MR. E, A. FISHER OX THE MATHEMATICAL 
540 
instead of 
we must write 
tlien 
hence 
0 = P log g-g 
<P = p log- £+p — 1 — g+p — 1 ; 
*' = —E—-L 
f+JP-1 
0 ==“ 
P 
g+P~ 1 
, 2 ’ 
a 2 L i 
a « 2 a 
= - 2 S(f0"-l) 
« \ £+jp—l ^+p-i 
of which the mean value is 
n , 
2 n 
- 2 (-» + 2»-l — p — 1 —l) = —— 2 > 
Oj cl 
hence 
<T,; 
2 _ 
a_ 
2n 
For one particular point of origin, therefore, the variations of the abscissa 
uncorrelated with those of a ; this point may be termed the centre of location. 
Example :—To determine the centre of location of the curve of Type IV., 
Here 
rlfcce~ vUm ( (l + f 2 ) 
r + 9 
0 = 
— v tan 1 £— ) + - ~ log I + f 2 , 
from these we find 
so that 
0' = - (v+-r + 2g) l+f , 
0 =“ 
r + 1 r + 2 r + 4 
r + 4 + ; 
i<p 
r +1 r + 2 
r + 4 +i 
£0 
</> = r + 2 l + f“ +2 (j/f—r + 2) ! + £' 
<p" r + 4 
The centre of location, therefore, at the distance from the mode, 
vU 
v + 4 
are 
