H. Waite 
481 
Part of this hyperbola is shown on the left of Diagram I as a broken line 
from which it appears that in a population of a thousand, there can be no stable 
condition with a smaller average number of infected persons than about 4-5. 
The numbers in Table A are all found for a population of a thousand, but the 
general form of Equation (iii) is applicable to a population of any magnitude so 
long as the number of infecting bites does not fall below one per month. For 
example, when p = 20000, and vi = 200, Equation (iii) gives a = 893941, while the 
formulae on p. 42G give a = 893966, the difference being less than '003 per cent. 
It will be of interest to compare the values of a found from E(|uation (iii) with 
those of Table A in a few typical cases : i 
a, by Equation (iii) 
a, from Table A 
10 
42554 
42553 
50 
46249 
46251 
100 
49067 
49069 
500 
88676 
88680 
In the last three cases the term - f*'^ is negligible, while in the last case 
12m-^ o o 
the term ~- is only about "01 per cent, of the whole. 
2m ^ 
Numerical Examples. In the numerical illustrations which follow, the increase 
or decrease iu malaria, month by month, has been obtained by successive applica- 
tions of Equation (A), p. 425, in the form 
1 - 
ms = m,_,R,^\ 
where ? 
1- R, 
192p' 
Rs = l-^-y\, 
P 
1 n ^ -100343 . 
log(l-n) = ~ [n>l\ 
n = -2063 [n :}> 1]. 
Seven-figure tables have been used throughout in the calculations but the 
results are given to one place of decimals only. 
[Note. It is assumed, in all the examples, that Professor Ross' recovery rate 
holds. This would rapidly reduce a large number of cases to the vanishing point 
in the absence of new infections, whereas it is well known that a few persons 
suffer from relapses after living many years in countries where there is no 
iibility of re-infection. (See Report, p. 16.)] 
55—2 
