Karl Pearson 
37 
were what the mathematician terms the conjugate diameters of the variate axes. 
He discovered that the sections parallel to the variate axes were ' apparently ' 
normal curves of equal S.D. but that this s.D. was reduced and bore a constant 
ratio to the s. D. of the general population. He knew 8 years earlier the relation 
of c7 Vl — to the 'reversion' coefficient r. That Galton should have evolved all 
this from his observations is to my mind one of the most noteworthy scientific 
discoveries arising from pure analysis of observations. 
Why Galton did not at once write down the equation to his surface as 
_Lr _ -L^^ ^,_,<L^2,y 
has always been a puzzle to me. Actually he carried the problem, stated in the 
language of probability, to Mr J. D. Hamilton Dickson, a mathematician of 
Peterhouse, Cambridge, who after stating the wording of Gal ton's problem, wrote 
down the answer substantially as above in the fourth line of his memoir* ! The 
fact is that Galton's statement of his problem, involving as it did the assumption 
of normal distribution, homoscedasticity and linear regression, provided the answer 
the moment his results were read in symbols. The explanation of Galton's action 
po.ssibly lies in the fact that Galton was very modest and throughout his life under- 
rated his own mathematical powers. 
Thus in 1885 Galton had completed the theory of bi-variate normal correlation. 
The next stage in the theory of correlation, multi-variate correlation, was directly 
indicated by the general problem of ancestry. As is now well known the funda- 
mental regression equation is 
where R^g is the p. 
q minor of the determinant 
R = 
1 
■''oi 
1'q2 ■ ■ ■ 
' 0)1 
1 
1\, ... 
''no 
r,n 
?-„o ... 
1 
and the variability 
of the array is 
o"o ^ 
.(il). 
Galton endeavoured to reach this by a short cut, and thus evolved his law of 
ancestral heredity. This was a brilliant and suggestive step, but he was not able 
to state the conditions under which it is theoretically correct or bring forward data 
at that time to confirm its observational accuracy. 
* R. S. Proc. Vol. xi>. p. 63, 1886. Galton himself writes (B. A. Report, 1885, p. 1211), "J may be 
permitted to say that I never felt such a glow of loyalty and respect towards the sovereignty and 
magnificent sway of mathematical analysis as when his answer reached me, confirming, by purely 
mathematical reasoning, my various and laborious statistical conclusions with far more minuteness than 
I had dared to hope, for the original data ran somewhat roughly, and I had to smooth them with 
tender caution." 
