Method of Least Squares. 371 
that which makes a maximum, 
1 
When two observations are close together, the root of x which 
lies close to the two observations is evidently the appropriate 
value. The weight of those two observations is then high; 
the weight of the third observation, if it lies at a distance from 
the other two, is small. These considerations may easily be 
extended to the case of any number of observations given by 
probability-curves. The equation 
i + ^ +&0 . + ^ 
X — Xx x — x 2 
is easily formed, and admits of approximative treatment for 
one or two observations remote from the majority ; and doubt- 
less in other cases. 
In case of laws of error other than probability-curves, the 
method of course does not afford the most probable value. But 
I submit that the method is still a very advantageous method; 
more advantageous both in respect of accuracy and conve- 
nience than the method proposed by DeMorgan and Mr. 
Glaisher. Our method is at least accurate in one case, and 
that the very important and typical case of the law of error 
being a probability-curve ; comparable in that respect to La- 
place's treatment of the sought value as a linear function of 
the observations; a procedure which leads to the most probable 
value in the case of probability-curves, but is in general only 
a convenient, an advantageous, procedure*. But their method 
is never (except by chance) accurate, and always inconvenient. 
As I understand Mr. Glaisher, if three observations of un- 
known weight are given, say x 1} x 2) x 3 , his procedure is first 
to take the mean — -^ -; then to form the apparent 
o 
errors — — ^ — &c. ; then to form what may be called the 
o 
provisional weight (for all the observations), 
1 
h 2 = 
Then put 
[( * + y**) V&».] 
* See ante, p. 361. 
2D2 
