430 
Mosquitoes and Malaria 
curves differ considerably and it is nece^saiy to proceed with Equation (i) to 
a higher degree of approximation. 
TABLE B. (Equation (ii).) 
a 
0 
44360 
10 
44808 
50 
46695 
100 
49288 
150 
52188 
200 
55450 
250 
59146 
300 
63371 
Writing Equation (i) in the form 
am ° 
and expanding the right-hand side, we have 
Vp mj 2 tnj 3 V^* mj 
pc p — m^l{p — mf ^ 1 (/) — vif 
pc 
am 
am 
p — 7 
o — m 1 {p — mf 1 (p 
pm 2 p'^m^ 3 phyi^ 
Putting z for , this may be written : 
^ pm ^ 
pc 
am 
- 2^ + - 2^ approx. 
ain 
pc 
4 2 
a 1 ,^ 
1,1, 
3 4 
approx., : 
pc^ _ c(p-m) 
2m U'ln-" ^ ^' 
The above relations cease to hold good when n< 1, i.e. when am <19'2p; 
hence the limit of applicability of the Stable Population Curve, obtained from 
Equation (iii), is given by its intersection with the hyperbola 
am = 192p. - ; > 
