.IITI.U .1 I l(i\ <•! ^ /./ / /s //( .//. Mil lli'I'.s (i.t 



If P is otiual to (/, the nuinlHT of causes must l)e very small iiuloed 

 l)cfore we are able to tietert the dilTerence between the terms of the 

 binumial expansion and those given by the normal law. To show 

 that this is true I have chosi-n a case corresponding to a physical 

 condition where there are only Hi causes and where p is equal to q. 

 The data are given in Table I\'. 



TABLE IV 



Obviously, therefore, the limitations imposed by the assumptions 

 as to the number of causes and the equality of p and q are not as 

 important as they might at first appear. It is probable that this is 

 one of the reasons why we find approximately normal distributions. 

 If, however, p is sufficiently small, the difference between the observed 

 distribution and that consistent with the normal law can easily be 

 detected. We shall show in a later section th.it this is true for Ruther- 

 ford's data." 



Is ThKRK .\ rNIVKRS.M, L.WV OF KrROR ? 



Obviously from what has already been said, the normal law is not a 

 universal law of nature. It is probable that no such law exists. We 

 do, however, have certain laws which are more general than the 

 normal. We shall consider briefly some of these types in an effort to 

 indicate the arlvantagcs that can be gained by an application of them 

 to physical data. 



" Loc. cit. 



