154 Mansfield Merriman — List of Writings relating 



Seventh Proof- - see 1825 Ivory. 



Eighth Proof --- 1826 Ivory. 



Proof of the Arithmetical Mean 1832 Encke. 



Ninth Proof 183'? Hagen. 



Tenth Proof 1838 Bessel. 



Laplace's Proof extended and improved. 1844 Ellis. 



Eleventh Proof 1844 Donkin. 



Adrain's Second Proof rediscovered 1850 Herschel. 



Twelfth Proof 1856 Donkin. 



On the Arithmetical Mean 1864 DeMorgan. 



[Thirteenth Proof]... 1870 Crofton. 



Analysis of several Proofs 1872 Glaisher. 



Proof of the Arithmetical Mean 1875 Schiaparelli. 



I have drawn information from every source within my reach. On 

 the Proofs of the Method I have found Glaisher's memoir of 1872 

 of the greatest value, and while working on the early writers Tod- 

 hunter's Slstory of Probability was continually before me. It is 

 here also the place to acknowledge my indebtedness to Prof. H. A. 

 Newton of Yale College for valuable suggestions and kind assistance. 



1722 Cotes, '^stimatio errorum in mixta mathesi, per variationes 

 partium trianguli plani et sphierici.' Opera vniscellanea (appended 

 to Harmotiia niensurarum y Cantabrigise, 4to), pp. 1-22. — Memoir 

 republished, Lemgoviae, 1768, 8vo. 



Only the closing paragraph relates to accidental errors of observa- 

 tion; this gives the following rule: "Sit^j locus Objecti alicujus ex 

 Observatione prima definitus, q, r, s ejusdem Objecti loca ex Obser- 

 vationibus subseqi;entibus ; sint insuper P, Q, P, /S' pondera reciproce 

 proportionalia spatiis Evagationum, per quiie se diffundere possint 

 Errores ex Observationibus singulis prodeuntes, qua^que dantur ex 

 datis Errorum Limitibus ; & ad puncta p, q, r, s posita intelligantur 

 pondera P, Q, P, S, & inveniatur eorum gravitatis centrum Z : dico 

 punctum Z fore Locum Objecti maxime probabilem, qui pro vero ejus 

 loco tutissime haberi potest." 



Cotes's rule only agrees with modern methods when the observa- 

 tions are directly made upon one quantity. See Laplace, Theorie 

 analytique des ProbablUtes, third edition, p. cxxxviii, p. 346; and 

 Ivory, Phil. Mag., 1825, Vol. LXV, p. 4. 



1 749 EuLER. Pihce qui a remjmrte le prix de VAcademie royale 



des sciences en 1748, sur les vnegalities du mouvement de Saturne et de 



Jupiter. Paris, 4to. 



Contains a method for the combination of linear equations similar 

 to the following^. 



