to the Method of Least Squares. 179 



T]ie g-eiieral term of the l>inonii:il tlieorem is shown to take the ex- 

 ponential form ee-M% when the number of teims is indefinitely great: 

 See Laplace, Theorie des .... Prob., Chap. Ill, and 1837 Hagen. 

 Formulae for probability of errors between given limits and for prob- 

 able errors are also developed. See 1836 Poisson. 



1830 RiESK. '[Eine Recension.]' Jahrb. filr loissen. Kritik for 



1830, Pt. I, col. 269-284. 



A review of Gauss's memoirs Tlieoria combinationis , 1823, 



and Supplementum. theoriae , 1827, giving an account of their 



contents and a popular ex))osition of the subject. 



1831 (yAucHT. ' Meraoire sur le systeme de valeurs qu'il faut 



attribuer a divers Elemens, determines par un grand nombre d'ob- 



servations, pour que la plus grande de toutes les erreurs, abstraction 



faite du signe, devienne un minimum.' Jour. Kcole Poly.., Vol. XIII 



(cahier 20), pp. 175-221. 



This was perhaps published aljout 1814, See Bidl. Soc. Philoni. 

 Paris, for 1824, pp. 92-99. The methods of 1760 Boscovich and 

 1792 Laplace, are particular cases of Cauchy's solution. See La- 

 place's Theorie . . . des Prob., Chap. IV, Art. 24. 



1831 Degex. ' Recherches sur la parabole, determinee par la 

 methode des moindres carres et qui represente le moins defectueuse- 

 ment, quil il soit possible, un systeme quelconque de points donnes 

 dans un plan.' 3fan. Acad. St. Peters, par divers savants, Vol. I, 

 pp. 13-28. 



1831 Grunert. ' Berechnung der wahrscheinlichsten Resultate 

 aus gegebenen Beobachtungen. Methode der kleinsten Quadi*ate.' 

 KiugeFs Mathematisches Worterbuch, Vol. V, Art. " Wahrscheinlich- 

 keitsrechnung,' pp. 983-1027. 



A clear presentation of the Method of Least Squares according to 

 Gauss, the proof being that of 1809. 



1831 Hansen. ' Darlegimg einer neuen Methode, bei AuAvendung 



der Methode der kleinsten Quadrate, die Gewichte der unhekannten 



Grossen zu berechnen.' Astron. Nachr., Vol. VIII, col. 463-468. 



A simplification of Gauss's method of 1823 for finding weights. 

 Not the same as 1830 Hansen. See 1832 Encke. 



1831 Hansen. ' Ueber die Anwendung der Wahrscheinlichkelts- 

 rechnung auf geodatische Vermessungen ini Allgemeinen, und iiber 

 die MAUPEKTUis'sche Gradmessung.' Astron. Nachr., Vol. IX, col. 

 189-220, 237-262. 



