Great Astronomers by Robert Stawell Ball (best ereader for students .txt) 📖

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 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