Bishop of Cloyne, and the professorship of astronomy thereupon became
vacant. Such was Hamilton's conspicuous eminence that,
notwithstanding he was still an undergraduate, and had only just
completed his twenty-first year, he was immediately thought of as a
suitable successor to the chair. Indeed, so remarkable were his
talents in almost every direction that had the vacancy been in the
professorship of classics or of mathematics, of English literature or
of metaphysics, of modern or of Oriental languages, it seems
difficult to suppose that he would not have occurred to every one as
a possible successor. The chief ground, however, on which the
friends of Hamilton urged his appointment was the earnest of original
power which he had already shown in a research on the theory of
Systems of Rays. This profound work created a new branch of optics,
and led a few years later to a superb discovery, by which the fame of
its author became world-wide.
At first Hamilton thought it would be presumption for him to apply
for so exalted a position; he accordingly retired to the country, and
resumed his studies for his degree. Other eminent candidates came
forward, among them some from Cambridge, and a few of the Fellows
from Trinity College, Dublin, also sent in their claims. It was not
until Hamilton received an urgent letter from his tutor Boyton, in
which he was assured of the favourable disposition of the Board
towards his candidature, that he consented to come forward, and on
June 16th, 1827, he was unanimously chosen to succeed the Bishop of
Cloyne as Professor of Astronomy in the University. The appointment
met with almost universal approval. It should, however, be noted
that Brinkley, whom Hamilton succeeded, did not concur in the general
sentiment. No one could have formed a higher opinion than he had
done of Hamilton's transcendent powers; indeed, it was on that very
ground that he seemed to view the appointment with disapprobation.
He considered that it would have been wiser for Hamilton to have
obtained a Fellowship, in which capacity he would have been able to
exercise a greater freedom in his choice of intellectual pursuits.
The bishop seems to have thought, and not without reason, that
Hamilton's genius would rather recoil from much of the routine work
of an astronomical establishment. Now that Hamilton's whole life is
before us, it is easy to see that the bishop was entirely wrong. It
is quite true that Hamilton never became a skilled astronomical
observer; but the seclusion of the observatory was eminently
favourable to those gigantic labours to which his life was devoted,
and which have shed so much lustre, not only on Hamilton himself, but
also on his University and his country.
In his early years at Dunsink, Hamilton did make some attempts at a
practical use of the telescopes, but he possessed no natural aptitude
for such work, while exposure which it involved seems to have acted
injuriously on his health. He, therefore, gradually allowed his
attention to be devoted to those mathematical researches in which he
had already given such promise of distinction. Although it was in
pure mathematics that he ultimately won his greatest fame, yet he
always maintained and maintained with justice, that he had ample
claims to the title of an astronomer. In his later years he set
forth this position himself in a rather striking manner. De Morgan
had written commending to Hamilton's notice Grant's "History of
Physical Astronomy." After becoming acquainted with the book,
Hamilton writes to his friend as follows:--
"The book is very valuable, and very creditable to its composer. But
your humble servant may be pardoned if he finds himself somewhat
amused at the title, 'History of Physical Astronomy from the Earliest
Ages to the Middle of the Nineteenth Century,' when he fails to
observe any notice of the discoveries of Sir W. R. Hamilton in the
theory of the 'Dynamics of the Heavens.'"
The intimacy between the two correspondents will account for the tone
of this letter; and, indeed, Hamilton supplies in the lines which
follow ample grounds for his complaint. He tells how Jacobi spoke of
him in Manchester in 1842 as "le Lagrange de votre pays," and how
Donkin had said that, "The Analytical Theory of Dynamics as it exists
at present is due mainly to the labours of La Grange Poisson,
Sir W. R. Hamilton, and Jacobi, whose researches on this subject
present a series of discoveries hardly paralleled for their elegance
and importance in any other branch of mathematics." In the same
letter Hamilton also alludes to the success which had attended the
applications of his methods in other hands than his own to the
elucidation of the difficult subject of Planetary Perturbations.
Even had his contributions to science amounted to no more than these
discoveries, his tenure of the chair would have been an illustrious
one. It happens, however, that in the gigantic mass of his
intellectual work these researches, though intrinsically of such
importance, assume what might almost be described as a relative
insignificance.
The most famous achievement of Hamilton's earlier years at the
observatory was the discovery of conical refraction. This was one of
those rare events in the history of science, in which a sagacious
calculation has predicted a result of an almost startling character,
subsequently confirmed by observation. At once this conferred on the
young professor a world-wide renown. Indeed, though he was still
only twenty-seven, he had already lived through an amount of
intellectual activity which would have been remarkable for a man of
threescore and ten.
Simultaneously with his growth in fame came the growth of his several
friendships. There were, in the first place, his scientific
friendships with Herschel, Robinson, and many others with whom he had
copious correspondence. In the excellent biography to which I have
referred, Hamilton's correspondence with Coleridge may be read, as
can also the letters to his lady correspondents, among them being
Maria Edgeworth, Lady Dunraven, and Lady Campbell. Many of these
sheets relate to literary matters, but they are largely intermingled
With genial pleasantry, and serve at all events to show the affection
and esteem with which he was regarded by all who had the privilege of
knowing him. There are also the letters to the sisters whom he
adored, letters brimming over with such exalted sentiment, that most
ordinary sisters would be tempted to receive them with a smile in the
excessively improbable event of their still more ordinary brothers
attempting to pen such effusions. There are also indications of
letters to and from other young ladies who from time to time were the
objects of Hamilton's tender admiration. We use the plural
advisedly, for, as Mr. Graves has set forth, Hamilton's love affairs
pursued a rather troubled course. The attention which he lavished on
one or two fair ones was not reciprocated, and even the intense
charms of mathematical discovery could not assuage the pangs which
the disappointed lover experienced. At last he reached the haven of
matrimony in 1833, when he was married to Miss Bayly. Of his married
life Hamilton said, many years later to De Morgan, that it was as
happy as he expected, and happier than he deserved. He had two sons,
William and Archibald, and one daughter, Helen, who became the wife
of Archdeacon O'Regan.
[PLATE: SIR W. ROWAN HAMILTON.]
The most remarkable of Hamilton's friendships in his early years was
unquestionably that with Wordsworth. It commenced with Hamilton's
visit to Keswick; and on the first evening, when the poet met the
young mathematician, an incident occurred which showed the mutual
interest that was aroused. Hamilton thus describes it in a letter to
his sister Eliza:--
"He (Wordsworth) walked back with our party as far as their lodge,
and then, on our bidding Mrs. Harrison good-night, I offered to walk
back with him while my party proceeded to the hotel. This offer he
accepted, and our conversation had become so interesting that when we
had arrived at his home, a distance of about a mile, he proposed to
walk back with me on my way to Ambleside, a proposal which you may be
sure I did not reject; so far from it that when he came to turn once
more towards his home I also turned once more along with him. It was
very late when I reached the hotel after all this walking."
Hamilton also submitted to Wordsworth an original poem, entitled
"It Haunts me Yet." The reply of Wordsworth is worth repeating:--
"With a safe conscience I can assure you that, in my judgment, your
verses are animated with the poetic spirit, as they are evidently the
product of strong feeling. The sixth and seventh stanzas affected me
much, even to the dimming of my eyes and faltering of my voice while
I was reading them aloud. Having said this, I have said enough. Now
for the per contra. You will not, I am sure, be hurt when I tell you
that the workmanship (what else could be expected from so young a
writer?) is not what it ought to be. . .
"My household desire to be remembered to you in no formal way.
Seldom have I parted--never, I was going to say--with one whom after
so short an acquaintance I lost sight of with more regret. I trust
we shall meet again."
The further affectionate intercourse between Hamilton and Wordsworth
is fully set forth, and to Hamilton's latest years a recollection of
his "Rydal hours" was carefully treasured and frequently referred
to. Wordsworth visited Hamilton at the observatory, where a
beautiful shady path in the garden is to the present day spoken of as
"Wordsworth's Walk."
It was the practice of Hamilton to produce a sonnet on almost every
occasion which admitted of poetical treatment, and it was his delight
to communicate his verses to his friends all round. When Whewell was
producing his "Bridgewater Treatises," he writes to Hamilton in
1833:--
"Your sonnet which you showed me expressed much better than I could
express it the feeling with which I tried to write this book, and I
once intended to ask your permission to prefix the sonnet to my book,
but my friends persuaded me that I ought to tell my story in my own
prose, however much better your verse might be."
The first epoch-marking contribution to Theoretical Dynamics after
the time of Newton was undoubtedly made by Lagrange, in his discovery
of the general equations of Motion. The next great step in the same
direction was that taken by Hamilton in his discovery of a still more
comprehensive method. Of this contribution Hamilton writes to
Whewell, March 31st, 1834:--
"As to my late paper, a day or two ago sent off to London, it is
merely mathematical and deductive. I ventured, indeed, to call it
the 'Mecanique Analytique' of Lagrange, 'a scientific poem'; and
spoke of Dynamics, or the Science of Force, as treating of 'Power
acting by Law in Space and Time.' In other respects it is as
unpoetical and unmetaphysical as my gravest friends could desire."
It may well be doubted whether there is a more beautiful chapter in
the whole of mathematical philosophy than that which contains
Hamilton's dynamical theory. It is disfigured by no tedious
complexity of symbols; it condescends not to any particular problems;
it is an all embracing theory, which gives an intellectual grasp of
the most appropriate method for discovering the result of the
application of force to matter. It is the very generality of this
doctrine which has somewhat impeded the applications of which it is
susceptible. The exigencies of examinations are partly responsible
for the fact that the method has not become more familiar to students
of the higher mathematics. An eminent professor has complained that
Hamilton's essay on dynamics was of such an extremely abstract
character, that he found himself unable to extract from it problems
suitable for his examination papers.
The following extract is from a letter of Professor Sylvester to
Hamilton, dated 20th of September, 1841. It will show how his works
were appreciated by so consummate a mathematician as the writer:--
"Believe me, sir, it is not the least of my regrets in quitting this
empire to feel that I forego the casual occasion of meeting those
masters of my art, yourself chief amongst the number, whose
acquaintance, whose conversation, or even notice, have in themselves
the power to inspire, and almost to impart fresh vigour to the
understanding, and the courage and faith without which the efforts of
invention are in vain. The golden moments I enjoyed under your
hospitable roof at Dunsink, or moments such as they were, may
probably never again fall to my lot.
"At a vast distance, and in an humble eminence, I still promise myself
the calm satisfaction of observing your blazing course in the
elevated regions of discovery. Such national honour as you are able
to confer on your country is, perhaps, the only species of that
luxury for the rich (I mean what is termed one's glory) which is not
bought at the expense of the comforts of the million."
The study of metaphysics was always a favourite recreation when
Hamilton sought for a change from the pursuit of mathematics. In the
year 1834 we find him a diligent student of Kant; and, to show the
views of the author of Quaternions and of Algebra as the Science of
Pure Time on the "Critique of the Pure Reason," we quote the
following letter, dated 18th of July, 1834, from Hamilton to Viscount
Adare:--
"I have read a large part of the 'Critique of the Pure Reason,' and
find it wonderfully clear, and generally quite convincing.
Notwithstanding some previous preparation from Berkeley, and from my
own thoughts, I seem to have learned much from Kant's own statement
of his views of 'Space and Time.' Yet, on the whole, a large part of
my pleasure consists in recognising through Kant's works, opinions,
or rather views, which have been long familiar to myself, although
far more clearly and systematically expressed and combined by him.
. . . Kant is, I think, much more indebted than he owns, or, perhaps
knows, to Berkeley, whom he calls by a sneer, 'GUTEM Berkeley'. . .
as it were, 'good soul, well meaning man,' who was able for all that
to shake to its centre the world of human thought, and to effect a
revolution among the early consequences of which was the growth of
Kant himself."
At several meetings of the British Association Hamilton was a very
conspicuous figure. Especially was this the case in 1835, when the
Association met in Dublin, and when Hamilton, though then but thirty
years old, had attained such celebrity that even among a very
brilliant gathering his name was perhaps the most renowned. A
banquet was given at Trinity College in honour of the meeting. The
distinguished visitors assembled in the Library of the University.
The Earl of Mulgrave, then Lord Lieutenant of Ireland, made this the
opportunity of conferring on Hamilton the honour of knighthood,
gracefully adding, as he did so: "I but set the royal, and therefore
the national mark, on a distinction already acquired by your genius
and labours."
The banquet followed, writes Mr. Graves. "It was no little addition
to the honour Hamilton had already received that, when Professor
Whewell returned thanks for the toast of the University of Cambridge,
he thought it appropriate to add the words, 'There was one point
which strongly pressed upon him at that moment: it was now one
hundred and thirty years since a great man in another Trinity College
knelt down before his sovereign, and rose up Sir Isaac Newton.' The
compliment was welcomed by immense applause."
A more substantial recognition of the labours of Hamilton took place
subsequently. He thus describes it in a letter to Mr. Graves of 14th
of November, 1843:--
"The Queen has been pleased--and you will not doubt that it was
entirely unsolicited, and even unexpected, on my part--'to express
her entire approbation of the grant of a pension of two hundred
pounds per annum from the Civil List' to me for scientific services.
The letters from Sir Robert Peel and from the Lord Lieutenant of
Ireland in which this grant has been communicated or referred to have
been really more gratifying to my feelings than the addition to my
income, however useful, and almost necessary, that may have been."
The circumstances we have mentioned might lead to the supposition
that Hamilton was then at the zenith of his fame but this was not
so. It might more truly be said, that his achievements up to this
point were rather the preliminary exercises which fitted him for the
gigantic task of his life. The name of Hamilton is now chiefly
associated with his memorable invention of the calculus of
Quaternions. It was to the creation of this branch of mathematics
that the maturer powers of his life were devoted; in fact he gives us
himself an illustration of how completely habituated he became to the
new modes of thought which Quaternions originated. In one of his
later years he happened to take up a copy of his famous paper on
Dynamics, a paper which at the time created such a sensation among
mathematicians, and which is at this moment regarded as one of the
classics of dynamical literature. He read, he tells us, his paper
with considerable interest, and expressed his feelings of
gratification that he found himself still able to follow its
reasoning without undue effort. But it seemed to him all the time as
a work belonging to an age of analysis now entirely superseded.
In order to realise the magnitude of the revolution which Hamilton
has wrought in the application of symbols to mathematical
investigation, it is necessary to think of what Hamilton did beside
the mighty advance made by Descartes. To describe the character of
the quaternion calculus would be unsuited to the pages of this work,
but we may quote an interesting letter, written by Hamilton from his
death-bed, twenty-two years later, to his son Archibald, in which he
has recorded the circumstances of the discovery:--
"Indeed, I happen to be able to put the finger of memory upon the year
and month--October, 1843--when having recently returned from visits
to Cork and Parsonstown, connected with a meeting of the British
Association, the desire to discover the laws of multiplication
referred to, regained with me a certain strength and earnestness
which had for years been dormant, but was then on the point of being
gratified, and was occasionally talked of with you. Every morning in
the early part of the above-cited month, on my coming down to
breakfast, your (then) little brother William Edwin, and yourself,
used to ask me, 'Well papa, can you multiply triplets?' Whereto I
was always obliged to reply, with a sad shake of the head: 'No, I
can only ADD and subtract them,'
"But on the 16th day of the same month--which happened to be Monday,
and a Council day of the Royal Irish Academy--I was walking in to
attend and preside, and your mother was walking with me along the
Royal Canal, to which she had perhaps driven; and although she talked
with me now and then, yet an UNDERCURRENT of thought was going on in
my mind which gave at last a RESULT, whereof it is not too much to
say that I felt AT ONCE the importance. An ELECTRIC circuit seemed
to CLOSE; and a spark flashed forth the herald (as I FORESAW
IMMEDIATELY) of many long years to come of definitely directed
thought and work by MYSELF, if spared, and, at all events, on the
part of OTHERS if I should even be allowed to live long enough
distinctly to communicate the discovery. Nor could I resist the
impulse--unphilosophical as it may have been--to cut with a knife on
a stone of Brougham Bridge as we passed it, the fundamental formula
which contains the SOLUTION of the PROBLEM, but, of course, the
inscription has long since mouldered away. A more durable notice
remains, however, on the Council Books of the Academy for that day
(October 16, 1843), which records the fact that I then asked for and
obtained leave to read a Paper on 'Quaternions,' at the First General
Meeting of the Session; which reading took place accordingly, on
Monday, the 13th of November following."
Writing to Professor Tait, Hamilton gives further particulars of the
same event. And again in a letter to the Rev. J. W. Stubbs:--
"To-morrow will be the fifteenth birthday of the Quaternions. They
started into life full-grown on the 16th October, 1843, as I was
walking with Lady Hamilton to Dublin, and came up to Brougham
Bridge--which my boys have since called Quaternion Bridge. I pulled
out a pocketbook which still exists, and made entry, on which at the
very moment I felt that it might be worth my while to expend the
labour of at least ten or fifteen years to come. But then it is fair
to say that this was because I felt a problem to have been at that
moment solved, an intellectual want relieved which had haunted me for
at least fifteen years before.
"But did the thought of establishing such a system, in which
geometrically opposite facts--namely, two lines (or areas) which are
opposite IN SPACE give ALWAYS a positive product--ever come into
anybody's head till I was led to it in October, 1843, by trying to
extend my old theory of algebraic couples, and of algebra as the
science of pure time? As to my regarding geometrical addition of
lines as equivalent to composition of motions (and as performed by
the same rules), that is indeed essential in my theory but not
peculiar to it; on the contrary, I am only one of many who have been
led to this view of addition."
Pilgrims in future ages will doubtless visit the spot commemorated by
the invention of Quaternions. Perhaps as they look at that by no
means graceful structure Quaternion Bridge, they will regret that the
hand of some Old Mortality had not been occasionally employed in
cutting the memorable inscription afresh. It is now irrecoverably
lost.
It was ten years after the discovery that the great volume appeared
under the title of "Lectures on Quaternions," Dublin, 1853. The
reception of this work by the scientific world was such as might have
been expected from the extraordinary reputation of its author, and
the novelty and importance of the new calculus. His valued friend,
Sir John Herschel, writes to him in that style of which he was a
master:--
"Now, most heartily let me congratulate you on getting out your
book--on having found utterance, ore rotundo, for all that labouring
and seething mass of thought which has been from time to time sending
out sparks, and gleams, and smokes, and shaking the soil about you;
but now breaks into a good honest eruption, with a lava stream and a
shower of fertilizing ashes.
"Metaphor and simile apart, there is work for a twelve-month to any
man to read such a book, and for half a lifetime to digest it, and I
am glad to see it brought to a conclusion."
We may also record Hamilton's own opinion expressed to Humphrey
Lloyd:--
"In general, although in one sense I hope that I am actually growing
modest about the quaternions, from my seeing so many peeps and vistas
into future expansions of their principles, I still must assert that
this discovery appears to me to be as important for the middle of the
nineteenth century as the discovery of fluxions was for the close of
the seventeenth."