LI— LII] 



Introduction 



Ixxvii 



The binomial is ( ^i-vr + ^r^m 

 V114 114 



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 = 'Ol.oQo. 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 : 



Annual 



Frequency 



Frequency 



Deaths 



Observed 



Poisson's Series 







109 



108^72 



1 



65 



m-i-2 



2 



22 



20^22 



3 



3 



4-12 



h 



1 



•63 



5 







•08 



6 and over 





•01 



Totals ... 



200 



200 



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

 and taking •O the series for 0'6 and 1 times the series for O'l , 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, 

 Biometnka, Vol. x. pp. 36—71.) 



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

 Then if Wj 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 



if 1- 



+ 



«s 



N ' N 



* See Eugenics Laboratory Memoirs, XIII. 

 22. 



' A Second Study of the Influence of Parental Alcoholism,'' 



