Astronomical Discovery Part 5

"You know that I attach importance to the examination of that part of the heavens in which there is ... reason for suspecting the existence of a planet exterior to _Ura.n.u.s_. I have thought about the way of making such examination, but I am convinced that (for various reasons, of declination, lat.i.tude of place, feebleness of light, and regularity of superintendence) there is no prospect whatever of its being made with any chance of success, except with the Northumberland telescope.

"Now, I should be glad to ask you, in the first place, whether you could make such an examination?

"Presuming that your answer would be in the negative, I would ask, secondly, whether, supposing that an a.s.sistant were supplied to you for this purpose, you would superintend the examination?

"You will readily perceive that all this is in a most unformed state at present, and that I am asking these questions almost at a venture, in the hope of rescuing the matter from a state which is, without the a.s.sistance that you and your instruments can give, almost desperate.

Therefore I should be glad to have your answer, not only responding simply to my questions, but also entering into any other considerations which you think likely to bear on the matter.

"The time for the said examination is approaching near."

[Sidenote: Challis undertakes the search.]

[Sidenote: He finds too late that he had observed the planet.]

Professor Challis did not require an a.s.sistant, but determined to undertake the work himself, and devised his own plan of procedure; but he also set out on the undertaking with the expectation of a long and arduous search. No such idea as that of finding the planet on the first night ever entered his head. For one thing, he had no map of the region to be examined, for although the map used by Galle had been published, no copy of it had as yet reached Cambridge, and Professor Challis had practically to construct a map for himself. In these days of photography to make such a map is a simple matter, but at that time the process was terribly laborious. "I get over the ground very slowly," he wrote on September 2nd to Airy, "thinking it right to include all stars to 10-11 magnitude; and I find that to scrutinise thoroughly in this way the proposed portion of the heavens will require many more observations than I can take this year."

With such a prospect, it is not surprising that one night's observations were not even compared with the next; there would be a certain economy in waiting until a large amount of material had been acc.u.mulated, and then making the comparisons all together, and this was the course adopted. But when Le Verrier's third paper, with the decided opinion that the planet would be bright enough to be seen by its disc, ultimately reached Professor Challis, it naturally gave him an entirely different view of the possibilities; he immediately began to compare the observations already made, and found that he had observed the planet early in August. But it was now too late to be first in the field, for Galle had already made his announcement of discovery. Writing to Airy on October 12, Challis could only lament that after four days' observing the planet was in his grasp, _if_ only he had examined or mapped the observations, and _if_ he had not delayed doing so until he had more observations to reduce, and _if_ he had not been very busy with some comet observations. Oh! these terrible _ifs_ which come so often between a man and success! The third of them is a peculiarly distressing one, for it represents that eternal conflict between one duty and another, which is so constantly recurring in scientific work. Shall we finish one piece of work now well under way, or shall we attend to something more novel and more attractive? Challis thought his duty lay in steadily completing the comet observations already begun. We saw in the last lecture how the steady pursuit of the discovery of minor planets, a duty which had become tedious and apparently led nowhere, suddenly resulted in the important discovery of Eros. But Challis was not so fortunate in electing to plod along the beaten track; he would have done _better_ to leave it. There is no golden rule for the answer; we must be guided in each case by the special circ.u.mstances, and the dilemma is consequently a new one on every occasion, and perhaps the more trying with each repet.i.tion.

[Sidenote: Sensation caused by the discovery.]

[Sidenote: Not all _national_ jealousy.]

Such are briefly the events which led to the discovery of Neptune, which was made in Germany by direction from France, when it might have been made in Cambridge alone. The incidents created a great stir at the time. The "Account" of them, as read by Airy to the Royal Astronomical Society on November 13, 1846, straightforward and interesting though it was, making clear where he had himself been at fault, nevertheless stirred up angry pa.s.sions in many quarters, and chiefly directed against Airy himself.

Cambridge was furious at Airy's negligence, which it considered responsible for costing the University a great discovery; and others were equally irate at his attempting to claim for Adams some of that glory which they considered should go wholly to Le Verrier. But it may be remarked that feeling was not purely national. Some foreigners were cordial in their recognition of the work of Adams, while some of those most eager to oppose his claims were found in this country. In their anxiety to show that they were free from national jealousy, scientific men went almost too far in the opposite direction.

[Sidenote: The position of Cambridge in the matter.]

[Sidenote: Challis the weakest point.]

Airy's conduct was certainly strange at several points, as has already been remarked. One cannot understand his writing to Le Verrier in June 1846 without any mention of Adams. He could not even momentarily have forgotten Adams' work; for he tells us himself how he noticed the close correspondence of his result with that of Le Verrier: and had he even casually mentioned this fact in writing to the latter, it would have prepared the way for his later statement. But we can easily understand the unfavourable impression produced by this statement after the discovery had been made, when there had been no previous hint on the subject at all. Of those who abused him Cambridge had the least excuse; for there is no doubt that with a reasonably competent Professor of Astronomy in Cambridge, she need not have referred to Airy at all. It would not seem to require any great amount of intelligence to undertake to look in a certain region for a strange object if one is in possession of a proper instrument. We have seen that Challis had the instrument, and when urged to do so was equal to the task of finding the planet; but he was a man of no initiative, and the idea of doing so unless directed by some authority never entered his head.

He had been accustomed for many years to lean rather helplessly upon Airy, who had preceded him in office at Cambridge. For instance, when appointed to succeed him, and confronted with the necessity of lecturing to students, he was so helpless that he wrote to implore Airy to come back to Cambridge and lecture for him; and this was actually done, Airy obtaining leave from the Government to leave his duties at Greenwich for a time in order to return to Cambridge, and show Challis how to lecture. Now it seems to me that this helplessness was the very root of all the mischief of which Cambridge so bitterly complained. I claimed at the outset the privilege of stating my own views, with which others may not agree: and of all the mistakes and omissions made in this little piece of history, the most unpardonable and the one which had most serious consequences seems to me to be this: that Challis never made the most casual inquiry as to the result of the visit to Greenwich which he himself had directed Adams to make. I am judging him to some extent by default; because I a.s.sume the facts from lack of evidence to the contrary: but it seems practically certain that after sending this young man to see Airy on this important topic, Challis thereupon washed his hands of all responsibility so completely that he never even took the trouble to inquire on his return, "Well! how did you get on? What did the Astronomer Royal say?" Had he put this simple question, which scarcely required the initiative of a machine, and learnt in consequence, as he must have done, that the sensitive young man thought Airy's question trivial, and did not propose to answer it, I think we might have trusted events to right themselves. Even Challis might have been trusted to reply, "Oh! but you must answer the Astronomer Royal's question: you may think it stupid, but you had better answer it politely, and show him that you know what you are about." It is unprofitable to pursue speculation further; this did _not_ happen, and something else did. But I have always felt that my old University made a scapegoat of the wrong man in venting its fury upon Airy, when the real culprit was among themselves, and was the man they had themselves chosen to represent astronomy. He was presumably the best they had; but if they had no one better than this, they should not have been surprised, and must not complain, if things went wrong. If a University is ambitious of doing great things, it must take care to see that there are men of ability and initiative in the right places. This is a most difficult task in any case, and we require all possible incentives towards it. To blink the facts when a weak spot is mercilessly exposed by the loss of a great opportunity is to lose one kind of incentive, and perhaps not the least valuable.

[Sidenote: Curious difference between actual and supposed planet.]

[Sidenote: Professor Peirce's contention that the discovery was a mere accident.]

[Sidenote: The explanation.]

Let us now turn to some curious circ.u.mstances attending this remarkable discovery of a planet by mathematical investigation, of which there are several. The first is, that although Neptune was found so near the place where it was predicted, its...o...b..t, after discovery, proved to be very different from that which Adams and Le Verrier had supposed. You will remember that both calculators a.s.sumed the distance from the sun, in accordance with Bode's Law, to be nearly twice that of Ura.n.u.s. The actual planet was found to have a mean distance less than this by 25 per cent., an enormous quant.i.ty in such a case. For instance, if the supposed planet and the real were started round the sun together, the real planet would soon be a long way ahead of the other, and the ultimate disturbing effect of the two on Ura.n.u.s would be very different. To explain the difference, we must first recall a curious property of such disturbances. When two planets are revolving, so that one takes just twice or three times, or any exact number of times, as long to revolve round the sun as the other, the usual mathematical expressions for the disturbing action of one planet on the other would a.s.sign an _infinite_ disturbance, which, translated into ordinary language, means that we must start with a fresh a.s.sumption, for this state of things cannot persist. If the period of one were a little _longer_ than this critical value, some of the mathematical expressions would be of contrary sign from those corresponding to a period a little _shorter_. Now it is curious that the supposed planet and the real had orbits on opposite sides of a critical value of this kind, namely, that which would a.s.sign a period of revolution for Neptune exactly half that of Ura.n.u.s; and it was pointed out in America by Professor Peirce that the effect of the planet imagined by Adams and Le Verrier was thus totally different from that of Neptune. He therefore declared that the mathematical work had not really led to the discovery at all; but that it had resulted from mere coincidence, and this opinion--somewhat paradoxical though it was--found considerable support. It was not replied to by Adams until some thirty years later, when a short reply was printed in _Liouville's Journal_. The explanation is this: the expressions considered by Professor Peirce are those representing the action of the planet throughout an indefinite past, and did not enter into the problem, which would have been precisely the same if Neptune had been suddenly created in 1690; while, on the other hand, if Neptune had existed up till 1690 (the time when Ura.n.u.s was first observed, although unknowingly), and then had been destroyed, there would have been no means of tracing its previous existence. In past ages it had no doubt been perturbing the orbit of Ura.n.u.s, and had effected large changes in it; but if it had then been suddenly destroyed, we should have had no means of identifying these changes. There might have been instead of Neptune another planet, such as that supposed by Adams and Le Verrier; and its action in all past time would have been very different from that of Neptune, as is properly represented in the mathematical expressions which Professor Peirce considered. In consequence the orbit of Ura.n.u.s in 1690 would have been very different from the orbit as it was actually found; but in either case the mathematicians Adams and Le Verrier would have had to take it as they found it; and the disturbing action which they considered in their calculations was the comparatively small disturbance which began in 1690 and ended in 1846. During this limited number of years the disturbance of the planet they imagined, although not precisely the same as that of Neptune, was sufficiently like it to give them the approximate place of the planet.

Still it is somewhat bewildering to look at the mathematical expressions for the disturbances as used by Adams and Le Verrier, when we can now compare with them the actual expressions to which they ought to correspond; and one may say frankly that there seems to be no sort of resemblance. Recently a memorial of Adams' work has been published by the Royal Astronomical Society; they have reproduced in their Memoirs a facsimile of Adams' MS. containing the "first solution," which he made in 1843 in the Long Vacation after he had taken his degree, and which would have given the place of Neptune at that time with an error of 15. In an introduction describing the whole of the MSS., written by Professor R. A.

Sampson of Durham, it is shown how different the actual expressions for Neptune's influence are from those used by Adams, and it is one of the curiosities of this remarkable piece of history that some of them seem to be actually _in the wrong direction_; and others are so little alike that it is only by fixing our attention resolutely on the considerations above mentioned that we can realise that the a.n.a.lytical work did indeed lead to the discovery of the planet.

[Sidenote: Suggested elementary method for finding Neptune illusory.]

A second curiosity is that a mistaken idea should have been held by at least one eminent man (Sir J. Herschel), to the effect that it would have been possible to find the place of the planet by a much simpler mathematical calculation than that actually employed by Adams or Le Verrier. In his famous "Outlines of Astronomy" Sir John Herschel describes a simple graphical method, which he declares would have indicated the place of the planet without much trouble. Concerning it I will here merely quote Professor Sampson's words:--

"The conclusion is drawn that _Ura.n.u.s_ arrived at a conjunction with the disturbing planet about 1822; and this was the case. Plausible as this argument may seem, it is entirely baseless. For the maximum of perturbations depending on the eccentricities has no relation to conjunction, and the others which depend upon the differences of the mean motions alone are of the nature of forced oscillations, and conjunction is not their maximum or stationary position, but their position of most rapid change."

Professor Sampson goes on to show that a more elaborate discussion seems quite as unpromising; and he concludes that the refinements employed were not superfluous, although it seems _now_ clear that a different mode of procedure might have led more certainly to the required conclusion.

[Sidenote: The evil influence of Bode's Law.]

For the third curious point is that both calculators should have adhered so closely to Bode's Law. If they had not had this guiding principle it seems almost certain that they would have made a better approximation to the place of the planet, for instead of helping them it really led them astray. We have already remarked that if two planets are at different distances from the sun, however slight, and if they are started in their revolution together, they must inevitably separate in course of time, and the amount of separation will ultimately become serious. Thus by a.s.suming a distance for the planet which was in error, however slight, the calculators immediately rendered it impossible for themselves to obtain a place for the planet which should be correct for more than a very brief period. Professor Sampson has given the following interesting lists of the dates at which Adams' six solutions gave the true place of the planet and the intervals during which the error was within 5 either way.

I. II. III. IV. V. VI.

Correct 1820 1835 1872 1830 1861 1856

Within 5 {1812 1827 1865 1813 1815 1826 {1827 1842 1877 1866 1871 1868

Now the date at which it was most important to obtain the correct place was 1845 or thereabouts when it was proposed to look for the planet; but no special precaution seems to have been taken by either investigator to secure any advantage for this particular date. Criticising the procedure after the event (and of course this is a very unsatisfactory method of criticism), we should say that it would have been better to make several a.s.sumptions as regards the distance instead of relying upon Bode's Law; but no one, so far as I know, has ever taken the trouble to write out a satisfactory solution of the problem as it might have been conducted. Such a solution would be full of interest, though it could only have a small weight in forming our estimation of the skill with which the problem was solved in the first instance.

[Sidenote: Le Verrier's erroneous limits.]

Fourthly, we may notice a very curious point. Le Verrier went to some trouble not only to point out the most likely place for the planet, but to indicate limits outside which it was not necessary to look. This part of his work is specially commented upon with enthusiasm by Airy, and I will reproduce what he says. It is rather technical perhaps, but those who cannot follow the mathematics will be able to appreciate the tone of admiration.

[Sidenote: The visible disc.]

"M. Le Verrier then enters into a most ingenious computation of the limits between which the planet must be sought. The principle is this: a.s.suming a time of revolution, all the other unknown quant.i.ties may be varied in such a manner that though the observations will not be so well represented as before, yet the errors of observation will be tolerable. At last, on continuing the variation of elements, one error of observation will be intolerably great. Then, by varying the elements in another way, we may at length make another error of observation intolerably great; and so on. If we compute, for all these different varieties of elements, the place of the planet for 1847, its _locus_ will evidently be a discontinuous curve or curvilinear polygon. If we do the same thing with different periodic times, we shall get different polygons; and the extreme periodic times that can be allowed will be indicated by the polygons becoming points. These extreme periodic times are 207 and 233 years.

If now we draw one grand curve, circ.u.mscribing all the polygons, it is certain that the planet must be within that curve. In one direction, M. Le Verrier found no difficulty in a.s.signing a limit; in the other he was obliged to restrict it, by a.s.suming a limit to the eccentricity. Thus he found that the longitude of the planet was certainly not less than 321, and not greater than 335 or 345, according as we limit the eccentricity to 0.125 or 0.2. And if we adopt 0.125 as the limit, then the ma.s.s will be included between the limits 0.00007 and 0.00021; either of which exceeds that of _Ura.n.u.s_.

From this circ.u.mstance, combined with a probable hypothesis as to the density, M. Le Verrier concluded that the planet would have a visible disk, and sufficient light to make it conspicuous in ordinary telescopes.

"M. Le Verrier then remarks, as one of the strong proofs of the correctness of the general theory, that the error of radius vector is explained as accurately as the error of longitude. And finally, he gives his opinion that the lat.i.tude of the disturbing planet must be small.

"My a.n.a.lysis of this paper has necessarily been exceedingly imperfect, as regards the astronomical and mathematical parts of it; but I am sensible that, in regard to another part, it fails totally.

I cannot attempt to convey to you the impression which was made on me by the author's undoubting confidence in the general truth of his theory, by the calmness and clearness with which he limited the field of observation, and by the firmness with which he proclaimed to observing astronomers, 'Look in the place which I have indicated, and you will see the planet well.' Since Copernicus declared that, when means should be discovered for improving the vision, it would be found that _Venus_ had phases like the moon, nothing (in my opinion) so bold, and so justifiably bold, has been uttered in astronomical prediction. 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."

[Sidenote: Peirce's views of the limits.]

But now this process of limitation was faulty and actually misleading. Let us compare what is said about it by Professor Peirce a little later.

"Guided by this principle, well established, and legitimate, if confined within proper limits, M. Le Verrier narrowed with consummate skill the field of research, and arrived at two fundamental propositions, namely:--

"1st. That the mean distance of the planet cannot be less than 35 or more than 37.9. The corresponding limits of the time of sidereal revolution are about 207 and 233 years.

"2nd. 'That there is only one region in which the disturbing planet can be placed in order to account for the motions of Ura.n.u.s; that the mean longitude of this planet must have been, on January 1, 1800, between 243 and 252.'

"'Neither of these propositions is of itself necessarily opposed to the observations which have been made upon Neptune, but the two combined are decidedly inconsistent with observation. It is impossible to find an orbit, which, satisfying the observed distance and motion, is subject to them. If, for instance, a mean longitude and time of revolution are adopted according with the first, the corresponding mean longitude in 1800 must have been at least 40 distant from the limits of the second proposition. And again, if the planet is a.s.sumed to have had in 1800 a mean longitude near the limits of the second proposition, the corresponding time of revolution with which its motions satisfy the present observations cannot exceed 170 years, and must therefore be about 40 years less than the limits of the first proposition.'

"Neptune cannot, then, be the planet of M. Le Verrier's theory, and cannot account for the observed perturbations of Ura.n.u.s under the form of the inequalities involved in his a.n.a.lysis"--(_Proc. Amer.

Acad. I._, 1846-1848, _p._ 66).

[Sidenote: Newcomb's criticism.]

At the time when Professor Peirce wrote, the orbit of Neptune was not sufficiently well determined to decide whether one of the two limitations might not be correct, though he could see that they could not both be right, and we now know that they are _both wrong_. The mean distance of Neptune is 30, which does _not_ lie between 35 and 37.9; and the longitude in 1800 was 225, which does _not_ lie between 243 and 252. The ingenious process which Airy admired and which Peirce himself calls "consummately skilful" was wrong in principle. As Professor Newcomb has said, "the error was the elementary one that, instead of considering all the elements simultaneously variable, Le Verrier took them one at a time, considering the others as fixed, and determining the limits between which each could be contained on this hypothesis. No solver of least square equations at the present day ought to make such a blunder. Of course one trouble in Le Verrier's demonstration, had he attempted a rigorous one, would have been the impossibility of forming the simultaneous equations expressive of possible variations of all the elements."

[Sidenote: Element of good fortune.]