Great Astronomers by Robert Stawell Ball (uplifting novels .txt) 📕
Ptolemy commences with laying down the undoubted truth that the shape of the earth is globular. The proofs which he gives of this fundamental fact are quite satisfactory; they are indeed the same proofs as we give today. There is, first of all, the well-known circumstance of which our books on geography remind us, that when an object is viewed at a distance across the sea, the lower part of the object appears cut off by the interposing curved mass of water.
The sagacity of Ptolemy enabled him to adduce another argument, which, though not quite so obvious as that just mentioned, demonstrates the curvature of the earth in a very impressive manner to anyone who will take the trouble to understand it. Ptolemy mentions that travellers who went to the south
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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 deathbed, 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
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