436 
Mosquitoes and Malaria 
no stable condition and the malaria cases will gradually decrease and finally 
disappear. 
The differences are : (c) the number of cases in the " stable population," 
corresponding to a given number of anophelines, is higher in Professor Ross' 
treatment than in mine, and {d) tl)e changes in the malaria rate are more rapid ; 
e.g., in a particular example, where the population is 1000, the number of 
anophelines per person 100 and the initial number of cases 500, we have : 
Months 0 1 2 3 4... finally 
Cases (Eoss) 500 525 544 560 571 600 
„ (Waite) 500 512 521 529 535 556 
The divergence seems to be chiefly due to the difference in the time units 
employed in the two methods of treatment. Professor Ross has used the month 
throughout and has taken the value of m constant during each month, while 
I have used the average time between two consecutive infecting bites as my unit. 
The fact that m is increased by unity each time a healthy person is bitten by an 
infected mosquito and is continually being diminished owing to recoveries, fully 
justifies, in my opinion, the adoption of this unit. 
Part of the difference (d) is easily accounted for as follows : Suppose m is 
increasing; then in finding mj+i from m^, the number of new cases obtained by 
Professor Ross is too great ; for iiig is the smallest value of m during the month, 
and therefore the chance of malarial sufferers being bitten again is greater and 
that of healthy persons being infected less than that found. Again, the number of 
recoveries found for the month is, for the same reason, too small, and thus both 
causes combine to make the value of m^+i too great. 
Similar reasoning shows that when the malaria is decreasing the value found 
for mg+T, is too small ; i.e. in both cases the changes in the malaria rate are too 
rapid. It is evident, however, that the difference on this account becomes smaller 
as the stable value is approached. H. W.] 
