40 Rosenberger on Halley's Comet at its last Appearance. 

 The other observers, 



— 77 = 0-67333 = $U locr m"^ = 3-88248 



Combining at last all the observations, I gave to the right 

 ascension of the different observers the following values: To 

 Messier =1; Maraldi-411; Cassini -386 ; Bradley •2475 ; 

 Hell -218; Darquier, &c. -120, as resulting from the last 

 determinations of ?«". In order, however, to enable others 

 to use other combinations at pleasure, I quote here separately 

 the products (act), (ae), &c. as applied by me to the difft3- 

 rent series of observations*. 



Assuming the semi-major axis of the comet on January 

 1759, = 18-083275+ ( A«), I find according to the well-known 

 method of elimination of Gauss, and its beautiful extension 

 in the Theoria Combiiiationis Observ. Error, ruin, obnoxice, the 

 sum of the least squares of the remaining errors. 



M = 270264." + 1-4.924 W = 270264" + ( A fl.) 30895". 

 whence the mean error of Messier's right ascensions observed 

 in the equator = 32''-23. Moreover, 



V = 1-49516-3 ?J + TO. 7-89055-1 n (ee) = 8-80683 

 u = 0-81963-3 n + w . 7-24225-5 n (88) = 9*47798 

 z = 1-90024-6 w + TO. 9-99058-7 (yy) = 9*55376 

 y = 1-56770-1 n + w . 8-29886-2 (/3 ^) = 0-48475 

 X = 1-24440-8 n + w. 7-57634-1 n (««) = 0-51459 

 where the numbers given are logarithms. 



Hence we obtain the corrections of the elements laid down 

 for our basis ; and the mean errors of this determination, and 

 the elements of the comet's path at noon of January 1759, 

 referred to the mean equinox at the same time, are : 



Semi-major axis =18-083275 + (Aa) 



Eccentricity = 0-96767572 + ( A«)0-0017766 



T. of perihelion passage = March 12. 57093 + (Aa) 0-04281 

 Long, of ascending node = 53° 47' 46"-88 - ( Aa) 44"-29 

 Dist.of perih. from node = 110 37 29-55 +(Aa) 237"-61 

 Inclination of the orbit. = 162 21 43-70 -(Aa) 41 '90 



The mean error of the elements may, at least, serve the 

 purpose of judging in some measure of the proportional un- 

 certainty of single" determinations. With this view I have 

 also tried what would liave resulted from Messier's observa- 

 tions by themselves ; whence I easily obtained the system of 

 elements, corresponding with all the other observations. I sub- 



» The author here gives a table of the values of vK ai/,ev,Tv, a v, n »< 

 %»,a^, ae, nT, a oi, an,ai, c^, eT,eu, en,ei,T\ T a, T n, T i, a', a n, 

 u i, 7»', n i and »', for each observer. _ ^ 



join 



