696 



SCIENCE. 



[N. S. Vol. XXII. No. 570. 



tinue as before to cross over it into the 

 drained country; but, in the latter, on the 

 right of the line, propagation 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 cessa- 

 tion 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 demarcation, 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 immigration 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 inta the drained 

 country must be exactly lost by the un- 

 drained country. This fact can be seen 

 to be obviously true if we imagine an im- 

 mense mosquito bar put up along the line 

 of demarcation so as to cheek all migration 

 across it, when, of course, the mosquito- 

 density would remain as at first on the left, 

 and would become absolute zero on the 

 right: then on removing the mosquito-bar 

 an overflow would commence from left to 

 right, which would increase the density on 

 the right by exactly as much as it would 

 reduce the density on the left. 



The dotted line on the diagram indicates 

 the effect on the mosquito-density which 

 must be produced by the drainage. If L 

 is the possible limit of migration of mos- 

 quitoes (it may be one mile or a hundred, 

 for all we know), the effect of the drainage 

 will first begin to be felt at that distance 

 to the left of the boundary line. From this 

 point the density will begin to fall gradu- 



ally until the boundary is reached, when 

 it must be exactly one half the original 

 density. This follows because of the equiva- 

 lence of the emigration and immigration on 

 the two sides. Next, as we proceed from 

 the boundary into the drained country, 

 the density continues to fall, until at a 

 distance L on the right of the line, it be- 

 comes zero, the country now becoming en- 

 tirely free of mosquitoes because they can 

 no longer penetrate so far from the un- 

 drained country. 



In the diagram the line giving the mos- 

 quito-density falls very slowly at first, and 

 then, near the boundary, very rapidly, sub- 

 sequently sinking slowly to zero. ^ The 

 mathematical analysis on which this curve 

 is based is too complex to be given here; 

 but it is not difftcult to see that the centrip- 

 etal law of random migration must de- 

 termine some such curvature. The mos- 

 quitoes which are bred in the pools lying 

 along the boundary line must remain for 

 the most part in its proximity, only a few 

 finding their way further into the drained 

 country, and only a very few reaching, or 

 nearly reaching, the limit of migration. 

 Though an infinitesimal proportion of them 

 may wander as far as ten, twenty or more 

 miles into the drained country (and we do 

 not know exactly how far they may not 

 occasionally wander) the vast bulk of the 

 immigrants must remain comparatively 

 close to the boundary. And as, for the 

 reason just given, the mosquito-density on 

 the boundary itself must always be only 

 one half the original density, it follows 

 that it must become very rapidly still less, 

 the further we proceed into the drained 

 country. In fact, the analysis shows that 

 the total number of emigrants must be in- 

 significant when compared with the number 

 of insects which remain behind — that is, 

 when they are not drawn particularly in 

 one direction. We are, therefore, justified 



