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