# Lectures on Ten British Physicists of the Nineteenth Century/Lecture 9

JOHN COUCH ADAMS
(1819-1892)
John Couch Adams was born on the 5th of June, 1819, at a farmhouse seven miles from Launceston in Cornwall. His father was a tenant farmer, and so had been his ancestors for several generations. His mother, née Tabitha Knill Grylls, owned a small estate, inherited from an aunt named Grace Couch; hence the middle name of the mathematician. John Couch Adams was the oldest of seven children; he had three brothers and three sisters; his brother William Grylls Adams became a professor of physics, and has attained to scientific distinction although not comparable to that of his brother. Adams was thus of the old Welsh stock located in the south-western peninsula of England. He received his primary education at the village school near the farm, where at ten years of age he studied algebra. In his own home there was a small library, which also had been inherited by his mother, and which included some books on astronomy. He constructed a simple instrument to determine the elevation of the sun. "It consisted of a vertical circular card with graduated edge, from the centre of which a plumb bob was suspended. Two small square pieces of card, with a pinhole in each, projected from the circular disc at right angles to its face at opposite ends of a diameter. The card was to be so placed that the sun shone through the pin holes, and the elevation was read off on the circle."
At twelve years of age he was placed in a private school taught by the Rev. John Couch Grylls, a cousin of his mother, the subjects of instruction being classics and mathematics. Here ​he had access to a public library, where he studied more books on astronomy, and also Vince's Fluxions, then the principal testbook at Cambridge on the higher mathematics. Thus early was he introduced to Newton's methods. While at this school he watched for three weeks for a predicted return of Encke's comet; at last he saw it (1835) and he wrote home, "You may conceive with what pleasure I viewed this, the first comet which I had ever had a sight of, which at its visit 380 years ago threw all Europe into consternation, but now affords the highest pleasure to astronomers by proving the accuracy of their calculations and predictions." The following year an annular eclipse of the Sun took place. For the people on the farm he made a calculation of the times of the eclipse for that meridian and latitude, and also a diagram of the eclipse as it would appear to them. Next year his account of observations of an eclipse appeared in the London papers. He was now 18 years old; and had shown such signs of mathematical power that preparations were made to send him to Cambridge.
In 1839, when 20 years old, he entered St. John's College; while an undergraduate he was invariably the first man of his year in the college examinations. It was his custom to keep a memorandum book, in which at the end of his second college year (July 3, 1841) he made the following entry: "Formed a design, in the beginning of this week, of investigating as soon as possible after taking my degree, the irregularities in the motion of Uranus, which are yet unaccounted for, in order to find whether they may be attributed to the action of an undiscovered planet beyond it; and if possible thence to determine the elements of its orbit, etc., approximately, which would probably lead to its discovery." His attention had been drawn to the phenomenon by reading Airy's report on Astronomy to the British Association (1831-2); but no explanation is suggested there. Meanwhile he kept to the beaten path of training for the Tripos; as a result in 1843 he won the first place in that examination, the first Smith's prize and a fellowship from his college. After taking his degree, Adams attempted a first solution of his problem on the assumption that the orbit ​was a circle with a radius equal to twice the mean distance of Uranus from the Sun—an assumption suggested by Bode's law. The result showed that a good general agreement between his theory and observation might be obtained. He now in 1844, if not before, acquainted Prof. Challis, Airy's successor with his scientific enterprise; and through him made a request to Airy for the errors of the tabular geocentric longitude of Uranus for 1818-26, with the factors for reducing them to errors of heliocentric longitude. Airy at once supplied all the results of the Greenwich observations of Uranus from 1754 to 1830.
With these improved data Adams now undertook a more elaborate discussion of the problems, retaining however the former assumption with respect to the mean distance; and by September of the following year (1845) he had the investigation completed. He communicated the results to Prof. Challis in the form of a note giving numerical values for the new planet, of its mean longitude at a given epoch, the longitude of its perihelion, the eccentricity of its orbit, its mass and its geocentric longitude for the last day of the month but without any account of his method. Challis on the 22d of September wrote to Airy a letter to introduce Adams; the first sentence in that letter has been already quoted in my lecture on Airy. Challis further said that he considered Adams' deductions to be made in a trustworthy manner. Challis had the best facilities in England to search for the predicted planet, yet he turned the matter over to Airy. Provided with the letter Adams called at the Greenwich Observatory, and met with the experiences described in my last lecture. Adams was naturally of a shy disposition and he felt mortified. In reply to the paper of results that he had left at the Observatory, Airy sent, a fortnight later, a letter to Adams: "I am very much obliged by the paper of results which you left here a few days since, showing the perturbations on the place of Uranus produced by a planet with certain assumed elements. . . . I should be very glad to know whether this assumed perturbation will explain the error of the radius-vector of Uranus." The prin​cipal result was that the mean longitude of the planet for 1st of October, 1845, was 323° 34′. Adams was hurt at the reception which his results had obtained; regarding Airy's question as of trifling importance he did not send any answer immediately but applied himself to a new calculation on the assumption of a smaller mean distance.
That same November a French astronomer, M. Leverrier, presented a paper to the French Academy on the perturbations of Uranus produced by Jupiter and Saturn, and concluded that these were quite incapable of explaining the observed irregularities. In June of the next year he presented his second paper which showed that there was no other possible explanation of the discordance, except that of an exterior planet. Further, like Adams, he assumed the distance to be double that of Uranus, and calculated that its longitude at the beginning of the next year (1847) would be 325°. Leverrier communicated his results by letter on the 24th of June to Airy, who on comparison found that there was only about one degree of difference in the predicted places of Adams and Leverrier. The next day (June 29) a meeting of the Board of Visitors took place at the Greenwich Observatory; Sir John Herschel and Prof. Challis were present as visitors. In the course of a discussion, Airy referred to the probability of shortly discovering a new planet, giving as his reason the close coincidence of Adams' and Leverrier's predictions. Early in July Airy thought it time that a search should be made for the planet. He considered the Cambridge telescope the best for the purpose, and he asked Prof. Challis whether he would undertake it, and the latter agreed to do so. Airy suggested the formation of three successive maps of the stars down to the 4th magnitude, in a band of the heavens 30° long by 10° wide having the predicted place of the planet as its centre. When the successive sets of observations were mapped, the planet could be detected by its motion in the interval.
At the end of August Leverrier presented his third memoir to the French Academy in which he gave the calculated elements of the orbit of the planet. He also restricted as far as possible ​the limits within which the planet should be sought; he predicted that it would have a visible disc, and sufficient light to make it conspicuous in ordinary telescopes. By this time Adams had completed his new investigation on the assumption of a distance 1/30 less than before; the results agreed still better with observation. In a letter to Airy he communicated the new results, answered his question about the errors of the radius-vector, and intimated that he was thinking of presenting a brief account of his investigation at the coming meeting of the British Association. Airy at this time was again absent on the Continent; the British Association met; Adams came with his paper, but the section of mathematics and physics had adjourned the day before he arrived. Had he been present at the beginning of the meeting he would have heard Sir John Herschel say in his address on resigning the chair to his successor, after referring to the astronomical events of the year, which included a discovery of a new minor planet: "The year has done more. It has given us the probable prospect of the discovery of another 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 that of ocular demonstration."
In this same month of September Leverrier sent his predictions to Dr. Galle of the Berlin Observatory in a letter received September 23, 1846. Dr. Galle was already provided with a map of the part of the heavens prescribed, and that very evening he found a star of the eighth magnitude which did not exist on the map; observation on the following evening showed that its motion was nearly the same as that of the predicted planet. On October 1st Challis heard of the discovery of the planet at Berlin. He then found that he had actually noted it on August 4 and August 12, the third and fourth nights of his search, so that had the observations been compared as the work proceeded, the planet might have been discovered by him before the middle of August. The discovery of the planet by Dr. Galle, in consequence of Leverrier's prediction, was received with the greatest enthusiasm by astron​omers of all countries, and in France the planet was at once called Leverriers' planet or even "Leverrier." Sir John Herschel was the first to speak for Adams. He wrote a letter to the Athenæum in which he recalled his works at the Southampton meeting, and explained that the ground of his confidence was the near coincidence of the results of two independent investigations—that by Leverrier, and another by a young Cambridge mathematician named Adams. He invited Adams to place his calculations in full before the public; this Adams did on the 13th of November, 1846, in a memoir read before the Royal Astronomical Society.
At the time of Galle's discovery Airy was on the Continent. On returning to Greenwich he wrote to Leverrier (October 14, 1846), "I was exceedingly struck with the completeness of your investigations. May you enjoy the honors which await you! and may you undertake other work with the same skill and the same success, and receive from all the enjoyment which you merit! I do not know whether you are aware that collateral researches had been going on in England, and that they had led to precisely the same result as yours. I think it probable that I shall be called on to give an account of these. If in this I shall give praise to others, I beg that you will not consider it as at all interfering with my acknowledgment of your claims. You are to be recognized beyond doubt as the real predicter of the planet's place. I may add that the English investigations, as I believe, were not quite so extensive as yours. They were known to me earlier than yours." Leverrier naturally felt much hurt by Herschel's article and Airy's letter. He could not understand why Adams had not published his results. Other French astronomers were at first very unwilling to admit that Adams had any rights whatever in connection with the planet, but later, at the suggestion of the great French astronomer Arago, the name Neptune was adopted and has since been universally used. It was now time for Prof. Challis to publish what he knew of the matter. He gave in the Athenæum for October 17 an account of Adams' investigations, and it was then publicly known for the first time that Adams' con​clusions had been in the hands of Airy and Challis since 1845, and that Challis had actually been engaged in searching for the planet. The British astronomers were divided in opinion; some held that the fact that Adams' results had not been publicly announced deprived him of all claims in relation to the discovery. The Royal Society of London rather hastily (1846) awarded it highest honor, the Copley medal, to Leverrieral one; and in the Royal Astronomical Society a majority of the Council were in favor of awarding their gold medal to him; but a sufficient minority of the Council protested. Two years later the Royal Society made some amends by awarding the Copley medal to Adams.
In 1847 the Queen with Prince Albert visited the University of Cambridge; on this occasion the honor of knighthood was offered to Adams, then 28 years old, but he felt obliged to decline for the same reason as Airy had done before. The members of St. John's College, in honor of the brilliant achievement of one of their number founded the Adams prize, to be awarded biennially for the best essay on some prescribed subject in pure or applied mathematics; its value is about £225. In this year also, Prof. Benjamin Pierce of Harvard College published a paper in which he criticized the methods of Adams and Leverrier, contending that the period of Neptune differed so considerably from that of the hypothetical planet that the finding of the planet was partly due to a happy accident. Adams, on the occasion of the republication of his memoir in Lionville's Journal in 1877, replied that the objection did not hold on account of the perturbations considered lying within a fraction of the synodic periods of Neptune and Uranus. In this year Leverrier attended the meeting of the British Association at Oxford, in the company of Airy. The two discoverers of Neptune met then, and ever after manifested a high appreciation for each other. In 1876 when Adams was president of the Royal Astronomical Society he made an address on presenting a second gold medal to Leverrier for his theories of the four great planets, Jupiter, Saturn, Uranus, and Neptune.
Adams was by nature a calculator, not an observer or experi​menter. Hence it is not surprising to find that his next research work was the determination of the constants in Gauss' theory of terrestrial magnetism—a subject to which he devoted much time in his later years, and which he left unfinished. In 1851 Adams was elected president of the Royal Astronomical Society. In 1852 his fellowship at St. John's College expired, because he had not taken clerical orders; he was however elected to a fellowship at Pembroke College, which he retained till his death. In 1853 Adams communicated to the Royal Society his celebrated memoir on the secular acceleration of the Moon's mean motion. Halley was the first to detect this acceleration by comparing the Babylonian observations of eclipses with those of Albatagnius and of modern times, and Newton referred to his discovery in the second edition of the Principia. The first numerical determination of the value of the acceleration is due to Dunthorne, who found it to be about 10″ in a century. Laplace was the first to deduce the acceleration theoretically from Newtonian principles; the result is given by an infinite series of which he calculates only the first term. Plana, an Italian mathematician, found the next term to be $-{\frac {2187}{128}}m^{4}$; Adams by his investigation found it to be $-{\frac {3771}{64}}m^{4}$, which reduced the value of the first term from 10″ to 6″. This paper gave rise to a violent controversy; those opposed holding that the result was contradictory to observation. But Adams was safe; his result depended entirely on algebraical considerations—on the solution of a differential equation, not on observation; consequently his result finally prevailed.
In 1858 Adams' life at Cambridge was interrupted; he was appointed professor of mathematics in the University of St. Andrews, Scotland. At the end of a year he returned to Cambridge as Lowndean professor of astronomy and geometry. As Lowndean professor he lectured during one term in each year, generally on the lunar theory, but sometimes on the theory of Jupiter's satellites, or the figure of the Earth. Two ​years later he succeeded Challis as the Director of the Cambridge Observatory and settled down as a married man. Henceforth the center of his scientific activity was the Observatory house, where Airy and Challis had lived, situated on an eminence about a mile west of Cambridge on the Huntington road. The observatory was well equipped, thanks to Airy's efficient incumbency; but Adams was by nature a calculator, and the instruments were not much used during his tenure of office.
In 1866 Adams took up the problem of the November meteors, drawn thereto by the remarkable display of that year. Prof. Newton of Yale had published a memoir in the American Journal of Science and Arts in which he collected and discussed the original accounts of thirteen displays of these meteors in years ranging from A.D. 902 to A.D. 1833; he inferred that these displays recur in cycles of 33.25 years, and that during a period of two or three years at the end of each cycle a meteoric shower may be expected. He concluded that the most natural explanation of these phenomena is, that the November meteors belong to a system of small bodies describing an elliptic orbit about the Sun, and extending in the form of a stream along an arc of that orbit which is of such a length that the whole stream occupies about one-tenth or one-fifteenth of the periodic time in passing any particular point. He showed that in one year the group must have a periodic time of either 180.0 days, 185.4 days, 354.6 days, 376.6 days or 33.25 years. Prof. Newton found that the node of the orbit of the meteors is gradually increasing; that the rate is 52″.4 with respect to the fixed stars; and he remarked that with this datum and the position of the radiant point, computation might be able to determine which of the five periods is the correct one. He considered 354.6 days the most probable. Adams then took up the problem. He found that none of the first four periods satisfied the data, while the fifth one of 33.25 years did. He concluded that he had settled the question of the periodic time of the November meteors beyond a doubt. The elements of their orbit obtained by Adams agreed very approximately with those of a comet ​observed in 1866, and it seemed probable that the meteors and the comet constituted one moving aggregation. In 1899, thirty-three years later, an exceptional display of meteors was predicted on the strength of Adams' result; there was much popular lecturing on the subject beforehand; the citizens of London on the predicted night went to bed having previously arranged with the policeman on the beat to call them up, but their slumbers were not disturbed.
Eleven years later (1877) Adams recognized the merits of an American astronomer George W. Hill, who was then an assistant in the office of the American Nautical Almanac, and whose eminence as an astronomer is now universally recognized in the world of science. Hill in 1877 published a paper on the motion of the moon's node in the case when the orbits of the Sun and Moon are supposed to have no eccentricities, and when their mutual inclination is supposed to be definitely small. He made the solution of the differential equations depend on the solution of a single linear differential equation of the second order which is of a very simple form. This equation is equivalent to an infinite number of algebraical linear equations, and Hill showed how to develop the infinite determinant corresponding to these equations in a series of powers and products of the small quantities forming their coefficients. Adams in his unpublished investigations had discovered the same infinite determinant, and was thus in a position to immediately recognize the value of Hill's work. This same year (1877) Adams communicated to the British Association at Plymouth the results of a calculation of Bernoulli's numbers. Bernoulli's numbers are the coefficients of $x^{n}/n!$ in the expansion of $x/(1-e^{-x})$. Now ${\frac {x}{(1-e^{-x})}}=1+{\frac {1}{2}}x+B_{1}{\frac {x^{2}}{2!}}-B_{2}{\frac {x^{4}}{4!}}+B_{3}{\frac {x^{6}}{6!}}-\ldots$ in which $B_{1}={\frac {1}{6}},B_{2}={\frac {1}{30}},\ldots B_{9}={\frac {43867}{798}}$. . . . The first fifteen $B's$ were calculated by Euler, the next 16 by Rothe; and in this communication Adams supplied the following 31 numbers. The difficulty of this calculation may be judged from the facts. that the denominator of $B_{3}2$ is 510 and the numerator is a ​number of 42 figures. By means of these numbers and calculations which Adams made of the logs. of 2, 3, 5 and 7 to 263 places, he made a calculation of Euler's constant 0.577215 to 263 places. He also made a calculation of the modulus of the common logarithms to the same number of places. Mr. Shanks had previously calculated the above logarithms and the modulus of the common logarithms to 205 places, and Euler's constant to 110 places of decimals.
In 1881 on Airy's retirement from the Royal Observatory, the appointment was offered to Adams, but he declined it. He was not a business man, and probably already felt the effects of age. In 1884 he visited America, coming as a delegate to the International Prime Meridian Conference held at Washington. He also took part in the British Association meeting at Montreal, and the American Association meeting in Philadelphia. In 1889 he was afflicted by a severe illness, and after two further attacks he died on the 21st of January, 1892, in the 73d year of his age. He was buried in the Cambridge cemetery, which is not far from the Observatory. A medallion of Adams has been placed in Westminster Abbey close to the grave of Newton.
A Cambridge physician who knew him well thus sketches his character: "His earnest devotion to duty, his simplicity, his perfect self-lessness, were to all who knew his life at Cambridge a perpetual lesson, more eloquent than speech. From the time of his first great discovery scientific honors were showered upon him, but they left him as they found him— modest, gentle, and sincere. Controversies raged for a time around his name, national and scientific rivalries were stirred up concerning his work and its reception, but he took no part in them, and would generously have yielded to other's claims more than his greatest contemporaries would allow to be just. With a single mind for pure knowledge he pursued his studies, here bringing a whole chaos into cosmic order, there vindicating the supremacy of a natural law beyond the imagined limits of its operation; now tracing and abolishing errors that had crept into the calculations of the acknowledged masters of his craft, ​and now giving time and strength to resolving the self made difficulties of a mere beginner, and all the while with so little thought of winning recognition or applause that much of his most perfect work remained for long, or still remains, unpublished."
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