In the year 1838 a scheme was adopted by the Royal Irish Academy for
the award of medals to the authors of papers which appeared to
possess exceptionally high merit. At the institution of the medal
two papers were named in competition for the prize. One was
Hamilton's "Memoir on Algebra, as the Science of Pure Time." The
other was Macullagh's paper on the "Laws of Crystalline Reflection
and Refraction." Hamilton expresses his gratification that, mainly
in consequence of his own exertions, he succeeded in having the medal
awarded to Macullagh rather than to himself. Indeed, it would almost
appear as if Hamilton had procured a letter from Sir J. Herschel,
which indicated the importance of Macullagh's memoir in such a way as
to decide the issue. It then became Hamilton's duty to award the
medal from the chair, and to deliver an address in which he expressed
his own sense of the excellence of Macullagh's scientific work. It
is the more necessary to allude to these points, because in the whole
of his scientific career it would seem that Macullagh was the only
man with whom Hamilton had ever even an approach to a dispute about
priority. The incident referred to took place in connection with the
discovery of conical refraction, the fame of which Macullagh made a
preposterous attempt to wrest from Hamilton. This is evidently
alluded to in Hamilton's letter to the Marquis of Northampton, dated
June 28th, 1838, in which we read:--

"And though some former circumstances prevented me from applying to
the person thus distinguished the sacred name of FRIEND, I had the
pleasure of doing justice...to his high intellectual merits...I
believe he was not only gratified but touched, and may, perhaps,
regard me in future with feelings more like those which I long to
entertain towards him."