G4 
MR. RUMKER’S OBSERVATIONS 
Hence, Ellipsis. 
Passage over Periliel. 1825, Dec. ll d 4 h 45 m 
T . , - f Periliel.. 3 18° 28' 54" 
Longitude of | Node >>215 44 58 __ 
Inclination 33 31 3 
Logarithm of Perihelion Distance 
Logarithm 9.9802984 
4> 72° 52' 19" 
Logar. half Parameter . .0.3866458 
Logar. half Major Axis 1.4438875 
Logar. half Minor Axis 0.9152666 
Logar. Sidereal Motion 1.3841754 
Logar. Sidereal Revolution 53509.3 Days. 
8 s 
Parabola. 
. . . .Dec. 10 d 16 h 36 m 23 s M. T. Stargard. 
319° 6' 39" \ From Mean Equinox, Decem- 
215 44 58 / her 20, 1825. 
33 31 3 
0.0950103 
Motion retrograde. 
The elements of this Comet might have been found, without the assistance 
of the usual methods, in the following manner : — 
The time of the Comet’s passage through its node could be deduced from 
the observations, by finding through interpolation when its geocentric and 
consequently also its heliocentric latitude was =0. But the Comet was at 
that time near its opposition, so that a rough estimation of its distance § from 
the earth was sufficient to find the longitude of the node by the formula 
p sin (« — L) 
tang (8 — L) = 
R + p cos (a. — L) 
where L is the heliocentric longitude of the earth, R its radius vector, and a the 
Comet’s geocentric longitude ; for as a — L is small near the opposition, can 
but little influence the angle of commutation. 
We had also the opportunity of observing the Comet when the node was in 
opposition. For this time is a plane passing through Sun, Comet, and Earth, 
the plane of the Comet’s orbit consequently • ^ g ^ = tang I., (3' being the 
Comet’s geocentric latitude, and I the inclination of the orbit. Having thus 
obtained approximate values of 8 and I, the rest of the elements might be 
found as usual, and corrected by three Hypotheses. We had also the oppor- 
tunity of observing the Comet in its opposition, when its heliocentric and 
geocentric longitudes were equal. Consequently, tang c ^. 8 ^ = tang u', u' 
being the argument of latitude whence r" is known, and the interval of time 
found according to Lambert’s Theorem with r", r and u', if this interval does 
