30 
Notes on the History of Correlation 
rid of constant sources of error which arise chiefly from vices of method of 
observation, ignorance of physical laws, etc. That they can be removed by 
increasing the number of our observations, and in surveying — which he has 
essentially in mind — by using the repeating circle, which destroys the majority of 
constant errors and lessens the influence of variable causes by the fact itself of 
repeating the observed angles. It is clear that he is thinking solely of theodolite 
work, and that his x, y, z are Gauss' indirectly observed quantities, his directly 
observed quantities being angles and bases a, b, c, 
He now changes his notation ; he uses iv, y, z for the errors S*', hy, Sz, and 
m, n, p for Sa, 8b, 8c, and takes equations 
:v = A m + Bn + Cj) + ... 
and calls x, y, z the dependent variables, m, n, p the independent variables. He says 
that Laplace has shown that a variation of x between x and x + hx will be of 
the form 
where is given by 
da 
It is therefore clear that he supposes that his observed quantities m,v,p,... are 
■uncorrelated in our sense of the word. In fact he gives for two and three variates 
the expressions 
pjnrK ^ ^- (/,,„ + /,^^„->) ^^^^^^^^ ), 
V TT.TT 
/ g - ( /,,„ + !,„n^ + h„ir) ^^^^^ ^^^^ ( 264). 
V TT. TT.TT 
There is obviously not a single step, not a line in this, which does not occur 
in Gauss, except that Gauss would use 
II- = h,„m' + flan- 4- lij,p- 
and not trouble to state that the probability was given by the exponential. 
Now Gauss' problem was to express the variability of a; in terms of the variability 
of the observed quantities a, b,c, ... or m, n, p, and of the differential coefficients 
A, B, C. This is absolutely the same as Bravais' problem, and Bravais' treatment 
goes very little further than Gauss' — indeed it is essentially narrower as while 
Gauss neither limits the number of his variables nor their nature, Bravais treats 
only of position in space. 
I will now give the value of the expression Bravais reaches for his surface of 
two dimensions, expressing by d'-io the briquette of frequency on dxdy : 
