AL de Zach’s Agronomical Obfervatiom » 145 
be employed in preference, b'ecaufe the perihelial didance being 
a condant quantity, the angle of podtion 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 obfervations of right afcendon and 
declination, the heliocentric longitudes and latitudes mud 
fird be calculated ; but as thofe data are not diffident, what is 
not given mud be arbitrarily fuppofed, vi%. the Shortened dif- 
tancesf dijiantias. curtains ). This 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 diortened didaiices in the plane of the 
ecliptic ; the whole reduced to the plane bf 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 perihelial 
diftance, and the time the comet puts in running its anomalies. 
Let therefore T 23 reprefent the ecliptic at an infinite dii~ 
fance ; QFR 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 fird obferved in C ; I the earth’s 
place when the comet was obferved in K ; ST “ d, SI = <£, the 
didances from the earth to the fun at the fird and iecond obfer- 
Vation known by adronomical tables ; let Cm and K n be two 
perpendiculars to the plane of the ecliptic, it will be Sm = u y 
Sn = v the two diortened didances. 
The obferved geocentric longitude of the comet in T~za — are V yyG ; 
the obferved geocentric longitude of the comet in I — atrrare V wH j 
the geocentiic longitude of the fun by tables in T~£~arc 
the geocentric longitude of the fun by tables in I“2~arc ^ 
Vol, LXXV. U 
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