64 



MR. RUMKER'S observations 



Hence, Ellipsis. Parabola. 



Passage over Perihel. 1825, Dec. 11'' 4:^ '15" 8' Dec. IC 16^ 36" 23» M. T. Stargard. 



T . J »rPerihel..318° 28' 54" 319° 6' 39" "1 From Mean Equinox, Decem- 



Longitudeot|j;,^jg ..215 44 58 215 44 58 / ber 20, 1825. 



Inclination 33 31 S..' 33 31 3 



Logarithm of Perihelion Distance 0.0950103 



Logarithm 9.9802984 Motion retrograde. 



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. 



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 g from 

 the earth was sufficient to find the longitude of the node by the formula 



/ T \ p sin (a — L) 



tang (8 — L) == -^ ^-— ^-r 



° ^ ^ 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 « — L is small near the opposition, f 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 



tang g' 



sin(«'-e) = tang I., ^' being the 

 Comet's geocentric latitude, and I the inclination of the orbit. Having thus 

 obtained approximate values of & 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, ' ^ T — - = 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 



