194 Mansfield Merriman — List of 'Writings relating 



Part III of this paper ofters some critical remarks on the Theory 

 of Least Squares with particubir reference to Ellis's paper of 1850. 

 Herschel's proof, it is said, "should be treated with respect." The 

 Method of Least Squares may be used, if for no other reason, because 

 "it is a very good method," as shown by Gauss's proof of 1823. 



1851 HossAKD. ' Note sur la methode des moindres carres.' ]^ouv. 



Annal. Math., Vol. X, pp. 456-460. 



Ivory's first proof (1825) is here rediscovered under a slightly dif- 

 ferent form. 



1851 Paucker. Uebei'einstimmung der ausgeglichenen LTrsachen 

 mit den durch Bessel's Verfahren gefundenen. Arbeit KiXrland. 

 GeselL, Vol. IX, pp. 170-18:3. 



1851 Paucker. Einfluss der Gewichte auf die Ausgleichung. 

 Arbeit Kilrland. Gesell, Vol. IX, pp. 183-193. 



The substance of this and the preceding article is given in the fol- 

 lowing. 



1851 Paucker. • Zur Theorie der kleinsten Quadrate.' Bull, 

 phys. math. Acad. /St. Peters., Vol. IX, col. 113-125; Vol. X, col. 33- 

 43, 233-238. — MM. math. Acad. >St. Peters., Vol. I, pp. 188-204, 

 333-346, 433-439. 



Contains new methods of computation, tests of accuracy, etc., 

 which appear to be of little value. 



1852 Biexayme. ' Memoire sur la ])robabilite des erreurs d'apres 

 la methode des moindres carres.' Liouville'' s Jour. Math., Vol. 

 XVII. pp. 33-78, — Mem. . par divers savans.. Inst. France, Vol. 

 XV, pp. 615-663. 



After some interesting critical remarks, Laplace's analysis (1812) 

 is given considerably simplified. According to Bienayme's investi- 

 gation the formula? for probable error ordinarily used are only cor- 

 rect for one unknown quantity. For two, three and four unknown 

 quantities, he finds that the probable errors should be respectively 

 1.746, 2.281 and 2.716 times larger than those given by the usual 

 formuhii. His expression for the proljability that an error is included 

 between given limits differs sensibly for several unknown quantities 

 from the common probability integral, particularly for limits but 

 little removed from £c=:0. See 1873 Wrede. 



See Coniples Pendus Acad. Paris, Vol. XXXIV, pp. 90-92, or 

 Liouville's Joxir. Math., Vol. XVII, pp. 31-32 for a report on this 

 memoir. See also Meyer's (Jalcul des Prohabilites, pp. 377-408. 



1852 Biver. Tli'eorie des moindres carres etablie par Vatialyse 

 pxf.re. Bruxelles, 8vo. 



Pi'obably similar to Iiis memoir of 1853. 



