AN EXPLANATION OF DEVIATIONS FEOM POISSON'S 
LAW IN PRACTICE. 
In her paper on the Poisson Law of small numbers, Biometrika, X, p. 36 et seq. 
Miss Whitaker after a very interesting analysis of the various attempts which 
have been made to test Poisson's Law on actual statistics concludes that "A general 
interpretation based on a very simple conception seems needed for those demo- 
gi'aphic cases, in which the law of small numbers appears far more often to 
correspond to a negative than to a positive binomial." 
The following is an attempt to explore the general question of what effect 
various departures from the conditions which lead to Poisson's Law have on the 
resulting statistics, and especially which conditions lead to positive and which to 
negative binomials when the exponential might at first sight be expected. 
Poisson's Law has been applied to the occurrence of different numbers of 
individuals in divisions of space or time : thus of yeast cells in squares of a 
haemacytometer, of deaths from the kick of a horse in Prussian Army Coi'ps which 
may be taken as individuals occurring in divisions of space, or of suicides of 
children per year in Prussia which are individuals occurring in divisions of time. 
In such cases it has been asserted that if the chance of an individual being found 
in a given division is so small that when multiplied by the very large number of 
individuals the product is still a reasonably small number, then the frequency of 
divisions containing 0, 1, 2...r individuals will be given by the terms of the 
exponential 
where N is the number of divisions and 7// the mean number of individuals 
occurring in a division. 
(1) That the chance of falling in a division is the same for each individual. 
(2) That the chance of an individual falling in it is the same for each 
(3) That the fact that an individual has fallen in a division does not affect 
the chance of other individuals falling therein. 
By "STUDENT." 
For the above to be true it is necessary 
division. 
