219 
n = 
g 
crown cover 
ìable c. 
l 
n 
P 
plots results: 
plot measure- 
. When c 
n 
P 
population, 
Developing this form gives: 
S . n . n = p.n +q.n , of which 
g p P H g 
n and n are derived as follows: 
g P 
p. n 
„ and n = —k 
,2 p ^2 
q. n 
n 
g 
& S np - q 
Sng- p 
Considering now the first of the two conditions: a minimum of cost for a given 
2 
standard error, the product CS must be developed first: 
CS = ( n c + n c ) 
g g P P 
J2_ + _£L 
n n 
g P 
n g ÜP % “g . q.c 
= —. p. c + —. q. c + —. p. c + —“ g 
n ^ g n p n p n 
g 5 p g p 
q. n 
Substituting n = ~ 2 —in order to find n , gives: 
S - p 
n 
g 
2 n g 
CS = P- c g + c l- C p + n ' P ' C 
+ —^ . c (n S 2 - p) 
p . 0 2 . n q ' g ' g 
y (n g S - p) g h & & 
p. q. c 2 
q. cp + Ö—^ + p. c + n c . S - p. c 
(n g S 2 - p) S g S g 
p. q. c 2 
q. cp + 9 + * c p- * S * 
(n g S Z - p) g S 
Differentiating for n gives: 
o 
ÉJCSZL . c s 
d n^, g 
2 p - q • V S 
(n S 2 - p) 2 
g ' 
Equating to zero: 
s 2 
(n S 2 - p) 2 
v g 
2 2 
c (n S - p) - p. q. c 
g v g vi P 
= 0 
or 
g g 
which leads to: 
. c 2 ,2 A 
c.. ( n S - p ) - p. q. c = 0, 
P • q • C