No. 603] MENDELIAN CLASS FREQUENCY 147 



as when 71 is very large as compared with m, and neither 

 p nor q are very small, (i) and (iii) are obviously capable 

 of being put in much simpler form and still giving a 

 sufficiently close approximation to the true result. For 

 Mendelian work, however, where frequently neither of 

 these conditions are even approximately realized, it will 

 in general be better to use the full expression as given 

 above. 



The ordinates of the error distribution (the chances of 

 different occurrences) are given by the successive terms 

 of the hypergeometrical series 



Cr=Co 



^ y+1 m(m-l) (ff+l)( y +2) 

 [ ' 2 * (9+m)(9+m-l) 



n(ni-l){m-2) (j?+l)(p+2 )(p+3) 



13 •(9+m)(9+m-l)(9+m-2) 



n(m-l){m-2)(m-S) 



(p+l)(p+2)(p+3)(p+4) , ^ 1 



r( g+m+l )r(n+2) 

 r(9+l)r(n+m+2)- 



(v) 



As we shall presently see, the calculation of the terms 

 in (iv) becomes a tedious and laborious matter when the 

 number needed is at all considerable. Under such cir- 

 cumstances, and when in addition m and n are even mod- 

 erately large, equation (iv) may be greatly simplified, 

 without significant loss of accuracy, by the use of Ster- 

 ling's theorem (to the bracket) or by Forsyth's approxi- 

 mation for such of the factorials as are not included in 

 the range of the Pearson^*' tables. Thus we have, by 

 Sterling's theorem, remembering that r denotes any term 

 m the series, and writing s = m — r, 



Tables for Statisticians and Biometricians, " edited by Karl Pear- 



