92 PREVENTIVE MEDICINE 



propagation there for as long as we please, provided that we can 

 obliterate all their breeding-waters or persistently destroy all their 

 larvae which we may assume can generally be done for an ade- 

 quate expenditure. We must, therefore, ask what will be the exact 

 effect of completely arresting propagation within a given area 

 under the assumed conditions? 



The first obvious point is that the operation must result in a 

 decrease of mosquitoes. If we kill a single gnat there must be one 

 gnat in the world less than before. If we kill a thousand every day 

 there must be so many thousands less at the end of a given period; 

 and the arrest of propagation over any area, however small, must 

 be equivalent to the destruction of a certain number of the insects. 

 But this does not help us much. It may be suggested that, after 

 the arrest of propagation over even a considerable area, the diminu- 

 tion of mosquitoes within the area remains inappreciable.. What 

 is the law governing the percentage of diminution in the mosquito 

 density due to arrest of propagation within an area? 



The number of gnats (or any animal) within an area must always 

 be a function of four variables, the birth-rate and death-rate within 

 the area, and the immigration and emigration into and out of it. 

 If we could surround the area by an immense mosquito-bar, the 

 insects within it (after the death of old immigrants) would consist 

 entirely of native insects; on the other hand, if we arrest propa- 

 gation, the gnat population must hereafter consist entirely of immi- 

 grants. The question, therefore, resolves itself into this one: What 

 is what must be the ratio of immigrants to natives within 

 any area? What factors determine that ratio? 



Ceteris paribus, one factor must be the size of the area. If the 

 area be a small one, say of ten yards radius, suppression of propa- 

 gation will do little good, because the proportion of mosquitoes 

 bred there will be very small (under our assumed conditions) com- 

 pared with those which are bred in the large surrounding tracts 

 of country, and which will have no difficulty in traversing so small 

 a distance as ten yards. But if we completely suppress propaga- 

 tion over an area of ten miles radius, the case must be very different 

 every gnat reaching the centre must now traverse ten miles to 

 do so. And if we increase the radius of the no-propagation area still 

 further, we must finally arrive at a state of affairs when no mos- 

 quitoes at all can reach the centre, and when, therefore, that centre 

 must be absolutely free from them. In other words, we can re- 

 duce the mosquito-density at any point by arresting propagation 

 over a sufficient radius around that point. 



But we now enter upon more difficult ground. How large must 

 that radius be in order to render the centre entirely mosquito-free? 

 Still further, what will be the proportion of mosquito-reduction 



