SIR WILLIAM ROWAN HAMILTON, LL. D., M. R. I. A.,

D. C. L. CANTAB.;

FELLOW OF THE AMERICAN SOCIETY OF ARTS AND SCIENCES;

OF THE SOCIETY OF ARTS FOR SCOTLAND; OF THE ROYAL ASTRONOMICAL SOCIETY OF LONDON; AND OF THE
ROYAL NORTHERN SOCIETY OF ANTIQUARIES AT COPENHAGEN:
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE;

HONORARY OR CORRESPONDING MEMBER OF THE IMPERIAL OR ROYAL ACADEMIES OF ST. PETERSBURGH,
BERLIN, AND TURIN; OF THE ROYAL SOCIETIES OF EDINBURGH AND DUBLIN ;
OF THE NATIONAL ACADEMY OF THE UNITED STATES;

OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY; THE NEW YORK HISTORICAL SOCIETY;

THE SOCIETY OF NATURAL SCIENCES AT LAUSANNE; THE PHILOSOPHICAL SOCIETY OF VENICE:
AND OF OTHER SCIENTIFIC SOCIETIES IN BRITISH AND FOREIGN COUNTRIES;
ANDREWS' PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF DUBLIN ;
AND ROYAL ASTRONOMER OF IRELAND.

INGEGNERI

EDITED BY HIS SON,

WILLIAM EDWIN HAMILTON, A. B. T. C. D., C. E.

DEGLI

BLIOTECA

LIZABORAVAODVE

10418

LONDON:

LONGMANS, GREEN, & CO.

DUBLIN:

Printed at the University Press,

BY M. H. GILL.

TO THE

RIGHT HONORABLE WILLIAM EARL OF ROSSE,

CHANCELLOR OF THE UNIVERSITY OF DUBLIN,

This Volume

IS, BY PERMISSION, DEDICATED,

BY

THE EDITOR.

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 develope, 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