104 A Calculation of the Orbit of the Comet. 



vals of time, as would be requisite for an exact deter- 

 mination of what astronomers call the elements of its 

 orbit. Nevertheless, I endeavored, for this purpose, 

 to improve such advantages and opportunities as were 

 presented ; and the common distance from some known 

 lixed star was taken every night when the sky was 

 clear, from the 1st of October, to the time of its becom- 

 ing invisible. The only instrument which could be 

 used for this purpose, was a well divided Sextant be- 

 lono'lnsr to the United States. From the nature of the 

 instrument, and the unfavorable state of the atmosphere 

 during a considerable portion of the time, when the ob- 

 servations were made, I am far from thinking, that they 

 will bear a comparison with such as may be made at 

 European observatories. In my opinion, however, they 

 will be sufficient for determining the orbit of this Comet, 

 with as much or more accuracy, than some of those of 

 the preceding centuries, on which Dr. Halley and other 

 astronomers have grounded their calculations of a num- 

 ber of comets. 



With a view of investigating the elements of the orbit 

 of this comet, I selected three observations made at 

 equal intervals of time, viz. those of October 3d and 

 i9th, and of November 4th. Others might have been 

 used for this purpose, but these superseded the necessi- 

 ty of interpolation, or of using the differential method 

 of Newton. The geocentric longitudes and latitudes of 

 the comet for those times, were calculated, and its ve- 

 locity, and the apparent direction of its motion in respect 

 to the earth, were thereby found. The direction of the 

 plane of its orbit, and its distance from the sun, at one 

 of those times, were found nearly, by a comparison of 

 the absolute quantity and rate of its velocity in a para- 

 bolic orbit, with its apparent angular motion as seen 

 from the earth, during the intervals of time between the 

 observations. A calculation was then made, of different 

 orbits varying in excess or defect of distance from that 

 assumed, and an orbit was found by proportion, which 

 gave the comet's place "mery nearly as observed. 



These calculations being veiy tedious, and there be- 

 ing great danger of incurring mistakes, I have not been 



