LOGICAL BASIS OF MOSQUITO-REDUCTION 95 



wander up to the end of each stage; and the continuous line shows 

 the course followed by one which has wandered straight onward 

 all its life and has died at the extreme limit to which an insect of 

 its species can generally go, namely, the outermost circle, L. On 

 the other hand, the dotted line shows a course which is likely to 

 be followed by the largest number of the 1024 insects liberated 

 from the pool that is to say, a quite irregular to-and-fro course, 

 generally terminating somewhere near the point of origin. The 



DIAGRAM I. The chance-distribution of mosquitoes. P, central breeding- 

 pool. L, limit of migration. The numbers denote the proportions of 1024 mos- 

 quitoes starting from P which die at the distances 1, 2, 3, 4, 5, respectively. 

 The continuous line denotes a continuous migration always in one direction; 

 the dotted line, the usual erratic course. 



numbers placed on each ring show the number of mosquitoes calcu- 

 lated from the binomial coefficients when n = 5, which are likely 

 to reach as far as that ring at the time of their death. Thus only 

 2 out of the 1024 mosquitoes are ever likely to reach the extreme 

 limit; while, on the other hand, no less than 912, or 89 per cent, 

 are likely to die somewhere within the second ring around the 

 centre. 



The same reasoning will apply whatever may be the number 

 of mosquitoes liberated from the pool, or the number of stages 

 into which we arbitrarily divide their subsequent life. Suppose, 

 for example, that 1,048,576 mosquitoes escape from the pool and 

 that we divide their life into 10 stages. Then only 2 of all these 

 insects are ever likely to reach the extreme limit of the outermost 

 circle; only 40 will die at the next circle; only 190 at the next; 

 and so on the large majority perishing within the circles com- 

 paratively close to the point of origin. 



This fact should be clearly grasped. The law here enunciated may, 

 perhaps, be called the centripetal law of random wandering. It ordains 

 that when living units wander from a given point guided only by 

 chance, they will always tend to revert to that point. The principle 



