192 Mansfield 3ferriinan — List of Writings relating 



1850 Bache. ' Comparison of the Results obtained in Geodesy by 

 the Application of the Theory of Least Squares.' Proc. Amer. Assoe. 

 for 1849, pp. 102-105. 



A statement of probable errors of measurements of angles in U. S. 

 Coast Survey triangulations. At the end of the paper, wliieh seems to 

 be a biief abstract of the original, there are some remarks by Peirck, 

 Gould and Henry, which probably were incorrectly reported. 



1850 Encke. 'Ueber die Anwendung der Wahrscheinlichkeits- 

 Rechnung auf Beobachtungen.' Berlin, Astron. Jahrh. for 1853, pp. 

 310-351. 



The object of this paper is to establish greater confidence in the 

 practice of taking the ai-ithmetical mean and in the validity of tlie 

 exponential law of facility of error. Six of the ten problems of I;A- 

 grange's memoir of 1774 are translated and a few comments added. 

 Hagen's demonstration of 1837 is also given in full and spoken of in 

 very favorable terms. Encke alludes to the use of the " Erfahrungs- 

 satz des Prinzips des ai'ithmetischen Mittels" in his memoir of 1832 

 and says, "so blieb doch immer eine willktihrliche Annahme iibrig." 

 At the end of the article is an attempt to explain whyy_ ^ (p{x)dxz^\^ 

 when (p{x) is the probability of the error x. 



1850 Guy. 'On the Relative Value of Averages derived from 

 different Observations.' Joitr. Statis. Soc, Vol. VIII, pp. 30-45. 

 The observations discussed are statistical facts. 



1850 Herschel. ' Quetelet on Probabilities.' Edinlmrgh Ren., 

 Vol. XCII, pp. 1-57. — HerschePs Essags (London, 1857, 8vo), pp. 

 365-465. 



This paper contains in a popular form another proof of the Method 

 of Least Squares. Supposing a stone dropped with the intention that 

 it shall hit a mark on a horizontal plane, the reasoning assumes that 

 the deflections from rectangular axes tlirough the mark are independ- 

 ent ; and deduces the exponential form ce~^' *" for the law of devia- 

 tion or error. From this the Method of Least Squares at once 

 follows. This proof was put into algebraic language by Ei.ijs (see 

 below) and the unwarrantable character of the assumption clearly 

 pointed out. See above 184r) Bravais, and below 1857 Boole, 1867 

 Thompson and Tait, 1872 Schlomilcii, and particularly 1872 Glai- 

 SHER. See also 1808 ^^drain, where this proof was first given. 



1850 Ellis. 'Remarks on an alleged Proof of the "Method of 

 Least Squares," contained in a late number of the Edinhnrgh Review.'^ 

 Lond. Phil. Mag., Vol. XXXVII, pp. 321-328, 462. —Also Ellis's 

 Mathematical Writings (Cambridge, 1863, 8vo), pp. 51-62. 



