to the Method of Least Squares. 197 



Further remarks by Bienayme referring to tliis discussion are 

 given in pages (58-69, 197, 206 of Vol. XXXVII of the Couiptes 

 Rendus. 



1853 Cauchy. 'Memoire sur I'interpohition, ou Remarques sur 



les Remarques de M. Jules Bienayme.' (Joniptes Rendus Acad. 



Paris, Vol. XXXVII, pp. 64-68. 



Gives an extract from the memoir of 1835, and maintains that in 

 many investigations the method of interpolation is preferable to that 

 of Least Squares. 



1853 Cauchy. 'Sur la nouvelle nic'thode d'interpolation comparee 

 a la methode des moindres carres.' Comptes Rendus Acad. Paris, 

 Vol. XXXVII, pp. 100-109. 



The new method is claimed to be often the shortest, and the 

 Method of Least Squares is said to give most probable results only 

 under certain conditions. 



1853 Cauchy. 'Memoire sur les coefficients limitateurs ou restric- 

 teurs.' Comptes Rendus Acad. Paris, Vol. XXXVII, pp. 150-162. 



In the latter part of the article the " restricteurs" are applied to 

 the theory of Least Squares, and it is concluded that that Method 

 furnishes most probable results only when the law of facility of error 

 is the same for all the errors, when no limits can be assigned to the 

 magnitude of an error, and when the probability of an error x is 

 proportional to e-'i^^*. 



1853 Cauchy. ' Sur les resultats moyens d'observations de meme 

 nature, et sur les resultats les plus probables.' Co)iiptes Rendus 

 Acad. Paris, Vol. XXXVII, pp. 198-206. 



The conclusions of the preceding article are confirmed. 



185;-5 CAU(mY. 'Sur la probabilite des erreurs qui affectent des 

 resultats moyens d'observations de raenie nature.' Comptes Rendus 

 Acad. Paris, Vol. XXXVII, pp. 264-272. 



Shows that the most probable values may sometimes differ from 

 those found by the Method of Least Squares. 



1853 Bienayme. 'Considerations a I'appuf de la decouverte de 

 Laplace sur la loi des probabilites dans la methode des moindres 

 carres.' Comptes Rendus Acad. Paris, Vol. XXXVII, pp. 309-324. 

 —Liouville's Jour. Math., 1867, Vol. XII, pp. 158-176. 



An answer and review of some of Cauchy's articles: also main- 

 tains that the mean of the sum of the squares of the errors is under 

 all circumstances a measm-e of the precision of the observations. 



