LI LII] 



Introduction 



Ixxvii 



/113 1 X 882 

 The binomial is I = ^ + - j . n is accordingly large and q small, while 



749 = 5 "8 nearly. We look out 5'8 in Table L and sum the terms for 12 and beyond. 

 We find the chance of 12 or more = '01595. Actually worked from the binomial, 

 it is "01564. Or about once in five years, we might expect in Canton Vaud a 

 month with 12 imbecile births*. 



Illustration (ii). Bortkewitsch (loc. cit. p. 25) gives the following deaths from 

 kicks of a horse in ten Prussian Army Corps during 20 years, reached after 

 excluding four corps for special reasons: 



The mean m of the observed frequency is - 61, whence using Table LI (p. 113) 

 and taking '9 the series for 0'6 and - 1 times the series for 0'7, we reach figures, 

 which multiplied by 200 give us the column headed " Frequency, Poisson's Series " 

 above. Such good agreement, however, is very rare. A good fit to actual data 

 with the Exponential Binomial Limit is not often found. Its chief use lies in 

 theoretical investigations of chance and probable error : see Whitaker, Biometriku, 

 Vol. x. p. 36. 



TABLE LII (pp. 122124) 



Table of Poisson's Exponential for Cell Frequencies 1 to 30. (Luoy Whitaker, 

 Biometrika, Vol. x. pp. 3671.) 



Given a cell in which the frequency is n, corresponding to the population N. 

 Then if n, and N are very large (or we suppose, without this, the individual to be 

 returned before a second draw), the number in this sth cell will be distributed in 

 M samples of m according to the binomial law 



* See Eugenia Laboratory Memoirs, XIII. 

 p. 22. 



A Second Study of the Influence of Parental Alcoholism, " 



