208 Mansfield Merrinuiii — TAst of Writhigs relating 



1863 KuRZ. ' Ueber der Metliode der kleinsten Quadrate.' Vier- 



teljahrsschr. Gesell. Zurich., Vol. VIII, pp. 22.3-240. 



On the various methods of formiug and sohini;' normal e(]uations, 

 of determining- weights, ete, 



1863 LoBATTO. Over de waarschijnlijkheid van gemiddelde uit- 

 korasten uit een groot aantal waarnemingen. Archief. Wish: 

 Genoots, Vol. II, pp. 96-127. 



1864 CiiAuvENET. 'Method of Least Squares.' Appendix to 

 Munual of SpJierical and Practical Astrononiy (l^hiladel])hia, 8vo), 

 Vol. II, pp. 469-566. — Also as separate issue under title ' A Treatise 

 on the Method of Least Squares,. . . .' Philadelphia, 1868. 



This is mainly an abridgment of Encke's memoirs of 1832. 

 Excke's demonstration of the rule of the arithmetical mean is in 

 particular set forth Avith confidence. The reasoning showing that if 

 (p{ii') is the probability of the error x, qj{x)dx is the rigorous proba- 

 bility that an error falls between x and x-\-dx is very illogical. At 

 the end are valuable tables, two of the probability integral, and 

 others for using Peirce's criterion which is given nearly in the woids 

 of its author; see 1852 and 1856. Chauvenet adds an approximate 

 criterion for the rejection of one doubtful observation, which is de- 

 rived " directly from the fundamental formula upon which the whole 

 theory of the Method of Least Squares is based." 



1864 Christo¥Fkt.. 2 B<^''^tim»iung einer Oberfldche dwell lokale 

 3fessum/en. [Berlin], 4to. 



1864 DeMorgan. ' On the Theory of the Errors of Observation.' 

 7rans. Catvb. Phil Soc, Vol. X, pp. 409-427. 



This is a very valuable contribution to the theory of the arithmet- 

 ical mean. It is shown that the average "is not merely the w?e</?i 

 value of all the given values: it is also the tnean supposition of all 

 possible suppositions as to the mode of obtaining that value," but 

 that " the average is the most probal)le result only so long as we 

 know nothing of the law of facility of error." See Glaisher, Mem. 

 Astron. Soc.^Lond, 1872, Vol. XXXIX, p. 90. 



DeMorgan suggests the name '•'■critical error'''' instead oi probable 

 error. The entire paper, like all of DeMougan's writings, is very 

 interesting and suggestive. 



1864 ScHOTT. ' Development of Bessel's function for the effect of 

 periodic forces, for durations of periods frequently occurring in mete- 

 orological and magnetical investigations; with examples.' Pep. Coast 

 Snrmy IT. 8. for 1862, pp. 232-235. 



See above 1828 Besskl. 



