Lucy Whitaker 
We have said tliat tlie results for II. and IV. are fairly satisfactory, i.e. we 
mean that they are consistent with q being small and positive and n being large ; 
but of course they are also consistent with q being negative and n being small and 
negative. 
It will be obvious from these results for "Student's" data that it is extremely 
difficult to test the legitimacy of the hypothesis on which the " Law of Small 
Numbers" is based. In none of the cases dealt with by Bortkewitsch, much less 
in those dealt with by Mortara, are the populations (N) anything like as extensive 
as those considered by " Student." But populations of even 400 give, as we see, too 
large values of the probable errors of q and n for us to be certain of our conclusions. 
(8) Bortkewitsch' s Gases. Taking Bortkewitsch next, he deals with the 
following cases : 
I. Suicides of Children in Prussia for 25 years: (a) Boys, {b) Girls, 25 cases. 
II. Suicides of Women in eight German States for 14 years: 112 cases or 
8 subseries of 14. 
III. Accidental Deaths in 11 Trade Societies in 9 years: 99 cases, or 11 sub- 
series of 9. 
IV. Deaths from the Kick of a Horse in 14 Prussian Army Corps for 20 years : 
280, or, as Bortkewitsch, 200 cases. 
It will be noted at once that Bortkewitsch 's populations (iV) are far too small 
for any effective determination of the legitimacy of his application of Poisson's 
forniula to his data. 
We take his cases in order ; 
I. (a) Suicides of Boys. 
TABLE III. 
Number of Suicides 
0 
1 
3 
3 
4 
5 
6 
7 and over 
Number of Years 
4 
8 
5 
3 
4 
0 
1 
0 
The binomial is : 
25 [1-2033 -•2033]-'' «^^\ 
Mean 1-9600 and = 3-2584. 
We have q=- -2033 ± -2421, n = - 9-6425 ± 10-9416. 
If q were really zero its probable error would be + "1908. Clearly 25 cases are 
wholly inadetpiate to test the legitimacy of applying the Poisson-Exponential to the 
frequency*. But to what extent is the reader made conscious by Bortkewitsch 
that his cases fail entirely to demonstrate the legitimacy of applying his hypotheses ? 
* The x'-^ for the binomial is 2'H79 and for the exponential '2-83G, showing a somewhat better 
result for the binomial. 
Biometrika x 7 
