200 Mansfield Merrhnan — Ijist of Writings relating 



1855 Lloyd. On the mean results of observations. Trans. Irish 

 Acad., Vol. XXII, pp. 61-73. 



See abstract in Proc. Irish Acad., Vol. IV, pp. 180-183. 



1855 Peiroe (B.). ' Report upon the Determination of Longitude by 

 Moon Culminations.' Jiej). Coast Sur. U. S. for 1854, pp. 109*-120*, 



" The small errors which are beyond the limits of human percep- 

 tion, are not distributed according to the mode recognized by the 

 Method of Least Squares, but either with the uniformity which is the 

 ordinary characteristic of matters of chance, or more frequently in 

 some arbitrary form dependant upon individual peculiarities " 



1855 ScHOTT. 'Adjustment of horizontal angk^s of a triangulation.' 

 Hep. Coast Sur. U. S., for 1854, pp. 70*-86*. 



This and many of Schott's following papers are very valuable, 

 but they are not usually clear except to those who already understand 

 the subject. 



1855 ScHoiT. ' Probal»le error of observation derived from^ obser- 

 vations of horizontal angles at any single station, and depending on 

 directions.' Eep. Coast Sur. U. S. for 1854, pp. 86* -95*. 



A discussion of 350 measurements taken at eleven stations. 



1856 Airy. 'Letter from . . . [liemarks on Peirce's Criterion.]' 

 Gould's Astron. Jour., Vol. IV, pp. 137-138. 



The Criterion is strongly opposed. ". . . . the whole theory is 

 defective in its foundations and illusory in its results." It must be 

 said, however, that some of Airy's objections are not sup])orted by 

 very good logic. 



1856 WiNLOCK. ' On Professor Airy's objections to Peirce's Cri- 

 terion.' GoiikVs Astron. Jour., Vol. IV, pp. 145-147. 



Airy's objections are taken up in detail ; some of them are shown 

 to apply equally well to the Method of Least Squai-es. 



1856 Peters. ' Ueber die Bestinunung des wahrscheinlichen Feh- 

 lers einer Beobachtung aus den Abweichungen der Beobachtungen 

 von ihrem arithraetischen Mittel.' Astron. Nachr., Vol. XLIV, col. 

 29-32. —Trans, in Rep. Coast Sur. U. S. for 1856, pp. 307-308. 



Let '^x be the sum of the residual errors all taken positive, and n 

 the number of direct observations of equal weight. Then Peters' 

 result is, tliat r, the probable error of a single observation is, 



r = 0.845347 - y-^^ — - 

 Vw(?^— 1) 



See on this formula 1869 Lijroth, and 1875 Helmert 



