M. DE TjACus AJlronomkal ObfeiVc7tions. 145 



Le employed in preference, b^caufe the periheliiU dlftance being 

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

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

 ■only geocentric longitudes and latitudes of the comet, de- 

 duced from the immediate oblervations of right afceniion and 

 declination, the heliocentric longitudes and latitudes mufl 

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

 not given mud be arbitrarily fuppofed, viz. the (hortened ^\(' 

 t2inQts(diJiantias cur tat as). This fuppofitionis 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 (hortened diftances in the planeof 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 vedors being given, with the angle 

 comprehended, to find the two true anomalies, the perihelial 

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

 Let therefore t s =^yf reprcfent the ecliptic at an infinite dlf- 

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

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

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

 place when the comet was obferved in K ; ST =r ^, S\ — ^, the 

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

 vation known by aflronomical tables ; let Cm and K^ be two 

 perpendiculars to the plane of the ecliptic, it will be Sm^Uy 

 S« s= u the two fhortened di{lances> 



The obferved geocentric long-itude of the comet in T:^5=:arc T "v^G j 

 the obferved geocentric longitude of the comet in I=ra~arc V ViJ'H; 

 the geocentric longitude of the fun by tables in T~^r=arc TVy=^A; 

 'the geocentric longitude of the fun by tables in Ir:^ — arc T ViJ'riBii 



Vol. LXXV. U Now 



