M. DE Zach's /^Jlronomical Obfervaiions, 14-^ 



be employed in preference, becaufe the perihellal diflance being 

 a conftant quantity, the angle of pofition then becomes the true 

 anomaly of the comet ; but as the data of this problem aie 

 only geocentric longitudes and latitudes of the comet, de- 

 duced from the immediate obfervations of right afcenhon and 

 declination, the heliocentric longitudes and latitudes mufl 

 firfl be calculated ; but as thofe data are not fiifficient, what is 

 not given mufl be arbitrarily fuppofed, 'viz. the fhortened dif- 

 t2incQ^(dlflantias curtatasyTKis fuppofition is changed and altered 

 until the calculation will agree with the three obfervations, 

 then the difference between two longitudes is the angle com- 

 prehended between the two fhortened diftances in the plane of the 

 ecliptic ; the whole reduced to the plane of the comet's orbit by 

 means of the heliocentric latitude, gives the difference between 

 the anomalies comprehended by two radius vectors, the problem 

 then is reduced : two radius vectors being given, with the angle 

 •comprehended, to find the two true anomalies, the perlhelial 

 diflance, and the time the comet puts in running its anomalies. 

 Let therefore T^^^ys reprcfent the ecliptic at an infinite dif- 

 tance ; QPR the apparent elliptical or parabolical path of a co- 

 met; S the fun's center; P the comet's perihelion ; T the place of 

 the earth when the comet was flrft obferved in C ; I the earth's 

 place when the comet was obferved in K ; ST = ^, SI = (?, the 

 dlflances from the earth to the fun at the firfl and fecond obfer- 

 vation known by aftronomical tables ; let Qm and K;z be two 

 perpendiculars to the plane of the ecliptic, it will be Sm=zUf 

 Sn = v the two fhortened diftances, 



The obferved geocentric longitude of the comet in Tzzazzarc T Vj'G ; 

 the obferved geocentric longitude of the comet in I— azrarc TVfH; 

 the geocentric longitude of the fun by tables in Trz^~arc *Y*VS=s=A.; 

 the geocentric longitude of the fun by tables in I=^=:arc T ^^"B, 



Vol. LXXV. U Now 



