College, and the President of the Royal Irish Academy. Three
candidates were put forward by their respective friends for the
vacant Presidency. One was Humphrey Lloyd, the son of the late
Provost, and the two others were Hamilton and Archbishop Whately.
Lloyd from the first urged strongly the claims of Hamilton, and
deprecated the putting forward of his own name. Hamilton in like
manner desired to withdraw in favour of Lloyd. The wish was strongly
felt by many of the Fellows of the College that Lloyd should be
elected, in consequence of his having a more intimate association
with collegiate life than Hamilton; while his scientific eminence was
world-wide. The election ultimately gave Hamilton a considerable
majority over Lloyd, behind whom the Archbishop followed at a
considerable distance. All concluded happily, for both Lloyd and the
Archbishop expressed, and no doubt felt, the pre-eminent claims of
Hamilton, and both of them cordially accepted the office of a
Vice-President, to which, according to the constitution of the
Academy, it is the privilege of the incoming President to nominate.
In another chapter I have mentioned as a memorable episode in
astronomical history, that Sir J. Herschel went for a prolonged
sojourn to the Cape of Good Hope, for the purpose of submitting the
southern skies to the same scrutiny with the great telescope that his
father had given to the northern skies. The occasion of Herschel's
return after the brilliant success of his enterprise, was celebrated
by a banquet. On June 15th, 1838, Hamilton was assigned the high
honour of proposing the health of Herschel. This banquet is
otherwise memorable in Hamilton's career as being one of the two
occasions in which he was in the company of his intimate friend De
Morgan.
In the year 1838 a scheme was adopted by the Royal Irish Academy for
the award of medals to the authors of papers which appeared to
possess exceptionally high merit. At the institution of the medal
two papers were named in competition for the prize. One was
Hamilton's "Memoir on Algebra, as the Science of Pure Time." The
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, and 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 anything 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.