J 4 6 . M. de.Zach's- Ajh-momlcal Observations. 
Now for the firft obfervation the angle of elongation is b~a; 
for the angle ATG = arc AG = r yju&A - n| vj G — loinwo - lon°x 
comet, ~b — a\ 
the angle of the annual parallax Sm'X ~^b'- h ~ a )-..== e ; 
o° 
the angle of commutation »?ST ±± 1 go o - e-\- (b~ a) ~f ; 
from whence the heliocentric longitude of the comet™ 
b ~ i 8 o° -f / = tr. 
V 1 J o 
The fame at the fecond obfervation in L 
Angie of elongation w /S’ - & 
Angle of annual parallax e — «, 
• o ^ 
Angie of commutation <p-.= jgo o — s + (/3 — a) ; 
heliocentric longitude of the comet in 1 = 0 - + 
putting -now the heliocentric latitude foen from S = k ; 
the geocentric latitude feen from T=,/^ 
the heliocentric latitude will be fi D v tang. A';- 
fin. ( b — a ) o 5 
the fame with IOz it will be - n ■ ? ' ta ' 1g \ x - =s tang., k heliocentric 
un. ((3—ssj Q 
latitude in K. 
Having thus determined the heliocentric latitudes of two- 
obfervatrorts, the radius vectors wilheafily be found in the fup- 
pofition made for the fhortened dijdances,. for they are in the. 
fame ratioito the radius vectors as the cofine of the heliocen- 
tric latitudes. are to the radius — . i ; therefore the radius vector 
• « Zl' 
m of the firfc obfervation will he tz — and the radius vector of 
cpi. k . 
the fecond obfervation b — — 7 - 
' COf. K 
Takingmow the difference between • the found, heliocentric' 
longitudes, we get 1 the heliocentric motion of the comet upon 
the ecliptic between two Ihortened diftances, which is to be; 
reduced upon the comef’s orbit, this heliocentric motion is 
therefore y ~ g =* m. No.w.to reduce this motion we have, firft, 
fin.ua 
