150 ON THE COMET OF SEPTEMBER 1862. No. 2. 



Adopting the above elements, we have the following expres- 

 sions for the comet's heliocentric co-ordinates referred to the plane 

 of the Equator and the two corresponding planes : 

 Log sin X =[9-9976609] + log sin (191 e 23'.96 + v.) 

 Log tan A =[+ 9-0149823] + log tan (19123'.96 + v.) 



x = r cos (141 21 ' 22 + A) cos X 



y = r sin (141 21' 22 + A) cos X = x tan (141 21' 22 + A) 



z = r sin X 



where r is the comet's radius vector and v the true anomaly, 

 reckoned according to the order of the signs, or contrary to the 

 direction of the comet's motion. 



I believe the elements above given, will be found to be a 

 pretty close approximation to the true ones, considering the 

 difficulty attending exact observations of the comet, and the 

 liability to error of the positions of the stars of comparison. In 

 all cases, I have adopted the beso authorities at command for the 

 positions of the stars of comparison. In three instances, I have 

 been enabled to avail myself of corrections deduced from meridian 

 observations made at the Sydney Observatory in 1859 and 

 18CO. As an instance of the liability to error of the Southern 

 catalogues, I may refer to my observations of the 13th 

 October. In the comparisons of that evening, I employed 

 B. A. C. 5558 a star of the sixth magnitude, and Lacaille 6907 

 one of the seventh. The latter corresponds with 5789 of the 

 Brisbane Catalogue. My comparisons of the two stars showed 

 that Lacaille 6907 was thirty-five seconds of time west of 

 B. A. C. 5558. Lacaillle's catalogue gives the same result, but 

 Brisbane makes it only sixteen seconds west of B. A. C. 5558. 

 The position of Brisbane 5789 depends on one observation only, 

 and this is the case with many other stars in that catalogue. It 

 appears, therefore, we must be cautious in placing much depen- 

 dence on the star positions of the Southern catalogues. A 

 complete and accurate re-observation of the Southern stars, 

 down to the eighth magnitude inclusive, more especially those 

 between the parallels of 20 and 50 degrees declination, is a work 

 of the highest importance, and without which we cannot expect 

 any great advance in the astronomy of this hemisphere. The 

 best observations of a planet or comet cannot be made available 

 for any accurate purpose till the origins from which its position 



