to the Met/bod of Least Squares. 187 



1843 Akgelander, ' Ueber die Anwendung der Methode der 

 kleinsteu Quadrate auf einen besondern Fall.' Astron. Machr.^ Vol. 

 XXI, col. 163-168. 



Simplifies the formation of normal equations, etc., when the obser- 

 vations are made on the simple sums or differences of the unknown 

 quantities. 



1843 BERKHA>f. (Teher die Methode der kleinsteu Quadrate. 

 Blankenburg, 8vo. 



1843 CouRNOT. ' E.v^yositioti. de la theorie des chances et des proh- 



abilites.'' l^aris, 8vo, pp. viii, 448. — German trans., Braunschweig, 



1849, 8vo. 



Chapters on the theory of means and the adjustment of observa- 

 tions are given. At the end is a table of values of the error function. 

 Courxot''s methods are often quite awkward. 



1843 Gerlixg. ' Die Ausgleichungs-Rechnung der practischen 

 Geometric^ oder die Methode der Meinsten Quadrate mit ikren An- 

 wendungen auf geoddtische Aufgabevi.'' Hamburg and Gotha, 8vo, 

 pp. xix, 409, and 4 pi. 



This book is dedicated to Gauss. The principle of Least Squares 

 is assumed as the basis of the methods of adjustment. It consists of 

 four parts ; the first treats of direct, the second of indirect, and the 

 third of conditioned observations, while the fourth discusses the form 

 and number of conditional equations which need to be considered in 

 the adjustment of triangulations. 



The book is fully illustrated with practical examples, and contains 

 the best systematized development of the application of the method 

 to the treatment of simple geodetic measurements that has yet ap- 

 peared. Gerling issued later (1845, 1855, 1862) some papers sup- 

 plementary to the work, one of which contains a long list of errata. 



1843 Reuschle. ' Ueber die Deduction der Methode der kleinsteu 

 Quadrate aus Begriffen der Wahrscheinlichkeitsrechnung.' Crelle's 

 Jour. Math., Vol. XXVI, pp. 333-364 ; Vol. XXVII, pp. 182-184. 



This is a critical examination of the deduction of the expression 

 for the probability of an error between given limits and of other 

 points in the " Metaphysik" of the Method. Encke's proof of the 

 validity of the arithmetical mean (1832) is also examined and found 

 to be imperfect. 



1844. Encke. ' Bemerkungen zu der Abhandlung No. 22. Band 

 26. Heft 4, dieses Journals." Crelle's Jour. Math., Vol. XXVIII, 

 pp. 213-222. 



