to the Method of Least /Squares. 155 



1750 Mayer. Abhandlung iiber die Umwiilzung des Mondes um 

 seine Axe. Kosmographische Nachrichten u. Sammlungevi for 1748, 

 pp. 52-183. 



By twenty-seven observations npon the position of a moon spot 

 Mayer obtained twenty-seven equations each containing three un- 

 known quantities. To solve these he added together those nine 

 equations in which the values of the coefficients of one of the un- 

 known quantities were the greatest, then the nine in which these co- 

 efficients were the least and lastly the remaining nine ; thus obtaining 

 three resulting equations with three unknown quantities. 



May'er's method is given by Lalande, Astronornie, second edition, 

 Vol. Ill, pp. 418-428.^ See Wolf, Handhmh der Math., Vol. I, p. 

 279, Vol II, p. 199; and also below, 1830 Francoeur. 



[1754] KisTNER. Om geometriska aberrationer. SvenskaVetensk. 

 Acad. Handl. for 1753, p. 126. — German translation in Schwedische 

 AJcad. Ahhandl. for 1753, p. 131, 



Treats of errors in Surveying and probably contains nothing of 

 value on the theory of accidental errors. See also the same memoirs 

 for 1708, p. 147 and p. 159. 



1755 BoscovioH. I)e llttera ex/peditione per Poiitifieam ditionetn 



ad diiitetietidos duos nieridiani (/nidus. Romae, 4to, pp. xxii, 516. 



— Fi'ench translation by Hugon entitled Voyage astronomique et 



geograpJiique . . . . ; Paris, 1770, 4to. 



A method of combination of observations for the determination ot 

 the mean ellipticity of the earth from measured arcs of the meridian 

 is here used. The method itself is proved in the French translation ; 

 see below 1760. For description of the book see Touhunter, His- 

 tory of Theories of Attraction . . . ., Vol. I, pp. 305-321, 332-334. 



1756 Simpson. ' A letter to the Right Honourable George Earl 

 of Macclesfield, President of the Royal Society, on the Advantage of 

 taking the Mean of a number of Observations, in practical Astron- 

 omy.' Phil. Trans. Lond. for ] 755, Vol. XLIX, Pt. I, pp. 82-93. 

 — Reprint, see 1757. 



This memoir is interesting and valuable as being the first in which 

 the Theory of Probability is applied to the discussion of errors of 

 observation and in which the idea of a law of facility of error is im- 

 plied. At the beginning of the letter Simpson says that his attention 

 had been called to the subject by the fact that " some persons, of 

 considerable note, have been of opinion, and even jjublickly main- 

 tained, that one single observation, taken with due care, was as much 

 to be relied on as the Mean of a great number." 



The letter contains two propositions ; the first gives a method of 

 determining the probability that the error of the mean of n observa- 

 tions shall be less than an assigned value, provided it is equally prob- 



