CHANCE. 73 



So that if the first collision multiplied the deviation 

 by a very large number, A, after n collisions it will be 

 multiplied by A". It will, therefore, have become very 

 great, not only because A is large — that is to say, 

 because small causes produce great effects — but be- 

 cause the exponent n is large, that is to say, because 

 the collisions are very numerous and the causes very 

 complex. 



Let us pass to a second example. Why is it that 

 in a shower the drops of rain appear to us to be 

 distributed by chance? It is again because of the 

 complexity of the causes which determine their 

 formation. Ions have been distributed through the 

 atmosphere ; for a long time they have been sub- 

 jected to constantly changing air currents, they have 

 been involved in whirlwinds of very small dimensions, 

 so that their final distribution has no longer any 

 relation to their original distribution. Suddenly the 

 temperature falls, the vapour condenses, and each of 

 these ions becomes the centre of a raindrop. In 

 order to know how these drops will be distributed 

 and how many will fall on each stone of the pave- 

 ment, it is not enough to know the original position 

 of the ions, but we must calculate the effect of a 

 thousand minute and capricious air currents. 



It is the same thing again if we take grains of dust 

 in suspension in water. The vessel is permeated by 

 currents whose law we know nothing of except that 

 it is very complicated. After a certain length of 

 time the grains will be distributed by chance, that 

 is to say uniformly, throughout the vessel, and this 

 is entirely due to the complication of the currents 

 If they obeyed some simple law — if, for instance 



