377, i\^=l74. 
Truncating at 47 '5 we have 
2^ = 3-4341, = 2-7869, 
whence i^-^ = -4422, and from the Table 
/i' = -679, -</r2 = -908, ■»/r3= 1-331. 
These lead to A = 1-7182 
and Mean = 49-22, o-= 2-530, iV^=162, 
i.p. to a "tail" of 40 not one of 52 below 47*5. Actually this tail disti'ibutes itself 
a^ follows : 
i Under 45 45 ^6 lf[ 
\ Gaussian tail 5 6 12 17 
Against Parsons' 0 9 10 33 
This confirms our previously expressed view that probably a considerable 
number of the bones classed as 47 mm. are really female femora, and that the 
male distribution runs considerably beyond 45 mm. into the range treated as 
purely female. 
Finally let us try the result of pooling male and female bones and breaking up 
the composite frequency by the method of Phil. Trans. Vol. 185 A, p. 84. 
We have now 279 bones distributed as follows: 
Diameter of Head ^ 
in mm. ( 
36 
37 
38 
39 
40 
4i 
4f 
J,3 
44 
45 
46- 
47 
Jf8 
49 
50 
51 
52 
53 
54 
55 
Total 
Frequency 
1 
1 
4 
10 
18 
16 
24 
13 
23 
13 
33 
18 
38 
20 
18 
12 
6 
8 
3 
279 
The constants are Mean = 46-63, S.D. = 3-93, 
M2 = 15-4040, /i3 = - 6-7791, 
/i4 = 541-5162, /is =-530-5339. 
The nonic is 
q.^ - b-mi^qJ + -0689^^./ + 9-8357g./ - 3-4275g,/ - 8 2041g/ - -3020^/ 
+ -0144^2 ~ -0097 = 0, 
giving the root §2= — 934 and jt>3 = — 9-34, 
