List of Papers, Memoirs, Addresses, and Books published by Sir William Rowan Hamilton, and of Notices of Communications.

Robert Perceval Graves
[Life of Sir William Rowan Hamilton, Vol. III, pp. 645-658.]

An asterisk is prefixed to items not contained in the Royal Society's Catalogue.


AS AN ADDENDUM to the foregoing List, it may here be stated that there remain in manuscript the following Papers by Sir W. R. Hamilton, considerable both for their extent and importance; and other mathematical investigations of value may probably be found in his numerous Manuscript-books. All these remains are, or shortly will be, deposited for reference in the Manuscript Room of the Library of Trinity College, Dublin:-

  1. A criticism on the work of Scheffler, entitled Der Situations-Kalkul. 1856.
  2. An extension by means of Quaternions of some propositions laid down by Gauss in his Disquisitiones Arithmeticae. 1856. As to Nos. 1 and 2 vid. supra, p. 52.
  3. Two Letters to Professor De Morgan on Multiple and Definite Integrals. 96 folio pages. 1858. Vid. supra, p. 95.
  4. Letter (with Postscript) to Andrew S. Hart, LL. D., S.F.T.C.D., on Anharmonic Co-ordinates. 280 folio pages. 1864. Vid. supra, p. 123, also Note to p. 124.
  5. `Lines of Curvature and Curvatures of Surfaces, partly by Quaternions, partly by the Methods of Monge and Dupin.' 38 pages, 130 articles. 1864. Vid. supra, p. 201.
  6. `Gauss's Measure of Curvature of a Surface.' 2 pages, 11 articles. 1864. Vid. supra, p. 201.
  7. `Intersections of Normals to Quadrics.' 74 pages, 262 articles, 1864. Vid p. supra, 201.
  8. `Locus of the Vertex of a Quadric Cone having Six-point contact with a Curve in Space.' 48 pages, 224 particles. Vid. supra, p. 201.

I TRANSFER from the conclusion of Professor Tait's article Quaternions,in the ninth Edition of the Encyclopædia Britannica, the following list of works on the subject:-

To this list Prof. Tait adds:-

``Sylvester and others have recently published extensive contributions to the subject, including quaternions under the general class matrix, and have developed much farther than Hamilton lived to do the solution of equations in quaternions.''

Without any pretension to rendering complete the above bibliography I here set down some further references as likely to be useful to the student:-

Vol. XX. contains a paper by Dino Padelletti, entitled, Principii della Teoria dei Quaternioni elementarmente espositi (47 pages).

Extract from the introductory Section: - ``Il calcolo dei Quaternioni mi sembra in fatti degno di essere maggiormente conosciuto ed apprezzato fra noi: esso fornisce un mezzo efficace per le ricerche geometriche e meccaniche, specialmente adesso che i metodi geometriche tendono a prevalere sempre più nel campo della Meccanica razionale, l'algoritmo hamiltoniano sembra naturalmente indicato per tradurre i teoremi meccanici in formule concise e di facile interpretazione.''

``The Calculus of Quaternions seem to me, in fact, worthy of being more known and appreciated among us; it furnishes an instrument efficacious in carrying on geometrical and mechanical researches, and especially now that geometrical methods tend to prevail more and more in the field of rational Mechanics, the Hamiltonian algorithm seems naturally indicated for the expression of mechanical theorems in formulæ at once concise and of easy interpretation.''

Professor Padelletti mentions some studies in Quaternions: all of them have been named above except the three which here follow:

Clifford, Mathematical Papers (Macmillan, London, 1882) contains towards the close exercises on Quaternions.

[In the Introduction by Prof. Henry J. Stephen Smith, at pp. lxii-lxvi., will be found some estimate of the comparative merits of the Ausdehnungslehre of Grassmann and the Quaternions of Hamilton. For Hamilton's own statement of the position of Quaternions in reference to the Ausdehnungslehre see LECTURES ON QUATERNIONS, Preface (p. 62).]

A.S. Hardy, Ph. D.: Elements of Quaternions, second edition, revised, 240 pp., 8vo.

[Dr. Hardy is Professor of Mathematics at Dartmouth College, U.S.A. ``The Chief aim has been to meet the wants of beginners in the class-room.'']

Elementos de Calulo de los Cuaterniones y sus Aplicaciones principales á la Geometria, al Análisis, y á la Mecanica, por Valentin Balbin, Doctor en Ciencias fisico-matematicas, Catedratico di matematicas superiores en la Universidad Nacional di Buenos Ayres, &c.; Buenos Ayres, 1887.