221 
mditure, the 
a fixed 
proportion 
P- c 
q. c 
q. c + p. c 
__e l ..._g... 
q. c + p. c 
P g 
P- c T 
q. c 
S . c 
v. c p 
,2 2 
. b . s . c 
1 c g 
n 
p 
2 
This form can be further developed, s can be written as: 
v. c 
As 
V. c 
Z < v i - v 
n - 2 
g 
U (c - c ) (v 
n n 
g g_ 
2 (v -v) 2 - b 2 z (c n -c n ) 2 
1 g g 
(n g - 2) 
I-*] 
I (Vj - V) 2 
[l<‘n - ] 2 
L g g J 
r^v (c - c ) (V. - V ) I 
n _g ^ 1 J 
we write for s' 
v. c 
Y (c - c ) 
Z_ n_ n. 
g g ± 
[y (c - c 
L 2 - n 
V. c 
(n - 2) 
g g J 
As furthermore 
2 
V. c 
[l (v i - <c n - c 
JL 
n>] 
g J 
I < v i - ^ 2>n ' )2 
g g 
r- . -,2 ... 2, 
(v. - V) (1 - r ) 
2 2 (n e' 1} 
= s v (1 - r ) 
g 
2 ,2 X 
» s v (1 - r ) . 
2 2 
Developing b .¡s c 
.2 2 
b . s 
c 
P [x {c n ~ l n > (v i"*>] T {C n ~ l * Y 
L g g J ^— D o 
Hp 
b (c - c 
n n 
(n p - X > 
g g 
2