A. Ritchie-Scott 
421 
Substituting in (85), 
= r>c^n-, + (n - 1) /3,_., + t"-^c^ (105). 
Similarly for the A face 
h'Py"'z' (h', y') dij = N^A. h'» . 1„, , 
A' 3"' h' 
'"-^_L/,. iv-^n, '1-2 . 1^ ^ 01 a IV /in(3\ 
n=r + - 1) -u7»^ + • IT ~ • .s^-^ • • ■ 
KJy >.Jii ^1/ 
A on 
h' 
A'o 
J' ' 
on 
rh' E{k- ri) 
«i = - "TF-— - ^7 = ri + c„ (107), 
«n = »van_i + (?i - 1) a„-2 + «:"-'Ca (108). 
11. The moments in terms of the tetrachoric coefficients. 
We have already seen (77) that 
^^=e,_,(.) and = 
Drop the arguments and write 6p, 9q for Op{x), 6,i{y) respectively, 
= 6p_-i 9q - r 6p_2 9'q-i + . dp--, 6',]_.i . . . 
= 6p—i^q 
Similarly ^^dy ' ^ ^i'-i.'i-i' 
dOp^ q 
dx dy 
But ^if^ = i_ (ep9.; - r0p_,0'q., + dp.,,q_, . . . 
Hence 
dr drV^ -y-i-'y-i ■ 2! 
dp-id q-i + vdp-., ii—<, — ^ dp—3,q--i 
d6p^ q 
dxdy 
de. 
d 
.(109). 
.(110). 
.(111). 
The result in (111) corresponds to that deduced by Pearson (in Phil. Trans. 
Vol. 195, pp. 1-47), viz. 
^^-i'^- (113). 
dr dxdy 
Biometrika xii 27 
