to the Method of Least Squwes. 195 



1852 DiENGER. ' Ueber die Ausgleichung der Beoljaclitungs- 

 fehler.' Archiu. 3Iath. u. Phys., Vol. XVIII, pj.. 149-193 ; Vol XIX, 

 pp. 211-227. 



Hagen's demoiisti'ation (1837) is followed. The article forms an 

 almost complete elementary treatise on the Method of Least Squares. 



In the Supplement Hagen's proof is abandoned, as resting on a 

 questionable hypothesis and Gauss's first proof is given in its place. 

 DiEXGEK appreciates clearly the defects of Gauss's method, for he 

 requires the number of observations to be infinite in order that the 

 value given by the arithmetical mean shall coincide with the true 

 value of the measured quantity. 



1852 DiENGER, 'Ueber die Bestimmung des Gewichts der nach 

 der Methode der kleinsten Quadrate erhaltenen wahrscheinlichsten 

 Werthe der Unbekannten, wenn Bedingungsgleicluingen vorhanden 

 sind.' Arc/iiv. 3Iath. u. P/ujs., Vol. XIX, pp. 197-202. 



Contains valuable practical formula? for the computer. 



1852 Hartner. Handbuch der niederyi Oeoddsie, nebst eineni An- 

 hange uher die Elemente der Mctrhscheidehunst. Wien, 8vo. — Sec- 

 ond edition, 1856, 8vo, pp. xvi, 611. — Fourth edition, 1872, 8vo. 



See 1863 Bursch. 



1852 LiAGRE. 'Sur la valeur la plus probable d'un cote geode- 



sique commun a deux triangulations.' Bxdl. Acad. Jielgique, Vol. 



XIX, Pt. I, pp. 513-534. 



A clear exposition and solution of the problem. An example from 

 1 849 Baeyer is discussed. 



1852 LiAGRE. 'Sur la loi de repartition des hauteurs baro- 



raetriques, par rapport a la hauteur moyenne.' Pull. Acad. Pelgique^ 



Vol. XIX, Pt. II, pp. 502-514. 



The law is shown to agree with the exponential law of facility of 

 error. 



1852 Peirce (B.) " Criterion for the Rejection of doubtful observa- 

 tions.' GoukPs Astron. Jour.., Vol. II, pp. 161-163. 



This Criterion, founded on a principle of the Theory of Probability, 

 proposes a method for determining by successive approximation, 

 whether or not a suspected observation may be rejected. Tables are 

 needed for its application: for these see below 1855 Gould and 1864 

 Chauvenet. 



It is a fatal objection to this criterion that its use involves a con- 

 tradiction of reasoning. The arithmetical mean, for instance, can 

 only be used when tlie observations are all of equal weight, and the 

 rejection of an observation which deviates considerably from the 



