1887. | Corrigendum on Mr F. Y. Edgeworth’s paper. 101 
Corrigendum of F. Y, Edgeworth’s paper on Observations and 
Statistics in the Cambridge Philosophical Transactions for 1885, 
Vol. xiv. Part 11. p. 140. 
Mr Edgeworth desires to retract or retouch some passages in 
this paper. At p. 159 in the paragraph headed (e) he would 
cancel the statement that “in the general case” (of facility-curves 
differmg from the probability-curve and from each ee the 
method of least squares is not “theoretically correct”. The 
method is defensible in that case on the same principle » as that 
on which it is defended in the less general case headed (6) (p. 158) 
(when the facility-curves appear in homogeneous clusters). The 
principle is, that it is allowable to ignore (especially if we are 
ignorant of) part of the data (or danda), namely the specialities 
of the facility-curves; and to utilise only our knowledge (1) of 
the Arithmetical Mean (simple or weighted) of the observations, 
and (2) of the mverse-mean-square-of-error for the respective 
facility-curves. Confining our attention to these two circumstances, 
we may reason by Inverse Probability that the probability of 
the observed Arithmetic Mean differing from the real point by 
any assigned extent w is measured by (the integral of) a Proba- 
2 
bility-curve y= Ge e *, whose modulus-squared c? is the mean 
TT 
(simple or weighted) of the inverse-mean-square-of-error for the 
different facility-curves. It cannot be denied that there is some- 
thing arbitrary in selecting one portion of our information to be 
utilised (for instance one weighted Arithmetic Mean, rather than 
another). The practice is explained by the parallel procedure 
of an Insurance Company, when they cannot utilise all their in- 
formation. As pointed out by Dr Venn in his Logie of Chance, 
(chap. VII. § 22 et seq.) they have often a choice as to what portion 
of the data is to be neglected. For example given mortality 
statistics for (a) English-residents-in-Madeira, and (8) Con- 
sumptive-residents-in-Madeira; upon which basis should an 
English-consumptive-resident be insured? Hither plan would 
come right in the long run; but the run would be much longer, 
the deviations between the average and the particulars would 
doubtless be much greater, upon plan (a); since “the state of a 
man’s lungs has probably more to do with his health than the 
place of his birth has”, Similarly any weighted Arithmetic 
Mean will come right in the long run of numerous applications 
of the method. But some systems of weight will afford much 
shorter excursions from the true Mean, will deviate less from the 
real point in the course of repeated use, than others. The method 
of least squares assiges the system which (as compared with other 
linear combinations of the observations) is attended with the 
