Charles the Obscure, The one you never heard of, but should have.

  

JAC Charles

My good and generous friend, Dave Renfro, sometimes finds time in his busy writing and research schedule to send me copies of some of the old documents he's working through.  Recently a collection from him included a 1979 Isis article by J. B. Gough.

One in particular, which I opened only weeks after the anniversary of the death of the unfortunate Jacques Charles, called the Geometer in his lifetime to avoid confusing him with Charles the Balloonist, and sometimes Charles the inventor, who is J. A. C Charles, and the namesake for the chemistry law that is sometimes, probably without merit, called Charles' Law.  Unfortunately, the point of Gough's article is that they did become confused, often due to lack of effort or interest on the part of historical writers, to the point that now you can find little or nothing about the "geometer" and much of what you find about the more famous Charles is, in fact, a mis-credit for the work of Charles the Geometer. 
I would have assumed that articles like the one by Gough in 1979, and another by the famous science historian Roger Hahn a few years later would have set the record straight, but in fact as I scanned a couple of biographies on the internet they still contain the residue of the confusion.
One of the first points of confusion is that you may see the date for the induction of the famous Charles into the Academy of Sciences as 1785.  This is off by almost a full decade, and is the actual date of the induction of Charles the Geometer.   The famous Charles would be inducted into the  Académie des Science in 1795, almost four years after the other Charles had gone to an early grave.

The image is an illustration of JAC Charles first Balloon flight on 1 Dec, 1783

*Wik

A second, and even more common error is that you will often still see biographies of the famous J A C Charles that list him as a mathematician, and sometimes add something like, "most of his papers were in mathematics."  

Wikipedia currently lists JAC Charles as " French inventor, scientist, mathematician, and balloonist.,"and then follow up with, "Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences, entering on 12 May 1785." 

Searching for Jacque, the Geometer may be a long search, and unless you stumble across a copy of this blog, or the document I started from, you may find nothing at all.

 JAC Charles, the famous, it seems, was NOT a mathematician, and wrote almost nothing, including nothing about mathematics, and only the sketchiest outline of the law which, due to the graciousness of more capable scientists (you can read the name Joseph Louis Gay-Lussac here) would eventually bear his name.  J. B. Gough goes so far in his article in Isis to declare that this Charles was "nearly a mathematical illiterate."  He points out that of the eight articles credited to J. A. C Charles by Poggendorf, seven were actually by the more obscure (and more mathematical) Charles.

Here is how Wikipedia credits his axquiring credit for the law.

Charles's law (also known as the law of volumes), describing how gases tend to expand when heated, was first published by natural philosopher Joseph Louis Gay-Lussac in 1802,[2] but he credited it to unpublished work by JAC Charles, and named the law in his honour.

Around 1787 Charles did an experiment where he filled five balloons to the same volume with different gases. He then raised the temperature of the balloons to 80 °C (not at constant temperature) and noticed that they all increased in volume by the same amount. This experiment was referenced by Gay-Lussac in 1802 when he published a paper on the precise relationship between the volume and temperature of a gas. Charles' law states that under constant pressure, an ideal gas' volume is proportional to its absolute temperature. The volume of a gas at constant pressure increases linearly with the absolute temperature of the gas. The formula he created was V1/T1 = V2/T2.

Today many sources use the expression Gay-Lussac's Law. This law was independently and nearly simultaneously stated by John Dalton.

Gau-Lussac

In 1804, Gay Lussac and Jean-Baptiste Biot made a hydrogen-balloon ascent; a second ascent the same year by Gay-Lussac alone attained a height of 7,016 metres (23,018 ft) in an early investigation of the Earth's atmosphere. He wanted to collect air samples at different heights to record differences in temperature and moisture.

In 1752, when the obscure Jacque Charles was only 20 years old, Minutes of the French Academy of Science kept by Lavoisier of the meeting at which the report was read identify Charles as "professeur de mathematiques 'a l'ecole de Nanterre, a suburb of France.  His work was so advanced that, in the words of Roger Hahn in his 1981 Isis article, "More Light on Charles the Obscure", : 

{The committee of academicians examining it inferred that Charles was familiar with Euler's text on differential calculus, and that he showed promise. They said, "les solutions de ces deux problemes nous paraissent meriter les encouragements de l'Academie, mais elles ont pour objet des questions trop elementaires pour que nous les jugeions dignes d'etre impri-mees."}

Gay-Lussac, in his published paper about the law credits Charles with this statement (English translation) "Before going further, I must jump ahead. Although I had recognized on many occasions that the gases oxygen, nitrogen, hydrogen, carbonic acid, and atmospheric air all expand identically from 0° to 80°, citizen Charles had noticed the same property in these gases 15 years ago; however, since he never published his results, it is only by great luck that I knew it. He had also sought to determine the expansion of water-soluble gas, and he had found for each a particular dilation different from that of other gases. In this respect, my experiments differ strongly from his".
Gough points as far back as 1870 with evidence to the ongoing confusion.  A donation of the physics lectures of the more famous Charles to the Institute de France prompted a notice in Comptes Rendes with a brief description of Charles life and career on February 7 of 1870.  Shortly after the publication a letter to the Perpetual Secretary questioned if the article had not confused Charles the balloonist with the geometer.  A followup with a brief description of the lives of both men was given in Comptes Rendes on March 7 of the same year.

I first wrote about this in 2013, and today, nine years later, there is no biography of Charles the geometer in St Andrews MacTutor.  Encyclopedia dot com also has no article about Charles the geometer, but writes about J A C Charles, "Charles published almost nothing of significance." 

"Assertions to the contrary notwithstanding, there is no evidence that Charles knew anything but the rudiments of mathematics. Through an unfortunate confusion of names, biographers and bibliographers have completely confounded J. A. C. Charles with another contemporary known only as Charles le Géomètre.

 Wikipedia also has no page for Jacque Charles the geometer, but says, "(J A C )Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences,... He was sometimes called Charles the Geometer."

So what of the mathematical Charles, who has so sadly been overlooked for several hundred years?  It seems that he was born around 1752 in Cluny, France in the Burgendy region of France.  He seems to have attempted to gain entry to the Paris Academy of Science, to which both Charleses would eventually belong, at the ripe age of about 18 while still living in Cluny.  His article, on a problem in Algebra, probably reflecting his youth, was rejected by the academy as being too elementary.  Two years later, he  submit a second paper two years later, "sur le dynamique" impressed the judges who inferred that the author must be aware of Euler's differential calculus.  When it was read to the full meeting of the  academy, Lavoisier's minutes of the meeting list Charles as a Professor of Mathematics at the school at Nanterre, most probably referring to a popular academy in that suburb of Paris that trained young Nobles who were intending to proceed to Engineering colleges.
 Over the period from 1779 to 1785, Charles continued to submit articles to the Academy.  In all he submitted seven articles all of which were deemed appropriate for publication.  After the seventh, Condercet, who had reviewed the paper for the Academy, pointed out that this, and any of the previous six, certainly merited his admission to the Academy.  His major obstacle seems to have been the opposition to his appointment by Laplace, who was motivated more by his rivalry with Charles' sponsor, Charles Bossut(famed for his textbooks in France).  Finally a vote on May 11, 1785 (this date is often given as May 12, I use Hahn's date as few have better records to the history of the Paris Academy) secured Charles his membership.

Charles, through his association with Bossut, had already obtained the position as the Chair of Hydrolics, which brought with it, admission to the Paris Academy of Architecture, which made Charles a duel academician.

Somewhere around 1789 Charles was onset with a paralysis which greatly affected his ability to write.  It is said that he had, for a short while,  to request another member to sign him in at meetings.  He did manage to learn to write with his other hand, but never with full control.  A few years later, in 1791, he died apparently from the same paralytic problem.  Only sketchy records exist of his death and burial due to the confusion created by events related to the revolution.  It appears he died on (or near) August 20, 1791 and it is reported that he was buried at Saint-Germain-l'Auxilles on the 22nd of the same month.  A memorial service was held at the Oratoire on Dec 29,1971.  Due to the events of the revolution, no M'emoires of the Paris Academy were produced that year, and hence no obituary for members who died.

I am still trying to learn more about the actual writings of Jacques Charles, the Geometer and would love to hear from those who have greater knowledge on this subject, and the man himself, to share.

Here is the post I have about the lesser known Charles at On This Day in Math:

1791 Jacques Charles, (probably 1752, August 20, 1791) Mathematician, born in Cluny, France. He is often confused with the Jacques A. C. Charles who is credited (or mis-credited) with Charles' Law and much of the work of this Jacques Charles. During the Late 18th Century both were active in Paris scientific circles and both were members of the Paris Scientific Academy. They were often distinguished by calling this one Charles the Geometer, and the other Charles the Balloonist since JAC Charles was active in promoting the use of hydrogen balloons and had designed the first balloon that is known to have been used.
This Jacques Charles is also frequently referred to by the historians who are aware of the confusion between them as Charles the Obscure.
Jacques Charles first contact with the Paris Acad of Sci was in a 1770 letter in which he submitted an article on a problem in Algebra at about the age of 18. It was turned down by the academy due to it's elementary level. The address shows that he was living in Cluny at the time. But two years later a second correspondence to the academy is read to the Academy, and Lavosier's minutes list his position as a professor of Mathematics as the school at Nanterre, on the outskirts of Paris. It is suspected that this was a preparatory school for young nobles who were training to become engineers that had been located there since the 1760's.
Between 1779 and 1785 Jacques Charles submitted seven articles to the Paris Academy, all of which were deemed worthy of publication, but only the last seemed to merit his admittance to this esteemed group. Condorcet, who was then perpetual secretary of the Academy said that this, as well as his prior papers certainly warranted his admission. It seems that Laplace, who had a conflict with Charles' mentor/sponsor, Bossut, and had been blocking his entry. With some behind the scenes effort by Lavosier had created a new geometry section, he was voted into the Academy on May 11 (often given as May 12).
By 1792 due to the confusion of their names, much of the mathematical work of Charles the Geometer would be credited to Charles the Balloonist and the "Geometer" would become the "obscure". Even the energetic J. C. Poggendorf would miscredit eight papers by the geometer to the other, and in biographies of J. A. C. Charles written even in the 20th century, you will see him credited as a "mathematician" and statements that suggest that "most of his writings were in mathematics." J. B. Gough, writing in an article in Isis in 1979 describes the ballooning Charles as, "nearly a mathematical illiterate."
The confusion between the two men of common names was exacerbated by the timing of this Charles' death. The year 1791 and the problems related to the Revolution made this the Academy of Sciences did not publish a Memoires, and as a result, no eloge's for the members who died in that year. Strangely, this was still four years before the better remembered Charles was admitted to the Academy.
He was buried (according to an old note to Cvomptes Rendes) at St. Germain l'auxerrois, but this seems hard to confirm in the church records. (*J. B. Gough)
Charles was also the Royal Professor of Hydrodynamics, and as such was also inducted into The Academy of Architecture. *Roger Hahn, More Light on Charles the Obscure, Isis, Vol. 72, No. 1 (Mar., 1981), pp. 83-86