The Philosophical Breakfast Club

by Laura J. Snyder

  Babbage noticed that “Sir RP seemed excessively angry and annoyed during the whole interview.” The prime minister refused to concede that he deserved more money, or any particular honors or position, for his work on the Difference Engine. “I then said,” Babbage recounted proudly, “Sir Peel, if those are your views, I wish you good morning.” And that was the end of the line for government funding for Babbage, and the end to any chance that the computer age would begin in the nineteenth, rather than the twentieth, century.100 Even the publication of the article on the Analytical Engine by his “good fairy” nine months later could not alter history.

  11

  NEW WORLDS

  ALL OF SOUTHAMPTON WAS ABUZZ WITH THE LATEST TANTALIZING gossip: a new planet, still unseen, was traveling around the sun beyond the orbit of Uranus. At the 1846 meeting of the British Association, Herschel referred to this planet obliquely, but everyone knew what he was talking about. “We see it,” Herschel announced dramatically, “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 that of ocular demonstration.”1

  The planet’s existence had not been divined by any telescopic observations. Rather, its existence, position, and mass had been calculated mathematically, by two men working independently: U. J. J. Le Verrier, the famous French astronomer, and a little-known Englishman, John Couch Adams. Barely two weeks after Herschel’s comments, the astronomer Johann Gottfried Galle, at the Berlin observatory, working from Le Verrier’s calculations, found the planet, less than one astronomical degree from its predicted location. It was only the second planet ever discovered, and the first time a celestial body had been found after theoretical mathematical prediction of its existence. (The erstwhile planet Pluto would later be discovered in a similar way.)

  It had all started in 1821, when the French astronomer Alexis Bouvard published astronomical tables for the planet Uranus. Applying Newton’s law of universal gravitation, Bouvard made predictions about the future position of the planet, based on the gravitational force Newton’s law dictated would be exerted on Uranus by the sun and the other known planets. Soon, however, it became clear to Bouvard, and to others, that the orbit of Uranus in fact deviated quite substantially from its predicted positions. After checking all his calculations, Bouvard became convinced that there must be a yet-unnoticed celestial body causing the deviations, or “perturbations,” in the planet’s orbit by exerting additional gravitational force upon it. The only other possible explanation, barring observational error, was that Newton’s law of universal gravitation was not truly universal: perhaps, so far away from the sun, gravitational force is weaker or stronger than Newton’s law stipulated. Yet the work of William and John Herschel on binary stars had shown that Newton’s law held true as far away as the most distant stars, so most astronomers discounted this possibility.

  Although astronomers soon became convinced that there must be some planet or other celestial body causing the perturbations of Uranus, finding it was another matter; the task was like seeking a tiny pebble amid the grains of sand in an entire beach—a pebble whose position would change each day of the search. It would help if one could somehow calculate the approximate position of the planet on a certain night or series of nights, so that astronomers could carefully and systematically search just one part of the sky. This kind of calculation, however, had never been done before. Astronomers were familiar with the problem of perturbations, a classic type of calculation in mechanics, whereby one calculates the effect of known bodies (of known positions and masses) on another given body. But this case was different; here, the disturbances upon a known body must somehow be used to infer the mass and position of the unseen perturbing body. This became known as the problem of “inverse perturbation.”2

  In June of 1841, a student at St. John’s College, Cambridge, was browsing in Johnson’s bookstore in Trinity Street. He came upon a copy of the proceedings of the Oxford meeting of the British Association in 1832, and began to read Airy’s report on the current state of astronomy. In his report, Airy had noted that the difference between the predicted and actual positions of Uranus was nearly half a minute of arc, a value much too high to be explained by observational error alone. Airy had proposed that astronomers take up the challenge of finding the solution to this problem.

  The student, John Couch Adams, was struck by the fact that nearly a decade had passed since Airy’s call to action, and the problem remained unsolved. He confided to his diary a few days later that, as soon as he took his degree, he would begin working on the irregularities in the orbit of Uranus, to tease out the secret of the invisible planet—“wh[ich] w[oul]d probably lead to its discovery,” he predicted confidently.3 After graduating as senior wrangler and first Smith’s prizeman in 1843, and receiving a fellowship from St. John’s, Adams began to tackle the problem.

  Had Babbage’s Analytical Engine been built, Adams’s task could have been much simpler. As it was, it involved much laborious hand calculation. Adams began by assuming a position for the invisible planet using Bode’s law, a rule of thumb that predicts the spacing of planets in the solar system (in 1778, J. E. Bode had used it to predict the existence of a planet between Mars and Jupiter—what turned out to be the Asteroid Belt). This gave Adams the rough estimate that the distance of the invisible planet from the sun was at twice the mean distance of Uranus from the sun. He then calculated what the path of Uranus would be if the perturbing body was in this position. He next determined the difference between his calculated path and the observations, what we would call today the “residuals.” Adams used what is now known as “regression analysis” to adjust the positions of the invisible planet in a way suggested by the residuals, and continued to repeat the process.4

  By October 1843 he had worked out a provisional solution. He took his work to James Challis, Plumian Professor of Astronomy and head of the Cambridge Observatory, who was impressed enough to write Airy and request more observations of Uranus so that Adams could continue his calculations with fresh data. Challis sent his request to Airy in February 1844, and Airy promptly sent back all the observations made of Uranus from the Greenwich Observatory between 1754 and 1830.

  Adams finally finished his arduous calculations in early September 1845. He presented Challis with his solution to the elements of the orbit of the “invisible” planet, and predicted its location in the nighttime sky on September 30. Challis wrote a letter of introduction to Airy for Adams, and, ignoring the usual social conventions, the younger man traveled from Cambridge to Greenwich without an appointment to impart his prediction to him. But Airy was in France at the time. A disappointed Adams left the letter from Challis and went home to Cornwall for a holiday. When Airy returned from France, he sent a letter to Challis saying that he would be “delighted to hear” of Adams’s investigations. Adams returned to try to see Airy two times on the same day in late October, but, once again, left without seeing Airy. The first time Airy was absent; the next he was having his dinner, and the servant refused to admit the young man. Adams left a statement of his results and another prediction of the location of the planet.

  When he looked over the single sheet that Adams had left him, Airy was skeptical—no doubt in part because of Adams’s youth and inexperience, but also because Adams had given only his results, not the whole series of calculations. Airy wrote to Adams asking whether his calculations also explained another aspect of Uranus’s orbit—its “radius vector,” the fact that the planet was farther from the sun than it ought to be. Airy considered this a Baconian crucial experiment for judging the accuracy of Adams’s results. Oddly, Adams never replied. Nor did he publish his results, which would have been the usual way to establish priority of scientific discovery, as it is today.

  At the same time, in France, Le Verrier independently began to work on the complex calculations to determine the mass and position of the unseen planet. In November 1845 he presen
ted a paper to the Royal Academy of Sciences in Paris. In this paper Le Verrier discussed the perturbations of Uranus’s orbit and the likelihood that there was an eighth planet causing the disturbances. On June 1, 1846, he presented a second paper, in which he predicted the location of this eighth planet on the night of January 1, 1847.

  Airy read this memoir soon after it was printed in the proceedings of the Royal Academy. He dug up Adams’s calculations, which he had put aside when the insolent young man had not even bothered to respond to his query—and was shocked to recognize that Le Verrier’s and Adams’s results were extremely close. At around this time Airy received a letter from Whewell, who was working on the revisions for his second edition of the History of the Inductive Sciences. Whewell asked Airy if he should include any updated information about Uranus’s eccentric behavior. Airy replied, “People’s notions have been long turned to the effects of an external planet, and upon this there are two remarkable calculations. One is by Adams of St. John’s.… The other is by LeVerrier.… Both have arrived at the same result!”5

  At a meeting of the Board of Visitors at the Royal Observatory at Greenwich a few days later, on June 29, Airy informed the twelve men present—including Herschel and Babbage—that there was an “extreme probability” that the planet would be found in a short time. Yet Airy suggested, rather strangely, that the Cambridge Observatory, rather than his Royal Observatory, undertake the search for the new planet. He had told Whewell in his letter a few days earlier that “if I were a rich man or had an unemployed staff I would immediately take measures for the strict examination of that part of the heavens containing the position of the postulated planet.” But even if Airy’s staff really was too busy to search for a new planet (one would think the discovery of a new planet would be considered a worthy task for the Royal Observatory), Britain had several other quite powerful telescopes that might have been enlisted in the search, including Lord Rosse’s famed thirty-six-inch and newly operational seventy-two-inch reflectors at Birr Castle in Ireland. Perhaps Airy thought it apt that the planet’s optical as well as its mathematical discovery should belong to his alma mater.

  Not only did Airy err in not assigning other telescopes to take part in the search, but he also devised an overly cumbersome method for seeking the new planet. In the nighttime sky, planets are distinguishable from stars in two ways. One is that the planets move with respect to the stars, which appear to be fixed in their places on the heavenly vault (that is why the planets have their name, meaning “little wanderers”). So an astronomer can find a planet by looking for a body that moves in relation to the stars. The second way in which a planet can be distinguished from a star is that, in a powerful enough telescope, the light from a planet can be resolved into a disk, a round spot of light with defined edges, whereas since the stars are so far away, the light from them is more diffuse, and thus the stars appear to twinkle; they cannot be resolved into disks with defined edges, no matter how powerful the telescope. Le Verrier had recommended that the planet be sought by combing the predicted part of the sky for a disk. That would be like taking the sand from a section of the beach and sifting it through a sieve to find the slightly larger, but still tiny, pebble. Airy, on the other hand, suggested a much more unwieldy procedure to Challis: map all the “stars” in the zone three times, and then compare their positions, to find the one that had moved. That would be like marking the position of each grain of sand in a cubic meter of sand, repeating the procedure three times, and comparing the maps in order to discover which tiny grain had moved in the intervening time.

  Challis’s search for the new planet began on July 29. Several days later, Le Verrier, still unaware of the British efforts, presented a third paper to the Royal Academy, giving a new prediction of the mass and orbit of the planet. Since no observatory in France took up the search, Le Verrier sent his results to a young astronomer who had recently sent Le Verrier his doctoral dissertation: Johann Gottfried Galle at the Berlin Observatory. Galle received the letter on the twenty-third of September. He and his student, Heinrich Louis d’Arrest, began the search for the new planet that very night. After fewer than sixty minutes of searching, the two men found the planet—near the constellations Capricorn and Aquarius, less than one degree from the position predicted by Le Verrier. As Le Verrier’s mentor François Arago would later put it, Le Verrier had discovered a new planet not with a telescope but “with the point of his pen.”

  Galle triumphantly wrote to Le Verrier, “Monsieur, the planet of which you indicated the position really exists!” Le Verrier replied, “I thank you for the alacrity with which you applied my instructions. We are thereby, thanks to you, definitely in possession of a new world.”6 That new world would soon be dubbed “Neptune.”

  ON OCTOBER 1, the Times headline screamed, “Le Verrier’s Planet Found!” By this point Challis had mapped three thousand stars. Going back over his laboriously drawn star maps, Challis’s heart sank when he realized that he had, in fact, observed Neptune on August 4 and 12, but had not recognized it as a planet.7 At the same time, Herschel became aware that on the night of July 14, 1830, he had nearly been the one to discover Neptune; he had swept a portion of the sky only one half of a degree north of where the planet must have been at the time. The magnifying power of his telescope would have been enough to show the celestial object as a small but recognizable disk—a planet. What a wonderful coincidence it would have been for both new planets to be discovered by Herschels! But upon realizing how close he had been to finding the new planet, Herschel mused that “it is better as it is. I should be sorry it [sic] had been detected by any accident or merely by its aspect. As it is, it is a noble triumph for science.”8

  Herschel was pleased that the planet had been discovered by prediction rather than by merely stumbling upon it with the telescope—the way his father had discovered Uranus. As Herschel had claimed in his Preliminary Discourse, the most striking kind of discoveries are made by prediction. Successful prediction compels the man of science to accept the truth of the theory that had led to the prediction, Herschel believed.9 Whewell had also made this point in his Philosophy of the Inductive Sciences. He argued there that if a theory makes a prediction of some novel phenomenon, and that prediction turns out to be correct, it is very strong confirmation of the truth of the theory; how, after all, could a false theory make a successful prediction, especially a prediction of something entirely unsuspected before, like a new planet? As Whewell put it, predictive success is extremely strong proof for the truth of a theory, because the agreement of the prediction with what does happen is “nothing strange, if the theory be true, but quite unaccountable, if it be not.”10

  Constructing a true theory, Whewell argued, was like breaking a coded message. “If I copy a long series of letters of which the last half-dozen are concealed, and if I guess these aright, as is found to be the case when they are afterwards uncovered, this must be because I have made out the import of the inscription,” Whewell explained.11 Successful prediction of formerly unknown facts is evidence that we have broken the code of nature, that we have “detected Nature’s secret.”12 As Bacon would have put it, we have demonstrated our ability to read God’s “second book,” the book of nature.

  Indeed, it seemed obvious to Herschel and Whewell that if Newton’s theory of gravitation were not true, the fact that from the theory we could correctly predict the existence, location, and mass of Neptune would be bewildering and indeed miraculous. The successful prediction of Neptune using Newton’s theory showed that astronomy truly was, as Whewell had put it at the British Association meeting in 1833, the “Queen of the Sciences.” Herschel agreed, calling astronomy “the most perfect science.”13 Here was a perfect case to show the world the way that science should work.

  AS SOON AS this new world was discovered, the race was on to claim it for the conquering nation.14 British scientists were united in feeling that an opportunity for making the discovery had slipped through their grasp. The fact that
it was a Frenchman receiving the honors made it even worse. The British rushed to publicize the fact that a Cambridge man, Adams, had also made essentially the same predictions as Le Verrier, and that the Cambridge Observatory had begun the search before the Berlin astronomers. Tensions between the British and the French were once again running high—and Herschel would soon make things worse.

  In a letter he wrote to the magazine the Athenaeum after learning of the discovery of the planet, Herschel surprisingly claimed that Le Verrier’s calculations alone had not been enough to convince astronomers of the existence of a new planet; it was the congruence of his and Adams’s results that had done so. Le Verrier was outraged. As Herschel well knew, Galle had undertaken the search for the new planet solely on the basis of Le Verrier’s prediction, without any knowledge of Adams’s work. Wagging a finger at Herschel, he chastised, “Among men of science of different countries, there ought to remain only that friendly rivalry, which, as leading to the benefit of science, so far from hindering, does but cement, the frank and brotherly friendship of those who cultivate it.”15 Replying to Le Verrier in the pages of the same newspaper, Herschel backpedaled, assuring his French colleague of “the frank and brotherly friendship” of all those who cultivate science, and that “there is not a man in England who will begrudge him” the “possession” of the discovery.16 Yet, in his diary that evening, Herschel recorded, “In bed half day after a sleepless night wrote to Editor of the Guardian in reply to M. Le Verrier’s savage letter—These Frenchmen fly at one like wildcats.”17 To a friend he confided that “this matter has really made me ill.”18

  The French, understandably, thought it rather suspicious that no one had ever heard of Adams’s calculations until after the discovery of the planet by Galle. In early November, a cartoon appeared in the French magazine L’illustration, which depicted Adams peering into a telescope that was aimed at Le Verrier’s memoir to the Royal Academy; it was provocatively captioned, “M. Adams decouvrant la nouvelle planète dans le rapport de M. Leverrier.” (Mr. Adams discovering the new planet in Leverrier’s report.)19