to the Method of Least Squares. 221 



Shows that the arithMictical moan is the most ])rol)al)le results for 

 n-\-\ observations, provided it is the most probable result for n ob- 

 servations, and as it is undoubtedly sueh for n-=^2, " ... it can b(> 

 shown to be generally true." 



lS7o Wrkde. ' Nagra anmarlsuingar rorande niinste qvradt- 

 methoden.' (Jfoersigt Fot'Juaidl. AraJ. Stoek/wlm, Vol. XXX, No. 

 8, pp. :5-;U ; Xo. 10, pp. 21-26. 



The prol)able error is said to be not always 0.6745 of the mean 

 error but depends upon tiie number of unknown quantities involved. 

 See 1852 Bienayme. Bessel's investigation of 1838 is also discussed. 



1873 GlaishePw 'On the Rejection of Discordant Observations.' 

 Monthly Notices Astron. Soe. Zo?id., Vol. XXXIII, pp. 391-402. 



It is here clearly pointed out how inconsistent is the rejection of 

 discordant observations by a criterion founded on the supposition of 

 the validity of the arithmetical mean. The idea first advanced by 

 DeMokgan [Encyc. Metroj)., 1847) that the mean is only an approxi- 

 mate value to be used in weighting the observations from which a 

 new mean is to be deduced, and so on, is here developed to a certain 



extent. See 1821 . The criterion given by Stone in 1868 is 



examined and pronounced untrustworthy and wrong. 



1873 Stone. 'On the Rejection of Discordant Observations.' 

 Monthly Notices, Vol. XXXIV, pp. 9-15. 



A reply to the preceding in which Glaisher's arguments are ex- 

 amined at length and the validity of the criterion maintained. 

 Glaisher's method for weighting observations is also discussed and 

 regarded "as mathematically unsound." 



1874 Glaisher. ' Note on a paper by Mr. Stone, " On the Rejec- 

 tion of Discordant Observations." ' Monthly Notices, Vol. XXXIV, 

 p. 251. 



1874 Stone. 'Note on a Discussion relating to the Rejection of 

 Discordant Observations.' Monthly Not., Vol. XXXV, pp. 107-108. 



1874 Cantor. '■ Ilistorische Notizenuber die Wahrscheinlichkeits- 



rechnung.'' Halle, 8vo, pp. 8, 



This is of no value. Gauss alone is mentioned in connection with 

 Least Squares. 



1874 Fechner, ' Ueber die Bestimmung des wahrscheinlichen 

 Fehlers eines Beobachtungsmittels durch die Summe der einfachen 

 Abweichungen.' Poggendorffs A^mal. P/iys., Jubelband, pp. 66-81. 



