32 
Notes on the Historji of Correlation 
are functions of certain independent and directly observed quantities. When he 
thinks of c and a at all, it is not in terras of observations on x and y but of the 
differential coefficients A, B, G the geometrical relations between position in 
space and the angles by which that position is found. 
Next we come to his surface of three variates and the treatment is identical. 
Ho writes 
^^^^^-(ax- + hif + cz-^-2ezii + 2fxz + %j.r,i) 296), 
and his primary object is lo determine a, h, c, e, /, g in terms of the differential 
coefficients A, B, C and the variabilities of the observed independent variates. 
Thus he gives 
"' = G'^T^{i^'B")r-, e = G-^Sj^{{A"B)(A"B')l ^ S 
There is throughout merely the standpoint of the Gaussian method of treating 
errors of observation, and if we are to attribute any discovery of the idea of 
correlation to Bravais we must with the same confidence assert that Gauss was the 
primary originator of the whole idea. To my mind this is absurd*. In the case 
of both these distinguished men the quantities they were observing were absolutely 
independent ; they neither of them had the least idea of correlation between 
observed quantities. The product terms in their expressions — never analysed in 
the sense of correlation — arise solely not IVom organic relationships, but from the 
geometrical relationships which exist between their observed quantities and the 
indirectly observed quantities they deduce from them. Bravais himself (p. 331) 
says that the application of his results are narroAvly circumscribed by the nature of 
his assumptions — astronomy and the great geodesic surveys alone provide sufficiently 
accurate material. As far as Gauss and Bravais are concerned we raust, I think, 
hold that they contributed nothing of real importance to the problem of correlation, 
and that my statement of 1895 was a totally erronocjus one. 
The same criticism applies to all the treatment of the normal surfaces by later 
Avriters, which are described at very considerable length by Czuber in his Theorie 
der Beobachtungfehler, Leipzig, 1891. In all cases the variables are indirectly 
observed quantities and the product terms arise because they are mathematically 
supposed to be linear functions of the directly observed, but quite indeperident 
variables. That the directly measured quantities might themselves be correlated 
does not seem to have occurred to the many writers on the theory of observations. 
As far as I am aware there is nothing to record on our subject beyond the work 
of the writers on the theory of observations referred to above until we reach 
Francis Galton himself. His first statement of his ideas was in a lecture at the 
■* I feel quite certain tbat if any one had told either Gauss or Bravais that ^ (ah) for their observed 
measurements need not be zero, they would have been laughed out of court, as the astronomers now 
laugh at us, when we assert that their measurements of different stellar magnitudes are very probably 
correlated ! 
