Things Certain and Uncertain: Popular Accounts of Balloon Flights

Once the Mongolfiers’ balloons demonstrated the possibility of lighter-than-air travel, news traveled fast. Accounts of the various balloon flights circulated around the world, attesting to both the exhilaration of such a voyage and the scientific principles that made it possible.

Augustin-Charles Piroux’s L’Art de Voyager Dans les Airs introduced the subject of air travel with a flourish: "The astonishment of the multitude joins the admiration of the scholars; Experiments multiply, intrepid men rise into the air, and the globes that carry them merge with the stars" [Piroux 1784, pp. 1–2, translated by the authors]. Benjamin Franklin (then serving as the newly-independent United States’ minister to France) described how, when a balloon was launched from the Tuileries Palace [on 1 December 1783], “all Eyes were gratified with seeing it rise majestically from among the Trees, and ascend gradually above the Buildings, a most beautiful Spectacle!” [Rotch 1907, p. 270]. The excitement is palpable in this conclusion from the Journal de Paris's account: “M. Montgolfier was already known for the manufacture of the most beautiful papers that have been made in France. The experiment which we have just related announces a curiosity and enlightenment of another kind” [Journal de Paris 1783, p. 862, translated by the authors].

And balloon flights were not limited to the Montgolfier brothers—around the same time, the French scientist Jacques Charles was exploring the uses of hydrogen as a method for raising balloons. Charles, in collaboration with the engineers Anne-Jean and Nicolas-Louis Robert, oversaw the launch of a hydrogen balloon from Paris on 27 August 1783. It happened that Benjamin Franklin was also present at this flight, describing how they obtained hydrogen for the balloon by “pouring Oil of Vitriol upon Filings of Iron,” and reporting that “it was found to have a tendency upwards so strong as to be capable of lifting a Weight of 39 Pounds, exclusive of its own Weight which was 25 lbs. and the Weight of the Air contain’d” [Rotch 1907, pp. 260–261]. Indeed, the flight from the Tuileries that Franklin observed on 1 December was by another of Charles’s and the Robert brothers’ hydrogen balloons. Over the next several years, similar voyages were made repeatedly across France. Piroux, writing in 1784, noted that “Everyone wants to repeat the wonderful experiment of MM. Montgolfier, each according to his means. Aerostatic Globes are part of the show at all parties: the workers of Paris cannot supply the demands of the Province” [Piroux 1784, p. 29, translated by the authors].

Figure 3. An illustration of the hydrogen balloon flight
over the Tuileries Palace on 1 December 1783. Library of Congress.

Of equal interest to observers were the mechanical principles that made balloon flights possible. Many accounts combined the description of the event with an attempt at rigorous, scientific description of the forces at play. For the most part, these reports described the volume and weight of the balloon, with some stating the force exerted by the elevating agent (either heated air or hydrogen):

• Franklin described Charles’s balloon of 27 August as “A hollow Globe 12 feet Diameter was formed of what is called in England Oiled Silk,” and relayed that “some observers say, the Ball was 150 Seconds in rising, from the Cutting of the Cord till hid in the Clouds; that its height was then about 500 Toises” [Rotch 1907, pp. 260–262]. He further noted that “One of 38 feet Diameter is preparing by Mr. Montgolfier himself, at the Expence of the Academy, which is to go up in a few Days. I am told it is constructed of Linen & Paper, and is to be filled with a different Air” [Rotch 1907, p. 262].
• According to Piroux, “Montgolfier's machine of 19 September weighed seven or eight hundred pounds, contained forty thousand cubic feet of gas, and could, it is said, lift about twelve hundred pounds (its load was only six hundred)” [Piroux 1784, p. 15]. He also claimed that “the species of air employed by M. de Montgolfier offers an absolutely new phenomenon, since to obtain it, it is enough to simply burn wet straw and an animal substance such as wool. A very small quantity of these combustible materials, and ten minutes’ time, furnished the necessary 37,500 cubic feet of air, and such a volume of inflammable air [hydrogen] would not have been procured without perhaps eight or ten thousand francs, and five to six working days” [Piroux 1784, pp. 74–75, both quotations translated by the authors].
• In a report by Barthélemy Faujas de Saint-Fond, published under the auspices of the Royal Academy of Sciences in Paris, the balloon flown by the Montgolfiers at the Château de la Muette on 21 November “was 70 feet high, 46 feet in diameter: it contained 60,000 cubic feet [of air], and the weight it lifted was about sixteen to seventeen hundred pounds” [Faujas de Saint-Fond 1784, p. 22, translated by the authors]. (Notably, this was the first balloon flight crewed by humans.)

Given the widespread interest in the mechanics of balloon flight, it is not surprising that Euler would become engaged in his own version of these calculations. In fact, Anders Lexell, Euler’s dining companion on the night of his death, recalled their dinner conversation a couple of weeks afterward (in a letter to J. H. de Magellan):

Talking afterwards upon the principles on which the aerostatic globes are constructed, he remarked that it was a curious mathematical problem to determine the motion of such a globe, from knowing the proportion between the density of the air contained in the globe and of the common air. He observed also, that supposing this proportion to be as one to two, the greatest velocity of the globe would be 41 feet in a second [Stén 2014, p. 234].

However, Euler’s goals were slightly different from those described above: Instead of reporting the specific size and weight of a hot-air balloon, or determining the expense required to obtain enough hydrogen for a flight, or even determining the force such a balloon could exert, he sought to use more general principles of mechanics to determine its maximum velocity. Of course, Euler’s death prevented us from reading the complete article he would likely have published on the matter. However, the preservation of his blackboard notes and the relatively rapid publication of E579 made his basic derivation available to the general public (and, eventually, to us).