176 Mansfield Merrimmi — List of Writings relating 



likely, and that the law of facility of error is the same at every ob- 

 servation ; but PoissoN makes neither of these assumptions." — Tod- 

 hunter in Trans. (Jamb. Phil. Soc, 1869, Vol. XI, p. 219. 



1824 Puissant. 'Application de la methode la plus avantageuse 

 a la determination de I'aplatissement du spheroide osculateur en 

 France, par le comparaison d'un arc de meridien avee un arc de par- 

 allele.' Ferii.ssac's Bull. ^ci. Math., Vol. I, pp. 271-2*74, — Connaiss. 

 des Terns for 1827, pp. 230-232. 



A general statement of the method, which seems to have been else- 

 whei'e published in detail. 



1825 Ivory. 'On the Method of the Least Squares.' T'illodi's 

 Phil. 3Iag., Vol. LXV, pp. 3-10, 81-86, 161-168. 



This paper contains two attempted proofs of the principle of Least 

 Squares by methods independent of the Theory of Probability. The 

 first, in page 5, rests on a vague analogy with the properties of a 

 lever and is in the words ef Elus " little more than a petitio prin- 

 eipii concealed by a metaphor." The second, in pages 6-7, rests on 

 the supposition that " the mean of the sum of the squares of the 

 errors may be taken as a measure of the precision of the observa- 

 tions" which can scarcely be assumed as evident ; this is similar to 

 Gauss's proof of 1823. 



Pages 81-86 are devoted to discussing the probability of errors. 

 Ivory makes no distinction between true errors and residuals, and 

 does not recognize that the probability of any definite error mixst be 

 an infinitessimal. The remaining pages attempt to show that the 

 Method of Least Squares cannot give the most advantageous or 

 probableresultsunlessthelawof facility of error is <p (a;) = ce~"' ^ , and 

 that Laplace's demonstration " whatever merit it may have in other 

 respects is neither more or less general than the other solutions of the 

 problem." 



These two proofs are examined and exposed by Ellis in 1844, and 

 the second proof with the criticisms on Laplace are analyzed by 

 Glaishek in 1872. See also 1851 Hossard. 



1825 MuNCKE. ' Beobachtung.' Art. in Gehler^s PhysiJcalisches 

 Worterbuch, second ed. Vol. I, ])p. 884-912. 



Contains matter from 1823 Gauss and 1819 Paucker. 



1826 Gauss. 'Chronometrische Lilngenbestimmung.' Astron. 

 JVachr., Vol. V, col. 227-240, 245-248. — See also 1855 Bertrand. 



The Method of Least Squares is used and formulae for finding 

 mean errors of the results given. 



