390 Mr, L. Isserlis : Application of Solid Hyper geometrical 

 Hence (21), (22), (40), (41), (42), (43) give 



*2[fe (ra ~fS~ 3) --(3n-6)] =^ + « 3 + 6(.V-» 2 ~~0 • (60) 

 *&%rF= n4+ *(*i'-»*.-i) ........ (61) 



*'[/8,' ( "^"~ 3) -(3»-6)] =n«.+«»+6(*»--«V) 



... (62) 



2! '[ ft '"»-l ! ] = " H4(:i ' ! "" V) - ...... (63) 



Eliminating.^, ^'we obtain 



But &' = ^VlZL i s known from (50), (52) ; 

 z 2 r n — r < s ' 



. V /r'V(n\ 2 n-r' r (1 + ?) 2 ^ ,,,, 



in fact — = (-)(-) — , = ^t- — T2> =7 say . (64) 



z 2 WW r' n—r (1 + V)s ' J 



. 3A(n-2)-2ft(n-3 ) +6n-6 _ ( „ 



' " 3/3 1 '(n-2)-2f3 2 '(n-3) + 6n-6 7 ' * V •' 



orw=6 f Ttft^'+D-M+D ] . . (66> 



l7(3A / -2A' + 6)-(3A-2A + 6)i 

 n being known, q is given by (58) since 

 (l-2# ,(71-2)'. 









2(1-2) -" 



n- 



-1 



The 



values 



of 



r and r r are given 



by 











n 



r "f+i"' 



/ 



71 



Equations (21) and (22) will give c and c' and (7), (8) will 

 give the position of the mean. 



Let N be the total number of observations, then to obtain 

 the various ordinates of the hypergeometrical frequency 

 polyhedron we must take the various terms of 



which is equivalent to the double series AF X (a, a', 0, 7) of §3. 



