H. Waite 
425 
and therefore, for the end of the month 
Din = >l>oR'' + J _ (A). 
Now, for any particular month n = fsbaim where m is the number of cases at 
the beginning of the month, (or the average number for the first half of the 
month and the second half of the previous month) ; and Professor Ross has 
estimated the approximate values of the constants f, s, b, i to be \,\, and ^ 
respectively ; hence 
n = ^- ^ - ^ am 
4 ■ 3 ■ 4^ ■ 4 ■ 
am 
also r == '2063 when ?i :j> 1, . 
, X -100343 , 
and log (1 —r)= when n <j: 1. 
We can thus by successive applications of the formula (A) obtain a series of 
values of m at the ends of consecutive months when we know^ the value at the 
beginning of the period, the total population and the average number of 
anophelines in the neighbourhood. Although it is impossible to estimate this 
last quantity with any degree of accuracy, yet by comparing the results of 
numerical examples, using different values of a, we get an idea of the effect on the 
malaria rate of reducing the anophelines in any given proportion. 
Condition for a Stable Population. Suppose that a certain locality has a 
population p and cases of malaria. This latter will remain stationary if the 
number of new cases is equal to the number of recoveries. With a given value 
of mo and p the number of new infections depends on the number of anophe- 
lines in the neighbourhood. Hence with the anophelines present in a certain 
proportion to the human population, the malaria rate is stationary and if they are 
present in a greater or less proportion there will be a corresponding increase or 
decrease in the number of cases. 
Let be the number of cases at the end of the month ; then, by Equation (A) 
mi = ?Ho-K" + YZTJi' 
The value of m is stationary if = = m, i.e. 
1 — i2™ 
jither 1 - i2« = 0 (i), 
1 
0 
