166 Mansfield Merriman — List of Writings relating 



Least Squares on the ground that any other process would lead to 

 impracticable calculations. 



I quote a historical remark on page 221 : "Ceterum principium 

 nostrum, quo jam inde ab anno 1795 usi suraus, nuper etiam a clar. 

 Legendre in opere Nouvelles methodes . . .com^tes, 1S06 prolatum 

 est " 



1810 Bessel. Zhttersaclmngen ilber die scheinbare und loahre 

 Bahn der grossen Cometen von 1 807, Konigsberg, 4to. 



The Method of Least Squares is used in determining the orbit and 

 is called " den nioindres quarres.'''' See Zach^s Monatl. Corres., 1810, 

 Vol. XXII, pp. 205-212. 



1810 Laplace. ' Memoire sur les approximations des formules 

 qui sont fonctions de tres-grands nombres, et sur leur application aux 

 probabilites.' Mem. Inst. France for 1809, pp. 853-415, 559-565. 



Pages 38:3-389 and 559-565 are devoted to the Theory of Errors, 

 and the principle of Least Squares is proved " lorsque les resultats 

 entre lesquels on doit prendre un milieu, sont donnt's cliacun par un 

 tres-grand noml)re d'observations, quelles que soient d'ailleurs les lois 

 de facilite des erreurs de ces observations." 



The matter of these pages is reproduced in the Theorie analytique 

 des Probabilites, pp. 329-335, 340-342 ; see below under 1812 for re- 

 marks concerning the proof. See Ball. Soc. Philom. Paris, 1810, 

 Vol. II, pp. 132-136 for an account of the contents of the memoir. 



1811 (tAUSS, ' Disquisito de dementis ellipticis Palladis ex oppo- 

 sitionibus 1803, 1804, 1805, 1807, 1808, 1809.' Comment. Soc. Got- 

 tingen, Vol. I, 26 pp. — French translation, see 1855 Bertrand. 



Twelve equations involving six unknown corrections to the ele- 

 ments of the orbit are solved by the Method of Least Squares. We 

 here find for the first time the notation 



[a6]=a' b'+a" b" +«'" V" +.... 



and also the algorithm for the solution of normal equations by suc- 

 cessive substitution, since univei'sally followed in lengthy computa- 

 tions. 



A partial translation of the above with comments is given by Zach 

 in the Monatl. Corres., 1811, Vol. XXIV, pp. 449-465. 



1811 Laplace. 'Du milieu qii'il faut choisir entre les resultats 

 des observations.' 3Iem. Inst. France for 1810, Ft. I, pp. 317-347. 



Contains " the theory of errors substantially coincident with so 

 much of the same theory as we find in pages 314-328 and 340-342 of 

 the Theorie. .. .des Prob?^ — Todhunter, History of Probability, 

 p. 490. See below 1812. 



