196 Mansfield Merriman — JList of Writings relatiiui 



mean asserts that the weights of the several vahies are not equal. 

 See below 1856 Airy and Winlock, 1S68 Stone and particularly 

 18V2 and 1873 Glaisher. 



The criterion has been used to some extent in the U. S. Coast Sur- 

 vey office, but has elsewhere, I believe, found no acceptance. 



1852 QuETELET. ' Sur quelques proprietes curieuses qui presentent 

 les resultats d'une sc'rie d'observations, faites dans la vue de deter- 

 miner une constant, lorsqxie les chances de rencontrer des ecarts en 

 plus et en moins soint egales et independantes les unes des autres.' 

 Bull. Acad. Belgique, Vol. XIX, Pt. II, pp. 303-317. 



An interesting investigation, illustrated by a discussion of meteoro- 

 logical observations. 



1852 Wolf. Beitrag zur Lehre von der Wahrscheinlichkeit. 

 Mittheil. Gesell. Bernior 1852, i)p. 133-134. 



1853 BivEi;. ' Theorie analytique des moindres carres.' Liou- 

 viUe's Jour. Math., Vol. XYIII, i)p. 169-200. 



The principle of the arithmetical mean is proved according to 1832 

 Encke. The term "risque de erreur" is given to the function 

 A-\-B2x^-\- (''^x^I)-\-2x^-\- . . . and it is shown that this becomes 

 a minimum when 2x^ is a minimum, and this condition is regarded 

 as furnishing " les valeurs les plus plausibles des inconnues." Form- 

 ulae for weights and mean errors aie also developed. 



1853 Caught, ' Memoire sur revaluation d'inconnues determinees 

 par uu grand nombre d'equations approximatives du premier degre.' 

 Com2J>tes Rendiis Aead. Paris, Vol. XXVI, pp. 1114-1122. 



It is maintained that the method of interpolation (1835 Cauchy) 

 can be used for determining several unknown quantities from a re- 

 dundant number of equations, witli results nearly as accurate as by 

 the Method of Least Squares. 



1853 Biekayme. 'Remarque sur les diiierences qui distinguent 

 I'interpolation de M. Cauchy de la methode des moindres carres, et 

 qui assurent la superiorite de cette methode.' Vomptes Rendus 

 Acad. Paris, Vol. XXVII, pp. 5-13. — LiouviUe's Jour. Math., Vol. 

 XVIII, pp. 299- 308. 



It is maintained that the two methods differ '■ completement," and 

 that even a contradiction exists. Cauchy's method, it is said, is only 

 a modiiication of the ordinary pi-ocess of elimination, which assures 

 no especial degree of probability to the results and which requires in 

 practice as many operations as the Method of Least Squares. See 

 below Cauchy. 



