Karl Pkarson 
29 
their naines. Again Edgeworth (Hd not obtain results identical with Bravais', he 
went on a route of his own to find the true multiple correlation surface and gave as 
I said in 1S95 only doubtful results. But I fear they were not all due to printer's 
errors. On re-e.xamining his memoir 25 years later I think he harnessed imperfect 
mathematical analysis to a jolting car and drove it into an Irish bog on his road, 
and that it w;is doubtful analysis not errors of printing which led to his obscure 
conclusions. I was scarcely justified in 1895 in calling the multiple regression 
result Edgeworth's Theorem. He had tried in 1892 to solve the problem, and he 
can hardly be said to have succeeded properly. It is very difficult to explain now 
how my errors of ascription came about, still less possible is it to understand why 
later writers have not corrected my false history, but merely repeated it. 
As far as I can remember what happened at all, it was as fjllows. I know that 
I was immensely excited by Clalton's book of 1889 — Natural Iii/ienta.nce — and that 
I read a paper on it in the year of its appearance. In 1891 — 2 I lectured popularly 
on probability at Gresham College, taking skew whist contours as illustrations of 
correlation. In 1892 I lectured on variation, in 1893 on correlation to research 
students at University College, the material being afterwards published as the first 
four of my Phil. Trans, memoirs on evolution. At this time I dealt with correlation 
and worked out the general theory for three*, four and ultimately n variables. The 
field was very wide and I was far too excited to stop to investigate properly what 
other people had done. I wanted to reach new l esults and apply them. Accordingly 
I did not examine carefully eithei- Bravais or Edgeworth, and when I came to put 
my lecture notes on correlation into written form, probably asked somebody who 
attended the lectures io examine the pajjers and say what was in them. Only when 
I now come back to the papers of Bravais and Edgeworth do I realise not only that 
I did grave injustice to others, but made most misleading statements which have 
been spread broadcast by the text-book writers. 
(3) Let us now examine Bravais' memoir. He commences by stating that 
he is going to measure the errors of the determination of the coordinates x, y, z of a 
point in space. These coordinates are not measured directly but are functions 
of the observed elements a, b, c, and he puts 
x = 1^ {a, b, c, ...), 
y = ^{a,b,G,...), 
z = X f>, c, ■■■). 
He then expands x, y, z linearly in terms of (/, b, c assuming that mathematical 
differentials may be used for errors ; thus he writes 
Bx = ASa + BSb + CBc + ..,, 
8y=^A'Ba + B'Bb + C'Bc + ..., 
Bz==A"8a + B"Bb + C"Bc+.... 
He tolls us that the A, B, C are differential coefficients, i.e. of the known functions 
(f), -yjr, X, and that t(j justify the neglect of higher powers and products we must get 
* Published iu the li. S. Pruc. Vol. lvui. p. 241, 1895. 
