An Update of the Paper, ‘On known and less known relations of Leonhard Euler with Poland’

In this note we publish a short letter from Leonhard Euler’s son, Johann Albrecht Euler, the Secretary of the Imperial Academy in St. Petersburg, to Marcin Poczobutt-Odlanicki, the Vilnius PUBLICATION


Introduction
In his paper (Sznajder 2016), the author highlighted connections between Leonhard Euler and Polish scientists of his era.The aim of that work was to put attention to less known relations of the Swiss mathematician and Polish mathematicians, physicists, astronomers, and geographers.Sznajder notes: Among individual Polish scholars, J.A. Euler corresponded with a Vilnius astronomer Marcin Poczobutt-Odlanicki (1728-1810), whom he informed in a letter of December 19, 1777, about the discovery of a new comet by A.J. Lexell 66 (Sznajder 2016, p. 100).
At that time, J. A. Euler (Leonhard Euler's son) was the secretary of the Imperial Academy in St. Petersburg.
This letter was recently found at the Vilnius University Library by Dr. Veronika Girininkaitė, the first author of this note.The letter, written in French, bears no salutation and was discovered in a folder dedicated to M. Poczobutt-Odlanicki, so he was presumably the addressee.It bears no signature, so it is not certain whether the letter was penned by Johann Albrecht Euler himself.
Handwriting comparison with copies of original letters written by J.A. Euler came out positive, so we may state with considerable certainty that the letter to M. Poczobutt-Odlanicki was indeed written by J.A. Euler.
Below, we present three documents.The first one is a copy of the original letter from J.A. Euler to M. Poczobutt-Odlanicki, the second is its transcribed version, and the third one is the English translation.Thus, we are now able to provide primary documentation for a statement made in the 2016 article.

The original letter
The letter was recently digitized by Vilnius University Library.

English translation
I am mortified that for all the important new literary works that you have the kindness to communicate to me, I may not give you anything in my return which was worthy of your attention.The first volume of the new academic transactions 2 , which includes that first half of the current year, will not appear before the upcoming Spring.The Academy had ordered new types from the letter foundry, and as this foundry was completely ruined by the great flood of September 10, it was not possible to provide these new types until the end of last month.Mr. Lexell, our astronomer, has made a lot of noise by the discovery of a comet, which according to his calculations, should reappear every five and a half years, but which is also so small in mass that it seems impossible to see it even with these small research telescopes, unless it approaches the Earth very considerably, as it happened in the year 1770 and 1771.This is the reason why this comet has been, so far, able to escape the vigilance of the astronomers, but since Mr. Lexell has determined exactly its orbit, we can at each return to the Sun find it by directing good glasses to the places of the sky that calculation gives, we will see this in the year 1781.

A brief biography of Anders Johan Lexell
Anders Johan Lexell (1740-1784) was a Finnish-Swedish astronomer, mathematician, and physicist.He was born in Turku, Finland.At the age of 14, he matriculated at the Academy of Åbo (Turku) and in 1760, received the Doctor of Philosophy degree (dissertation: Aphorismi mathematico-physici).In 1763, he moved to Uppsala (Sweden) and worked at Uppsala University as a lecturer.Starting in 1766, Lexell served as a professor of mathematics at the Uppsala Nautical School.
Lexell spent 16 years of his professional life at the Imperial Academy in St. Petersburg, Russia.He was known for his work in celestial mechanics and polygonometry; one of the theorems in spherical trigonometry bears his name (Lexell 1781).Lexell applied his findings to research comets and planetary motion.He was one of the most prolific and prominent scientists of his time.During his stay at the Imperial Academy, Lexell authored 62 papers and authored four additional works; his coauthors were L. Euler, J.A. Euler, Wolfgang Ludwig Krafft and others.D. Bernoulli (1700-1782) and L. Euler had a very high opinion of Lexell's research achievements.Apparently, Euler wrote: "Besides Lexell, such a paper could only be written by D'Alembert or me" (Euler 1784).
Soon after his arrival from Berlin (1766), Euler interceded after A. J. Lexell, who in 1768 wrote a paper, Methodus integrandi nonnulis aequationum exemplis illustrate (Lexell 1769) to get accepted to the Imperial Academy of Sciences.Again, Euler praised this work highly.In the meantime, Lexell was granted permission by the Swedish king to leave Sweden (that time, Finland was part of Sweden) and move to St. Petersburg, Russia.In 1771, Lexell became an Astronomy academician; in 1773, he became a member of the Academy of Stockholm and Academy of Uppsala.In 1774, Lexell became a corresponding member of the Paris Royal Academy of Sciences.Later, he became a corresponding member of the Turin Royal Academy.
The scope of Lexell's work was quite wide.He was interested in integrating nonlinear differential equations and using an integrating factor to solve higher order differential equations.Another field of Lexell's interest was polygonometry, considered as generalized trigonometry.These themes occupied a significant part of his work.The Lexell's continuator in this direction was a Geneva-born mathematician Simon Antoine Jean L'Huillier (1750-1840), see Sznajder 2016 for a list of some of the L'Huillier's works.
The third part of his research interests were celestial mechanics and astronomy.He studied parameters of several planets, members of the Solar System, including Uranus (Lexell was the first astronomer to calculate its orbit), Venus, Mars, and Jupiter.Most of all, he was interested in observation of comets.
In 1780-1781, Lexell visited Germany, England, and France on a scientific trip, and he then returned to St. Petersburg via Sweden.During this trip, he wrote 28 letters to Johann A. Euler, which have been archived in the Russian Academy of Sciences.Formal reports to the Director of the academy were lost.The private letters to J.A. Euler contain many interesting details regarding people and places Lexell had encountered, Lyubimienko 1936.He was present at the deathbed of Euler in 1783 and succeeded him as the Chair of Mathematics at the Imperial Academy, but died just one year later at the young age of 44.The asteroid 2004 Lexell and the lunar crater Lexell were named in his honor.For more bibliographic details, we refer to Stén 2014.