Recherches sur les mouvements d’Uranus.

Paris: Bachelier, 1846.

First edition, first offprint issue, extremely rare, of Le Verrier’s mathematical prediction of the existence of Neptune, “undeniably one of the major scientific events of the nineteenth century” (Lequeux, p. 22). This issue precedes both the journal appearance in Connaissance des Temps and the second offprint issue, in both of which ‘Uranus’ in the title was changed to ‘le planète Herschel’ (and a related footnote was added). “Neptune, whose existence was visually confirmed in 1846, was the first planet to be discovered by mathematical rather than observational means. The discovery of Neptune not only represents the greatest triumph for Newton’s gravitational theory since the return of Halley’s Comet in 1758, but it also marks the point at which mathematics and theory, rather than observation, began to take the lead in astronomical research … The discovery of Neptune resulted from the need to develop a theory explaining the motion of the solar system’s seventh planet, Uranus, the movements of which could not be completely accounted for by the gravitational effects of Jupiter and Saturn. Several astronomers since the planet’s discovery in 1781 had suggested that the perturbations in Uranus’s orbit could be caused by an as yet unknown trans-Uranian planet. However, the complex mathematics required for proving this hypothesis was so daunting that no one had attempted the task … Le Verrier had begun his own work on the Uranus problem in the summer of 1845, encouraged by François Arago, who by then had become France’s leading astronomer. On November 19, 1845 Le Verrier published his first brief paper on the subject in the Comptes rendus de l’Académie des sciences, following it with three more equally brief papers published on June 1, August 31 and October 5, 1846. These short papers, totaling only 34 pages, were preliminary to the full and detailed account Le Verrier gave of his results in [the present work]; on p. 5 of that work Le Verrier referred to the Comptes rendus papers as ‘publications partielles. Le Verrier communicated the result of his investigations to several astronomers who had powerful instruments at their disposal. Among them was J. G. Galle, at the Berlin observatory, who was notified by Le Verrier on 23 September. Two days later he wrote to Le Verrier, announcing that he had observed the planet within 1° of Le Verrier’s predicted position. “During the time that Le Verrier was conducting his research on the movements of Uranus, the English astronomer J. C. Adams was independently arriving at the same conclusions, which he communicated to the Astronomer Royal, George Biddell Airy. Adams’s paper remained unpublished until 1847” (Norman 1343). OCLC lists only the BNF copy of this first offprint issue (and nine copies of the second issue); only one other copy of this first issue in auction records (Sotheby’s 1983).

“In his celebrated treatise on celestial mechanics, Pierre Simon de Laplace had developed mathematical expressions for the mutual perturbations exerted by the planets as a result of their gravitational attraction. Using these expressions, one could carry out numerical calculations to produce tables of the positions of the planets over time. The responsibility for doing so was claimed by the Bureau of Longitudes, headed by Laplace himself, though the work of actually performing these backbreaking calculations was distributed among several astronomers at the Bureau, including Delambre, Alexis Bouvard, and Burckhardt. Bouvard, Laplace’s student, was assigned the most thankless task. In 1821, he began the laborious calculation of tables predicting the movements of the three giant planets: Jupiter, Saturn, and Uranus. The calculation of the tables of Jupiter and Saturn proved to be relatively straightforward. Uranus, however, proved to be highly intractable. Even after taking into account the perturbations exerted by the other planets, Bouvard could not derive a set of orbital elements that would successfully account for the movements of Uranus during the entire period over which it had been observed …

“Resigned to defeat, Bouvard wrote in the introduction of his Tables of Uranus in 1821 that it would remain the task of future investigators to determine whence arose the difficulty in reconciling these two data sets: whether the failure of the observations before 1781 to fit the tables was due to the inaccuracy of the older observations or whether they might depend on ‘some foreign and unperceived source of disturbance acting upon the planet’ … It seems, then, that Alexis Bouvard himself had been the first to speculate that the anomalous motion of Uranus could be occasioned by the gravitational action of a new planète troublante (disturbing planet) … Following Alexis Bouvard’s death in 1843, his nephew Eugène was charged by the Bureau of Longitudes to work on new tables of the planets. He submitted his results to the Academy of Sciences on September 1, 1845, but they were never published. By then he had come to regard the discrepancies between observation and theory as irreconcilable without adding another factor, and personally found ‘entirely plausible the idea suggested by my uncle that another planet was perturbing Uranus.’

“Arago evidently hoped that the problem of Uranus would be taken up at the Paris Observatory, but he lacked confidence in Eugène Bouvard, whose measurements at the eclipse expedition of 1842 had been of poor quality. Since there was no one else at the observatory he deemed capable of tackling such a difficult problem, he turned to Le Verrier (1811-77). He had great faith in Le Verrier’s mathematical abilities, and so, at Arago’s request, Le Verrier abandoned the investigation of comets in which he was then involved and devoted himself to Uranus …

“Le Verrier scrupulously examined all the available observations up until 1845, notably those made recently at the Paris Observatory, which Arago put in his hands, and which were of excellent quality; and also those made at Greenwich which were sent by the director, Airy. He also examined carefully Alexis Bouvard’s calculations (he seems not to have considered those of his nephew, Eugène). He discovered that certain terms had been neglected unjustifiably, and he also turned up several outright errors, which required him to redo parts of the calculation. Next he undertook to determine the actual location of the perturbing planet.

“The problem was entirely novel: hitherto, the position of each planet was determined by taking into account the perturbations of the others whose positions were known by observation. In the present case, it was a matter of determining the position of a planet about which one knew nothing except the perturbations that it exerted on the other planets. In mathematics, this is called an inverse problem. It is both difficult and complex, because there are many unknowns to be determined. Le Verrier simplified the problem from the outset by supposing as known the distance of the planet from the Sun and the inclination of its orbit. He wrote on 1 June 1846:

‘It would be natural to suppose that the new body is situated at twice the distance of Uranus from the Sun, even if the following considerations didn’t make it almost certain. First, it is obvious that the sought-after planet cannot come too close to Uranus [since then its perturbations would have been very evident]. However, it is also difficult to place it as far off, say, as three times the distance of Uranus, for then we should have to give it an excessively large mass. But then its great distance both from Saturn and Uranus would mean that it would disturb each of these two planets in comparable degree, and it would not be possible to explain the irregularities of Uranus without at the same time introducing very sensible perturbations of Saturn, of which however there exist no trace.’

We might add that since the orbits of Jupiter, Saturn, and Uranus all have a very small inclination to the ecliptic, it is reasonable to suppose, as a first approximation, that the same must apply to the sought-after planet.

“By such legerdemain, Le Verrier had reduced the number of unknowns by two: he assumed the semi-major axis of the orbit, a quantity that would have been particularly difficult to determine otherwise, and the inclination of the orbit. Nevertheless, there remained more than enough other unknowns, in part because the orbital elements of Uranus were themselves poorly determined owing to the lack of any solution fitting all the observations … Seeing this, Le Verrier was obliged to determine simultaneously both the orbital elements of Uranus and those of the new planet. This is a problem with 12 unknowns. However, as we have seen, Le Verrier had already settled on two for the unknown planet, and using the same reasoning he settled on the same ones for Uranus: the semi-major axis and the orbital inclination. With this simplification, there remained eight unknowns in the orbital elements, to which he added a ninth, the mass of the perturbing planet … Le Verrier affirmed, in his presentation to the Academy of sciences on 1 June 1846:

‘I demonstrate that all the observations of the planet [Uranus] can be represented with the exactitude they deserve … I conclude also that one can effectively model the irregularities of Uranus’s movements by the action of a new planet placed at a distance of twice that of Uranus from the Sun; and what is just as important, that one can arrive at the solution in only one way. To say that the problem is susceptible to only one solution, I mean that there are not two regions in the sky in which one can choose to place the planet in a given epoch (such as, for instance, 1 January 1847). Within this unique region, we can limit the object’s position within certain bounds.’

“Next Le Verrier indicates within 10° the possible positions occupied by the perturbing planet for 1 January 1847. The uncertainty was still considerable, and Le Verrier added that he could do no better at the time of his presentation, since the work for which he had just presented an abstract to the Academy ‘must be considered a rough draft or outline of a new theory, which [was] only in the initial stages.’ The orbital elements he calculated were provisional, but he hoped to extend his labors to provide more precise results …

“Despite Le Verrier’s seeming confidence, skepticism still reigned in certain quarters. Thus Airy wrote on 26 June to Le Verrier to ask for further clarifications, at the same time sending him additional Greenwich observations. Le Verrier thanked Airy for his assistance, and responded to Airy’s specific questions. He even proposed to communicate the orbital elements of the perturbing planet, if Airy were at all inclined to search for it. Airy was very impressed by Le Verrier’s confidence. Though his skepticism was completely overcome, he declined Le Verrier’s offer, for reasons that remain rather mysterious even today.

“Despite the novelty of the problem and the great mathematical difficulties involved, Le Verrier needed only 3 months to specify the orbital elements of the perturbing planet, guess at its mass, and even provide an order of magnitude estimate of the apparent diameter it would present in the telescope … On August 31 1846, Le Verrier presented a paper to the Academy of Sciences, containing the elements of the planet and the place where it ought to be found. He then wrote to several foreign astronomers in an effort to enlist a powerful instrument in the search. Sadly, there were at the time no suitable instruments at the Paris Observatory itself. Furthermore, the observatory did not then have at its disposal any good maps of this part of the sky. Despite all that Arago and Le Verrier between them had done, the planet would not, and indeed could not, be discovered in Paris.

“Among the foreign astronomers contacted by Le Verrier was Johann Gottfried Galle, of the Berlin observatory. Le Verrier wrote to him on 18 September. The letter reached Berlin on 23 September; that night Galle, after seeking and receiving permission from the observatory’s director, Johann Franz Encke, and being assisted by a graduate student from Copenhagen, Heinrich Louis d’Arrest, quickly discovered the planet. On 25 September, Galle wrote to Le Verrier (in French; the latter did not know German): ‘Monsieur, the planet whose position you had indicated really exists. On the very day I received your letter I found an eighth magnitude star, which did not appear in the excellent chart Hora XXI (drawn up by Dr. Carl Bremiker) from the collection of celestial charts published by the Academy of Berlin. The observation of the next night clinched the matter: here was indeed the planet we were looking for. Encke and I found with the great refractor of Fraunhofer (with an objective 9 1⁄2 inches [23 cm] in diameter) that in brightness it was comparable to a ninth magnitude star’ …

“Shortly after the announcement of the discovery, the planet was viewed in Paris by Le Verrier himself, as well as by several other astronomers, including Otto Struve and his father Wilhelm at the Pulkova Observatory near Saint Petersburg, by Emil Plantamour in Geneva, by Carl Ludwig von Littrow in Vienna, by John Russell Hind and James Challis in England, and by Carl Friedrich Gauss in Göttingen, etc. Many wrote to congratulate him, notably Otto Struve and Father Angelo Secchi at the Jesuit Collegio Romano in Rome …

“Though a torrent of salutations rained down on Le Verrier, those of his own colleagues meant the most to him. He became famous overnight, and received countless honors: Officer of the Legion of Honor (though he had only been a Chevalier for 4 months), assistant member of the Bureau of Longitudes, chair of celestial mechanics in the faculty of sciences in Paris – the latter was specifically created for him in honor of his achievement. King Louis-Philippe named him preceptor of astronomy for his grandson, Louis-Philippe d’Orléans. The Royal Society of London awarded him the prestigious Copley Medal, the very same that William Herschel had won for the discovery of Uranus, and inscribed him among its foreign members. Many other learned societies followed suit …

“After the discovery of the new planet, it was necessary to agree on a name for it. Normally, the astronomer who makes the discovery offers a proposal, and a learned scientific society votes on its appropriateness … Since Le Verrier was considered to be the true discoverer of the planet – as Arago put it so poetically, he had discovered it ‘at the tip of his pen’ – it was Le Verrier’s prerogative to name the planet. Indeed, it seems to have been Le Verrier himself who first proposed Neptune, asserting, moreover, to his correspondents that the Bureau of Longitudes had already selected this name … But now Le Verrier, having first proposed Neptune, seems to have had second thoughts. Unaccountably, he resigned the task of choosing the planet’s name to Arago. Arago, in turn, promptly proposed a different name – ‘Le Verrier’ …

“Le Verrier was evidently highly satisfied with Arago’s proposal. Moreover, he now attempted to regularize the situation by using for Uranus the name Herschel, a name which had hitherto been used only sporadically:

‘In my subsequent publications, I will consider it a strict duty to make disappear completely the name Uranus, and to only refer to the planet using the name HERSCHEL. I sorely regret that my already published writings do not permit me to follow the determination that I shall religiously observe henceforth.’

Nevertheless, the name ‘Le Verrier’ would encounter more and more fierce opposition, and finally the name Neptune would be adopted” (Lequeux).

Le Verrier’s initial announcement of his prediction precipitated a priority dispute with the Cambridge mathematical astronomer John Couch Adams. “Adams began his investigation of Uranus in 1843, and in 1845 sent his calculations and observations to the Astronomer Royal, George Biddell Airy, who failed to recognise the importance of the paper. In 1846, Urbain Jean Joseph Le Verrier published his own research and reached the same conclusion, leading to the immediate identification of Neptune by J.G. Galle. Only then was Adams’ work published, leading to a bitter dispute over priority” (Norman 7). But this standard account, in which Adams’ prediction preceded Le Verrier’s (although it was published later), has been brought into question by contemporary documents rediscovered in 1999. “In contrast to the traditional story of Adams’s wonderful prediction that went shamefully ignored by British astronomers, the real Adams appears to have been rather vague, and his predictions for the planet kept changing. At no point did he have the confidence to say, in effect, as Le Verrier did, ‘point your telescope here and you will find it.’ Instead, Adams’s predictions ranged over as much as 20° of sky, throwing British searchers at the Cambridge University Observatory on a six-week wild goose chase hunting the planet during the summer of 1846. The actual discovery of Neptune took Galle just a half hour at the telescope in Berlin (the planet was only 1° from Le Verrier’s predicted position). Afterward the British – and especially Airy – got together a carefully digested and heavily selected version of events. Adams’s vacillation and mathematical scrupulosity were hushed up and covered over, and only his early, preliminary result – which proved to be more accurate than his later ones – was made public. The result was a remarkable British takeover … Le Verrier protested at the time, but in vain. He never had an opportunity to read all the documents in the possession of the British, so he was forced to accept their version of Adams’s priority in the calculations” (Sheehan). For further details on the dispute, see Lequeux, pp. 44-49 and Kollerstrom, ‘Recovering the Neptune files’, Astronomy & Geophysics 44 (2003), pp. 5.23–5.24.

The detailed account of Le Verrier’s calculations contained in the present offprint was published three times in quick succession. It appeared in the Connaissance des Temps ou des Mouvements Célestes, a l’Usage des Astronomes et des Navigateurs, pour l’An 1849, Publiée par le Bureau des Longitudes (Additions, pp. 3-254), the French analogue of the British Nautical Almanac, under the title ‘Recherches sur les mouvements de la planète Herschel (dite Uranus)’, the article being dated 5 October 1846 at the end; the journal imprint gives its date of publication as November 1846. Two offprints of this article were published, which can be distinguished from the journal issue by the presence of the publisher’s imprint and the phrase ‘Extrait de la Connaissance des Temps pour 1849’ on p. 254. The second offprint issue differs from the version offered here in its title, ‘Recherches sur les mouvements de la planète Herschel’ (note that the phrase ‘dite Uranus’ has been omitted), and by the presence of the note referred to above stating Le Verrier’s intention to use the name Herschel instead of Uranus: this note is printed at the foot of p. 3 of the second offprint issue, and also appears in the journal issue, but not in the offprint offered here. This clearly indicates the following order of publication:

  1. The offprint offered here with title ‘Recherches sur les mouvements d’Uranus’;
  2. The publication in Connaissance des Temps with title ‘Recherches sur les mouvements de la planète Herschel (dite Uranus)’;
  3. The second offprint with title ‘Recherches sur les mouvements de la planète Herschel’.

Sparrow, Milestones of Science 132 (journal issue); Evans 25 (journal issue); Norman 1343 (second offprint issue), incorrectly stating that the offprint is a collected edition of the Comptes Rendus announcements. Lequeux, Le Verrier—Magnificent and Detestable Astronomer, 2013 (especially Chap. 2, ‘The Discovery of Neptune (1845–1846)’). Sheehan, ‘Secret Documents Rewrite the Discovery of Neptune,’ Sky & Telescope, July 2013.

8vo (230 x 151 mm), pp. [ii], [3], 4-254. Twentieth-century half-calf with original blue printed wrappers bound in (front wrapper with Japanese tissue repairs to a few minor marginal defects, rear wrapper with ink stain).

Item #4777

Price: $9,500.00