110 The Con-elation Coefficient of a Pohjcliorie Table 
§ 8. Computation of R\ and ct's. 
As the. computation of r^, even for an enneachoric table is somewhat lengthy, it 
is necessary to have a definite scheme to work to. In addition to this the values of 
the i2's when resolved into their constituents present some interesting features. 
A new expression for tetrachoric r has already been deduced from the degenera- 
tion of an enneachoric table. The following is a derivation of it directly and in a 
more symmetrical form. 
Consider the tetrachoric table 
D 
a 
b 
F E 
L 
c 
d 
G 
N 
Let A and B have the same significance as before, i.e. A is the fraction which 
the area of the plane DE is of the whole dichotomic plane and B the same for FE, 
^vi'it.e =An,. + Bn.^-a (79), 
where the a suffix is used to indicate that it is the P of the leading or a quadrant. 
Then since the fractional area of EG will be 1 — ^ and of EL, 1 — B, the 
corresponding P for b quadrant will be 
^P = An^. H- (1 - B) n.i - b 
■^A{N-~ n,.) + (1 - B) n., - {n., - a) 
= AN - {Aiij^. + Bn.i - a) 
-=AN-,P (80). 
Similarly ,P = BN ~ (81), 
aP=-N{A + B~\) + ,P (82). 
Hence we have + bP + cP + aP N (82) 6is. 
We have already seen (20) that 
- xf/r = Adm^. + Bdm.-^ - dm-^^ = S ^P^ (83). 
Using the symbol ^ as before to denote the operation " sum for all possible 
samples and divide by the number of samples"* we have 
* It would be useful to have a distinctive name for this operation, verb as well as substantive. 
