KiRSTiNE Smith 
73 
TABLE VI. 
a 
Maximum of 
a„ — from 
three groups 
at 0 and ± 1 
iViJlXinilllTl 01 (Ty 
<J 
from distribution 
A'' 
for wliicli <p (a*) = ^ 
Maximum oi a^— — 
from distribution for 
which 0(.t) = -2797A' 
and clusters at ± 1 
Maximum of 
a/A'' 
<r„ — from 
a 
best tliree 
groups 
•0 
1-732 

3-000 
1-862 
■1 
1-738 
3005 
1-868 
■2 
1-755 
3-020 
1-886 
•3 
1-783 
3045 
1-914 
•4 
1-822 
3079 
1-954 
•5 
1-871 
3-122 
2-003 
1-845 
•6 
1-929 
3-175 
2-062 
•7 
1-995 
3-236 
2-129 
•8 
2-069 
3-304 
2-205 
•9 
2-149 
3-381 
2-287 
2-076 
determining a single constant of the function. The investigations will be carried 
out for functions of the first and of the second degree for which the standard 
deviations of the observations are 
Sj, = cr (1 + ax^), a > — 1 
or s,, = a (1 + ax), l>a^O. 
We have in (3) of Section I given the formula (8) for ct;,^ and shall here give only 
the form to which it is transferred by putting 
0(x) = A:<^(x)/(;r). 
1 1 r 
The formula analogous to that given for d'„ (G6) is 
0 
0 
0 
.... 1 
0 
1 
.... fj.^ 
i"l 
/Xj,+j 
Ms 
IH 
/'•J)+2 
H'n+2 
Hp [J"p+i /^j)+2 f^iip 
Li„ fJ-n+l H'n+2 l^p+n 
(2) For a function of the first degree 
1/ = aQ-\- ai.T , 
for which the standard deviation of an observation is 
Sy= G (1 + as?), a > — 1, 
and therefore 
^ = 1 + 2a/X2 4- a2/i4 
= 0 
.(89). 
* 
