Great Astronomers
by
R. S. Ball
Part 5 out of 5
other was Macullagh's paper on the "Laws of Crystalline Reflection
and Refraction." Hamilton expresses his gratification that, mainly
in consequence of his own exertions, he succeeded in having the medal
awarded to Macullagh rather than to himself. Indeed, it would almost
appear as if Hamilton had procured a letter from Sir J. Herschel,
which indicated the importance of Macullagh's memoir in such a way as
to decide the issue. It then became Hamilton's duty to award the
medal from the chair, and to deliver an address in which he expressed
his own sense of the excellence of Macullagh's scientific work. It
is the more necessary to allude to these points, because in the whole
of his scientific career it would seem that Macullagh was the only
man with whom Hamilton had ever even an approach to a dispute about
priority. The incident referred to took place in connection with the
discovery of conical refraction, the fame of which Macullagh made a
preposterous attempt to wrest from Hamilton. This is evidently
alluded to in Hamilton's letter to the Marquis of Northampton, dated
June 28th, 1838, in which we read:--
"And though some former circumstances prevented me from applying to
the person thus distinguished the sacred name of FRIEND, I had the
pleasure of doing justice...to his high intellectual merits...I
believe he was not only gratified but touched, and may, perhaps,
regard me in future with feelings more like those which I long to
entertain towards him."
Hamilton was in the habit, from time to time, of commencing the
keeping of a journal, but it does not appear to have been
systematically conducted. Whatever difficulties the biographer may
have experienced from its imperfections and irregularities, seem to
be amply compensated for by the practice which Hamilton had of
preserving copies of his letters, and even of comparatively
insignificant memoranda. In fact, the minuteness with which
apparently trivial matters were often noted down appears almost
whimsical. He frequently made a memorandum of the name of the person
who carried a letter to the post, and of the hour in which it was
despatched. On the other hand, the letters which he received were
also carefully preserved in a mighty mass of manuscripts, with which
his study was encumbered, and with which many other parts of the
house were not unfrequently invaded. If a letter was laid aside for
a few hours, it would become lost to view amid the seething mass of
papers, though occasionally, to use his own expression, it might be
seen "eddying" to the surface in some later disturbance.
The great volume of "Lectures on Quaternions" had been issued, and
the author had received the honours which the completion of such a
task would rightfully bring him. The publication of an immortal work
does not, however, necessarily provide the means for paying the
printer's bill. The printing of so robust a volume was necessarily
costly; and even if all the copies could be sold, which at the time
did not seem very likely, they would hardly have met the inevitable
expenses. The provision of the necessary funds was, therefore, a
matter for consideration. The Board of Trinity College had already
contributed 200 pounds to the printing, but yet another hundred was
required. Even the discoverer of Quaternions found this a source of
much anxiety. However, the board, urged by the representation of
Humphrey Lloyd, now one of its members, and, as we have already seen,
one of Hamilton's staunchest friends, relieved him of all liability.
We may here note that, notwithstanding the pension which Hamilton
enjoyed in addition to the salary of his chair, he seems always to
have been in some what straitened circumstances, or, to use his own
words in one of his letters to De Morgan, "Though not an embarrassed
man, I am anything rather than a rich one." It appears that,
notwithstanding the world-wide fame of Hamilton's discoveries, the
only profit in a pecuniary sense that he ever obtained from any of
his works was by the sale of what he called his Icosian Game. Some
enterprising publisher, on the urgent representations of one of
Hamilton's friends in London, bought the copyright of the Icosian
Game for 25 pounds. Even this little speculation proved unfortunate
for the purchaser, as the public could not be induced to take the
necessary interest in the matter.
After the completion of his great book, Hamilton appeared for awhile
to permit himself a greater indulgence than usual in literary
relaxations. He had copious correspondence with his intimate friend,
Aubrey de Vere, and there were multitudes of letters from those
troops of friends whom it was Hamilton's privilege to possess. He
had been greatly affected by the death of his beloved sister Eliza, a
poetess of much taste and feeling. She left to him her many papers
to preserve or to destroy, but he said it was only after the
expiration of four years of mourning that he took courage to open her
pet box of letters.
The religious side of Hamilton's character is frequently illustrated
in these letters; especially is this brought out in the
correspondence with De Vere, who had seceded to the Church of Rome.
Hamilton writes, August 4, 1855:--
"If, then, it be painfully evident to both, that under such
circumstances there CANNOT (whatever we may both DESIRE) be NOW in
the nature of things, or of minds, the same degree of INTIMACY
between us as of old; since we could no longer TALK with the same
degree of unreserve on every subject which happened to present
itself, but MUST, from the simplest instincts of courtesy, be each on
his guard not to say what might be offensive, or, at least, painful
to the other; yet WE were ONCE so intimate, an retain still, and, as
I trust, shall always retain, so much of regard and esteem and
appreciation for each other, made tender by so many associations of
my early youth and your boyhood, which can never be forgotten by
either of us, that (as times go) TWO OR THREE VERY RESPECTABLE
FRIENDSHIPS might easily be carved out from the fragments of our
former and ever-to-be-remembered INTIMACY. It would be no
exaggeration to quote the words: 'Heu! quanto minus est cum reliquis
versari, quam tui meminisse!'"
In 1858 a correspondence on the subject of Quaternions commenced
between Professor Tait and Sir William Hamilton. It was particularly
gratifying to the discoverer that so competent a mathematician as
Professor Tait should have made himself acquainted with the new
calculus. It is, of course, well known that Professor Tait
subsequently brought out a most valuable elementary treatise on
Quaternions, to which those who are anxious to become acquainted with
the subject will often turn in preference to the tremendous work of
Hamilton.
In the year 1861 gratifying information came to hand of the progress
which the study of Quaternions was making abroad. Especially did the
subject attract the attention of that accomplished mathematician,
Moebius, who had already in his "Barycentrische Calculus" been led to
conceptions which bore more affinity to Quaternions than could be
found in the writings of any other mathematician. Such notices of
his work were always pleasing to Hamilton, and they served, perhaps,
as incentives to that still closer and more engrossing labour by
which he became more and more absorbed. During the last few years of
his life he was observed to be even more of a recluse than he had
hitherto been. His powers of long and continuous study seemed to
grow with advancing years, and his intervals of relaxation, such as
they were, became more brief and more infrequent.
It was not unusual for him to work for twelve hours at a stretch.
The dawn would frequently surprise him as he looked up to snuff his
candles after a night of fascinating labour at original research.
Regularity in habits was impossible to a student who had prolonged
fits of what he called his mathematical trances. Hours for rest and
hours for meals could only be snatched in the occasional the lucid
intervals between one attack of Quaternions and the next. When
hungry, he would go to see whether any thing could be found on the
sideboard; when thirsty, he would visit the locker, and the one
blemish in the man's personal character is that these latter visits
were sometimes paid too often.
As an example of one of Hamilton's rare diversions from the all-
absorbing pursuit of Quaternions, we find that he was seized with
curiosity to calculate back to the date of the Hegira, which he found
on the 15th July, 622. He speaks of the satisfaction with which he
ascertained subsequently that Herschel had assigned precisely the
same date. Metaphysics remained also, as it had ever been, a
favourite subject of Hamilton's readings and meditations and of
correspondence with his friends. He wrote a very long letter to Dr.
Ingleby on the subject of his "Introduction to Metaphysics." In it
Hamilton alludes, as he has done also in other places, to a
peculiarity of his own vision. It was habitual to him, by some
defect in the correlation of his eyes, to see always a distinct image
with each; in fact, he speaks of the remarkable effect which the use
of a good stereoscope had on his sensations of vision. It was then,
for the first time, that he realised how the two images which he had
always seen hitherto would, under normal circumstances, be blended
into one. He cites this fact as bearing on the phenomena of
binocular vision, and he draws from it the inference that the
necessity of binocular vision for the correct appreciation of
distance is unfounded. "I am quite sure," he says, "that I SEE
DISTANCE with EACH EYE SEPARATELY."
The commencement of 1865, the last year of his life saw Hamilton as
diligent as ever, and corresponding with Salmon and Cayley. On April
26th he writes to a friend to say, that his health has not been good
for years past, and that so much work has injured his constitution;
and he adds, that it is not conducive to good spirits to find that he
is accumulating another heavy bill with the printer for the
publication of the "Elements." This was, indeed, up to the day of
his death, a cause for serious anxiety. It may, however, be
mentioned that the whole cost, which amounted to nearly 500 pounds,
was, like that of the previous volume, ultimately borne by the
College. Contrary to anticipation, the enterprise, even in a
pecuniary sense, cannot have been a very unprofitable one. The whole
edition has long been out of print, and as much as 5 pounds has since
been paid for a single copy.
It was on the 9th of May, 1865, that Hamilton was in Dublin for the
last time. A few days later he had a violent attack of gout, and on
the 4th of June he became alarmingly ill, and on the next day had an
attack of epileptic convulsions. However, he slightly rallied, so
that before the end of the month he was again at work at the
"Elements." A gratifying incident brightened some of the last days
of his life. The National Academy of Science in America had then
been just formed. A list of foreign Associates had to be chosen from
the whole world, and a discussion took place as to what name should
be placed first on the list. Hamilton was informed by private
communication that this great distinction was awarded to him by a
majority of two-thirds.
In August he was still at work on the table of contents of the
"Elements," and one of his very latest efforts was his letter to Mr.
Gould, in America, communicating his acknowledgements of the honour
which had been just conferred upon him by the National Academy. On
the 2nd of September Mr. Graves went to the observatory, in response
to a summons, and the great mathematician at once admitted to his
friend that he felt the end was approaching. He mentioned that he
had found in the 145th Psalm a wonderfully suitable expression of his
thoughts and feelings, and he wished to testify his faith and
thankfulness as a Christian by partaking of the Lord's Supper. He
died at half-past two on the afternoon of the 2nd of September, 1865,
aged sixty years and one month. He was buried in Mount Jerome
Cemetery on the 7th of September.
Many were the letters and other more public manifestations of the
feelings awakened by Hamilton's death. Sir John Herschel wrote to
the widow:--
"Permit me only to add that among the many scientific friends whom
time has deprived me of, there has been none whom I more deeply
lament, not only for his splendid talents, but for the excellence of
his disposition and the perfect simplicity of his manners--so great,
and yet devoid of pretensions."
De Morgan, his old mathematical crony, as Hamilton affectionately
styled him, also wrote to Lady Hamilton:--
"I have called him one of my dearest friends, and most truly; for I
know not how much longer than twenty-five years we have been in
intimate correspondence, of most friendly agreement or disagreement,
of most cordial interest in each other. And yet we did not know each
other's faces. I met him about 1830 at Babbage's breakfast table,
and there for the only time in our lives we conversed. I saw him, a
long way off, at the dinner given to Herschel (about 1838) on his
return from the Cape and there we were not near enough, nor on that
crowded day could we get near enough, to exchange a word. And this
is all I ever saw, and, so it has pleased God, all I shall see in
this world of a man whose friendly communications were among my
greatest social enjoyments, and greatest intellectual treats."
There is a very interesting memoir of Hamilton written by De Morgan,
in the "Gentleman's Magazine" for 1866, in which he produces an
excellent sketch of his friend, illustrated by personal reminiscences
and anecdotes. He alludes, among other things, to the picturesque
confusion of the papers in his study. There was some sort of order
in the mass, discernible however, by Hamilton alone, and any invasion
of the domestics, with a view to tidying up, would throw the
mathematician as we are informed, into "a good honest thundering
passion."
Hardly any two men, who were both powerful mathematicians, could have
been more dissimilar in every other respect than were Hamilton and De
Morgan. The highly poetical temperament of Hamilton was remarkably
contrasted with the practical realism of De Morgan. Hamilton sends
sonnets to his friend, who replies by giving the poet advice about
making his will. The metaphysical subtleties, with which Hamilton
often filled his sheets, did not seem to have the same attraction for
De Morgan that he found in battles about the quantification of the
Predicate. De Morgan was exquisitely witty, and though his jokes
were always appreciated by his correspondent, yet Hamilton seldom
ventured on anything of the same kind in reply; indeed his rare
attempts at humour only produced results of the most ponderous
description. But never were two scientific correspondents more
perfectly in sympathy with each other. Hamilton's work on
Quaternions, his labours in Dynamics, his literary tastes, his
metaphysics, and his poetry, were all heartily welcomed by his
friend, whose letters in reply invariably evince the kindliest
interest in all Hamilton's concerns. In a similar way De Morgan's
letters to Hamilton always met with a heartfelt response.
Alike for the memory of Hamilton, for the credit of his University,
and for the benefit of science, let us hope that a collected edition
of his works will ere long appear--a collection which shall show
those early achievements in splendid optical theory, those
achievements of his more mature powers which made him the Lagrange of
his country, and finally those creations of the Quaternion Calculus
by which new capabilities have been bestowed on the human intellect.
LE VERRIER.
The name of Le Verrier is one that goes down to fame on account of
very different discoveries from those which have given renown to
several of the other astronomers whom we have mentioned. We are
sometimes apt to identify the idea of an astronomer with that of a
man who looks through a telescope at the stars; but the word
astronomer has really much wider significance. No man who ever lived
has been more entitled to be designated an astronomer than Le
Verrier, and yet it is certain that he never made a telescopic
discovery of any kind. Indeed, so far as his scientific achievements
have been concerned, he might never have looked through a telescope
at all.
For the full interpretation of the movements of the heavenly bodies,
mathematical knowledge of the most advanced character is demanded.
The mathematician at the outset calls upon the astronomer who uses
the instruments in the observatory, to ascertain for him at various
times the exact positions occupied by the sun, the moon, and the
planets. These observations, obtained with the greatest care, and
purified as far as possible from the errors by which they may be
affected form, as it were, the raw material on which the
mathematician exercises his skill. It is for him to elicit from the
observed places the true laws which govern the movements of the
heavenly bodies. Here is indeed a task in which the highest powers
of the human intellect may be worthily employed.
Among those who have laboured with the greatest success in the
interpretation of the observations made with instruments of
precision, Le Verrier holds a highly honoured place. To him it has
been given to provide a superb illustration of the success with which
the mind of man can penetrate the deep things of Nature.
The illustrious Frenchman, Urban Jean Joseph Le Verrier, was born on
the 11th March, 1811, at St. Lo, in the department of Manche. He
received his education in that famous school for education in the
higher branches of science, the Ecole Polytechnique, and acquired
there considerable fame as a mathematician. On leaving the school Le
Verrier at first purposed to devote himself to the public service, in
the department of civil engineering; and it is worthy of note that
his earliest scientific work was not in those mathematical researches
in which he was ultimately to become so famous. His duties in the
engineering department involved practical chemical research in the
laboratory. In this he seems to have become very expert, and
probably fame as a chemist would have been thus attained, had not
destiny led him into another direction. As it was, he did engage in
some original chemical research. His first contributions to science
were the fruits of his laboratory work; one of his papers was on the
combination of phosphorus and hydrogen, and another on the
combination of phosphorus and oxygen.
His mathematical labours at the Ecole Polytechnique had, however,
revealed to Le Verrier that he was endowed with the powers requisite
for dealing with the subtlest instruments of mathematical analysis.
When he was twenty-eight years old, his first great astronomical
investigation was brought forth. It will be necessary to enter into
some explanation as to the nature of this, inasmuch as it was the
commencement of the life-work which he was to pursue.
If but a single planet revolved around the sun, then the orbit of
that planet would be an ellipse, and the shape and size, as well as
the position of the ellipse, would never alter. One revolution after
another would be traced out, exactly in the same manner, in
compliance with the force continuously exerted by the sun. Suppose,
however, that a second planet be introduced into the system. The sun
will exert its attraction on this second planet also, and it will
likewise describe an orbit round the central globe. We can, however,
no longer assert that the orbit in which either of the planets moves
remains exactly an ellipse. We may, indeed, assume that the mass of
the sun is enormously greater than that of either of the planets. In
this case the attraction of the sun is a force of such preponderating
magnitude, that the actual path of each planet remains nearly the
same as if the other planet were absent. But it is impossible for
the orbit of each planet not to be affected in some degree by the
attraction of the other planet. The general law of nature asserts
that every body in space attracts every other body. So long as there
is only a single planet, it is the single attraction between the sun
and that planet which is the sole controlling principle of the
movement, and in consequence of it the ellipse is described. But
when a second planet is introduced, each of the two bodies is not
only subject to the attraction of the sun, but each one of the
planets attracts the other. It is true that this mutual attraction
is but small, but, nevertheless, it produces some effect. It
"disturbs," as the astronomer says, the elliptic orbit which would
otherwise have been pursued. Hence it follows that in the actual
planetary system where there are several planets disturbing each
other, it is not true to say that the orbits are absolutely elliptic.
At the same time in any single revolution a planet may for most
practical purposes be said to be actually moving in an ellipse. As,
however, time goes on, the ellipse gradually varies. It alters its
shape, it alters its plane, and it alters its position in that
plane. If, therefore, we want to study the movements of the planets,
when great intervals of time are concerned, it is necessary to have
the means of learning the nature of the movement of the orbit in
consequence of the disturbances it has experienced.
We may illustrate the matter by supposing the planet to be running
like a railway engine on a track which has been laid in a long
elliptic path. We may suppose that while the planet is coursing
along, the shape of the track is gradually altering. But this
alteration may be so slow, that it does not appreciably affect the
movement of the engine in a single revolution. We can also suppose
that the plane in which the rails have been laid has a slow
oscillation in level, and that the whole orbit is with more or less
uniformity moved slowly about in the plane.
In short periods of time the changes in the shapes and positions of
the planetary orbits, in consequence of their mutual attractions, are
of no great consequence. When, however, we bring thousands of years
into consideration, then the displacements of the planetary orbits
attain considerable dimensions, and have, in fact, produced a
profound effect on the system.
It is of the utmost interest to investigate the extent to which one
planet can affect another in virtue of their mutual attractions. Such
investigations demand the exercise of the highest mathematical
gifts. But not alone is intellectual ability necessary for success
in such inquiries. It must be united with a patient capacity for
calculations of an arduous type, protracted, as they frequently have
to be, through many years of labour. Le Verrier soon found in these
profound inquiries adequate scope for the exercise of his peculiar
gifts. His first important astronomical publication contained an
investigation of the changes which the orbits of several of the
planets, including the earth, have undergone in times past, and which
they will undergo in times to come.
As an illustration of these researches, we may take the case of the
planet in which we are, of course, especially interested, namely, the
earth, and we can investigate the changes which, in the lapse of
time, the earth's orbit has undergone, in consequence of the
disturbance to which it has been subjected by the other planets. In
a century, or even in a thousand years, there is but little
recognisable difference in the shape of the track pursued by the
earth. Vast periods of time are required for the development of the
large consequences of planetary perturbation. Le Verrier has,
however, given us the particulars of what the earth's journey through
space has been at intervals of 20,000 years back from the present
date. His furthest calculation throws our glance back to the state
of the earth's track 100,000 years ago, while, with a bound forward,
he shows us what the earth's orbit is to be in the future, at
successive intervals of 20,000 years, till a date is reached which is
100,000 years in advance Of A.D. 1800.
The talent which these researches displayed brought Le Verrier into
notice. At that time the Paris Observatory was presided over by
Arago, a SAVANT who occupies a distinguished position in French
scientific annals. Arago at once perceived that Le Verrier was just
the man who possessed the qualifications suitable for undertaking a
problem of great importance and difficulty that had begun to force
itself on the attention of astronomers. What this great problem was,
and how astonishing was the solution it received, must now be
considered.
Ever since Herschel brought himself into fame by his superb discovery
of the great planet Uranus, the movements of this new addition to the
solar system were scrutinized with care and attention. The position
of Uranus was thus accurately determined from time to time. At
length, when sufficient observations of this remote planet had been
brought together, the route which the newly-discovered body pursued
through the heavens was ascertained by those calculations with which
astronomers are familiar. It happens, however, that Uranus possesses
a superficial resemblance to a star. Indeed the resemblance is so
often deceptive that long ere its detection as a planet by Herschel,
it had been observed time after time by skilful astronomers, who
little thought that the star-like point at which they looked was
anything but a star. From these early observations it was possible
to determine the track of Uranus, and it was found that the great
planet takes a period of no less than eighty-four years to accomplish
a circuit. Calculations were made of the shape of the orbit in which
it revolved before its discovery by Herschel, and these were compared
with the orbit which observations showed the same body to pursue in
those later years when its planetary character was known. It could
not, of course, be expected that the orbit should remain unaltered;
the fact that the great planets Jupiter and Saturn revolve in the
vicinity of Uranus must necessarily imply that the orbit of the
latter undergoes considerable changes. When, however, due allowance
has been made for whatever influence the attraction of Jupiter and
Saturn, and we may add of the earth and all the other Planets, could
possibly produce, the movements of Uranus were still inexplicable. It
was perfectly obvious that there must be some other influence at work
besides that which could be attributed to the planets already known.
Astronomers could only recognise one solution of such a difficulty.
It was impossible to doubt that there must be some other planet in
addition to the bodies at that time known, and that the perturbations
of Uranus hitherto unaccounted for, were due to the disturbances
caused by the action of this unknown planet. Arago urged Le Verrier
to undertake the great problem of searching for this body, whose
theoretical existence seemed demonstrated. But the conditions of the
search were such that it must needs be conducted on principles wholly
different from any search which had ever before been undertaken for a
celestial object. For this was not a case in which mere survey with
a telescope might be expected to lead to the discovery.
Certain facts might be immediately presumed with reference to the
unknown object. There could be no doubt that the unknown disturber
of Uranus must be a large body with a mass far exceeding that of the
earth. It was certain, however, that it must be so distant that it
could only appear from our point of view as a very small object.
Uranus itself lay beyond the range, or almost beyond the range, of
unassisted vision. It could be shown that the planet by which the
disturbance was produced revolved in an orbit which must lie outside
that of Uranus. It seemed thus certain that the planet could not be
a body visible to the unaided eye. Indeed, had it been at all
conspicuous its planetary character would doubtless have been
detected ages ago. The unknown body must therefore be a planet which
would have to be sought for by telescopic aid.
There is, of course, a profound physical difference between a planet
and a star, for the star is a luminous sun, and the planet is merely
a dark body, rendered visible by the sunlight which falls upon it.
Notwithstanding that a star is a sun thousands of times larger than
the planet and millions of times more remote, yet it is a singular
fact that telescopic planets possess an illusory resemblance to the
stars among which their course happens to lie. So far as actual
appearance goes, there is indeed only one criterion by which a planet
of this kind can be discriminated from a star. If the planet be
large enough the telescope will show that it possesses a disc, and
has a visible and measurable circular outline. This feature a star
does not exhibit. The stars are indeed so remote that no matter how
large they may be intrinsically, they only exhibit radiant points of
light, which the utmost powers of the telescope fail to magnify into
objects with an appreciable diameter. The older and well-known
planets, such as Jupiter and Mars, possess discs, which, though not
visible to the unaided eye, were clearly enough discernible with the
slightest telescopic power. But a very remote planet like Uranus,
though it possessed a disc large enough to be quickly appreciated by
the consummate observing skill of Herschel, was nevertheless so
stellar in its appearance, that it had been observed no fewer than
seventeen times by experienced astronomers prior to Herschel. In
each case the planetary nature of the object had been overlooked, and
it had been taken for granted that it was a star. It presented no
difference which was sufficient to arrest attention.
As the unknown body by which Uranus was disturbed was certainly much
more remote than Uranus, it seemed to be certain that though it might
show a disc perceptible to very close inspection, yet that the disc
must be so minute as not to be detected except with extreme care. In
other words, it seemed probable that the body which was to be sought
for could not readily be discriminated from a small star, to which
class of object it bore a superficial resemblance, though, as a
matter of fact, there was the profoundest difference between the two
bodies.
There are on the heavens many hundreds of thousands of stars, and the
problem of identifying the planet, if indeed it should lie among
these stars, seemed a very complex matter. Of course it is the
abundant presence of the stars which causes the difficulty. If the
stars could have been got rid of, a sweep over the heavens would at
once disclose all the planets which are bright enough to be visible
with the telescopic power employed. It is the fortuitous resemblance
of the planet to the stars which enables it to escape detection. To
discriminate the planet among stars everywhere in the sky would be
almost impossible. If, however, some method could be devised for
localizing that precise region in which the planet's existence might
be presumed, then the search could be undertaken with some prospect
of success.
To a certain extent the problem of localizing the region on the sky
in which the planet might be expected admitted of an immediate
limitation. It is known that all the planets, or perhaps I ought
rather to say, all the great planets, confine their movements to a
certain zone around the heavens. This zone extends some way on
either side of that line called the ecliptic in which the earth
pursues its journey around the sun. It was therefore to be inferred
that the new planet need not be sought for outside this zone. It is
obvious that this consideration at once reduces the area to be
scrutinized to a small fraction of the entire heavens. But even
within the zone thus defined there are many thousands of stars. It
would seem a hopeless task to detect the new planet unless some
further limitation to its position could be assigned.
It was accordingly suggested to Le Verrier that he should endeavour
to discover in what particular part of the strip of the celestial
sphere which we have indicated the search for the unknown planet
should be instituted. The materials available to the mathematician
for the solution of this problem were to be derived solely from the
discrepancies between the calculated places in which Uranus should be
found, taking into account the known causes of disturbance, and the
actual places in which observation had shown the planet to exist.
Here was indeed an unprecedented problem, and one of extraordinary
difficulty. Le Verrier, however, faced it, and, to the astonishment
of the world, succeeded in carrying it through to a brilliant
solution. We cannot here attempt to enter into any account of the
mathematical investigations that were necessary. All that we can do
is to give a general indication of the method which had to be
adopted.
Let us suppose that a planet is revolving outside Uranus, at a
distance which is suggested by the several distances at which the
other planets are dispersed around the sun. Let us assume that this
outer planet has started on its course, in a prescribed path, and
that it has a certain mass. It will, of course, disturb the motion
of Uranus, and in consequence of that disturbance Uranus will follow
a path the nature of which can be determined by calculation. It
will, however, generally be found that the path so ascertained does
not tally with the actual path which observations have indicated for
Uranus. This demonstrates that the assumed circumstances of the
unknown planet must be in some respects erroneous, and the astronomer
commences afresh with an amended orbit. At last after many trials,
Le Verrier ascertained that, by assuming a certain size, shape, and
position for the unknown Planet's orbit, and a certain value for the
mass of the hypothetical body, it would be possible to account for
the observed disturbances of Uranus. Gradually it became clear to
the perception of this consummate mathematician, not only that the
difficulties in the movements of Uranus could be thus explained, but
that no other explanation need be sought for. It accordingly
appeared that a planet possessing the mass which he had assigned, and
moving in the orbit which his calculations had indicated, must indeed
exist, though no eye had ever beheld any such body. Here was,
indeed, an astonishing result. The mathematician sitting at his
desk, by studying the observations which had been supplied to him of
one planet, is able to discover the existence of another planet, and
even to assign the very position which it must occupy, ere ever the
telescope is invoked for its discovery.
Thus it was that the calculations of Le Verrier narrowed greatly the
area to be scrutinised in the telescopic search which was presently
to be instituted. It was already known, as we have just pointed out,
that the planet must lie somewhere on the ecliptic. The French
mathematician had now further indicated the spot on the ecliptic at
which, according to his calculations, the planet must actually be
found. And now for an episode in this history which will be
celebrated so long as science shall endure. It is nothing less than
the telescopic confirmation of the existence of this new planet,
which had previously been indicated only by mathematical
calculation. Le Verrier had not himself the instruments necessary
for studying the heavens, nor did he possess the skill of the
practical astronomer. He, therefore, wrote to Dr. Galle, of the
Observatory at Berlin, requesting him to undertake a telescopic
search for the new planet in the vicinity which the mathematical
calculation had indicated for the whereabouts of the planet at that
particular time. Le Verrier added that he thought the planet ought
to admit of being recognised by the possession of a disc sufficiently
definite to mark the distinction between it and the surrounding
stars.
It was the 23rd September, 1846, when the request from Le Verrier
reached the Berlin Observatory, and the night was clear, so that the
memorable search was made on the same evening. The investigation was
facilitated by the circumstance that a diligent observer had recently
compiled elaborate star maps for certain tracts of the heavens lying
in a sufficiently wide zone on both sides of the equator. These maps
were as yet only partially complete, but it happened that Hora. XXI.,
which included the very spot which Le Verrier's results referred to,
had been just issued. Dr. Galle had thus before his, eyes a chart of
all the stars which were visible in that part of the heavens at the
time when the map was made. The advantage of such an assistance to
the search could hardly be over-estimated. It at once gave the
astronomer another method of recognising the planet besides that
afforded by its possible possession of a disc. For as the planet was
a moving body, it would not have been in the same place relatively to
the stars at the time when the map was constructed, as it occupied
some years later when the search was being made. If the body should
be situated in the spot which Le Verrier's calculations indicated in
the autumn of 1846, then it might be regarded as certain that it
would not be found in that same place on a map drawn some years
previously.
The search to be undertaken consisted in a comparison made point by
point between the bodies shown on the map, and those stars in the sky
which Dr. Galle's telescope revealed. In the course of this
comparison it presently appeared that a star-like object of the
eighth magnitude, which was quite a conspicuous body in the
telescope, was not represented in the map. This at once attracted
the earnest attention of the astronomer, and raised his hopes that
here was indeed the planet. Nor were these hopes destined to be
disappointed. It could not be supposed that a star of the eighth
magnitude would have been overlooked in the preparation of a chart
whereon stars of many lower degrees of brightness were set down. One
other supposition was of course conceivable. It might have been that
this suspicious object belonged to the class of variables, for there
are many such stars whose brightness fluctuates, and if it had
happened that the map was constructed at a time when the star in
question had but feeble brilliance, it might have escaped notice. It
is also well known that sometimes new stars suddenly develop, so that
the possibility that what Dr. Galle saw should have been a variable
star or should have been a totally new star had to be provided
against.
Fortunately a test was immediately available to decide whether the
new object was indeed the long sought for planet, or whether it was a
star of one of the two classes to which I have just referred. A star
remains fixed, but a planet is in motion. No doubt when a planet
lies at the distance at which this new planet was believed to be
situated, its apparent motion would be so slow that it would not be
easy to detect any change in the course of a single night's
observation. Dr. Galle, however, addressed himself with much skill
to the examination of the place of the new body. Even in the course
of the night he thought he detected slight movements, and he awaited
with much anxiety the renewal of his observations on the subsequent
evenings. His suspicions as to the movement of the body were then
amply confirmed, and the planetary nature of the new object was thus
unmistakably detected.
Great indeed was the admiration of the scientific world at this
superb triumph. Here was a mighty planet whose very existence was
revealed by the indications afforded by refined mathematical
calculation. At once the name of Le Verrier, already known to those
conversant with the more profound branches of astronomy, became
everywhere celebrated. It soon, however, appeared, that the fame
belonging to this great achievement had to be shared between Le
Verrier and another astronomer, J. C. Adams, of Cambridge. In our
chapter on this great English mathematician we shall describe the
manner in which he was independently led to the same discovery.
Directly the planetary nature of the newly-discovered body had been
established, the great observatories naturally included this
additional member of the solar system in their working lists, so that
day after day its place was carefully determined. When sufficient
time had elapsed the shape and position of the orbit of the body
became known. Of course, it need hardly be said that observations
applied to the planet itself must necessarily provide a far more
accurate method of determining the path which it follows, than would
be possible to Le Verrier, when all he had to base his calculations
upon was the influence of the planet reflected, so to speak, from
Uranus. It may be noted that the true elements of the planet, when
revealed by direct observation, showed that there was a considerable
discrepancy between the track of the planet which Le Verrier had
announced, and that which the planet was actually found to pursue.
The name of the newly-discovered body had next to be considered. As
the older members of the system were already known by the same names
as great heathen divinities, it was obvious that some similar source
should be invoked for a suggestion as to a name for the most recent
planet. The fact that this body was so remote in the depths of
space, not unnaturally suggested the name "Neptune." Such is
accordingly the accepted designation of that mighty globe which
revolves in the track that at present seems to trace out the
frontiers of our system.
Le Verrier attained so much fame by this discovery, that when, in
1854, Arago's place had to be filled at the head of the great Paris
Observatory, it was universally felt that the discoverer of Neptune
was the suitable man to assume the office which corresponds in France
to that of the Astronomer Royal in England. It was true that the
work of the astronomical mathematician had hitherto been of an
abstract character. His discoveries had been made at his desk and
not in the observatory, and he had no practical acquaintance with the
use of astronomical instruments. However, he threw himself into the
technical duties of the observatory with vigour and determination. He
endeavoured to inspire the officers of the establishment with
enthusiasm for that systematic work which is so necessary for the
accomplishment of useful astronomical research. It must, however, be
admitted that Le Verrier was not gifted with those natural qualities
which would make him adapted for the successful administration of
such an establishment. Unfortunately disputes arose between the
Director and his staff. At last the difficulties of the situation
became so great that the only possible solution was to supersede Le
Verrier, and he was accordingly obliged to retire. He was succeeded
in his high office by another eminent mathematician, M. Delaunay,
only less distinguished than Le Verrier himself.
Relieved of his official duties, Le Verrier returned to the
mathematics he loved. In his non-official capacity he continued to
work with the greatest ardour at his researches on the movements of
the planets. After the death of M. Delaunay, who was accidentally
drowned in 1873, Le Verrier was restored to the directorship of the
observatory, and he continued to hold the office until his death.
The nature of the researches to which the life of Le Verrier was
subsequently devoted are not such as admit of description in a
general sketch like this, where the language, and still less the
symbols, of mathematics could not be suitably introduced. It may,
however, be said in general that he was particularly engaged with the
study of the effects produced on the movements of the planets by
their mutual attractions. The importance of this work to astronomy
consists, to a considerable extent, in the fact that by such
calculations we are enabled to prepare tables by which the places of
the different heavenly bodies can be predicted for our almanacs. To
this task Le Verrier devoted himself, and the amount of work he has
accomplished would perhaps have been deemed impossible had it not
been actually done.
The superb success which had attended Le Verrier's efforts to explain
the cause of the perturbations of Uranus, naturally led this
wonderful computer to look for a similar explanation of certain other
irregularities in planetary movements. To a large extent he
succeeded in showing how the movements of each of the great planets
could be satisfactorily accounted for by the influence of the
attractions of the other bodies of the same class. One circumstance
in connection with these investigations is sufficiently noteworthy to
require a few words here. Just as at the opening of his career, Le
Verrier had discovered that Uranus, the outermost planet of the then
known system, exhibited the influence of an unknown external body, so
now it appeared to him that Mercury, the innermost body of our
system, was also subjected to some disturbances, which could not be
satisfactorily accounted for as consequences of any known agents of
attraction. The ellipse in which Mercury revolved was animated by a
slow movement, which caused it to revolve in its plane. It appeared
to Le Verrier that this displacement was incapable of explanation by
the action of any of the known bodies of our system. He was,
therefore, induced to try whether he could not determine from the
disturbances of Mercury the existence of some other planet, at
present unknown, which revolved inside the orbit of the known
planet. Theory seemed to indicate that the observed alteration in
the track of the planet could be thus accounted for. He naturally
desired to obtain telescopic confirmation which might verify the
existence of such a body in the same way as Dr. Galle verified the
existence of Neptune. If there were, indeed, an intramercurial
planet, then it must occasionally cross between the earth and the
sun, and might now and then be expected to be witnessed in the actual
act of transit. So confident did Le Verrier feel in the existence of
such a body that an observation of a dark object in transit, by
Lescarbault on 26th March, 1859, was believed by the mathematician to
be the object which his theory indicated. Le Verrier also thought it
likely that another transit of the same object would be seen in
March, 1877. Nothing of the kind was, however, witnessed,
notwithstanding that an assiduous watch was kept, and the explanation
of the change in Mercury's orbit must, therefore, be regarded as
still to be sought for.
Le Verrier naturally received every honour that could be bestowed
upon a man of science. The latter part of his life was passed during
the most troubled period of modern French history. He was a
supporter of the Imperial Dynasty, and during the Commune he
experienced much anxiety; indeed, at one time grave fears were
entertained for his personal safety.
Early in 1877 his health, which had been gradually failing for some
years, began to give way. He appeared to rally somewhat in the
summer, but in September he sank rapidly, and died on Sunday, the
23rd of that month.
His remains were borne to the cemetery on Mont Parnasse in a public
funeral. Among his pallbearers were leading men of science, from
other countries as well as France, and the memorial discourses
pronounced at the grave expressed their admiration of his talents and
of the greatness of the services he had rendered to science.
ADAMS.
The illustrious mathematician who, among Englishmen, at all events,
was second only to Newton by his discoveries in theoretical
astronomy, was born on June the 5th, 1819, at the farmhouse of
Lidcot, seven miles from Launceston, in Cornwall. His early
education was imparted under the guidance of the Rev. John Couch
Grylls, a first cousin of his mother. He appears to have received an
education of the ordinary school type in classics and mathematics,
but his leisure hours were largely devoted to studying what
astronomical books he could find in the library of the Mechanics'
Institute at Devonport. He was twenty years old when he entered St.
John's College, Cambridge. His career in the University was one of
almost unparalleled distinction, and it is recorded that his
answering at the Wranglership examination, where he came out at the
head of the list in 1843, was so high that he received more than
double the marks awarded to the Second Wrangler.
Among the papers found after his death was the following memorandum,
dated July the 3rd, 1841: "Formed a design at the beginning of this
week of investigating, as soon as possible after taking my degree,
the irregularities in the motion of Uranus, Which are 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 approximately, which
would lead probably to its discovery."
After he had taken his degree, and had thus obtained a little
relaxation from the lines within which his studies had previously
been necessarily confined, Adams devoted himself to the study of the
perturbations of Uranus, in accordance with the resolve which we have
just seen that he formed while he was still an undergraduate. As a
first attempt he made the supposition that there might be a planet
exterior to Uranus, at a distance which was double that of Uranus
from the sun. Having completed his calculation as to the effect
which such a hypothetical planet might exercise upon the movement of
Uranus, he came to the conclusion that it would be quite possible to
account completely for the unexplained difficulties by the action of
an exterior planet, if only that planet were of adequate size and had
its orbit properly placed. It was necessary, however, to follow up
the problem more precisely, and accordingly an application was made
through Professor Challis, the Director of the Cambridge Observatory,
to the Astronomer Royal, with the object of obtaining from the
observations made at Greenwich Observatory more accurate values for
the disturbances suffered by Uranus. Basing his work on the more
precise materials thus available, Adams undertook his calculations
anew, and at last, with his completed results, he called at Greenwich
Observatory on October the 21st, 1845. He there left for the
Astronomer Royal a paper which contained the results at which he had
arrived for the mass and the mean distance of the hypothetical planet
as well as the other elements necessary for calculating its exact
position.
[PLATE: JOHN COUCH ADAMS.]
As we have seen in the preceding chapter, Le Verrier had been also
investigating the same problem. The place which Le Verrier assigned
to the hypothetical disturbing planet for the beginning of the year
1847, was within a degree of that to which Adams's computations
pointed, and which he had communicated to the Astronomer Royal seven
months before Le Verrier's work appeared. On July the 29th, 1846,
Professor Challis commenced to search for the unknown object with the
Northumberland telescope belonging to the Cambridge Observatory. He
confined his attention to a limited region in the heavens, extending
around that point to which Mr. Adams' calculations pointed. The
relative places of all the stars, or rather star-like objects within
this area, were to be carefully measured. When the same observations
were repeated a week or two later, then the distances of the several
pairs of stars from each other would be found unaltered, but any
planet which happened to lie among the objects measured would
disclose its existence by the alterations in distance due to its
motion in the interval. This method of search, though no doubt it
must ultimately have proved successful, was necessarily a very
tedious one, but to Professor Challis, unfortunately, no other method
was available. Thus it happened that, though Challis commenced his
search at Cambridge two months earlier than Galle at Berlin, yet, as
we have already explained, the possession of accurate star-maps by
Dr. Galle enabled him to discover the planet on the very first night
that he looked for it.
The rival claims of Adams and Le Verrier to the discovery of Neptune,
or rather, we should say, the claims put forward by their respective
champions, for neither of the illustrious investigators themselves
condescended to enter into the personal aspect of the question, need
not be further discussed here. The main points of the controversy
have been long since settled, and we cannot do better than quote the
words of Sir John Herschel when he addressed the Royal Astronomical
Society in 1848:--
"As genius and destiny have joined the names of Le Verrier and Adams,
I shall by no means put them asunder; nor will they ever be
pronounced apart so long as language shall celebrate the triumphs Of
science in her sublimest walks. On the great discovery of Neptune,
which may be said to have surpassed, by intelligible and legitimate
means, the wildest pretensions of clairvoyance, it Would now be quite
superfluous for me to dilate. That glorious event and the steps
which led to it, and the various lights in which it has been placed,
are already familiar to every one having the least tincture of
science. I will only add that as there is not, nor henceforth ever
can be, the slightest rivalry on the subject between these two
illustrious men--as they have met as brothers, and as such will, I
trust, ever regard each other--we have made, we could make, no
distinction between then, on this occasion. May they both long adorn
and augment our science, and add to their own fame already so high
and pure, by fresh achievements."
Adams was elected a Fellow of St. John's College, Cambridge, in 1843;
but as he did not take holy orders, his Fellowship, in accordance
with the rules then existing came to an end in 1852. In the
following year he was, however, elected to a Fellowship at Pembroke
College, which he retained until the end of his life. In 1858 he was
appointed Professor of Mathematics in the University of St. Andrews,
but his residence in the north was only a brief one, for in the same
year he was recalled to Cambridge as Lowndean Professor of Astronomy
and Geometry, in succession to Peacock. In 1861 Challis retired from
the Directorship of the Cambridge Observatory, and Adams was
appointed to succeed him.
The discovery of Neptune was a brilliant inauguration of the
astronomical career of Adams. He worked at, and wrote upon, the
theory of the motions of Biela's comet; he made important corrections
to the theory of Saturn; he investigated the mass of Uranus, a
subject in which he was naturally interested from its importance in
the theory of Neptune; he also improved the methods of computing the
orbits of double stars. But all these must be regarded as his minor
labours, for next to the discovery of Neptune the fame of Adams
mainly rests on his researches upon certain movements of the moon,
and upon the November meteors.
The periodic time of the moon is the interval required for one
circuit of its orbit. This interval is known with accuracy at the
present day, and by means of the ancient eclipses the period of the
moon's revolution two thousand years ago can be also ascertained. It
had been discovered by Halley that the period which the moon requires
to accomplish each of its revolutions around the earth has been
steadily, though no doubt slowly, diminishing. The change thus
produced is not appreciable when only small intervals of time are
considered, but it becomes appreciable when we have to deal with
intervals of thousands of years. The actual effect which is produced
by the lunar acceleration, for so this phenomenon is called, may be
thus estimated. If we suppose that the moon had, throughout the
ages, revolved around the earth in precisely the same periodic time
which it has at present, and if from this assumption we calculate
back to find where the moon must have been about two thousand years
ago, we obtain a position which the ancient eclipses show to be
different from that in which the moon was actually situated. The
interval between the position in which the moon would have been found
two thousand years ago if there had been no acceleration, and the
position in which the moon was actually placed, amounts to about a
degree, that is to say, to an arc on the heavens which is twice the
moon's apparent diameter.
If no other bodies save the earth and the moon were present in the
universe, it seems certain that the motion of the moon would never
have exhibited this acceleration. In such a simple case as that
which I have supposed the orbit of the moon would have remained for
ever absolutely unchanged. It is, however, well known that the
presence of the sun exerts a disturbing influence upon the movements
of the moon. In each revolution our satellite is continually drawn
aside by the action of the sun from the place which it would
otherwise have occupied. These irregularities are known as the
perturbations of the lunar orbit, they have long been studied, and
the majority of them have been satisfactorily accounted for. It
seems, however, to those who first investigated the question that the
phenomenon of the lunar acceleration could not be explained as a
consequence of solar perturbation, and, as no other agent competent
to produce such effects was recognised by astronomers, the lunar
acceleration presented an unsolved enigma.
At the end of the last century the illustrious French mathematician
Laplace undertook a new investigation of the famous problem, and was
rewarded with a success which for a long time appeared to be quite
complete. Let us suppose that the moon lies directly between the
earth and the sun, then both earth and moon are pulled towards the
sun by the solar attraction; as, however, the moon is the nearer of
the two bodies to the attracting centre it is pulled the more
energetically, and consequently there is an increase in the distance
between the earth and the moon. Similarly when the moon happens to
lie on the other side of the earth, so that the earth is interposed
directly between the moon and the sun, the solar attraction exerted
upon the earth is more powerful than the same influence upon the
moon. Consequently in this case, also, the distance of the moon from
the earth is increased by the solar disturbance. These instances
will illustrate the general truth, that, as one of the consequences
of the disturbing influence exerted by the sun upon the earth-moon
system, there is an increase in the dimensions of the average orbit
which the moon describes around the earth. As the time required by
the moon to accomplish a journey round the earth depends upon its
distance from the earth, it follows that among the influences of the
sun upon the moon there must be an enlargement of the periodic time,
from what it would have been had there been no solar disturbing
action.
This was known long before the time of Laplace, but it did not
directly convey any explanation of the lunar acceleration. It no
doubt amounted to the assertion that the moon's periodic time was
slightly augmented by the disturbance, but it did not give any
grounds for suspecting that there was a continuous change in
progress. It was, however, apparent that the periodic time was
connected with the solar disturbance, so that, if there were any
alteration in the amount of the sun's disturbing effect, there must
be a corresponding alteration in the moon's periodic time. Laplace,
therefore, perceived that, if he could discover any continuous change
in the ability of the sun for disturbing the moon, he would then have
accounted for a continuous change in the moon's periodic time, and
that thus an explanation of the long-vexed question of the lunar
acceleration might be forthcoming.
The capability of the sun for disturbing the earth-moon system is
obviously connected with the distance of the earth from the sun. If
the earth moved in an orbit which underwent no change whatever, then
the efficiency of the sun as a disturbing agent would not undergo any
change of the kind which was sought for. But if there were any
alteration in the shape or size of the earth's orbit, then that might
involve such changes in the distance between the earth and the sun as
would possibly afford the desired agent for producing the observed
lunar effect. It is known that the earth revolves in an orbit which,
though nearly circular, is strictly an ellipse. If the earth were
the only planet revolving around the sun then that ellipse would
remain unaltered from age to age. The earth is, however, only one of
a large number of planets which circulate around the great luminary,
and are guided and controlled by his supreme attracting power. These
planets mutually attract each other, and in consequence of their
mutual attractions the orbits of the planets are disturbed from the
simple elliptic form which they would otherwise possess. The
movement of the earth, for instance, is not, strictly speaking,
performed in an elliptical orbit. We may, however, regard it as
revolving in an ellipse provided we admit that the ellipse is itself
in slow motion.
It is a remarkable characteristic of the disturbing effects of the
planets that the ellipse in which the earth is at any moment moving
always retains the same length; that is to say, its longest diameter
is invariable. In all other respects the ellipse is continually
changing. It alters its position, it changes its plane, and, most
important of all, it changes its eccentricity. Thus, from age to age
the shape of the track which the earth describes may at one time be
growing more nearly a circle, or at another time may be departing
more widely from a circle. These alterations are very small in
amount, and they take place with extreme slowness, but they are in
incessant progress, and their amount admits of being accurately
calculated. At the present time, and for thousands of years past, as
well as for thousands of years to come, the eccentricity of the
earth's orbit is diminishing, and consequently the orbit described by
the earth each year is becoming more nearly circular. We must,
however, remember that under all circumstances the length of the
longest axis of the ellipse is unaltered, and consequently the size
of the track which the earth describes around the sun is gradually
increasing. In other words, it may be said that during the present
ages the average distance between the earth and the sun is waxing
greater in consequence of the perturbations which the earth
experiences from the attraction of the other planets. We have,
however, already seen that the efficiency of the solar attraction for
disturbing the moon's movement depends on the distance between the
earth and the sun. As therefore the average distance between the
earth and the sun is increasing, at all events during the thousands
of years over which our observations extend, it follows that the
ability of the sun for disturbing the moon must be gradually
diminishing.
[PLATE: CAMBRIDGE OBSERVATORY.]
It has been pointed out that, in consequence of the solar
disturbance, the orbit of the moon must be some what enlarged. As it
now appears that the solar disturbance is on the whole declining, it
follows that the orbit of the moon, which has to be adjusted
relatively to the average value of the solar disturbance, must also
be gradually declining. In other words, the moon must be approaching
nearer to the earth in consequence of the alterations in the
eccentricity of the earth's orbit produced by the attraction of the
other planets. It is true that the change in the moon's position
thus arising is an extremely small one, and the consequent effect in
accelerating the moon's motion is but very slight. It is in fact
almost imperceptible, except when great periods of time are
involved. Laplace undertook a calculation on this subject. He knew
what the efficiency of the planets in altering the dimensions of the
earth's orbit amounted to; from this he was able to determine the
changes that would be propagated into the motion of the moon. Thus
he ascertained, or at all events thought he had ascertained, that the
acceleration of the moon's motion, as it had been inferred from the
observations of the ancient eclipses which have been handed down to
us, could be completely accounted for as a consequence of planetary
perturbation. This was regarded as a great scientific triumph. Our
belief in the universality of the law of gravitation would, in fact,
have been seriously challenged unless some explanation of the lunar
acceleration had been forthcoming. For about fifty years no one
questioned the truth of Laplace's investigation. When a
mathematician of his eminence had rendered an explanation of the
remarkable facts of observation which seemed so complete, it is not
surprising that there should have been but little temptation to doubt
it. On undertaking a new calculation of the same question, Professor
Adams found that Laplace had not pursued this approximation
sufficiently far, and that consequently there was a considerable
error in the result of his analysis. Adams, it must be observed, did
not impugn the value of the lunar acceleration which Halley had
deduced from the observations, but what he did show was, that the
calculation by which Laplace thought he had provided an explanation
of this acceleration was erroneous. Adams, in fact, proved that the
planetary influence which Laplace had detected only possessed about
half the efficiency which the great French mathematician had
attributed to it. There were not wanting illustrious mathematicians
who came forward to defend the calculations of Laplace. They
computed the question anew and arrived at results practically
coincident with those he had given. On the other hand certain
distinguished mathematicians at home and abroad verified the results
of Adams. The issue was merely a mathematical one. It had only one
correct solution. Gradually it appeared that those who opposed Adams
presented a number of different solutions, all of them discordant
with his, and, usually, discordant with each other. Adams showed
distinctly where each of these investigators had fallen into error,
and at last it became universally admitted that the Cambridge
Professor had corrected Laplace in a very fundamental point of
astronomical theory.
Though it was desirable to have learned the truth, yet the breach
between observation and calculation which Laplace was believed to
have closed thus became reopened. Laplace's investigation, had it
been correct, would have exactly explained the observed facts. It
was, however, now shown that his solution was not correct, and that
the lunar acceleration, when strictly calculated as a consequence of
solar perturbations, only produced about half the effect which was
wanted to explain the ancient eclipses completely. It now seems
certain that there is no means of accounting for the lunar
acceleration as a direct consequence of the laws of gravitation, if
we suppose, as we have been in the habit of supposing, that the
members of the solar system concerned may be regarded as rigid
particles. It has, however, been suggested that another explanation
of a very interesting kind may be forthcoming, and this we must
endeavour to set forth.
It will be remembered that we have to explain why the period of
revolution of the moon is now shorter than it used to be. If we
imagine the length of the period to be expressed in terms of days and
fractions of a day, that is to say, in terms of the rotations of the
earth around its axis, then the difficulty encountered is, that the
moon now requires for each of its revolutions around the earth rather
a smaller number of rotations of the earth around its axis than used
formerly to be the case. Of course this may be explained by the fact
that the moon is now moving more swiftly than of yore, but it is
obvious that an explanation of quite a different kind might be
conceivable. The moon may be moving just at the same pace as ever,
but the length of the day may be increasing. If the length of the
day is increasing, then, of course, a smaller number of days will be
required for the moon to perform each revolution even though the
moon's period was itself really unchanged. It would, therefore, seem
as if the phenomenon known as the lunar acceleration is the result of
the two causes. The first of these is that discovered by Laplace,
though its value was overestimated by him, in which the perturbations
of the earth by the planets indirectly affect the motion of the
moon. The remaining part of the acceleration of our satellite is
apparent rather than real, it is not that the moon is moving more
quickly, but that our time-piece, the earth, is revolving more
slowly, and is thus actually losing time. It is interesting to note
that we can detect a physical explanation for the apparent checking
of the earth's motion which is thus manifested. The tides which ebb
and flow on the earth exert a brake-like action on the revolving
globe, and there can be no doubt that they are gradually reducing its
speed, and thus lengthening the day. It has accordingly been
suggested that it is this action of the tides which produces the
supplementary effect necessary to complete the physical explanation
of the lunar acceleration, though it would perhaps be a little
premature to assert that this has been fully demonstrated.
The third of Professor Adams' most notable achievements was connected
with the great shower of November meteors which astonished the world
in 1866. This splendid display concentrated the attention of
astronomers on the theory of the movements of the little objects by
which the display was produced. For the definite discovery of the
track in which these bodies revolve, we are indebted to the labours
of Professor Adams, who, by a brilliant piece of mathematical work,
completed the edifice whose foundations had been laid by Professor
Newton, of Yale, and other astronomers.
Meteors revolve around the sun in a vast swarm, every individual
member of which pursues an orbit in accordance with the well-known
laws of Kepler. In order to understand the movements of these
objects, to account satisfactorily for their periodic recurrence, and
to predict the times of their appearance, it became necessary to
learn the size and the shape of the track which the swarm followed,
as well as the position which it occupied. Certain features of the
track could no doubt be readily assigned. The fact that the shower
recurs on one particular day of the year, viz., November 13th,
defines one point through which the orbit must pass. The position on
the heavens of the radiant point from which the meteors appear to
diverge, gives another element in the track. The sun must of course
be situated at the focus, so that only one further piece of
information, namely, the periodic time, will be necessary to complete
our knowledge of the movements of the system. Professor H. Newton,
of Yale, had shown that the choice of possible orbits for the
meteoric swarm is limited to five. There is, first, the great
ellipse in which we now know the meteors revolve once every thirty
three and one quarter years. There is next an orbit of a nearly
circular kind in which the periodic time would be a little more than
a year. There is a similar track in which the periodic time would be
a few days short of a year, while two other smaller orbits would also
be conceivable. Professor Newton had pointed out a test by which it
would be possible to select the true orbit, which we know must be one
or other of these five. The mathematical difficulties which attended
the application of this test were no doubt great, but they did not
baffle Professor Adams.
There is a continuous advance in the date of this meteoric shower.
The meteors now cross our track at the point occupied by the earth on
November 13th, but this point is gradually altering. The only
influence known to us which could account for the continuous change
in the plane of the meteor's orbit arises from the attraction of the
various planets. The problem to be solved may therefore be attacked
in this manner. A specified amount of change in the plane of the
orbit of the meteors is known to arise, and the changes which ought
to result from the attraction of the planets can be computed for each
of the five possible orbits, in one of which it is certain that the
meteors must revolve. Professor Adams undertook the work. Its
difficulty principally arises from the high eccentricity of the
largest of the orbits, which renders the more ordinary methods of
calculation inapplicable. After some months of arduous labour the
work was completed, and in April, 1867, Adams announced his solution
of the problem. He showed that if the meteors revolved in the
largest of the five orbits, with the periodic time of thirty three
and one quarter years, the perturbations of Jupiter would account for
a change to the extent of twenty minutes of arc in the point in which
the orbit crosses the earth's track. The attraction of Saturn would
augment this by seven minutes, and Uranus would add one minute more,
while the influence of the Earth and of the other planets would be
inappreciable. The accumulated effect is thus twenty-eight minutes,
which is practically coincident with the observed value as determined
by Professor Newton from an examination of all the showers of which
there is any historical record. Having thus showed that the great
orbit was a possible path for the meteors, Adams next proved that no
one of the other four orbits would be disturbed in the same manner.
Indeed, it appeared that not half the observed amount of change could
arise in any orbit except in that one with the long period. Thus was
brought to completion the interesting research which demonstrated the
true relation of the meteor swarm to the solar system.
Besides those memorable scientific labours with which his attention
was so largely engaged, Professor Adams found time for much other
study. He occasionally allowed himself to undertake as a relaxation
some pieces of numerical calculation, so tremendously long that we
can only look on them with astonishment. He has calculated certain
important mathematical constants accurately to more than two hundred
places of decimals. He was a diligent reader of works on history,
geology, and botany, and his arduous labours were often beguiled by
novels, of which, like many other great men, he was very fond. He
had also the taste of a collector, and he brought together about
eight hundred volumes of early printed works, many of considerable
rarity and value. As to his personal character, I may quote the
words of Dr. Glaisher when he says, "Strangers who first met him were
invariably struck by his simple and unaffected manner. He was a
delightful companion, always cheerful and genial, showing in society
but few traces of his really shy and retiring disposition. His
nature was sympathetic and generous, and in few men have the moral
and intellectual qualities been more perfectly balanced."
In 1863 he married the daughter of Haliday Bruce, Esq., of Dublin and
up to the close of his life he lived at the Cambridge Observatory,
pursuing his mathematical work and enjoying the society of his
friends.
He died, after a long illness, on 21st January, 1892, and was
interred in St. Giles's Cemetery, on the Huntingdon Road, Cambridge.
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