H. Waitb 
435 
The foregoing results point to a stable population for any given number of 
mosquitoes, but it is perfectly clear that this number is itself subject to constant 
change, often of considerable magnitude, and that, in consequence, a stable 
population is rarely, if ever, attained in practice. 
The minor contributory causes mentioned on p. 421, will also affect the 
malaria rate to an extent which cannot be neglected, while another important 
item to consider is the distribution both of the human population and of the 
mosquitoes ; also whether the most densely populated districts are at the same 
time those most infected with mosquitoes. These and many other points will 
require careful investigation with the aid to be derived from the most recent 
and complete observations before the subject can be said to be exhausted, and 
I am quite well aware that the present paper merely traverses the outskirts of an 
important and extensive field of research. ; ^ i • ■ - ■ ,: . ■ > ■ 
But still it seems to me to establish two very important points, i.e., (i) Given 
a number of mosquitoes greater than that corresponding to the " stable population 
value," the number of malaria cases will tend to increase until a stable population 
value is reached, (ii) Given a number of mosquitoes less than that corresponding 
to the stable population value, the number of malaria cases will tend to decrease 
until that stable population is established. 
In both cases the number of malaria cases tends to asymptote to the stable 
value. The amount of malaria does not increase or decrease indefinitely, but 
tends to attain a definite prevalence. Where the "stable value" means a large 
number of malaria cases, the right step seems to be the reduction of the number 
of mosquitoes ; on the other hand, where it means a small number of cases it 
should be possible to segregate and isolate these cases. 
In conclusion I wish to express my grateful thanks to Professor Karl Pearson 
for much valuable assistance in the preparation of this paper. 
[Postsc7'ipt. Since completing this paper, I have, through the kindness of 
Professor Ross, been able to see proofs of part of his forthcoming treatise on 
Malaria. From a comparison of the two accounts it will be seen that there is 
complete agreement between us on the essential and fundamental points, but some 
difference in numerical details. This difference is due to an attempt on my part 
to treat the question by fuller and more rigid mathematical methods which would 
be out of place in a treatise written from the medical standpoint, while the 
simpler methods employed by Professor Ross give results which are sufficiently 
accurate for practical purposes. 
The principal points of agreement are : (a) for a given number of anophelines 
per unit of tlie population the number of malaria cases will gradually rise or fall 
to a fixed value at which it will remain stationary, and (b) when the anophelines are 
less than a certain number (about forty per unit of the population) there can be 
