December 1, 1905.] 



SCIENCE. 



691 



equally favorable to the propagation of 

 gnats (or of any other animal) ; and sup- 

 pose that every point of it is equally at- 

 tractive to them as regards food supply; 

 and that there is nothing, such for instance 

 as steady winds or local enemies, which 

 tends to drive them into certain parts of 

 the country. Then the density of the 

 gnat population will be uniform all over 

 the country. Of course, such a state of 

 things does not actually exist in nature; 

 but we shall nevertheless find it useful to 

 consider it as if it does exist, and shall 

 afterwards easily determine the variations 

 from this ideal condition due to definite 

 causes. Let us next select a circumscribed 

 area within this country, and suppose that 

 operations against the insects are under- 

 taken inside it, but not outside it. The 

 question before us is the following: How 

 far will these operations affect the mosquito 

 density within the area and immediately 

 around it? 



Now the operations may belong to two 

 categories — those aimed at killing the in- 

 sects within the area, and those aimed at 

 checking their propagation. The first can 

 never be completely successful ; it is in fact 

 impossible to kill every adult winged gnat 

 within any area. But it is generally pos- 

 sible to destroy at least a large proportion 

 of their larvce, which, it is scarcely neces- 

 sary to remind you, must live for at least 

 a week in suitable waters, and which may 

 easily be killed by larvacides, or by empty- 

 ing out the waters, or by other means. This 

 method of checking propagation consists, 

 in the case of these insects, of draining 

 away, filling up, poisoning or emptying out 

 the waters in which they breed. Obviously 

 the ultimate effect is the same if we drain 

 away a breeding pool or if we persistently 

 destroy the larvss found in it; though in 

 the first case the work is more or less per- 

 manent, and in the second demands con- 

 stant repetition. If we drain a breeding 



area we tend to produce the same effect 

 at the end of a year as if we had destroyed 

 as many gnats as otherwise that area would 

 have produced during that period. Thus, 

 though we can not kill all mosquitoes 

 within an area, even during a short period, 

 we can ahvays arrest their propagation 

 there for as long as we please, provided 

 that we can obliterate all their breed waters 

 or persistently destroy all their larvee — 

 which we may assume can generally be 

 done for an adequate 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 opera- 

 tion must result in a decrease of mos- 

 quitoes. 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 propaga- 

 tion over even a considerable area, the 

 diminution of mosquitoes within the area 

 remains inappreciable. What is the law 

 governing the percentage of diminution in 

 the mosquito density due to arrest of propa- 

 gation 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 propagation, the gnat 

 population must hereafter consist entirely 

 of immigrants. The question, therefore. 



