From: Astronomisches Jahrbuch für das Jahr 1786. nebst einer Sammlung der neuesten in die astronomischen Wissenschaften einschlagenden Abhandlungen, Beobachtungen und Nachrichten [Astronomical Yearbook for the Year 1786. in addition to a collection of the newest treatises, observations and news], edited by J.E. Bode. Berlin, 1783.
[16.] Ueber die Bahn des zweyten Kometen von 1781. Entdeckung einiger Nebelsterne; die Elemente der Bahn des neuen Planeten und astronomische Beobachtungen [On the orbit of the second comet of the year 1781. Discovery of some nebulous stars; the elements of the orbit of the new planet and astronomical observations], by Mr Méchain, in Paris, p. 231-237.

Translated from German by H. Frommert

>> Comets
>> Nebulae -- M105 -- M102 -- M104 -- M108/M109 -- M106 -- M107
>> Uranus
>> Observations

[On cometary orbits]
Herewith follow the elements requested by Mr. Bode of the orbits of the two last comets which appeared in the year 1781, and equally the positions of the new nebulous stars discovered by me.

The elements of the orbit of the first comet of the year 1781, are given in the Connoissance des tems [sic] for 1784. page 365, I think, that I have sent you such [elements] more than a year ago, and without doubt, you or Mr. Bode will have the volume for 1784. at hand. (*)

The main pieces of the orbit of the second comet of 1781 (**) I give here, as they have been calculated by me after the very beautiful method of Mr. de la Place, which will be published in the Memoirs of the Academy for 1780.

The ascending node                     2s 17d 22' 55"
The inclination of hte orbit              27  12   4
Longitude of perihelion in the orbit   0  16   3   7
Distance at perihelion                     0.9609951
Average time of the
  perihelion passage     the 29th of Nov. 12h 42' 46"

These elements differ only insignificantly from thise which I have found by the conventional methods. I have found most of my observations obtained from Octob. 9 to Dec. 25, acurate to 1 minute with this theory, and the largest deviations never exceed 2 minutes. Meanwhile the apparent path of this comet in the sky extended for almost 170 degrees. In its true orbit, it traversed an arc of 97d 20' and the heliocentric latitude changed by 27d 22' from the day I discovered it to Dec. 25. On Nov. 9 at 6 1/4 o'clock in the evening, it passed only 40 min near the north pole of the ecliptic. (****) It has passed its ascending node on Octob. 10. On Dec. 25, when its northern geocentric latitude was only 16d 30' yet, it was standing almost in opposition to the place where it had been discovered. At the end of October and the beginning of November it was visible to the naked eye. The tail was steadily quite short and almost only recognizable in the telescope.

(**) See astronom. Jahrbuch f. 1785. page 164 166 and following.

(***) Simultaneously, look at my [Bode's] main pieces of the orbit of this comet found by a casual drawing in the Jahrbuch for 1785. page 168.

(****) See astronomisches Jahrbuch for 1785. page 167. and Fig. 1 on the 3rd table.

[On nebulous objects]
Concerning the nebulous stars or nebulous patches, I'm not able to satisfy Mr. Bode['s] request, because up to now I was lacking time to determine the acurate positions of all those I have discovered. Therefore, I only want to give the positions of some which are not included in the Connoissance des tems [sic] f. 1784 [Messier's Catalog], and will indicate the others in such a manner that one will be able to recognize them. (**)
[M105] Mr. Messier mentions there on page 264 and 265 two nebulous stars, which I have discovered in the Lion [Leo; M95 and M96]. I find nothing to correct for the given positions which I have determined by comparison of their situation with respect to Regulus. There is, however, a third one, somewhat more northerly, which is even more vivid [brighter] than the two preceding ones. I discovered this one on March 24, 1781, 4 or 5 days after I had found the other two. On April 10, I compared its situation with Gamma Leonis from which followed its right ascension 159d 3' 45" and its northern declination of 13d 43' 58".

[M102] On page 267 of the Connoissance des tems [sic] f. 1784. Mr. Messier lists under No. 102 a nebula, which I have discovered between Omicron [actually Theta] Bootis and Iota Draconis; but this is a mistake. This nebula is the same as the preceding No. 101. Mr. Messier, caused by an error in the sky charts, has confused this one in the list of my nebulous stars communicated to him.

[M104] On May 11, 1781, I discovered a nebula above the Raven [Corvus], which did not appear to me to contain any single star. It is of a faint light and difficult to find when the wires of the micrometer are illuminated. I have compared it on this day and the following with Spica in the Virgin and from this derived its right ascension 187d 9' 42" and its southern declination 10d 24' 49". It does not appear in the Connoissance des tems.

[Virgo Cluster] On page 262 and 263, Mr. Messier mentions various nebulae, which I indicated to him. There are, however, in that region some others also, which he has not seen and the positions of which I intend to determine, as soon as I will have a comfortable observing place, which will not be delayed for long any more.

[M108, M109] Page 265 No. 97 [M97]. A nebula near Beta in the Great Bear. Mr. Messier mentions, when indicating its position, two others, which I also have discovered and of which one is close to this one [M108], the other is situated close to Gamma in the Great Bear [M109], but I could not yet determine their positions.

[M106] In July 1781 I found another nebula close to the Great Bear near the star No. 3 of the Hunting Dogs and 1 deg more south, I estimate its right ascension 181d 40' and its northern declination about 49d. I will be going to determine the more acurate position of this one shortly.

[M107] In April 1782 I discovered a small nebula in the left flank of Ophiuchus between the stars Zeta and Phi, the position of which I have not yet observed any closer.

This is, up to what is included in the mentioned Connoissance des tems [sic], all I have done concerning the nebulous stars. I will make up a separate memoir about that, and closer determine their positions and appearances.

[On the new planet]
Now I will report to you a little bit about the new planet of Mr. Herschel, which I have busily observed from April 25, 1781 to now. I have tried on different occasions to find a circular orbit, which meets the requirement of my observations and always noticed, that it was necessary with the progress of time to assume a smaller radius vector; for that given by Mr. de la Place was always too large. In the month of July 1782, I undertook the attempt to obtain an ellipse from 4 selected observations, of which the outermost two were about a year apart, by which I obtained an impression of the elements of the orbit. Aftr the last opposition, Mr. de la Place requested 4 acurate observations from me, of which the two outermost would lie as far apart as I ever had them; but the two others should just include the oppositions of 1781 and 1782. Consequently he has thought up a very simple and meaningful method, by which he has found the measures of an ellipse which represents the four observations mentioned above very well, and which leaves only an error of 8 to 9 seconds for the observation of April 26, 1782. For my part, I have made use of a very simple method which Mr. Boskovich has communicated to me, which is based on the same 4 observations, of which the outermost are 594 days apart. I have calculated an ellipse, according to which the outermost observations agree exactly, and the two between them differ only 4 or 8 seconds more. Just this exact agreement also occurs for the other observations. Eventually, this ellipse gives the longitude only 7 seconds larger that the observation of the last April 26 [1783], 121 days after the last which it was based upon. The planet has not yet traversed a sufficiently large piece of arc and the deviation of its motion is too insignificant to be able to find more acurate elements of the orbit. But I believe, however, that the elements derived by Mr. de la Place and myself approach the truth, or are at least sufficient to get a general impression of the extension and situation of the orbit. A more comprehensive series of observations will closer inform us about this.

Here follow the elements of the elliptical orbit I calculated for the new planet:

Place of perihelion, May 11, 1781       5s 22d 13' 17"
Time of passage of the perihelion, 
  November 7, 1799 at 7h 0m average time on the Paris meridian
Distance in perihelion                       18.25870
Distance in aphelion                         19.89938
Major half axis                              19.07904
Period of siderial revolution        83 years 4 months
Place of the ascending node             2s 11d 49' 17"
Inclination of the orbit                       43  35
Heliocentric longitude, on May 11
  1781 at 8h 47' average time           2  28  11  24 1/2
Average anomsly, taken from the
  perihelion, for this time             2  19   9  55

[Observations]
At the transit of Mercury on November 12 of last year 1782, weather in Paris was so fine as one can always only wish. (*)

I noticed the full entry of Mercury or the first inner contact of the edges at 3h 2' 8" true time.

The second inner contact of the edges on exit was at 4h 17' 46".

I have also measured various distances of the center of Mercury from the Sun's limb, abd calculated, that the true conjunction occured at 4h 3' 18" true time in 7s 20d 26' 39 1/2". The tables of Mr. de la Lande, give 11 sec. more in longitude and in latitude, for which I found 15' 52.1", only 1 sec less than the observation (**). Other observers have noticed the first contact later; but I coincide up to triffle with Mr. le Monnier, Dagelet and another one. Moreover also the observations most deviating from mine only give a difference of 6 sec. in view of the geocentric longitude of Mercury.

(**) Theerefore, they coincide very well with observation for this planet. My calculations of the transit, according to these tables, appears in the Ephemeris for 1782, p. 158. The calculation therein according to Halley's tables, as it appears in the 2nd volume of the Berlin collection of astronomical tables, therefore shows, that for entry and exit 21 minutes in time are missing.

This remarkable difference has its origin primarily in that Halley's tables put the ascending node of Mercury 10 minutes more east, and thus give the geocentric latitude 37" less; the chord, however, which Mercury traverses in front of the sun, is so close to the solar limb, that a small difference in latitude produces a very large one in duration and consequently in the times of entry and exit of Mercury.

At the occultation of the Pleiades by the Moon on February 9, 1783 the sky was less favorable; therefore, I have only been able to observe the entries of 3 stars:

Entry of Merope or d Plei. 6h 50m 45 1/2s true time, a good observation.
-- of Atlas or f Plei. 8h 22m 52s acurate to 3 or 4s.
-- of Pleione or h Plei. 8h 38m 1s rather acurate.

On the latitude of 48d 51' 50" and 2" time, west of the meridian of the Royal Observatory.

Also, we have observed the latest total lunar eclipse of March 18 of the year [1783] very well; (*) But because from such an event not much important can be derived and the indication of the entry and exit of separate patchesis loose, I only want to give here the phases mentioned, as I have observed them at Paris in the Cabinet of the King 14" west of the Royal Observatory.

Last Modification: January 29, 2005