Karl Pearson 
43 
Our object should be to find the ' best vaUie ' for r and not how it may be most 
easily determined at the obvious cost of accuracy. 
Although I am unable to follow some of Edgeworth's notation, he undoubtedly 
reaches something like the correct value for the correlation surface of three variates. 
In his notation 
i2 = A !(1 - p,,r) + (1 - p.J) + (1 - ^'Z 
- 2x^X., (/3,, - pr,P'^) - 2x,X., (p,3 - p-np-n) - 2a-.,X^ (p,, - p.o/Cl,,)) , 
where A^^ = {(1 - ^i:-.') ( 1 - Pr^) - {pv^p-i - PuY] 
according to him, but the factor 1 — py/ should be replaced by 1 — pss" I think. 
Even with this change I am unable to reach the value he gives in Galton's 
case of 
Pi. = -8, /3„=-9, p,,= -8, 
for these seem to give 
A = 9-9805, 
whereas Edgeworth's value is 1G'129. 
I do not grasp his equation at the foot of p. 196, nor follow how the equation 
at the top of p. 197 follows from it. 
Lastly we come to p. 201 where we should expect to find the general regression 
equation. Edgeworth tells us that the reasoning is quite general and accordingly 
we ought to anticipate that his results whatever they are would give our 
accepted values 
Pss=-^ and p,,. = ~, 
where R is the determinant of the coirelations. Instead of this simple rule 
Edgeworth sums up in the middle of the page with equations 
Ap,,= 4 AM/3.jP:;,P4->), 
A/3j4 = - A''(p,,j/3,,,p4;,), 
There is no explanation of what the symbolism means, and I cannot interpret it, so 
as to provide the requisite generalisation for n variates. 
On the other hand while unable to interpret Edgeworth's general analysis I 
agree in the case of four variates with the only two terms I have taken the trouble 
to test in his numerical illustration of this case, 
1 /r /I /2 /2 /I 
namely 2 as the coefficient of and —2^2 as the coefficient of x^x,^, my R 
being i^u being ^ and i?i2 being ^'^ . Edgeworth does not provide the 
needful external constant of the frequency surface, i.e. 
N 1_ 
(27r)''cr,(7, ... <7„ VS" 
