to the Method of Least Squares. 181 



ExcKE takes y=zq){x) as the equation of tlio curve expressing the 

 probability of error, and regarding x and y as contimious variables 

 recognizes clearly that for a given error <p(;'') must be an infinitesi- 

 mal. But strange to say he deduces 



'V TV 



in which A is a finite quantity. 



The second memoir contains tlie pi-actical features of the method — 

 Gauss's algorithm for the solution of normal equations, Gauss's 

 (1823) and Hansen's (1830 and 1831) methods of determining 

 weights, etc. The third is devoted to the discussion of conditioned 

 observations. At the time of publication these memoirs must have 

 been of great value to students. 



1832 LiTTKOA\\ THe WahrschelnUchkeitsreehnung und Hire An- 

 wenclung aiif das icissenschaftlicJte und prartische Leben. Wien, 8vo. 



1832 Puissant. ' Deuxieme memoire sur I'application du calcul 

 des probabilites aux mesures geodesiques.' Mem. Acad. Paris, Vol. 

 XI, pp. 123-156. 



Adjustment of triangulations, determinations of probable errors, etc. 



1834 Bessel. ' Betrachtung iiber die Methode der Yervielfal- 

 tigung der Beobachtungen.' Astron. JSTaehr., Vol. XI, col. 269-290. 

 — Ahhmidl. von Bessel (Leipzig, 1875), Vol. Ill, pp. 306-317. 



This valuable paper deduces rules for the adjustment of angles 

 taken by the method of repetitions, and formula? for finding their 

 weights and probable errors. 



1834 SxROOTjrAN. BevatteUjk onderrigt in de ICansrekening^ of 

 de leer der vx(c(rschijnlykheden. Breda, ] 2mo. 



1835 Caught, 'Memoire sur I'interpolation.' Lith. MS. — Trans- 

 lation in Lond. Phil. Mag., 1836, Vol. VIII, pp. 459-468. — Reprinted 

 in LiouvUle's Jour. Math., 1837, Vol. II, pp. 193-205; m Moigno's 

 Lemons de calcul differ entiel (Paris, 1840), pp. 513-526. 



When an empirical formula is to be derived from a great number 

 of observation equations, Cauchy's method may be used as easily 

 although perhaps with less accuracy than the Method of Least 

 Squares. See below 1853 Bienayme and Caught, 1842 Grunert 

 and 1861 Schott. See an article by Bartlett in Anier. Jour Sci 

 1862, Vol. XXXIV, pp. 27-33. ■ ■ ■' 



1836 PoissoN. 'Formules relatives aux probabilites qui dependent 

 de tres grand n ombres.' Gomptes Rend. Acad. Paris, Vol. II 

 pp. 603-613. 



