Suvat’s formulae

When I started teaching Newtonian mechanics, I was initially puzzled by the references that my students made to “Suvat’s formulae”. Like many mathematicians, I had assumed that the name of these formulae was purely an acronym; however, I was curious enough to do a little research on the subject. To my surprise, my students were correct, although the originator of the formulae, Cédric Gaspard Suvat, is little known even to Francophones and almost completely neglected in the English-speaking world. The most accessible biography appeared a few years ago in the Bulletin of the Poldavian Academy of Sciences, and although this periodical unfortunately doesn’t appear online they were kind enough to give me permission to publish a translation. Here it is.

From eponym to acronym: the sad case of Cédric Gaspard Suvat

[Translated from Bull. Acad. Poldavia 18(3): 667-669.]

This week marks the anniversary of the death of the French mathematical scientist Cédric Gaspard Suvat, now largely forgotten but known by name to millions of school and university students through his eponymous formulae.

Suvat was born in 1807 in the small town of Herbinville in the department of Gironde–Alpes, to a merchant family who had succeeded in prospering throughout the economic vicissitudes of the Revolution and the Napoleonic wars. Little is known of his early life, but he must have shown promise of brilliance because in 1825 he enrolled at the École Polytechnique in Paris, the city in which the rest of his life was to unfold. His subsequent academic career appears to have been undistinguished by formal accolades, but it is evident from his later work that he read widely and moved in radical political circles that would have caused considerable anxiety had his distant, and studiously apolitical, parents become aware of them.

In his early reading, Suvat had certainly come under the influence of the Goethean theory that Newtonian science had, at a fundamental level, perverted the understanding of nature, and this theory must have appealed strongly to the youthful patriotism of a frequenter of the notorious Café ABC. Although he came, reluctantly, to accept the validity of many of Newton’s contributions, he persisted in his suspicion that “l’achimiste anglais” had either unwittingly or with malice obscured the essential mathematical simplicity that underlay mechanics.

It was around the year 1835 that Suvat first conceived the notion of his “universal kinematics”, the system of simple algebraic equations that was to replace the lengthy and intricate apparatus of differential equations developed by Newton and his successors, although it took him several years to bring this notion to fruition. Suvat’s formulae were eventually revealed to the world in a pamphlet, printed in Paris in 1838 or 1839 and privately distributed. Their popular acceptance was delayed for some time by the poor quality of the letterpress and the unfortunate inclusion of a number of sign errors; Augustus de Morgan, in a review anthologised in volume 3 of his Budget of Paradoxes, was later to remark with typical callousness that “the typography perfectly reflects the mind of the paradoxer, insofar as the majority of the text is illegible, and such portions as are legible do little to encourage the reader’s confidence in the obscurer parts”. Nevertheless, the formulae were ultimately to prosper, and Suvat scored a significant victory over his insular opponents when in 1847 his pamphlet — assisted by a second and improved printing, and possibly also by the deployment of several thousand pounds in bribes — was adopted as a supplementary text to the Mathematical Tripos of the University of Cambridge. The formulae have never since been out of print.

The practical utility of Suvat’s formulae is, of course, impossible to dispute. However, what was arguably Suvat’s masterstroke was to introduce into them the notations for the displacement, initial and final velocities, acceleration and time which together ensure that his name, although often mistaken for a mere acronym, is still remembered. It remains uncertain whether this was intentional, or a coincidence arising naturally from Suvat’s happy conception of his own significance. (A pamphlet on alphabet reform, which bears his name and has been radiocarbon-dated to the period between 1835 and 1845, might shed further light on this matter if any of the 136 symbols that it contains, with the exception of the familiar Roman letters of Suvat’s name, could be related with confidence to those of any known language. The one extant copy of this pamphlet is currently in the possession of the Institut Voynich in Berlin, and may be viewed by curious visitors for a small fee.)

Sadly, the adoption of his formulae was to mark the zenith of Suvat’s career. Although regarded by his contemporaries as a strikingly original philosopher and a formidable disputant, Suvat appears never to have fully grasped certain principles of the differential calculus, and throughout his life he staunchly maintained that his “cinématique universelle” was not subject to “spécifications crétines” requiring the acceleration to be independent of time; contemporary and subsequent scientific opinion has not in general favoured his position. Perhaps more comprehensible was his resistance to the introduction of the “abomination hérétique” of vectors into his beloved mechanics, a resistance which engenders some sympathy to this day among undergraduate mathematicians. Nevertheless, his public activities rapidly descended into a seemingly endless round of disputation and recrimination, conducted through the medium of the letters pages (and subsequently the advertisement columns) of the Paris newspapers, while his private prosperity dwindled under the expenses associated with these activities. The final stages of the debate only reached the public through some unorthodox, though hardly unprecedented, channels, and as recently as a few years ago the traces of one exchange were still visible as graffiti scratched into the fabric of a canal bridge in the 21st arrondissement of Paris.

Suvat’s circle of scientific and philosophical colleagues was small, but nonetheless widespread. He was a lifelong correspondent of both the Irish philosopher de Selby and the cyclometer James Smith, of Liverpool, while the English mathematician James Moriarty based several passages of his celebrated work The Dynamics of an Asteroid upon Suvat’s calculations. Suvat, indeed, believed that Moriarty had in these passages strayed noticeably in the direction of plagiarism. This belief brought their correspondence to an acrimonious end, although Suvat was unable to enlist the help of any supporters in a scientific press which appeared incapable of criticising his adversary. It may be that the nervous strain engendered by the Asteroid controversy was instrumental in Suvat’s death — long the subject of fruitless speculation — in a locked room in his house in Paris, from unidentifiable but apparently natural causes at the age of 73.

Suvat retains a small but militant following in his home country, and his name was for several years in the 1950s inscribed among those of the great savants beneath the first balcony of the Eiffel Tower, until it was drawn to the attention of the competent authorities and unceremoniously removed.

Download full text in PDF: suvat-bio2.

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