LOGICAL BASIS OF MOSQUITO-REDUCTION 97 



must be immigrants which have crossed over the line from the left. 

 How many mosquitoes will there now be on the right side, compared 

 with those on the left side? The following diagram will enable us to 

 consider this question more conveniently. 



First, examine the state of affairs before the drainage was effected. 

 We may suppose that mosquitoes were then breeding fairly uni- 

 formly over the whole country, and that their density was much 

 the same on both sides of the line. A certain amount of migration 



BOUNDARY 



UNDRAINED COUNTRY 



NORMAL DENSITY MLL/(Vfi 



HALF DENSITY 



DRAINED COUNTRY 



ZERO DENSITY 



-x -L 



DIAGRAM II. Curve of falling mosquito-density due to drainage on right 

 boundary. L and L are the limit of migration on either side of the boundary. 



across the line, both from right to left and from left to right, must 

 always have been going on ; and since the density was equal on both 

 sides, this migration must also have been equal and opposite that 

 is, as many emigrants must have been constantly passing from right 

 to left as from left to right. Now, after the drainage has been effected 

 the following changes occur. The insects breed as before on the left 

 of the line, and some continue as before to cross over it into the 

 drained country; but, in the latter, on the right of the line, propa- 

 gation is entirely checked and, moreover, the migration from it to 

 the left of the line, which used to exist, now ceases. Hence not only 

 must there be a decrease of mosquito-density on the right of the line, 

 due to the local cessation of breeding, but also a decrease on the 

 left of the line, due to the cessation of the migration from the right 

 which formerly took place that is to say, the drainage has affected 

 the mosquito-density not only up to the line of demarkation, but 

 beyond it. And moreover, since the migration was formerly equal 

 from both sides of the line, it follows that now, after the drainage, 

 the loss on the left side of the line due to the cessation of immigra- 

 tion from the right is exactly equal to the gain on the right due to 

 the continuance of the immigration from the left. That is to say, the 

 mosquitoes gained by immigration into the drained country must 



