After the completion of his great book, Hamilton appeared for awhile to permit himself a greater indulgence than usual in literary relaxations.  He had copious correspondence with his intimate friend, Aubrey de Vere, and there were multitudes of letters from those troops of friends whom it was Hamilton’s privilege to possess.  He had been greatly affected by the death of his beloved sister Eliza, a poetess of much taste and feeling.  She left to him her many papers to preserve or to destroy, but he said it was only after the expiration of four years of mourning that he took courage to open her pet box of letters.

The religious side of Hamilton’s character is frequently illustrated in these letters; especially is this brought out in the correspondence with De Vere, who had seceded to the Church of Rome.  Hamilton writes, August 4, 1855:—­

“If, then, it be painfully evident to both, that under such circumstances there cannot (whatever we may both desire) be now in the nature of things, or of minds, the same degree of intimacy between us as of old; since we could no longer Talk with the same degree of unreserve on every subject which happened to present itself, but must, from the simplest instincts of courtesy, be each on his guard not to say what might be offensive, or, at least, painful to the other; yet we were once so intimate, an retain still, and, as I trust, shall always retain, so much of regard and esteem and appreciation for each other, made tender by so many associations of my early youth and your boyhood, which can never be forgotten by either of us, that (as times go) two or three very respectable friendships might easily be carved out from the fragments of our former and ever-to-be-remembered intimacy.  It would be no exaggeration to quote the words:  ’Heu! quanto minus est cum reliquis versari, quam tui meminisse!’”

In 1858 a correspondence on the subject of Quaternions commenced between Professor Tait and Sir William Hamilton.  It was particularly gratifying to the discoverer that so competent a mathematician as Professor Tait should have made himself acquainted with the new calculus.  It is, of course, well known that Professor Tait subsequently brought out a most valuable elementary treatise on Quaternions, to which those who are anxious to become acquainted with the subject will often turn in preference to the tremendous work of Hamilton.

In the year 1861 gratifying information came to hand of the progress which the study of Quaternions was making abroad.  Especially did the subject attract the attention of that accomplished mathematician, Moebius, who had already in his “Barycentrische Calculus” been led to conceptions which bore more affinity to Quaternions than could be found in the writings of any other mathematician.  Such notices of his work were always pleasing to Hamilton, and they served, perhaps, as incentives to that still closer and more engrossing labour by which he became more and more absorbed.  During the last few years of his life he was observed to be even more of a recluse than he had hitherto been.  His powers of long and continuous study seemed to grow with advancing years, and his intervals of relaxation, such as they were, became more brief and more infrequent.