290 On the Systematic Fitting of Curves 
and hence by (ix) 
^j = 0, = 5-449,636, /X3 = - 3-472,584, /ti, = 90-747,281. 
It will thus be seen that the determination of the four ijus about the mean 
neither a long nor a difficult process. I will now proceed to find them de novo 
applying (viii). 
Grade 
Frequency 
Z 
X 
Zx 
Zx"^ 
I. 
II. 
III. 
IV. 
a 
0 
2000 
0 
0 
0 
0 
b 
2 
1998 
1 
1998 
1998 
1998 
c 
7-5 
1990-5 
2 
3981 
7962 
15924 
d 
11-5 
1979 
3 
5937 
17811 
53433 
e 
21-5 
1957-5 
4 
7830 
31320 
125280 
f 
55 
1902-5 
5 
9512-5 
47562-5 
237812-5 
9 
104-5 
1798 
6 
10788 
64728 
388368 
h 
182 
1616 
7 
11312 
79184 
554288 
i 
271-5 
1344-5 
8 
10756 
86048 
688384 
J 
315 
1029-5 
9 
9265-5 
83389-5 
750505-5 
h 
337 
692-5 
10 
6925 
69250 
692500 
I 
293-5 
399 
11 
4389 
48279 
531069 
in 
204 
195 
12 
2340 
28080 
336960 
n 
127 
68 
13 
884 
11492 
149396 
P 
49 
19 
14 
266 
3724 
52136 
19 
0 
15 
0 
0 
0 
The chordal areas are here : 
Chordal area of Z = 17,989, 
Zx = 86,184, 
Zx'^ 580,828, 
Za? = 4,578,054. 
Whence by (xi) with the as zero, the moments about one end of the range : 
/i/ = 8-9945, 
fM,' = 86-350,667, 
,M,'= 871-242, 
yti/ = 9156-074,667. 
