748 



Mr. H. Bateman on some Problems 



n particles has a total charge r is zero if n — r is odd, and 

 equal to 



n! 1 



if 7i — r is even. The chance is in fact the coefficient of t r in 



Now we have seen that if v is the probable number of 

 particles in the given volume, the chance that at a given 

 time there are exactly n particles is 



e~\ 



n I 



Hence the chance that the volume contains a totsil charge 

 equal to r units is the coefficient of V in the expansion 



I nl{-2 + 2t) e ' 



that is in the expansion of the function 



Now if we use the notation employed by Basset *, we may 

 write 



V ( i \ <*> 



■ (2) 



Hence the chance of getting a total charge of r units is 

 represented by 



«-%(-) (3) 



The probable value of r is clearly zero, but we may find the 

 probable value of r 2 by summing the series 



Hydromechanics,' vol. ii. 



