LOGICAL BASIS OF MOSQUITO-REDUCTION 101 



quitoes which are really produced by faulty sanitation in the town 



itself. 



Another and similar statement is often made with all gravity to 

 the effect that mosquitoes are brought into towns in trains, carts, 

 and cabs. So they are; but a moment's reflection will assure us that 

 the number introduced in this manner must always be infinitesi- 

 mal compared with those that fly in or which are bred in the town 

 itself. Moreover, if vehicles may bring them in they may also take 

 them out. 



I will now endeavor to sum up the arguments which I have laid 

 before you --I fear very cursorily and inadequately. First, I sug- 

 gested that there must be for every living unit a certain distance 

 which that unit may possibly cover if it continues to move all its 

 life, with such capacity for movement as nature has given it, always 

 in the same direction. I called this distance the limit of migration. 

 It should perhaps be called the ideal limit of migration, because 

 scarcely one in many billions of living units is ever likely to reach 

 it not because the units do not possess the capacity for covering 

 the distance, but because the laws of chance ordain that they shall 

 scarcely ever continue to move always in the same direction. Next 

 I endeavored to show that, owing to the constant changes of direc- 

 tion which must take place in all random migration, the large 

 majority of units must tend to remain in or near the neighborhood 

 where they were born. Thus, though they may really possess the 

 power to wander much further away, right up to the ideal limit, 

 yet actually they always find themselves confined by the impalpable 

 but no less impassable walls of chance within a much more circum- 

 scribed area, which we may call the practical limit of migration 

 that is, a limit beyond which any given percentage of units which 

 we like to select do not generally pass. Lastly, I tried to apply this 

 reasoning to the important particular case of the immigration of 

 mosquitoes into an area in which their propagation has been arrested 

 by drainage and other suitable means. My conclusions are : 



(1) The mosquito-density will always be reduced, not only within 

 the area of operations, but to a distance equal to the ideal limit of 

 migration beyond it. 



(2) On the boundary of operations the mosquito-density should 

 always be reduced to about one half the normal density. 



(3) The curve of density will rise rapidly outside the boundary 

 and will fall rapidly inside it. 



(4) As immigration into an area of operations must always be at 

 the expense of the mosquito population immediately outside it, the 

 average density of the whole area affected by the operations must 

 be the same as if no immigration at all has taken place. 



