Karl Pp^arson 
483 
Clearly and /Jj are so small that the distribution fulfils our condition of 
being very closely symmetrical. The nonic, equation (v) above, is : 
- 3-057,789g/ + -QOO^Slblqi + 2-858,8l7g./ 
- -009,8679/ - -754,6789,3 _ -002,501190^ 
+ -000,000,054692 - -000,000,000,005 = 0, 
the last two terms being written down to many figures to show their inappreciable- 
ness. The root required is : 
9,= -•65679, 
which by (vi) leads to : 
7^ + -558,0507 - 24-755,802 = 0, 
and provides the solution : 
Females. Males. 
70-547 mm. 80-526 mm. 
255-4 285-6 1 (A). 
3-4842 mm. 3-6944 mm. ' 
29-24 30-84 
Mean: 
Total Frequency : 
Standard Deviation 
Modal Ordinate*: 
We have now to inquire how far the same result would be reached, if we had 
supposed as a first approximation equal Gaussian components and then proceeded 
to determine a second approximation by aid of (xvii) to (xix). 
Equations (ix) give us : 
??i = = " = 270-5, 
ry, = -^3 = 7 = 4-9912, 
Thus to a first approximation : 
Mean : 
Total Frequency : 
Standard Deviation : 
Modal Ordinate : 
(7,3=3-5750. 
Females. 
70-824 mm. 
270-5 
3-5750 mm. 
30-19 
Males. 
80-806 mm. 
270-5 
3 5750 mm. 
3019 
•(B). 
(B), statistically speaking, is so close to (A) that it gives every confidence of 
a second approximation practically reproducing (A). 
We find: 
= -•020,8112, 
7' 
-026,0386, 
= -513,2871, 
\= 1-948,228. 
Biometrika x 
i/o=^=^ of the normal curve. 
v27r(r 
62 
