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.