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:—­