THE DISCOVERY OF NEPTUNE
[Sidenote: Search for definite objects.]
In the last chapter we saw that the circumstances under which planets were
discovered varied considerably. Sometimes the discoveries were not
previously expected, occurring during a general examination of the
heavens, or a search for other objects; and, on one occasion at least, the
discovery may be said to have been even contrary to expectation, though,
as the existence of a number of minor planets began to be realised, there
have also been many cases where the discovery has been made as the result
of a definite and deliberate search. But the search cannot be said to have
been inspired by any very clear or certain principle: for the law of Bode,
successful though it has been in indicating the possible existence of new
planets, cannot, as yet, be said to be founded upon a formulated law of
nature. We now come, however, to a discovery made in direct interpretation
of Newton's great law of gravitation--the discovery of Neptune from its
observed disturbance of Uranus. I will first briefly recall the main facts
relating to the actual discovery.
[Sidenote: Disturbance of Uranus.]
After Uranus had been discovered and observed sufficiently long for its
orbit to be calculated, it was found that the subsequent position of the
planet did not always agree with this orbit; and, more serious than this,
some early observations were found which could not be reconciled with the
later ones at all. It is a wonderful testimony to the care and sagacity of
Sir William Herschel, as was remarked in the last chapter, that Uranus was
found to have been observed, under the mistaken impression that it was an
ordinary star, by Flamsteed, Lemonnier, Bradley, and Mayer, all observers
of considerable ability. Flamsteed's five observations dated as far back
as 1690, 1712, and 1715; observations by others were in 1748, 1750, 1753,
1756, and so on up to 1771, and the body of testimony was so considerable
that there was no room for doubt as to the irreconcilability of the
observations with the orbit, such as might have been the case had there
been only one or two, possibly affected with some errors.
[Sidenote: Suspicion of perturbing planet.]
It is difficult to mention an exact date for the conversion into certainty
of the suspicion that no single orbit could be found to satisfy all the
observations; but we may certainly regard this fact as established in
1821, when Alexis Bouvard published some tables of the planet, and showed
fully in the introduction that when every correction for the disturbing
action of other planets had been applied, it was still impossible to
reconcile the old observations with the orbit calculated from the new
ones. The idea accordingly grew up that there might be some other body or
bodies attracting the planet and causing these discrepancies. Here again
it is not easy to say exactly when this notion arose, but it was certainly
existent in 1834, as the following letter to the Astronomer Royal will
show. I take it from his well-known "Account of some Circumstances
historically connected with the Discovery of the Planet exterior to
Uranus," which he gave to the Royal Astronomical Society at its first
meeting after that famous discovery (Monthly Notices of the R.A.S., vol.
iii., and Memoirs, vol. xvi.).
NO. 1.--_The_ REV. T. J. HUSSEY _to_ G. B. AIRY.
[_Extract._]
"'HAYES, KENT, _17th November 1834_.
"'With M. Alexis Bouvard I had some conversation upon a subject I had
often meditated, which will probably interest you, and your opinion
may determine mine. Having taken great pains last year with some
observations of _Uranus_, I was led to examine closely Bouvard's
tables of that planet. 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. My first idea was to ascertain some
approximate place of this supposed body empirically, and then with
my large reflector set to work to examine all the minute stars
thereabouts: but I found myself totally inadequate to the former part
of the task. If I could have done it formerly, it was beyond me now,
even supposing I had the time, which was not the case. I therefore
relinquished the matter altogether; but subsequently, in conversation
with Bouvard, I inquired if the above might not be the case: his
answer was, that, as might have been expected, it had occurred to
him, and some correspondence had taken place between Hansen and
himself respecting it. Hansen's opinion was, that one disturbing body
would not satisfy the phenomena; but that he conjectured there were
two planets beyond _Uranus_. Upon my speaking of obtaining the places
empirically, and then sweeping closely for the bodies, he fully
acquiesced in the propriety of it, intimating that the previous
calculations would be more laborious than difficult; that if he had
leisure he would undertake them and transmit the results to me, as
the basis of a very close and accurate sweep. I have not heard from
him since on the subject, and have been too ill to write. What is
your opinion on the subject? If you consider the idea as possible,
can you give me the limits, roughly, between which this body or those
bodies may probably be found during the ensuing winter? As we might
expect an eccentricity [inclination?] approaching rather to that of
the old planets than of the new, the breadth of the zone to be
examined will be comparatively inconsiderable. I may be wrong, but I
am disposed to think that, such is the perfection of my equatoreal's
object-glass, I could distinguish, almost at once, the difference of
light of a small planet and a star. My plan of proceeding, however,
would be very different: I should accurately map the whole space
within the required limits, down to the minutest star I could
discern; the interval of a single week would then enable me to
ascertain any change. If the whole of this matter do not appear to
you a chimaera, which, until my conversation with Bouvard, I was
afraid it might, I shall be very glad of any sort of hint respecting
it.'
"My answer was in the following terms:--
[Sidenote: Airy's scepticism.]
NO. 2.--G. B. AIRY _to the_ REV. T. J. HUSSEY.
[_Extract._]
"'OBSERVATORY, CAMBRIDGE, _1834, Nov. 23_.
"'I have often thought of the irregularity of _Uranus_, and since the
receipt of your letter have looked more carefully to it. It is a
puzzling subject, but I give it as my opinion, without hesitation,
that it is not yet in such a state as to give the smallest hope of
making out the nature of any external action on the planet ... if it
were certain that there were any extraneous action, I doubt much the
possibility of determining the place of a planet which produced it. I
am sure it could not be done till the nature of the irregularity was
well determined from several successive revolutions.'"
[Sidenote: Le Verrier's papers.]
[Sidenote: Planet to be detected by disc.]
[Sidenote: Galle's discovery of the planet.]
Although only a sentence or two have been selected from Airy's reply (he
was not yet Astronomer Royal), they are sufficient to show that the
problem of finding the place of such a possible disturbing body was
regarded at that time as one of extreme difficulty; and no one appears
seriously to have contemplated embarking upon its solution. It was not
until many years later that the solution was attempted. Of the first
attempt we shall speak presently, putting it aside for the moment because
it had no actual bearing on the discovery of the planet, for reasons which
form an extraordinary episode of this history. The attempt which led to
success dates from November 1845. The great French astronomer Le Verrier,
on November 10, 1845, read to the French Academy a paper on the Orbit of
Uranus, considering specially the disturbances produced by Jupiter and
Saturn, and showing clearly that with no possible orbit could the
observations be satisfied. On June 1, 1846, followed a second paper by the
same author, in which he considers all the possible explanations of the
discordance, and concludes that none is admissible except that of a
disturbing planet exterior to Uranus. And assuming, in accordance with
Bode's Law, that the distance of this new planet from the sun would be
about double that of Uranus (and it is important to note this
assumption), he proceeds to investigate the orbit of such a planet, and to
calculate the place where it must be looked for in the heavens. This was
followed by a third paper on August 31st, giving a rather completer
discussion, and arriving at the conclusion that the planet should be
recognisable from its disc. This again is an important point. We remember
that in the discovery of Uranus it needed considerable skill on the part
of Sir William Herschel to detect the disc, to see in fact any difference
between it and surrounding stars; and that other observers, even when
their attention had been called to the planet, found it difficult to see
this difference. It might be expected, therefore, that with a planet twice
as far away (as had been assumed for the new planet) the disc would be
practically unrecognisable, and as we shall presently see, this assumption
was made in some searches for the planet which had been commenced even
before the publication of this third paper. Le Verrier's courageous
announcement, which he deduced from a consideration of the mass of the
planet, that the disc should be recognisable, led immediately to the
discovery of the suspected body. He wrote to a German astronomer, Dr.
Galle (still, I am glad to say, alive and well, though now a very old
man), telling him the spot in the heavens to search, and stating that he
might expect to detect the planet by its appearance in this way; and the
same night Dr. Galle, by comparing a star map with the heavens, found the
planet.
[Sidenote: Adams' work publicly announced.]
To two points to which I have specially called attention in this brief
summary--namely, the preliminary assumption that the planet would be,
according to Bode's Law, twice as far away as Uranus; secondly, the
confident assertion that it would have a visible disc--I will ask you to
add, thirdly, that it was found by the aid of a star map, for this map
played an important part in the further history to which we shall now
proceed. It may naturally be supposed that the announcement of the finding
of a planet in this way, the calculation of its place from a belief in the
universal action of the great Law of Gravitation, the direction to an
eminent observer to look in that place for a particular thing, and his
immediate success,--this extraordinary combination of circumstances caused
a profound sensation throughout not only the astronomical, but the whole
world; and this sensation was greatly enhanced by the rumour which had
begun to gather strength that, but for some unfortunate circumstances, the
discovery might have been made even earlier and as a consequence of
totally independent calculations made by a young Cambridge mathematician,
J. C. Adams. Some of you are doubtless already familiar with the story in
its abridged form, for it has been scattered broadcast through literature.
In England it generally takes the form of emphasising the wickedness or
laziness of the Astronomer Royal who, when told where to look for a
planet, neglected his obvious duty, so that in consequence another
astronomer who made the calculation much later and gave a more virtuous
observer the same directions where to look, obtained for France the glory
of a discovery which ought to have been retained in England. There is no
doubt that Airy's conduct received a large amount of what he called
"savage abuse." When the facts are clearly stated I think it will be
evident that many of the harsh things said of him were scarcely just,
though at the same time it is also difficult to understand his conduct at
two or three points of the history, even as explained by himself.
[Sidenote: Facts undoubted.]
There is fortunately no doubt whatever about any of the _facts_. Airy
himself gave a very clear and straightforward account of them at the time,
for which more credit is due to him than he commonly receives; and since
the death of the chief actors in this sensational drama they have been
naturally again ransacked, with the satisfactory result that there is
practically no doubt about any of the facts. As to the proper
interpretations of them there certainly may be wide differences of
opinion, nor does this circumstance detract from their interest. It is
almost impossible to make a perfectly colourless recital of them, nor is
it perhaps necessary to do so. I will therefore ask you to remember in
what I now say that there is almost necessarily an element of personal
bias, and that another writer would probably give a different colouring.
Having said this, I hope I may speak quite freely as the matter appears in
my personal estimation.
[Sidenote: Airy's "Account."]
[Sidenote: "A movement of the age."]
Airy's account was, as above stated, given to the Royal Astronomical
Society at their first meeting (after the startling announcement of the
discovery of the new planet), on November 13, 1846, and I have already
quoted an extract from it. He opens with a tribute to the sensational
character of the discovery, and then states that although clearly due to
two individuals (namely, Le Verrier and Galle), it might also be regarded
as to some extent the consequence of a movement of the age. His actual
words are these: "The principal steps in the theoretical investigations
have been made by one individual, and the published discovery of the
planet was necessarily made by one individual. To these persons the public
attention has been principally directed; and well do they deserve the
honours which they have received, and which they will continue to receive.
Yet we should do wrong if we considered that these two persons alone are
to be regarded as the authors of the discovery of this planet. I am
confident that it will be found that the discovery is a consequence of
what may properly be called a movement of the age; that it has been urged
by the feeling of the scientific world in general, and has been nearly
perfected by the collateral, but independent labours, of various persons
possessing the talents or powers best suited to the different parts of
the researches."
[Sidenote: Airy under-estimated Adams' work.]
I have quoted these words as the first point at which it is difficult to
understand Airy's conduct in excluding from them all specific mention of
Adams, knowing as he did the special claims which entitled him to such
mention; claims indeed which he proceeded immediately to make clear. It
seems almost certain that Airy entirely under-estimated the value of
Adams' work throughout. But this will become clearer as we proceed. The
"account" takes the form of the publication of a series of letters with
occasional comments. Airy was a most methodical person, and filed all his
correspondence with great regularity. It was jestingly said of him once
that if he wiped his pen on a piece of blotting-paper, he would date the
blotting-paper and file it for reference. The letters reproduced in this
"account" are still in the Observatory at Greenwich, pinned together just
as Airy left them; and in preparing his "account" it was necessary to do
little else than to have them copied out and interpolate comments. From
two of them I have already quoted to show how difficult the enterprise of
finding an exterior planet from its action on Uranus was considered in
1834. To these may be added the following sentence from No. 4, dated 1837.
"If it be the effect of any unseen body," writes Airy to Bouvard, "it will
be nearly impossible ever to find out its place." But the first letter
which need concern us is No. 6, and it is only necessary to explain that
Professor Challis was the Professor of Astronomy at Cambridge, and in
charge of the Cambridge Observatory, in which offices he had succeeded
Airy himself on his leaving Cambridge for Greenwich some eight years
earlier.
No. 6.--PROFESSOR CHALLIS _to_ G. B. AIRY.
[_Extract._]
"'CAMBRIDGE OBSERVATORY, _Feb. 13, 1844_.
[Sidenote: Challis mentions Adams to Airy, and suggests Adams' visit
to Greenwich.]
"'A young friend of mine, Mr. Adams of St. John's College, is working
at the theory of _Uranus_, and is desirous of obtaining errors of the
tabular geocentric longitudes of this planet, when near opposition,
in the years 1818-1826, with the factors for reducing them to errors
of heliocentric longitude. Are your reductions of the planetary
observations so far advanced that you could furnish these data? and
is the request one which you have any objection to comply with? If
Mr. Adams may be favoured in this respect, he is further desirous of
knowing, whether in the calculation of the tabular errors any
alterations have been made in Bouvard's _Tables of Uranus_ besides
that of _Jupiter's_ mass.'
"My answer to him was as follows:--
No. 7.--G. B. AIRY _to_ PROFESSOR CHALLIS.
[_Extract._]
"'ROYAL OBSERVATORY, GREENWICH, _1844, Feb. 15_.
"'I send all the results of the observations of _Uranus_ made with
both instruments (that is, the heliocentric errors of _Uranus_ in
longitude and latitude from 1754 to 1830, for all those days on which
there were observations, both of right ascension and of polar
distance). No alteration is made in Bouvard's _Tables of Uranus_
except in increasing the two equations which depend on _Jupiter_ by
1/50 part. As constants have been added (in the printed tables) to
make the equations positive, and as 1/50 part of the numbers in the
tables has been added, 1/50 part of the constants has been subtracted
from the final results.'
"Professor Challis in acknowledging the receipt of these, used the
following expressions:--
No. 8.--PROFESSOR CHALLIS _to_ G. B. AIRY.
[_Extract._]
"'CAMBRIDGE OBSERVATORY, _Feb. 16, 1844_.
"'I am exceedingly obliged by your sending so complete a series of
tabular errors of _Uranus_.... The list you have sent will give Mr.
Adams the means of carrying on in the most effective manner the
inquiry in which he is engaged.'
"The next letter shows that Mr. Adams has derived results from these
errors.
No. 9.--PROFESSOR CHALLIS _to_ G. B. AIRY.
"'CAMBRIDGE OBSERVATORY, _Sept. 22, 1845_.
"'My friend Mr. Adams (who will probably deliver this note to you)
has completed his calculations respecting the perturbation of the
orbit of _Uranus_ by a supposed ulterior planet, and has arrived at
results which he would be glad to communicate to you personally, if
you could spare him a few moments of your valuable time. His
calculations are founded on the observations you were so good as to
furnish him with some time ago; and from his character as a
mathematician, and his practice in calculation, I should consider the
deductions from his premises to be made in a trustworthy manner. If
he should not have the good fortune to see you at Greenwich, he hopes
to be allowed to write to you on this subject.'
"On the day on which this letter was dated, I was present at a
meeting of the French Institute. I acknowledged it by the following
letter:--
NO. 10.--G. B. AIRY _to_ PROFESSOR CHALLIS.
"'ROYAL OBSERVATORY, GREENWICH, _1845, Sept. 29_.
"'I was, I suppose, on my way from France, when Mr. Adams called
here; at all events, I had not reached home, and therefore, to my
regret, I have not seen him. Would you mention to Mr. Adams that I am
very much interested with the subject of his investigations, and that
I should be delighted to hear of them by letter from him?'
"On one of the last days of October 1845, Mr. Adams called at the
Royal Observatory, Greenwich, in my absence and left the following
important paper:--
No. 11.--J. C. ADAMS, Esq., _to_ G. B. AIRY.
[Sidenote: Adams' announcement of the new planet.]
"'According to my calculations, the observed irregularities in the
motion of _Uranus_ may be accounted for by supposing the existence of
an exterior planet, the mass and orbit of which are as follows:--
Mean distance (assumed nearly in accordance
with Bode's Law) 38.4
Mean sidereal motion in 365.25 days 1 deg.30'.9
Mean longitude, 1st October 1845 323 34
Longitude of perihelion 315 55
Eccentricity 0.1610.
Mass (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:--
_Observation--Theory._
"
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:--
_Observation--Theory._
"
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 assumed 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 _Uranus_
produced by a planet with certain assumed 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 assumed perturbation
will explain the error of the radius vector of _Uranus_. 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 _Uranus_ 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 Uranus, 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 orbit, &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, assuming the orbit of the unknown planet to be a circle with a
radius equal to twice the mean distance of Uranus from the sun (an
assumption 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
shell 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 Uranus 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 assumption
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 assumption on which he acted was the only possible one.
Or, to take a more peaceful illustration, 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 assume that this is the
fact, and play accordingly. Adams and Le Verrier played to win the game on
the particular assumption that the disturbance of Uranus was due to an
external planet revolving at a distance from the sun about twice that of
Uranus; _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 _Uranus_." Another
conceivable alternative is that there was some change in the law of
gravitation at the distance of Uranus, which, it must be remembered, is
twice as great as that of any planet previously known. Or some wandering
body might have passed close enough to Uranus to change its orbit somewhat
suddenly. We now know, for instance, that the swarm of meteorites which
gives rise to the well-known "November meteors" must have passed very
close to Uranus in A.D. 126, assuming 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 space, they met Uranus, and were swept by his
attraction into an orbit round the sun. Was there no reaction upon Uranus
himself? The probabilities are that the total mass of the swarm was so
small as to affect the huge planet inappreciably; but who was to say that
some other swarm of larger mass, or other body, might not have approached
near Uranus 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 attitude, 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.
[Illustration:
III--U. J. LE VERRIER.
(_From a print in the possession of the Royal Astronomical Society._)]
[Illustration:
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 assigned 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 _Uranus_, 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
_Uranus_ 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
Association assembled at Southampton: "We see it (the probable new planet)
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." 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_.
"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 _Uranus_. I have thought about the way of
making such examination, but I am convinced that (for various
reasons, of declination, latitude 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 assistant 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
assistance 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 assistant, 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 accumulated, 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 circumstances, and
the dilemma is consequently a new one on every occasion, and perhaps the
more trying with each repetition.
[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
passions 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 assume 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 circumstances 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 orbit, after discovery, proved to be very
different from that which Adams and Le Verrier had supposed. You will
remember that both calculators assumed the distance from the sun, in
accordance with Bode's Law, to be nearly twice that of Uranus. The actual
planet was found to have a mean distance less than this by 25 per cent.,
an enormous quantity 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 Uranus 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 assign an _infinite_ disturbance, which, translated into
ordinary language, means that we must start with a fresh assumption, 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 assign a period of revolution for Neptune exactly half that of
Uranus; 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 Uranus 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
Uranus, 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 Uranus 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 deg.. 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 analytical 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 _Uranus_ 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 assuming
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 deg. either way.
I. II. III. IV. V. VI.
Correct 1820 1835 1872 1830 1861 1856
Within +-5 deg. {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
assumptions 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: assuming a time of revolution, all the other unknown
quantities 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, circumscribing all the polygons, it
is certain that the planet must be within that curve. In one
direction, M. Le Verrier found no difficulty in assigning a limit; in
the other he was obliged to restrict it, by assuming a limit to the
eccentricity. Thus he found that the longitude of the planet was
certainly not less than 321 deg., and not greater than 335 deg. or 345 deg.,
according as we limit the eccentricity to 0.125 or 0.2. And if we
adopt 0.125 as the limit, then the mass will be included between the
limits 0.00007 and 0.00021; either of which exceeds that of _Uranus_.
From this circumstance, 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 latitude of the disturbing planet must be
small.
"My analysis 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 Uranus; that the
mean longitude of this planet must have been, on January 1, 1800,
between 243 deg. and 252 deg..'
"'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 deg.
distant from the limits of the second proposition. And again, if the
planet is assumed 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 Uranus under the
form of the inequalities involved in his analysis"--(_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 deg., which does _not_ lie between 243 deg. and 252 deg.. 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.]
[Sidenote: The map used by Galle.]
The account of Le Verrier's limits by Professor Peirce, though it exhibits
the error with special clearness, is a little unfair to Le Verrier in one
point. If, instead of taking the limits for the date 1800, we take them
for 1846 (when the search for Neptune was actually made), we shall find
that they do include the actual place of the planet, as Airy found. The
erroneous mean motion of Le Verrier's planet allowed of his being right at
one time and wrong at another; and Airy examined the limits under
favourable conditions, which explains his enthusiasm. But we can scarcely
wonder that Professor Peirce came to the conclusion that the planet
discovered was not the one pointed out by Le Verrier, and had been found
by mere accident. And all these circumstances inevitably contribute to a
general impression that the calculators had a large element of good
fortune to thank for their success. Nor need we hesitate to make this
admission, for there is an element of good fortune in all discoveries. To
look no further than this--if a man had not been doing a particular thing
at a particular time, as he might easily not have been, most discoveries
would never have been made. If Sir William Herschel had not been looking
at certain small stars for a totally different purpose he would never have
found Uranus; and no one need hesitate to admit the element of chance in
the finding of Neptune. It is well illustrated by a glance at the map
which, as has been remarked, Galle used to compare with the sky on the
night when he made the actual discovery. The planet was found down near
the bottom corner of the map, and since the limits assigned for its place
might easily have varied a few degrees one way or the other, it might
easily have been off the map; in which case, it is probable that the
search would not have been successful, or at any rate that success would
have been delayed.
[Illustration: V.--CORNER OF THE BERLIN MAP, BY THE USE OF WHICH GALLE
FOUND NEPTUNE.]
[Sidenote: Every one made mistakes.]
Thus, it is a most remarkable feature of the discovery of Neptune that
mistakes were made by almost every one concerned, however eminent. Airy
made a mistake in regarding the question of the Radius Vector as of
fundamental importance; Sir J. Herschel was wrong in describing an
elementary method which he considered might have found the planet;
Professor Peirce was wrong in supposing that the actual and the supposed
planet were essentially different in their action on Uranus; Le Verrier
was wrong in assigning limits outside which it was not necessary to look
when the actual planet was outside them; Adams was more or less wrong in
thinking that the eccentricity of the new planet could be found from the
material already at disposal of man. Both Adams and Le Verrier gave far
too much importance to Bode's Law.
To review a piece of history of this kind and note the mistakes of such
men is certainly comforting, and need not in any way lessen our
admiration. In the case of the investigators themselves, much may be set
down to excitement in the presence of a possible discovery. Professor
Sampson has provided us with a small but typical instance of this fact.
When Adams had carried through all his computations for finding Neptune,
and was approaching the actual place of the planet, he, "who could carry
through fabulous computations without error," for the first time wrote
down a wrong figure. The mistake was corrected upon the MS., "probably as
soon as made," but no doubt betrays the excitement which the great worker
could not repress at this critical moment. There is a tradition that,
similarly, when the mighty Newton was approaching the completion of his
calculations to verify the Law of Gravitation, his excitement was so great
that he was compelled to assign to a friend the task of finishing them.
Finally, we may remark how the history of the discovery of Neptune again
illustrates the difficulty of formulating any general principles for
guiding scientific work. Sometimes it is well to follow the slightest
clue, however imperfectly understood; at other times we shall do better to
refuse such guidance. Bode's Law pointed to the existence of minor
planets, and might conceivably have helped in finding Uranus: but by
trusting to it in the case of Neptune, the investigators were perilously
near going astray. Sometimes it is better to follow resolutely the work in
hand whatever it may be, shutting one's ears to other calls; but Airy and
Challis lost their opportunities by just this course of action. The
history of science is full of such contradictory experiences; and the only
safe conclusion seems to be that there are no general rules of conduct for
discovery.