Ma.s.s (that of the sun being unity) 0.0001656.
For the modern observations I have used the method of normal places, taking the mean of the tabular errors, as given by observations near three consecutive oppositions, to correspond with the mean of the times; and the Greenwich observations have been used down to 1830: since which, the Cambridge and Greenwich observations, and those given in the _Astronomische Nachrichten_, have been made use of. The following are the remaining errors of mean longitude:--
1780 +0.27 1783 -0.23 1786 -0.96 1789 +1.82 1792 -0.91 1795 +0.09 1798 -0.99 1801 -0.04 1804 +1.76 1807 -0.21 1810 +0.56 1813 -0.94 1816 -0.31 1819 -2.00 1822 +0.30 1825 +1.92 1828 +2.25 1831 -1.06 1834 -1.44 1837 -1.62 1840 +1.73
The error for 1780 is concluded from that for 1781 given by observation, compared with those of four or five following years, and also with Lemonnier's observations in 1769 and 1771.
"'For the ancient observations, the following are the remaining errors:--
1690 +44.4 1712 + 6.7 1715 - 6.8 1750 - 1.6 1753 + 5.7 1756 - 4.0 1763 - 5.1 1769 + 0.6 1771 +11.8
The errors are small, except for Flamsteed's observation of 1690.
This being an isolated observation, very distant from the rest, I thought it best not to use it in forming the equations of condition.
It is not improbable, however, that this error might be destroyed by a small change in the a.s.sumed mean motion of the planet.'
"I acknowledged the receipt of this paper in the following terms:--
NO. 12.--G. B. AIRY _to_ J. C. ADAMS, Esq.
"'ROYAL OBSERVATORY, GREENWICH, _1845, Nov. 5_.
[Sidenote: Airy's inquiry about the "radius vector."]
"'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 _Ura.n.u.s_ produced by a planet with certain a.s.sumed elements. The latter numbers are all extremely satisfactory: I am not enough acquainted with Flamsteed's observations about 1690 to say whether they bear such an error, but I think it extremely probable.
"'But I should be very glad to know whether this a.s.sumed perturbation will explain the error of the radius vector of _Ura.n.u.s_. This error is now very considerable, as you will be able to ascertain by comparing the normal equations, given in the Greenwich observations for each year, for the times _before_ opposition with the times _after_ opposition.'
"I have before stated that I considered the establishment of this error of the radius vector of _Ura.n.u.s_ to be a very important determination. I therefore considered that the trial, whether the error of radius vector would be explained by the same theory which explained the error of longitude, would be truly an _experimentum crucis_. And I waited with much anxiety for Mr. Adams' answer to my query. Had it been in the affirmative, I should at once have exerted all the influence which I might possess, either directly, or indirectly through my friend Professor Challis, to procure the publication of Mr. Adams' theory.
"From some cause with which I am unacquainted, probably an accidental one, I received no immediate answer to this inquiry. I regret this deeply, for many reasons."
[Sidenote: Adams' silence.]
Here we may leave Airy's "account" for a few moments to consider the reason why he received no answer. Adams was a very shy and retiring young man, and very sensitive; though capable of a great resolution, and of enormous perseverance in carrying it out. We know (what is not indicated in the above account), how steadily he had kept in view the idea of solving this great problem. It was characteristic of him that as early as 1841 he had formed a resolution to undertake it, although at the time he was not able to enter upon its accomplishment. The following memorandum, which is still in existence, having been found among his papers after his death, records these facts:
"1841, July 3. 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 Ura.n.u.s, which were as 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...o...b..t, &c., approximately, which would probably lead to its discovery."
Accordingly, "as soon as possible after taking his degree" he embarked upon the enterprise, and the first solution was made in the long vacation of 1843, a.s.suming the orbit of the unknown planet to be a circle with a radius equal to twice the mean distance of Ura.n.u.s from the sun (an a.s.sumption which, as we have seen, was also made by Le Verrier). Having satisfied himself that there was a good general agreement between his results and the observations, Adams began a more complete solution; indeed from first to last he made no less than six separate solutions, the one which he announced to Airy in the above letter being the fourth. Hence he had already done an enormous amount of work on the problem, and was in his own mind so justly convinced of the correctness and value of his results that he was liable to forget that others had not had the same opportunity of judging of their completeness; and he was grievously disappointed when his announcement was not received with full confidence.
[Sidenote: His disappointment at Greenwich, and at Airy's question.]
But perhaps it should first be stated that by a series of mischances Adams had been already much disappointed at the failure of his attempts to see the Astronomer Royal on his visits to Greenwich. This does not seem to have been exactly Airy's fault; he was, as may well be supposed, an extremely busy man, and was much occupied at the time on a question of great practical importance, at the direct request of the Government, namely, the settling of the proper gauge for railways throughout the country. The first time Adams called to see him, he was actually in London sitting on the Committee which dealt with this question, and Adams was asked to call later; when the visit was repeated, Airy was unfortunately at dinner (and it may be added that his hours for dinner were somewhat peculiar), and the butler, acting somewhat in the manner of his kind, protected his master's dinner by sending away one whom he doubtless regarded as a troublesome visitor. There is, as I have said, little doubt about any of the facts, and it seems well established that Airy himself did not learn of Adams' visits until afterwards, and it would scarcely be just to blame him for a servant's oversight. But Adams had left the paper above reproduced, and Airy with his business-like habits ultimately proceeded to deal with it; he wrote the answer given above asking Adams a definite question, filed a copy of it with the original letter, and then dismissed the matter from his thoughts until the reply from Adams, which he confidently expected should again bring it under notice.
This further disappointment was, however, too much for Adams; he regarded the question put by Airy as having so obvious an answer that it was intended as an evasion, though this was far from being the case. Airy was thoroughly in earnest about his question, though it must be admitted that a more careful study of the problem would have shown him that it was unnecessary. Later, when he learnt of Le Verrier's researches, he put the same question to him, and received a polite but very clear answer, showing that the suggested test was not an _experimentum crucis_ as he supposed.
But Adams did not feel equal to making this reply; he shrank into his sh.e.l.l and solaced himself only by commencing afresh another solution of the problem which had so engrossed his life at that time.
[Sidenote: The merits of Airy's question.]
[Sidenote: The range of possibilities.]
I have heard severe or contemptuous things said about this question by those who most blame Airy. Some of them have no hesitation in accusing him of intellectual incompetence: they say that it was the question of a stupid man. I think that in the first place they forget the difference between a deliberate error of judgement and a mere consequence of insufficient attention. But there is even more than this to be said in defence of the question. The "error of radius vector" came before Airy in an entirely independent way, and as an entirely independent phenomenon, from the "error of longitude," and there was nothing unnatural in regarding it as requiring independent explanation. It is true that, _as the event proved_, a mere readjustment of the orbit of Ura.n.u.s got rid of this error of radius vector (this was substantially Le Verrier's answer to Airy's question); but we must not judge of what was possible before the event in the light of what we now know. The original possibilities were far wider, though we have forgotten their former extent now that they have been narrowed down by the discovery. If a sentry during war time hears a noise in a certain direction, he may be compelled to make the a.s.sumption that it is the movement of an enemy; and if he fires in that direction and kills him, and thus saves his own army from destruction, he is deservedly applauded for the success which attends his action. But it does not follow that the a.s.sumption on which he acted was the only possible one.
Or, to take a more peaceful ill.u.s.tration, in playing whist it sometimes becomes apparent that the game can only be won if the cards lie in a certain way; and a good player will thereupon a.s.sume that this is the fact, and play accordingly. Adams and Le Verrier played to win the game on the particular a.s.sumption that the disturbance of Ura.n.u.s was due to an external planet revolving at a distance from the sun about twice that of Ura.n.u.s; _and won it_; and we applaud them for doing so. But it is easy to imagine a rearrangement of the cards with which they would have lost it; and Airy's question simply meant that he was alive to these wider possibilities, and did not see the need for attempting to win the game in that particular way.
One such alternative possibility has already been mentioned. "Hansen's opinion was, that one disturbing body would not satisfy the phenomena; but he conjectured that there were two planets beyond _Ura.n.u.s_." Another conceivable alternative is that there was some change in the law of gravitation at the distance of Ura.n.u.s, which, it must be remembered, is twice as great as that of any planet previously known. Or some wandering body might have pa.s.sed close enough to Ura.n.u.s to change its...o...b..t somewhat suddenly. We now know, for instance, that the swarm of meteorites which gives rise to the well-known "November meteors" must have pa.s.sed very close to Ura.n.u.s in A.D. 126, a.s.suming that neither the planet nor the swarm have been disturbed in any unknown manner in the meantime. It is to this encounter that we owe the introduction of this swarm to our solar system: wandering through s.p.a.ce, they met Ura.n.u.s, and were swept by his attraction into an orbit round the sun. Was there no reaction upon Ura.n.u.s himself? The probabilities are that the total ma.s.s of the swarm was so small as to affect the huge planet inappreciably; but who was to say that some other swarm of larger ma.s.s, or other body, might not have approached near Ura.n.u.s at some date between 1690 and 1845, and been responsible at any rate in part for the observed errors? These are two or three suppositions from our familiar experience; and there are, of course, limitless possibilities beyond. Which is the true scientific att.i.tude, to be alive to them all, or to concentrate attention upon one?
But we are perhaps wandering too far from the main theme. It is easy to do so in reviewing this extraordinary piece of history, for at almost every point new possibilities are suggested.
III--U. J. LE VERRIER.
(_From a print in the possession of the Royal Astronomical Society._)]
IV--J. G. GALLE.
WHO FIRST SAW THE PLANET NEPTUNE]
[Sidenote: Airy receives Le Verrier's memoir.]
We must return, however, to Airy's "account." We reached the point where he had written to Adams (on November 5, 1845), asking his question about the radius vector, and received no reply; and there the matter remained, so far as he was concerned, until the following June, when Le Verrier's memoir reached him; and we will let him give his own version of the result.
"This memoir reached me about the 23rd or 24th of June. I cannot sufficiently express the feeling of delight and satisfaction which I received from it. The place which it a.s.signed to the disturbing planet was the same, to one degree, as that given by Mr. Adams'
calculations, which I had perused seven months earlier. To this time I had considered that there was still room for doubt of the accuracy of Mr. Adams' investigations; for I think that the results of algebraic and numerical computations, so long and so complicated as those of an inverse problem of perturbations, are liable to many risks of error in the details of the process: I know that there are important numerical errors in the _Mecanique Celeste_ of Laplace; in the _Theorie de la Lune_ of Plana; above all, in Bouvard's first tables of _Jupiter_ and _Saturn_; and to express it in a word, I have always considered the correctness of a distant mathematical result to be a subject rather of moral than of mathematical evidence. But now I felt no doubt of the accuracy of both calculations, as applied to the perturbation in longitude. I was, however, still desirous, as before, of learning whether the perturbation in radius vector was fully explained. I therefore addressed to M. Le Verrier the following letter:--
No. 13.--G. B. AIRY _to_ M. LE VERRIER.
"'Royal Observatory, Greenwich, _1846, June 26_.
[Sidenote: He puts the "radius-vector" question to Le Verrier, but makes no mention of Adams.]
"'I have read, with very great interest, the account of your investigations on the probable place of a planet disturbing the motions of _Ura.n.u.s_, which is contained in the _Compte Rendu de l'Academie_ of June 1; and I now beg leave to trouble you with the following question. It appears, from all the later observations of _Ura.n.u.s_ made at Greenwich (which are most completely reduced in the _Greenwich Observations_ of each year, so as to exhibit the effect of an error either in the tabular heliocentric longitude, or the tabular radius vector), that the tabular radius vector is considerably too small. And I wish to inquire of you whether this would be a consequence of the disturbance produced by an exterior planet, now in the position which you have indicated?'"
There is more of the letter, but this will suffice to show that he wrote to Le Verrier in the same way as to Adams, and, as already stated, received a reply dated three or four days later. But the rest of the letter contains no mention of Adams, and thus arises a second difficulty in understanding Airy's conduct. It seems extraordinary that when he wrote to Le Verrier he made no mention of the computations which he had previously received from Adams; or that he should not have written to Adams, and made some attempt to understand his long silence, now that, as he himself states, he "felt no doubt of the accuracy of both calculations." The omission may have been, and probably was, mere carelessness or forgetfulness; but he could hardly be surprised if others mistook it for deliberate action.
[Sidenote: Airy announces the likelihood of a new planet, and suggests a search for it at Cambridge not having suitable telescope at Greenwich]
However, attention had now been thoroughly attracted to the near possibility of finding the planet. On June 29, 1846, there was a special meeting of the Board of Visitors of Greenwich Observatory, and Airy incidentally mentioned to them this possibility. The impression produced must have been definite and deep; for Sir John Herschel, who was present, was bold enough to say on September 10th following to the British a.s.sociation a.s.sembled at Southampton: "We see it (the probable new planet) as Columbus saw America from the sh.o.r.es of Spain. Its movements have been felt trembling along the far-reaching line of our a.n.a.lysis with a certainty hardly inferior to that of ocular demonstration." Airy discussed the matter with Professor Challis (who, it will be remembered, had originally written to him on behalf of Adams), suggesting that he should immediately commence a search for the supposed planet at Cambridge. It may be asked why Airy did not commence this search himself at Greenwich, and the answer is that he had no telescope which he regarded as large enough for the purpose. The Royal Observatory at Greenwich has always been, and is now, better equipped in some respects than any other observatory, as might be expected from its deservedly great reputation; but to possess the largest existing telescope has never been one of its ambitions. The instruments in which it takes most pride are remarkable for their steadiness and accuracy rather than for their size; and at that time the best telescope possessed by the observatory was not, in Airy's opinion, large enough to detect the planet with certainty. In this opinion we now know that he was mistaken; but, again, we must not judge his conduct before the event in the light of what we have since discovered. It may be recalled here that it was not until Le Verrier's third paper, published on August 31, that he (Le Verrier) emphatically pointed out that the new planet might be of such a size as to have a sensible disc; and it was this remark which led immediately to its discovery. Until this was so decisively stated, it must have seemed exceptionally improbable; for we saw in the last chapter how diligently the Zodiac had been swept in the search for minor planets,--how, for instance, Hencke had searched for fifteen years without success; and it might fairly be considered that if there were a fairly bright object (such as Neptune has since been found to be) it would have been discovered earlier. Hence Airy not unreasonably considered it necessary to spread his net for very small objects. On July 9 he wrote to Professor Challis as follows:--
No. 15.--G. B. AIRY _to_ PROFESSOR CHALLIS.
"THE DEANERY, ELY, _1846, July 9_.
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