lxx Tables for Statisticians and Biometricians [XXXV — XLVI 



with origin at the mode =161486 in actual percentages, = 3 - 2297 in working 

 units. To calculate y we take the origin at and have 



log y = 26-134,8705 + 20917 log (* + -6774) + 17-6838 log (362617 -x), 

 where x may be put 0, 1, 2, 3, 4, 5... working units corresponding to 0, 5, 10, 15, 

 20, 25... actual percentages. The curve is shewn in the accompanying diagram, 

 and considering the nature of the data is a reasonable graduation. 



200 



"fe. 



10 15 



20 25 30 35 40 45 50 55 

 Per cent, of Black in Skin Colour. 



60 65 70 



80 



Table XLVIII (pp. 89—97). 



Percentage frequency of Occurrences in a Second Sample of m after p Occur- 

 rences in a First Sample n. (M. Greenwood, Biometrika, Vol. ix. pp. 69 — 90.) 



If we assume the truth of Bayes' Theorem then an event having occurred 

 p times and failed q times in n trials, the chance that it will occur s times and fail 

 m — s times in a second series of m trials is : 



C' = 



[ af> +s {l-x) 



J 



i +m ~ s dx 



\s \m — 



[ X* (1 - x)i dx 



J 



These results can be evaluated as all the indices are integers and the series 

 C + C i + Cj+ ... + C s + ... expressed in the usual hypergeometrical form : 



\ q + m \ n+ 1 j m p + l m(m- 

 \q~]n+m+'l \ + |1 q + m + |2 



-1) (p + l)(p + 2) 



(q + m)(q +m- 1) 



2)(p+3) 



in (m — 1) (m — 2) 



ft 



(q + m) (q + m-l)(q+m-2) 



+ 



.(lxxx). 



