TABLES OF POISSON'S EXPONENTIAL 
BINOMIAL LIMIT. 
Bi^ H. E. SUPER, M.A. 
In his treatise, Reclierclien hi. Pruhabilite cles Jiigenieiits, Paris, liS37, 
Poisson* shows tliat the series of frecjuencies 
n(n — l) , , III 
given by the expanded terms of the binomial 
becomes in the limit, when q is diminished, and n increased, indefinitely, but so 
that nq remains finite and ecjual to m, the exponential series 
m- III'' \ 
e-(l + m + ^ + ... + ~ + ...y, 
and he points out that the terms of this series will give the proportional 
frequencies of the occurrences 
0, 1, 2, ... 7-, ... 
times, in any sample, of an event, every occurrence of which is equally likely in 
the sample and independent of the other occurrences, and which is of such 
frequency that m events occur in the sample on an average. 
The series is arrived at by " Student f," when considering the theoretical 
frequencies in sample drops of a liquid of minute corpuscles supposed distributed 
at random throughout the mass of the liquid. 
The event may also occur in time, each occurrence being supposed to take 
place with equal probability in any finite period taken as the sample, and to act 
independently of the occurrences of all the other events. A physical example, 
which appears by the closeness of the observed to the theoretical frequencies to 
* pp. 20.5 et seq. 
t Biometrika, Vol. v. p. 351, "On the Error of counting with a Haemacytometer. " 
Biometrika x 4 
