In my late father's Will no instructions were left as to the publication of his Writings, nor specially as to that of the Elements of Quaternions, which, but for his late fatal illness, would have been before now, in all their completeness, in the hands of the Public.
My brother, the Rev A H Hamilton, who was named Executor, being too much engaged in his clerical duties to undertake the publication, deputed this task to me.
It was then for me to consider how I could best fulfil my triple duty in this matter - First, and chiefly, to the dead; secondly, to the present public; and thirdly, to succeeding generations. I came to the conclusion that my duty was to publish the work as I found it, adding merely proof-sheets, partially corrected by my late father, and from which I removed a few typographical errors, and editing only in the literal sense of giving forth.
Shortly before my father's death, I had several conversations with him on the subject of the Elements. In these he spoke of anticipated applications of Quaternions to Electricity, and to all questions in which the idea of Polarity is involved - applications which he never in his own lifetime expected to be able fully to develop, bows to be reserved for the hands of another Ulysses. He also discussed a good deal the nature of his own forthcoming Preface; and I may intimate that, after dealing with its more important topics, he intended to advert to the great labour which the writing of the Elements had cost him - labour both mental and mechanical; as, besides a mass of subsidiary and unprinted calculations, he wrote out all the manuscript, and corrected the proof-sheets, without assistance.
And here I must gratefully acknowledge the generous act of the Board of Trinity College, Dublin, in relieving us of the remaining pecuniary liability, and thus incurring the main expense, of the publication of this volume. The announcement of their intention to do so, gratifying as it was, surprised me the less, when I remembered that they had, after the publication of my father's former book, Lectures on Quaternions, defrayed its entire cost; an extension of their liberality beyond what was recorded by him at the end of his Preface to the "Lectures," which doubtless he would have acknowledged, had be lived to complete the Preface of the Elements.
He intended also, I know, to express his sense of the care bestowed upon the typographical correctness of this volume by Mr M H Gill of the University Press, and upon the delineation of the figures by the Engraver, Mr Oldham.
I annex the commencement of a Preface, left in manuscript by my father, and which he might possibly have modified or rewritten. Believing that I have thus best fulfilled my part as trustee of the unpublished Elements, I now place them in the hands of the scientific public.
William Edwin Hamilton.
1st January 1866.
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