372 Mr. F. Y. Edgeworth on the 
Let p\ be the new provisional weight of the first observation. 
Then make 
p\{x-x x ) 2 +pl{x-x 2 ) 2 +p\{x-x 3 f 
a minimum. Let x be the new (weighted) mean. Calculate 
a new p x &c., and continue the process until you come to a 
standstill. 
It may be questioned whether this is exactly the procedure 
which DeMorgan had in view. Would not his language apply 
to the following process ? Find, as before, the prima facie 
value — — ~ — — ; then calculate the weights, upon the prin- 
ciples herein adopted, on the hypothesis that the putative is 
the real point ; and that the apparent errors are the result of 
divergence therefrom, according to probability-curves of dif- 
ferent moduli. The weights* are 
w 
fl 
+ x 3 -2x{ 
&c.= &c. 
Then make h\{x— ae^f + li\(x— x 2 y + hl(x— x 3 ) 2 a minimum, 
3B X x 2 
(x 2 + x 3 — 2x l )' 2 (x 3 + x x — 2x 2 f 
&G. 
x 1 
(x 2 + x 3 — 2x 2 f 
Find a new set of weights, and so on. 
Neither process leads directly, in the case of probability- 
curves, to the most probable value, which is 
The Mean ± V \x\ + x\ + x\ — (x 1 x 2 -f x 2 x 3 + x 3 Xi). 
Query whether the DeMorgan-Glaisher process would ulti- 
mately reach the most probable value. Their method, then, 
appears to be less advantageous in respect of accuracy than 
the method here suggested. Their method would perhaps be 
more advantageous in respect of convenience in some cases 
where the real weights are nearly equal, and not many ap- 
proximative steps are required. It must be remembered, 
however, that in these cases, as our analysis shows, the obser- 
vations must be close together; and therefore that our method 
also becomes facilitated in this case. For instance, taking the 
mean of the observations as origin, neglect powers higher 
than the second of x x , x 2 , &c. measured from this origin. 
* See I. A. (2). 
