CHAPTER XIV

SCIENTIFIC PREDICTION—THE DISCOVERY OF NEPTUNE

Under this heading we have to consider a single illustration—the prediction, and the discovery, in 1846, of the planet Neptune. This event roused great enthusiasm among scientists as well as in the popular mind, afforded proof of the reliability of the Newtonian hypothesis, and demonstrated the precision to which the calculation of celestial motions had attained. Scientific law appeared not merely as a formulation and explanation of observed phenomena but as a means for the discovery of new truths. "Would it not be admirable," wrote Valz to Arago in 1835, "to arrive thus at a knowledge of the existence of a body which cannot be perceived?"

The prediction and discovery of Neptune, to which many minds contributed, and which has been described with a show of justice as a movement of the times, arose from the previous discovery of the planet Uranus by Sir William Herschel in 1781. After that event Bode suggested that it was possible other astronomers had observed Uranus before, without recognizing it as a planet. By a study of the star catalogues this conjecture was soon verified. It was found that Flamsteed had made, in 1690, the first observation of the heavenly body now called Uranus. Ultimately it was shown that there were at least seventeen similar observations prior to 1781.

It might naturally be supposed that these so-called ancient observations would lead to a ready determination of the planet's orbit, mass, mean distance, longitude with reference to the sun, etc. The contrary, however, seemed to be the case. When Alexis Bouvard, the associate of Laplace, prepared in 1821 tables of Uranus, Jupiter, and Saturn on the principles of the Mécanique Céleste, he was unable to fix an orbit for Uranus which would harmonize with the data of ancient and modern observations, that is, those antecedent and subsequent to Herschel's discovery in 1781. If he computed an orbit from the two sets of data combined, the requirements of the earlier observations were fairly well met, but the later observations were not represented with sufficient precision. If on the other hand only the modern data were taken into account, tables could be constructed meeting all the observations subsequent to 1781, but failing to satisfy those prior to that date. A consistent result could be obtained only by sacrificing the modern or the ancient observations. "I have thought it preferable," says Bouvard, "to abide by the second [alternative], as being that which combines the greater number of probabilities in favor of the truth, and I leave it to the future to make known whether the difficulty of reconciling the two systems result from the inaccuracy of ancient observations, or whether it depend upon some extraneous and unknown influence, which has acted on the planet." It was not till three years after the death of Alexis Bouvard that the extraneous influence, of which he thus gave in 1821 some indication, became fully known.

Almost immediately, however, after the publication of the tables, fresh discrepancies arose between computation and observation. At the first meeting of the British Association in 1832 Professor Airy in a paper on the Progress of Astronomy showed that observational data in reference to the planet Uranus diverged widely from the tables of 1821. In 1833 through his influence the "reduction of all the planetary observations made at Greenwich from 1750" was undertaken. Airy became Astronomer Royal in 1835, and continued to take special interest in Uranus, laying particular emphasis on the fact that the radius vector assigned in the tables to this planet was much too small.

In 1834 the Reverend T. J. Hussey, an amateur astronomer, had written to Airy in reference to the irregularities in the orbit of Uranus: "The apparently inexplicable discrepancies between the ancient and modern observations suggested to me the possibility of some disturbing body beyond Uranus, not taken into account because unknown.... Subsequently, in conversation with Bouvard, I inquired if the above might not be the case." Bouvard answered that the idea had occurred to him; indeed, he had had some correspondence in reference to it in 1829 with Hansen, an authority on planetary perturbations.

In the following year Nicolai (as well as Valz) was interested in the problem of an ultra-Uranian planet in connection with the orbit of Halley's comet (itself the subject of a striking scientific prediction fulfilled in 1758), now reappearing, and under the disturbing influence of Jupiter. In fact, the probability of the approaching discovery of a new planet soon found expression in popular treatises on astronomy. Mrs. Somerville in her book on The Connection of the Physical Sciences (1836) said that the discrepancies in the records of Uranus might reveal the existence and even "the mass and orbit of a body placed for ever beyond the sphere of vision." Similarly Mädler in his Popular Astronomy (1841) took the view that Uranus might have been predicted by study of the perturbations it produced in the orbit of Saturn. Applying this conclusion to a body beyond Uranus we, he continued, "may, indeed, express the hope that analysis will one day or other solemnize this, her highest, triumph, making discoveries with the mind's eye in regions where, in our actual state, we are unable to penetrate."

One should not pass over in this account the labors of Eugène Bouvard, the nephew of Alexis, who continued to note anomalies in the orbit of Uranus and to construct new planetary tables till the very eve of the discovery of Neptune. In 1837 he wrote to Airy that the differences between the observations of Uranus and the calculation were large and were becoming continually larger: "Is that owing to a perturbation brought about in this planet by some body situated beyond it? I don't know, but that's my uncle's opinion."

In 1840 the distinguished astronomer Bessel declared that attempts to explain the discrepancies "must be based on the endeavor to discover an orbit and a mass for some unknown planet, of such a nature, that the resulting perturbations of Uranus may reconcile the present want of harmony in the observations." Two years later he undertook researches in reference to the new planet of whose existence he felt certain. His labors, however, were interrupted by the death of his assistant Flemming, and by his own illness, which proved fatal in 1846, a few months before the actual discovery of Neptune. It is evident that the quest of the new planet had become general. The error of Uranus still amounted to less than two minutes. This deviation from the computed place is not appreciable by the naked eye, yet it was felt, by the scientific world, to challenge the validity of the Newtonian theory, or to foreshadow the addition of still another planet to our solar system.

In July, 1841, John Couch Adams, a young undergraduate of St. John's College, Cambridge, whose interest had been aroused by reading Airy's paper on the Progress of Astronomy, made note of his resolution to attempt, after completing his college course, the solution of the problem then forming in so many minds. After achieving the B.A. as senior wrangler at the beginning of 1843, Adams undertook to "find the most probable orbit and mass of the disturbing body which has acted on Uranus." The ordinary problem in planetary perturbations calls for the determination of the effect on a known orbit exerted by a body of known mass and motion. This was an inverse problem; the perturbation being given, it was required to find the position, mass, and orbit of the disturbing planet. The data were further equivocal in that the elements of the given planet Uranus were themselves in doubt; the unreliability of its planetary tables, in fact, being the occasion of the investigation now undertaken. That thirteen unknown quantities were involved indicates sufficiently the difficulty of the problem.

Adams started with the assumptions, not improbable, that the orbit of the unknown planet was a circle, and that its distance from the sun was twice that of Uranus. This latter assumption was in accord with the so-called "Bode's Law," which taught that a simple numerical relationship exists between the planetary distances (4, 7, 10, 16, 28, 52, 100, 196), and that the planets as they lie more remote from the sun tend to be more nearly double the distance of the next preceding. Adams was encouraged, by his first attempt, to undertake a more precise determination.

On his behalf Professor Challis of Cambridge applied to Astronomer Royal Airy, who furnished the Reductions of the Planetary Observations made at Greenwich from 1750 till 1830. In his second endeavor Adams assumed that the unknown planet had an elliptical orbit. He approached the solution gradually, ever taking into account more terms of the perturbations. In September, 1845, he gave the results to Challis, who wrote to Airy on the 22d of that month that Adams sought an opportunity to submit the solution personally to the Astronomer Royal. On the 21st of October, 1845, the young mathematician, twice disappointed in his attempt to meet Airy, left at the Royal Observatory a paper containing the elements of the new planet. The position assigned to it was within about one degree of its actual place.

On November 5 Airy wrote to Adams and, among other things, inquired whether the solution obtained would account for the errors of the radius vector as well as for those of heliocentric longitude. For Airy this was a crucial question; but to Adams it seemed unessential, and he failed to reply.

By this time a formidable rival had entered the field. Leverrier at the request of Arago had undertaken to investigate the irregularities in the tables of Uranus. In September of the same year Eugène Bouvard had presented new tables of that planet. Leverrier acted very promptly and systematically. His first paper on the problem undertaken appeared in the Comptes Rendus of the Académie des Sciences November 10, 1845. He had submitted to rigorous examination the data in reference to the disturbing influence of Jupiter and of Saturn on the orbit of Uranus. In his second paper, June 1, 1846, Leverrier reviewed the records of the ancient and modern observations of Uranus (279 in all), subjected Bouvard's tables to severe criticism, and decided that there existed in the orbit of Uranus anomalies that could not be accounted due to errors of observation. There must exist some extraneous influence, hitherto unknown to astronomers. Some scientists had thought that the law of gravitation did not hold at the confines of the solar system (others that the attractive force of other systems might prove a factor), but Leverrier rejected this conception. Other theories being likewise discarded he asked: "Is it possible that the irregularities of Uranus are due to the action of a disturbing planet, situated in the ecliptic at a mean distance double that of Uranus? And if so, at what point is this planet situated? What is its mass? What are the elements of the orbit which it describes?" The conclusion reached by the calculations recorded in this second paper was that all the so-called anomalies in the observations of Uranus could be explained as the perturbation caused by a planet with a heliocentric longitude of 252° on January 1, 1800. This would correspond to 325° on January 1, 1847.

Airy received Leverrier's second paper on June 23, and was struck by the fact that the French mathematician assigned the same place to the new planet as had Adams in the preceding October. He wrote to Leverrier in reference to the errors of the radius vector and received a satisfactory and sufficiently compliant reply. At one time the Astronomer Royal had felt very skeptical about the possibility of the discovery which his own labors had contributed to advance. He had always, to quote his own rather nebulous statement, considered the correctness of a distant mathematical result to be the subject of moral rather than of mathematical evidence. Now that corroboration of Adams's results had arrived, he felt it urgent to make a telescopic examination of that part of the heavens indicated by the theoretical findings of Adams and Leverrier. He accordingly wrote to Professor Challis, July 9, requesting him to employ for the purpose the great Northumberland equatorial of the Cambridge Observatory.

Professor Challis had felt, to use his own language, that it was so novel a thing to undertake observations in reliance upon merely theoretical deductions, that, while much labor was certain, success appeared very doubtful. Nevertheless, having received fresh instructions from Adams relative to the theoretical place of the new planet, he began observations July 29. On August 4 in fixing certain reference points he noted, but mistook for a star, the new planet. On August 12, having directed the telescope in accordance with Adams's instructions he again noted the same heavenly body, as a star. Before Challis had compared the results of the observation of August 12 with the results of an observation of the same region made on July 30, and arrived at the inference that the body in question, being absent in the latter observation, was not a star but a planet, the prize of discovery had fallen into the hands of another observer.

On August 31 had appeared Leverrier's third paper, in which were stated the new planet's orbit, mass, distance from the sun, eccentricity, and longitude. The true heliocentric longitude was given as 326° 32' for January 1, 1847. This determination placed the planet about 5° to the east of star δ of Capricorn. Leverrier said it might be recognized by its disk, which, moreover, would subtend a certain angle.

The systematic and conclusive character of Leverrier's research, submitted to one of the greatest academies of science, carried conviction to the minds of astronomers. The learned world felt itself on the eve of a great discovery. Sir John Herschel, in an address before the British Association on September 10, said that the year past had given prospect of a new planet. "We see it as Columbus saw America from the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to ocular demonstration."

On September 18 Leverrier sent a letter to Dr. Galle, of the Berlin Observatory, which was provided with a set of star maps, prepared at the instance of Bessel. Galle replied one week later. "The planet, of the position of which you gave the indication, really exists. The same day that I received your letter [September 23] I found a star of the eighth magnitude, which was not inscribed in the excellent map (prepared by Dr. Bremiker) belonging to the collection of star maps of the Royal Academy of Berlin. The observation of the following day showed decisively that it was the planet sought." It was only 57' from the point predicted.

Arago said that the discovery made by Leverrier was one of the most brilliant manifestations of the precision of modern astronomic science. It would encourage the best geometers to seek with renewed ardor the eternal truths which, in Pliny's phrase, are latent in the majesty of theory.

Professor Challis received Leverrier's third paper on September 29, and in the evening turned his magnificent refractor to the part of the heavens that Leverrier had so definitely and so confidently indicated. Among the three hundred stars observed Challis was struck by the appearance of one which presented a disk and shone with the brightness of a star of the eighth magnitude. This proved to be the planet. On October 1 Challis heard that the German observer had anticipated him.

Arago, while recognizing the excellent work done by Adams in his calculations, thought that the fact that the young mathematician had failed to publish his results should deprive him of any share whatever in the glory of the discovery of the new planet, and that history would confirm this definite judgment. Arago named the new planet after the French discoverer, but soon acquiesced in the name Neptune, which has since prevailed.

Airy, in whose possession Adams's results had remained for months unpublished and unheeded, wrote Leverrier: "You are to be recognized beyond doubt as the predictor of the planet's place." A vigorous official himself, Airy was deeply impressed by the calm decisiveness and definite directions of the French mathematician. "It is here, if I mistake not, that we see a character far superior to that of the able, or enterprising, or industrious mathematician; it is here that we see the philosopher." This explains, if anything could, his view that a distant mathematical result is the subject of ethical rather than of mathematical evidence.

Adams's friends felt that he had not received from either of the astronomers, to whom he confided his results, the kind of help or advice he should have received. Challis was kindly, but wanting in initiative. Although he had command of the great Northumberland telescope, he had no thought of commencing the search in 1845, for, without mistrusting the evidence which the theory gave of the existence of the planet, it might be reasonable to suppose that its position was determined but roughly, and that a search for it must necessarily be long and laborious. In the view of Simon Newcomb,[3] Adams's results, which were delivered at the Greenwich Observatory October 21, 1845, were so near to the mark that a few hours' close search could not have failed to make the planet known.

Both Adams and Leverrier had assumed as a rough approximation at starting that the orbit of the new planet was circular and that, in accordance with Bode's Law, its distance was twice that of Uranus. S. C. Walker, of the Smithsonian Institution, Washington, was able to determine the elements of the orbit of Neptune accurately in 1847. In February of that year he had found (as had Petersen of Altona about the same time) that Lalande had in May, 1795, observed Neptune and mistaken it for a fixed star. When Lalande's records in Paris were studied, it was found that he had made two observations of Neptune on May 8 and 10. Their failure to agree caused the observer to reject one and mark the other as doubtful. Had he repeated the observation, he might have noted that the star moved, and was in reality a planet.

Neptune's orbit is more nearly circular than that of any of the major planets except Venus. Its distance is thirty times that of the earth from the sun instead of thirty-nine times, as Bode's Law would require. That generalization was a presupposition of the calculations leading to the discovery. It was then rejected like a discredited ladder. Man's conception of the universe is widened at the thought that the outmost known planet of our solar system is about 2,796,000,000 miles from the sun and requires about 165 years for one revolution.

Professor Peirce, of Harvard University, pointing to the difference between the calculations of Leverrier and the facts, put forward the view that the discovery made by Galle must be regarded as a happy accident. This view, however, has not been sustained.