Here we present the translation of Méchain's letter as printed in the Memoirs of the Berlin academy in original French language (probably Méchain's wording).
It was also translated, worked up, and published by Johann Elert Bode in German language in the Astronomisches Jahrbuch for 1786, p. 231-237. A translation of that publication is also available.
Translation from French done by H. Frommert
From: Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres, année MDCCLXXXII, avec l'Histoire pour la méme année [New Memoirs of the Royal Academy of Sciences and Arts, for the year 1782, with the History for the same year].
>> Nebulae -- M105 -- M104 -- M108/M109 -- M106 -- M107 -- M102
By M. Méchain, of the Royal Academy of Sciences.
Paris, May 6, 1783. - - -
I'm ashamed to have been for a long time without writing you; I have been very
busy & then sick for several months. - - -
M. de la Lande told me that M. Bode would desire to have the
element of the two last comets, & the positions of the new nebulae I have
[On cometary orbits]
The elements of the 1st comet are in the Connoissance des tems for 1784 p. 365; I think to have already had the honor to send them to you more than a year ago (*), & without doubt that you or M. Bode have at hand this Volume for 1784. Concerning those of the 2nd Comet of 1781, here they are such as I have deduced via a very beautiful analytical method by M. de la Place, which is published in the Mémoirs [of the French 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"The motion is retograde.
These elements differ only insignificantly from those which I have found by the conventional methods. I have represented all my observations from October 9 in the morning to Dec. 25 within less than a minute [of arc] for most of them, and the greatest deviation errors never exceed two minutes, & despite the apparent path of this comet has been almost 170 degrees. On its [true] orbit, it has traversed an angle of 97d 20'. & the heliocentric latitude has changed by 27d 22'. from the day when I have discovered it to Dec. 25. It passed at 40' from the north pole of the ecliptic on Nov. 9 at 6 1/4 in the evening; it has passed its [ascending] node on Oct. 10. On Dec. 25 it had a northern geographic latitude of no more than 16d 30' and was almost in opposition to the place where it had been discovered. It was visible to the naked eye at the end of October & the beginning of November. The tail was always quite short, & it was only visible in the telescope.
[On nebulous objects]
Concerning the new nebulae which I have discovered & of which M. Bode demanded the positions, I am not totally able to satisfy this, not having yet the ability to find time to determine all of those which I have discovered. I will report the positions of those which are not included in the Connoissance des tems for 1784, & I will indicate the others in such a manner that they can be found.
[M105] Mr. Messier reports in the Connoissance des temps 1784, p. 264 & 265 two nebulous stars, which I have discovered in the Leo [M95 and M96]; I find nothing to change for my positions which I have established by comparing these nebulae to Regulus; but there is also a third one to the north; it is a bit more beautiful [brighter] than the 2 others; I have discovered it on March 24, 1781, 4 or 5 days after the other two. On April 10, I compared it to Gamma Leonis & I have concluded the right ascension 159d 3' 45"; the declination 13d 43' 58" north.
[M104] On May 11, 1781, I have discovered a nebula above Corvus; it did not appear to me to contain stars; it is faint & very difficult to see when the wires of the micrometer are illuminated; I have compared it on this day & the following to the Ear of Virgo [Spica], & I have derived its right ascension 187d 9' 42", its south. declin. 10d 24' 49". It is not included in the Connoissance des tems.
On page 262 and 263, Mr. Messier mentions several nebulae in Virgo which
I have indicated to him; but there are of these some others which he has not
[M108, M109] Page 265. No. 97 [M97]. nebula near Beta Ursae Majoris. When reporting its position, Mr. Messier speaks of two others which I also have discovered, the one close to this one [M108], & the other close to Gamma [Ursae Majoris; M109] --
[M106] In July 1781, I have found another one close to Ursa Major near the star No. 3 of Canes Venatici & 1 deg more ore less to the south; I estimate its right ascension 181d 40' & its declination about 49d. --
[M107] Finally in April 1782, I have discovered a small nebula in the left flank of Ophiuchus between the stars Zeta & Phi. --
This is all what I have done on the nebulae which is more than what is reported in the Connoissance des tems [for] 1784; & I will determine exactly those which I have indicated, when I will have a more comfortable observing place, which will no more be delayed.
[M102] I will add only that No. 101 & 102 on the p. 267 of the Connoissance des tems [for] 1784 are nothing but the same nebula, which has been taken for two, by an error in the [sky] charts.
Rest preliminaty, under construction, to be corrected!
[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 , 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 anomaly, taken from the perihelion, for this time 2 19 9 55The first observation, which was used for calculating this orbit, is from May 11, 1781; the others have been improved with respect to the precession of the equinoxes, aberration and nutation, to have the true places and the siderial motion since May 11, 1781, as is required here.
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  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: May 18, 2005