694 



SCIENCE. 



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



We suppose that 1,024 mosquitoes have 

 escaped during a given period from the 

 central breeding-pool P, and we divide 

 their subsequent life into 5 stages— the 

 numbers 1,024 and 5 being selected merely 

 for illustration. Rings are drawn around 

 the central pool in order to mark the dis- 

 tance to which the insects may possibly 

 wander up to the end of each stage; and 

 the continuous line shows the course fol- 

 lowed by one which has wandered straight 

 onward all its life and has died at the ex- 

 treme 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 1,024 

 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 numbers placed on 

 each ring show the number of mosquitoes 

 calculated 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 1,024 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 center. 



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 subse- 

 quent life. Suppose, for example, that 

 1,048,576 mosquitoes escape from the pool 

 and that we divide their life into 10 stages. 

 Then only two 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 comparatively 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 wan- 

 dering. It ordains that when living units 

 wander from a given point guided only hy 

 chance they will always tend to revert to 

 that point. The principle which governs 

 their to-and-fro movements is that which 

 governs the drawing of black and red cards 

 from a shuffled pack. The chances against 

 our drawing all the twenty-six black cards 

 from such a pack without a single red card 

 amongst them are enormous; as are the 

 chances against a mosquito, guided only by 

 chance, always wandering on in one direc- 

 tion. On the other hand, just as we shall 

 generally draw black and red cards alter- 

 nately from the pack, or nearly so, so will 

 the random movements of the living unit 

 tend to be alternately backward and for- 

 ward — tend, in fact, to keep it near the 

 spot whence it started. As there is no par- 

 ticular reason why it should move in one 

 direction more than another, it will gen- 

 erally end by remaining near where it was. 

 But it will now be objected that the 

 movements of mosquitoes are not guided 

 only by chance, but by the search for food. 

 To study this point, take the diagram just 

 given, place a number of pencil dots upon 

 it at random, and suppose that each pencil 

 dot denotes a place where the insects can 

 obtain food — suppose, for example, that 

 the breeding pool lies in the center of a 

 large city and that the pencil dots are 

 houses around it. Consideration will show 

 that the centripetal law must still hold 

 good, because there is no reason why the 

 insects 'should attack one house more than 

 another. There is no reason why a mos- 

 quito which has flown straight from the 

 pool to the nearest house should next fly 

 to another house in a straight line away 

 from the pool, rather than back again, or 

 to the right or left. The same law of 

 chance will continue to exert the same in- 



