52 On the Polsso]} Law of Small Numbers 
III. Accidental Deaths in 11 Trade Societies. Bortkewitsch provides data 
fi'oin which the foUowiiig table is deduced: 
TABLE VII. 
Index Number 
Accidental Deaths 
Totals 
of Society 
0 
1 
2 
3 
5 
6 
7 
« 1 
11 
1,'? 
13 
U 
l.J 
1 
1 
1 
1 
3 
1 
1 
9 
U 
2 
3 
z 
, 1 
1 
9 
1:.' 
W 
2 
1 
3 
1 
3 
1 
2 
1 
2 
1 
1 
9 
9 
23 
z 
z 
1 
2 
1 
2 
1 
1 
1 
9 
27 
29 
4 
1 
2 
1 
3 
— 
1 
9 
9 
41 
1 
1 
1 
2 
T 
1 
2 
2 
1 
9 
40 
2 
1 
2 
1 
1 
1 
1 
9 
42 
1 
1 
1 
4 
1 
1 
9 
55 
z 
1 
1 
3 
1 
1 
9 
Totals ... 
1 
5 
9 
14 
13 
14 
16 
7 
7 
8 
2 
1 
1 
1 
1 
99 
The resulting binomials are : 
(13) 
9( 
4914 + 
.5086)'''-""»8, 
(14) 
9( 
6184 + 
•3816)^-'™-, 
(12) 
9(1 
9227 - 
.9227)---"«"', 
(20) 
9(1 
1282 - 
•1282)--'™, 
(23) 
9( 
•9921 + 
•0079)"«*'"-^'"=, 
(27) 
9( 
•5229 4- 
(29) 
9(1 
•4130- 
•4 130 )-»■-'*' 
(41) 
9( 
•8454 + 
•1546)^^"'"'2", 
(40) 
9 (2 
•0342 - 
l•0342)-2■'»3^ 
(42) 
9( 
•9322 + 
(55) 
9( 
•6154 + 
•3846)"'-«''^ 
Of these eleven binomials seven have a positive q ; only one of these (23) 
actually corresponds to a really small q and large n, although a second, (42), 
approximates to this condition. In the five other cases the q's are quite sub- 
stantial ; in (13) the q is larger than p. Of the four negative g's none can be said 
to be so small and the v so large as to suggest that they really correspond to the 
Poisson-Exponential. The probable error oi q ^ov q = Q is, however, + •3180, and 
thus for such small sei-ies, no test whatever can be really reached of the legitimacy of 
applying the Poisson-Exponential to such data. We may note, indeed, that seven 
of the eleven values of q exceed the probable error and two of these are more than 
three times the probable error. We should only expect two negative values of q 
as creat or greater than '9227 in 80 trials, whereas two have occurred in 9 trials, 
