Lucy Whitaker 
57 
number of men n in an army corps as 50,000* we have nq = '61 and -000,0122, 
thus reaching the binomial 
200 (-999,9878 + 000,01 2 2)^''.»»», 
giving as compared against Bortkewifcsch : 
Binomial Bortlcewitsch 
0 108-6876 108-6703 
1 66-3002 66-2889 
2 20-2213 20-2181 
3 4-1115 41110 
4 and over -7035 -7034 
and^^= -608,298 -608^318 
or, the slight advantage to the binomial exists but is of no significance. 
Now it seems to us that in this case the use of the exponential is justified for 
the total frequencies, but as far as describing those frequencies is concerned, it 
gives no better result than the binomial. But as in the other five of Bortke- 
witsch's cases the Exponential is not justified by the individual series themselvesf. 
It is perfectly true that the exponential has a definite theory behind it, and 
is interpretable in terms of that theory, i.e. we must suppose the probability of an 
occurrence very small and the chance of its repetition absolutely identical. But 
is the second of these conditions ever likely to be demonstrable a priori, or must 
* This supposes that every man in the army corps is equally liable to death from the kick of 
a horse; of course a very arbitrary assumption. 
t To illustrate the idleness of the application of the Poisson-Exponential even to these data for the 
Prussian Army Corps, we give here the binomials for the whole of the 14 corps. 
Index Number 
of Corps Binomial 
G 20(-95 + -05)i'i-oooo 
I 20 (1-325 - •325)-2-^<'i5 
II 20 (1-5667 --SBeTj-i-osss 
III 20 (-9 + -1)6-0000 
IV 20 (-6 + •4)1-0000 
V 20 (•6318 + -3682)i-«38 
VI 20 (1 -0912 - -0912)-9-3202 
VII -20 (-9 + •1)6-0000 
VIII 20 (-65 + -35)i^oooo 
IX 20(-8115+ •1885)3-«83 
X 20 (1^05 - ■05)-i5-oooo 
XI 20 (1-11 --ll)-ii '3036 
XIV 20(1-05- -0.5)~2J-oooo 
XV -20(1-1 - -l)-4-oooo 
One seeks in vain through these binomials for any approach to q very small and positive and n very 
large and positive. In no case does n approach the number of men in an army corps, say 50,000, 
or q equal the chance of a death from the kick of a horse, say, -0000122 ! It seems impossible by 
clubbing such equations together to give any satisfactory proof that the Poisson-Exponential really does 
apply to individual cases. In the 20 years involved, there were doubtless great changes in both 
the training and the personnel of each army corps, and the results obtained may be just as much due to 
such causes as to the errors of small samples. 
Biometrika x ^ 
