to the Method of Least Squares. 203 



obvious assumption (th(uioli I do not pretend that it is not an as- 

 sumption) tluit the prolxihiliti/ that x is between x and x-\-dx must be 



exjyressible In the form iNx , W,r." From this the exponential 



Law of facility of error is deduced. 



For an analysis of this reasoning see Glaisher, 3Iem. Astron. Sac. 

 Land., Vol. XXXIX, p. 118, who classes it among the proofs of the 

 Method. 



1857 LiactRe. Sur la mesure de precision des observations meridi- 

 ennes faites a I'Observatoire royal de Bruxclles. Bidl. Acad. Belgique, 

 Vol. Ill, pp. 330-338. 



1857 Petzval. ' Fortsetzung des Berichtes iiber optische Unter- 

 suchungen. [Ausgleichungstheorie].' Sitzungsber. math-nat. Acad. 

 Wien, Vol. XXIV, pp. 129-144. 



Petzval concludes that the Method of Least Squares is entirely 

 inapplicable in Optics. lie proposes "die Methode der numerisch 

 gleichen Maxima und ^limmia," which consists in making the sum of 

 the 2m powers a minimum, m being a variable which tends toward 

 infinity as a limit. The development and application of this method 

 is to constitute the First Part of Vol. Ill of his work on Optics. 

 This method was mentioned by Laplace in the Theorie. . . .des Proba 

 bilites, p. 345. 



1857 Sawitsch. Die A)rwendwig der WahrscheinlichkeitstJieorie 

 auf die Berechnung der Beobachtangen und geoddtische 3Iessimgen, 

 oder die Methode der Meinsten Qmidrate. (Russian). St. Petersburg, 

 8vo. — German edition, Leipzig, 1863, 8vo. 



1857 Vorlander. • Ueber das geodatische Vorwarts-Einschnei- 

 den.' Zeitschr. Math. n. Phys., Vol. II, pp. 299-316. 

 A practical application of the Method of Least Squares. 



1857 Wrede, 'Nagra anmarkningar rorande minsta quadrat- 

 methodens tillampning.' Of vers. Acad. Forhandl. Stockhohn, Vol, 

 XIV, pp. 73-81. 



On the error ellipse. 



1857 Zech. Einladung zur akadeniischen Feier des Geburtstags 

 des Konigs von Wiirttemberg, nehst einer Abhandlung zur Methode 

 der Meinsten Quadrate. Tiibingen, 4to. 



The first exhaustive discussion of the adjustment of indirect obser- 

 vations subject to conditional equations. See Joedan, Elemente der 

 Vermessungskunde (Stuttgart, 1877, 8vo), p. 6. 



