Lucy Whitaker 
71 
appears to be no valid reason for such a procedure, except the experience that 
many such cases actually give negative binomials*. It seems to us theoretically 
unjustifiable to apply the exponential to 8 cases say in a district of 100,000, and 
not apply it to 12 cases in a district of 200,000. Actually p may be 1'4 iu the 
first case and only 0'9 in the second. 
(e) We consider that the reasonable method in every case is not to start with 
the Poisson-Exponential, which screens the truth or falsity of the a priori 
hypotheses, but to fit a binomial regardless of the magnitude of p. The fact that 
quite as good fits are obtained with negative as with positive binomials suggests 
that a new interpretation of these cases of " negative probability " is requisite. 
Several cases of the interrelation of "contributory cause groups" which provide 
a series represented by a negative binomial (p — q)~^ have been recognised f. 
A general interpretation based on a very simple conception seems needed for 
these demographic cases in which the law of small numbers appears far more often 
to correspond to a negative than to a positive binomial. 
This paper was worked out in the Bioraetric Laboratory, and I have to thank 
Professor Karl Pearson for his aid at various stages. 
* Can we cite in addition perhaps, the fact that existing tables of m'^e~"'-jx \ do not extend beyond 
?/i = 10? 
+ Pearson, Biometrika, Vol. iv. p. 208. 
