Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: Grosse zu begehen; Hire Mittheilung muss ich bis auf eine andere Gelegenheit versparen. See 1816 Bessel, and also page 196 of the memoir 1816 Gauss. 1815 Laplace. ‘Sur 1'application du calcul des probabilites a la philosophie naturelle.’ Connaissance des Tems for 1818, pp. 361- 381. ?First Supplement to third edition of Theorie…. des Prob. (Paris, 1820, 4to), pp. 3-26. This is devoted partly to a general description of Laplace’s proof of. the Method of Least Squares, and partly to the discussion of the probability of results obtained by that method; a numerical example illustrates the use of his formulae. See Todhunter, Hist. of Probability, p. 610; also see 1869 Todhunter. 1816 Beeck-calkoen. Over de Theorie der Gemiddelde Waardij. Verhandl. Nederland. Inst., Vol. II, pp. 1-19. Treats of Laplace’s method of adjustment of 1792. 1816 Bessel. ‘ Untersuchungen tlber die Bahn des OLBERSSchen Kometen.’ Abhandl. Akad. Berlin for 1812-13, pp. 117-160 of the math. section. Bessel defines the probable error as follows:
Ich verstehe unter dieser Benennung die Grenze, die eine Anzahl kleinerer Fehler von einer gleichen Anzahl grosserer trennt, so dass es wahrscheinlicher ist, eine Beobachtung innerhalb jeder weiteren Grenze von der Wahr- heit abirren zu sehen, als aussernalb derselben. If we designate by 2x 2x2 ? the mean of the errors all taken positively, by the mean of the squares of those errors, and by r the probable error of a single observation, his demonstration shows that 5 fe n r=. 0.8453? or r =. 0.6745 n n Bessel does not distinguish between true errors and residuals. These formulas he uses in finding the probable errors of the elements of the orbits, which are deduced by the help of the Method of Least Squares. 1816 Gauss. ‘ Be…
