412 The Incomplete Moments of a Normal Solid 
From the operational point of view 
as before. 
I have hitherto considered the polychoric function with respect to one variable 
only. If now we consider two variables the query arises where there is a corre- 
sponding function such that 
<^'f'i{z)=T^^,{x, y).z{x,y) (63), 
where -v/r stands to y in the same relation that ^ stands to x. We have 
(n.n\ ,..11— a /'/•"X ^n— s 
,7.) = (-!)• (-;r^r = 
(to — s) ! ' 
and </>-^ h= </>M ;r, - oT;— ox , + 
(»! 2(h-2)! 22.2!(«-4)! 
|(?i-s)! 2.(H-s-2)! 2^2!(w-s-4)! 
(« - s) 
(-l)^^^'l (64), 
and similarly 
with reciprocal relations between i/r and Tniy). Hence 
qlpr q\\ pi ■ 
ql \ p 
+ (7:ny!-lT!"/'i!^ ^ 
(q-2)V\ p\ ;'2! 
+ 
I -{p-qy.^ {q-l)V{p-q + l)V 1! 
+ (g^!-(p-9 + 2)!- 2! + -j ^ 
It is more convenient to have the series in the reversed order. The s + 1th 
term is 
Tp-,-,s{x) TUf) ( - ry-^ ^ 
{p - q + s)\' s\ ' (q — s)l ' 
