370 Mr. F. Y. Edgeworth on the 
accuracy I impugn. How, then, can we be certain that the 
effect of a subexponential ingredient is extinguished? 
Agreeably to the distinction clearly exhibited by Mr. 
Glaisher (op. cit. p. 102 foot, and p. 103), the method of least 
squares belongs to B (3) or B (4) according as it is, or is 
not, given that all the observations have the same weight. The 
latter case presents the much vexed question, What shall be 
done with considerable outlying errors ? Shall the exceptional 
observation be omitted from the average, as Peirce* says ? Or 
shall it count for one, as Airy saysf ? Or shall it count indeed, 
but not count for one, as says DeMorgan ? Upon the hypo- 
thesis here entertained DeMorgan's view is undoubtedly cor- 
rect in theory, though in practice it may not differ from the 
practice of Peirce. The approximative method is justified in 
following the analogy of the exact method ; which would, 
according to the inverse method here all along contemplated, 
include all the data among the premises, though it may be 
that the conclusion, which is a function of them all, is less 
affected by (the variation or omission of) some than others. 
Thus, to take an example transferred here from its proper 
place (A 4) : suppose Ave have two observations, x x and x 2 , 
close together, and a third outlying, given that the generating 
facility- curves are probability-curves, but nothing further. 
Then we have to determine x, h 1} h 2 , A 3 , so that 
is a maximum. Whence 
(1) l-2/r 1 (x-x 1 f=^0, 
(2) l-2/#>-O 2 = 0, 
(3) l-27^-^ 3 ) 2 =0, 
(4) h%x-x 1 ) + hl(x-x 2 ) + hl(x-x 3 ) = Q. 
Whence 
i + * + _i o. 
(as—ai) (x—x 2 ) {x—x z ) 
Of the roots, that one is to be selected which makes a 
maximum 
or, as 
1 
1 2(x-x 1 y 
* Astron. Journ. vol. ii. p. 161 (Cambridge, America), 
t 'Astronomical Journal,' vol. iv. p. 137. 
