DISPERSAL OF MOSQUITOES 215 



about, to and fro, to left or right, where it wills in search of food or of mating, 

 over a country which is uniformly attractive and favorable to it. After a time it 

 will die. What are the probabilities that its dead body will be found at a given 

 distance from its birth-place ? " Doctor Eoss attacks the problem from the 

 mathematical standpoint. His address as a whole is full of interest, and may be 

 consulted on pages 89 to 102 of volume vi of the published report of the Con- 

 gress. We may, to advantage, quote his conclusions : 



" I will now endeavor to sum up the arguments which I have laid before you — 

 I fear ver}^ cursorily and inadequately. First I suggested that there must be for 

 every living unit a certain distance which that unit may possibly cover if it con- 

 tinues 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 direc- 

 tion. 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 cir- 

 cumscribed 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 partic- 

 ular case of the immigration of mosquitoes into an area in which their propaga- 

 tion had 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 operation 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. 



"5. As a general rule for practical purposes, if the area of operations be of 

 any considerable size, immigration will not very materially affect the result. 



" In conclusion, it must be repeated that the whole subject of mosquito- 

 reduction can not be scientifically examined without mathematical analysis. 

 The subject is really a part of the mathematical theory of migration — a theory 

 which, so far as I know, has not yet been discussed. It is not possible to make 

 satisfactory experiments on the influx, efflux, and varying density of mosquitoes 

 without such an analysis — and one, I may add, far more minute than has been 

 attempted here. The subject has suffered much at the hands of those who have 

 attempted ill-devised experiments without adequate preliminary consideration, 

 and whose opinions or results have seriously impeded the obviously useful and 

 practical sanitary policy referred to. The statement, so frequently made, that 

 local anti-propagation measures must always be useless, owing to immigration 

 from outside, is equivalent to saying that the population of the United States 



