LI— LII] 



Introduction 



lxxvii 



/113 1 \ m 

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



nq = 58 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 '01, 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, Biometrika, 

 Vol. x. p. 36. 



Table LII (pp. 122—124) 



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

 Biometrika, Vol. x. pp. 36—71.) 



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

 Then if n, anil 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 in according to the binomial law 



* See Eugenics Laboratory Memoirs, XIII. ' ' A Second Study of the Influence of Parental Alcoholism," 

 p. 22. 



