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. 645658.]
An asterisk is prefixed to items not contained in the Royal
Society's Catalogue.

*Review of two scientific memoirs of
James MAC CULLAGH,
B.A.: National Magazine, vol. I., pp. 145149.
Dublin, August, 1830.

THEORY OF SYSTEMS OF RAYS [1824]:
Irish Academy
Transactions, XV., 1828, pp. 69174; XVI.,
1830, pp. 462; XVI., Part II., 1831,
pp. 93125; XVII., pp. 1144.
[In this XVIIth volume is published Hamilton's ``Third
Supplement,'' containing ``CONICAL REFRACTION.''
Professor Lloyd's accounts of the experiments by which he
verified Hamilton's results are contained in the numbers of the
Philosophical Magazine for February and March 1832, pp.
112 and 207, and also in the XVIIth volume (pp.
145157) of the Irish Academy Transactions, above
mentioned. A paper on Caustics had been presented to the
R. I. A., December 13, 1824: and this Paper, when recast, was
called the Theory of Systems of Rays (supra
vol. i., pp. 176 and 187).  R. P. G.]

On the Error of a received principle of Analysis, respecting
Functions which vanish with their variables: Irish
Academy Transactions, XVI., 1830, pp. 63, 64;
Part II., 1831, pp. 129, 130.

On a view of mathematical Optics: British Association
Report, 18312, pp. 545547.

*Introductory Lecture on Astronomy: Dublin University
Review, January 1833, pp. 7285.

*Review of ARAGO'S work, ``The Comet,
translated by Colonel Charles Goold, London, 1833'': Dublin
University Review, April 1833, p. 365. (Two slight
contributions entitled The Comet will be found in the
Dublin Penny Journal, December 1832, p. 207, 208, and
January 1833, pp. 223, 224.'')

On some Results of the View of a Characteristic Function in
Optics: British Association Report, 1833, pp. 360370.

*On a New Method of investigating the relations of Surfaces to
their Normals, with results respecting the Curvatures of
Ellipsoids: Dublin University Review, July 1833, pp.
6534.

On the Effect of Aberration in prismatic Interference:
Philosophical Magazine, II., 1833, pp. 191194;
Poggendorff's Annalen der Physik und Chemie,
XXIX., 1833, pp. 316318.

On the undulatory Time of Passage of Light through a Prism:
Philosophical Magazine, II., 1833, pp. 284287;
Poggendorff's Annalen der Physik und Chemie,
XXIX., 1833, pp. 323327.

Note on Mr. POTTER'S Reply respecting his experiment of
prismatic Interference: Philosophical Magazine,
II., 1833, p. 371; Poggendorff's Annalen der
Physik und Chemie, XXIX., 1833, pp. 328, 329.

*On a General Method of expressing the Paths of Light and of the
Planets, by the Coefficients of a Characteristic Function:
Dublin University Review, November 1833, pp. 795826.

On the Application to Dynamics of a General Mathematical Method
previously applied to Optics: British Association Report,
1834, pp. 513518.

On Conjugate Functions, or Algebraic Couples, as tending to
illustrate generally the doctrine of Imaginary Quantities, and as
confirming the results of Mr. [J. T.] GRAVES respecting
the existence of two independent Integers in the complete
expression of an Imaginary Logarithm: British Association
Report, 1834, pp. 519523.

ON A GENERAL METHOD IN DYNAMICS, by which the study of
the motions of all free systems of attracting or repelling points
is reduced to the search and differentiation of one central
Relation or characteristic Function: Philosophical
Transactions of the Royal Society, 1834, pp. 247308;
Quetelet's Correspondance Mathématique,
VIII., 1834, pp. 6989, 200211.

Remarques sur un mémoire de M. PLANA, Tome
VII. [sur les rayons réfractés]: Quetelet's
Correspondance Mathématique. VIII., 1834,
pp. 2730.

*Address as Secretary of the Dublin Meeting of the British
Association: British Association Report, 1835, pp.
xli.lvi.; also, Philip Dixon Hardy's Proceedings of the
Fifth Meeting of the British Association for the Advancement of
Science, Dublin, 1835, pp. 2834.

*On a new theory of Logologues; also, On a new theory of
varying Orbits: British Association Report, 1835,
Part II., p. 7.

SECOND ESSAY ON A GENERAL METHOD IN DYNAMICS:
Philosophical Transactions of the Royal Society, 1835,
pp. 95144.

Inquiry into the Validity of a method recently proposed by
G. B. JERRARD, Esq., for Transforming and Resolving
Equations of Elevated Degrees: British Association
Report, 1836, pp. 295348.

Calculus of Principal Relations: British Association
Report, 1836, Part II., pp. 4144.

Theorem connected with the Question of resolving in finite Terms
the Equation of the Fifth Degree: Philosophical
Magazine, VIII., 1836, pp. 538543; and IX.,
1836, pp. 2832.

On Differences and Differentials of functions of Zero [1831]:
Irish Academy Transactions, XVII., 1837,
pp. 235, 236; Quetelet's Correspondance
Mathématique, VIII., 1834, pp. 2357.

*Exposition of the Argument of ABEL: British
Association Report, 1837, Part II., p. 1.

*New Applications of the Calculus of Principal Relations; and
Exposition of Mr. TURNER'S theorem of odd numbers, &c.:
British Association Report, 1837, Part II., p. 1.

Theory of CONJUGATE FUNCTIONS or Algebraic Couples, with
a preliminary and elementary Essay on ALGEBRA AS THE
SCIENCE OF PURE TIME [1835]: Irish Academy
Transactions, XVII, 1837, pp. 293422.

On the Propagation of Light in vacuo: British
Association Report, 1838, part II., pp. 26.

On the Propagation of Light in Crystals: British
Association Report, 1838, part II., p. 6.

On the Argument of ABEL, respecting the impossibility of
expressing a root of any General Equation above the Fourth Degree
by any finite combination of Radicals and Rational Functions
[1837]: Irish Academy Transactions, XVIII.,
1839, pp. 171259.

Investigations respecting Equations of the Fifth Degree [May 22,
1837]: Irish Academy Proceedings, I. 1841, pp. 7680.

*Inaugural Address as President of the Royal Irish Academy
[January 8, 1838]: Irish Academy Proceedings,
I., 1841, pp. 107120.

*Address as President of the Royal Irish Academy on Professor
MAC CULLAGH'S Paper on the Laws of Crystalline Reflexion
and Refraction [June 25, 1838]: Irish Academy
Proceedings, I., 1841, pp. 212221.

On the Dynamics of Light [communicated January 14,
and February 11, 1839]: Irish Academy
Proceedings, I., 1841, pp. 245, 267270.

Notice of a singular appearance of the clouds observed on the 16th
of December, 1838 [communicated January 14, 1839]:
Irish Academy Proceedings, I., 1841, p. 249.

*Address as President of the Royal Irish Academy on
Dr. APJOHN'S researches on the Specific Heats of Gases
[February 25, 1839]: Irish Academy Proceedings,
I., 1841, pp. 276284.

Researches respecting Vibration, connected with the Theory of
Light [communicated June 24, 1839]: Irish
Academy Proceedings, I., 1841, pp. 341349.

*Address as President of the Royal Irish Academy on
Mr. PETRIE'S Paper on the History and Antiquities of
Tara Hill [June 24, 1839]: Irish Academy Proceedings,
I., 1841, pp. 350354.

On FLUCTUATING FUNCTIONS [communicated June 22,
1840]: Irish Academy Proceedings, I., 1841,
pp. 475477; Irish Academy Transactions,
XIX., 1843, pp. 264321.
See also: Supplementary Remarks on Fluctuating Functions
[communicated February 28, 1842]: Irish Academy
Proceedings, II., 1844, pp. 232238.

On a Mode of deducing the Equation of FRESNEL'S Wave:
Philosophical Magazine, XIX., 1841, pp.
3813.

*New Demonstration of FOURIER'S theorem
[communicated June 28, 1841]; Irish Academy
Proceedings, II., 1844, p. 129.

On the Focal Lengths and Aberrations of a thin Lens of Uniaxal
Crystal, bounded by Surfaces which are of Revolution about its
Axis: Philosophical Magazine, XIX., 1841,
pp. 289294.

On certain discontinuous Integrals connected with the Development
of the Radical which represents the Reciprocal of the Distance
between two Points: Philosophical Magazine,
XX., 1842, pp. 288294.

*On a mode of expressing Fluctuating or Arbitrary Functions by
mathematical formulæ: British Association Report,
1842, Part II., p. 10.

On a Theorem in the Calculus of Differences: British
Association Report, 1843, Part II., pp. 2, 3.

On some investigations connected with the Calculus of
Probabilities: British Association Report, 1843,
Part II., pp. 3, 4.

On Equations of the Fifth Degree; and especially on a certain
System of Expressions connected with those Equations which
Professor BADANO has recently proposed [1842]:
Irish Academy Transactions, XIX., 1843,
pp. 329376.
*See also communications of August 4, 1842, and
of February 27, 1843: Irish Academy Proceedings,
II., pp. 275, 276, and p. 355.

On an Expression for the Numbers of BERNOULLI by means
of a Definite Integral, and on some connected Processes of
Summation and Integration: Philosophical Magazine,
XXIII., 1843, pp. 360367.

On the Composition of Forces [communicated Nov. 8,
1841]: Irish Academy Proceedings, II., 1844,
pp. 166170.

On the Day of the Vernal Equinox at the time of the Council of
Nice [communicated May 9, 1842]: Irish Academy
Proceedings, II., 1844, pp. 249, 250.

On Dr. ROBINSON'S Table of mean Refractions
[communicated May 22, 1843]: Irish Academy
Proceedings, II., 1844, pp. 400, 401.

*Address as President of the Royal Irish Academy, on
Dr. KANE'S Researches on the Nature of Ammonia [June 26,
1843]: Irish Academy Proceedings, II., 1844,
pp. 412419.

On the Calculus of Probabilities [communicated July 31,
1843]: Irish Academy Proceedings, II., 1844,
pp. 420422.

*On a new species of Imaginary Quantities connected with the
Theory of QUATERNIONS [communicated
November 13, 1843]: Irish Academy Proceedings,
II., 1844, pp. 424434.
See Life, vol. ii., pp. 443, 444. The intimation to
the Academy of the discovery had been made on October 16, 1843].

*On approximating to the calculation of Eclipses
[communicated May 27, 1844]: Irish Academy
Proceedings, II., 1844, p. 597.

*On Quaternions [November 11, 1844]: Irish Academy
Proceedings, III., 1847, pp. 116.

*On Quaternions [June 23, 1845]: Irish Academy
Proceedings, III., 1847, p. 109.

*On Quaternions [July 20, 1846]: Irish Academy
Proceedings, III., 1847, pp. 273292.

On Quaternions: Philosophical Magazine, XXV.,
1844, pp. 1013, 2416, 48995; XXVI., 1845,
pp. 22024; XXIX., 1846, pp. 2631, 113122, 3268;
XXX., 1847, pp. 458461; XXXI., 1847, pp.
214219, 278293, 511519; XXXII., 1848, pp.
367374; XXXIII., 1848, pp. 5860; XXXIV.,
1849, pp. 294297, 340343, 425439; XXXV., 1849,
pp. 133137, 200204; XXXVI., 1850, pp. 305, 306.

On Quaternions: British Association Report, 1844,
Part II., p. 2; 1845, Part II., p. 3.

Exercises in Quaternions: Cambridge and Dublin
Mathematical Journal, IV., 1849, pp. 161168.

Researches respecting Quaternions, First Series: Irish
Academy Transactions, XXI., 1848, pp. 199296.
[See Life, Vol. II., p. 444.]

Sur les Quaternions: Nouvelles Annales de
Mathématiques, XII., 1853, pp. 275283.

On Symbolical Geometry: Cambridge and Dublin Mathematical
Journal, I., 1846, pp. 4557, 137154, 256263;
II., 1847, pp. 4752, 130133, 204209;
III., 1848, pp. 6884, 220225; IV., 1849,
pp. 8489, 105118.

On two Theorems of Central Forces [communicated
November 30, 1846]: Irish Academy Proceedings,
III., 1847, pp. 308, 309.

A new method of expressing in symbolical language the Newtonian
Law of Attraction [the Law of the Circular Hodograph;
communicated December 14, 1846]: Irish Academy
Proceedings, III., 1847, pp. 344353.

On a Theorem of Hodographic Isochronism [communicated
March 16, 1847, and May 10, 1847]: Irish Academy
Proceedings, III., 1847, pp. 417, 465, 466.

On the application of the Calculus of Quaternions to the Theory
of the Moon [communicated June 14, 1847]: Irish
Academy Proceedings, III., 1847, pp. 507520.

Illustrations from Geometry of the Theory of Algebraic
Quaternions [communicated February 10, 1845]:
Irish Academy Proceedings, III., 1847,
Appendix, pp. xxxiixxxvi.
*[Note on p. xxxi of the appendix to Vol. III.,
1847, of the Irish Academy Proceedings: `The Abstract
of Sir W. R. Hamilton's memoir on Quaternions, read on
February 10, 1845, and referred to in page 64, has not been
received for insertion in this Appendix.
`Nor have the Abstracts of Sir W. R. Hamilton's Memoirs on the
New Imaginaries, read on July 14 and 21, 1845, and referred to in
pages 111, 112 been received.'
They were printed for private circulation. Copies are deposited
with the Hamilton Papers in the Library of Trinity College,
Dublin.  R. P. G.].

On the application of the Method of Quaternions to some Dynamical
questions [communicated July 14, and July 21,
1845]: Irish Academy Proceedings, III., 1847,
Appendix, xxxvil.

*Additional applications of the Theory of Algebraic Quaternions
[communicated December 8, 1845]: Irish Academy
Proceedings, III., 1847, Appendix,
pp. lilx.

*On an Isoperimetrical Problem treated by the Calculus of
Quaternions: British Association Report, 1847,
Part II., p. 4.

*On some applications of the Calculus of Quaternions to the
Theory of the Moon: British Association Report, 1847,
Part II., p. 4.

*On additional applications of Quaternions to Surfaces of the
Second Order [communicated November 30, 1847]:
Irish Academy Proceedings, IV., 1850,
pp. 1419.

*On Quaternions and the Rotation of a Solid Body
[communicated January 10, 1848]: Irish Academy
Proceedings, IV., 1850, pp. 3856.

*On Quaternions and the determination of the distances of any
recently discovered Comet or Planet [communicated
February 28, 1848]: Irish Academy Proceedings,
IV., 1850, p. 75.

*On the New Planet Metis [communicated May 22,
1848]: Irish Academy Proceedings, IV., 1850,
p. 169.

On the Double Mode of Generation of an Ellipsoid
[communicated May 22, 1848]: Irish Academy
Proceedings, IV., 1850, p. 173.

Additional theorems respecting certain reciprocal Surfaces
[communicated June 26, 1848]: Irish Academy
Proceedings, IV., 1850, pp. 192, 193.

*On Quaternions applied to Problems respecting the construction
of a Circle touching three given Circles on a Sphere, and of a
Sphere touching four given Spheres [communicated
December 11, 1848]: Irish Academy Proceedings,
IV., 1850, p. 255.

On Theorems relating to Surfaces, obtained by the method of
Quaternions [communicated February 26, 1849]:
Irish Academy Proceedings. IV., 1850,
pp 306308.

On the Equation of the Ellipsoid [communicated April 9,
1849]: Irish Academy Proceedings, IV., 1850,
pp. 324, 325.

On the inscription of certain ``gauche'' Polygons in Surfaces of
the Second Degree [communicated April 9, 1849]:
Irish Academy Proceedings, IV., 1850,
pp. 3256.

On the construction of the Ellipsoid by two sliding spheres
[communicated April 23, 1849]: Irish Academy
Proceedings, IV., 1850, pp. 341, 342.

On a Theorem respecting Ellipsoids, obtained by the method of
Quaternions [communicated May 28, 1849]: Irish
Academy Proceedings, IV., 1850, pp. 349355.

On some results obtained by the Quaternion analysis respecting
the inscription of `gauche' Polygons in Surfaces of the Second
Order [communicated June 25, 1849]: Irish
Academy Proceedings, IV., 1850, pp. 380387.

*On some new applications of Quaternions to Geometry:
British Association Report, 1849, Part II.,
p. 1.

On ``gauche'' Polygons in central Surfaces of the Second Order
[communicated May 13, 1850]: Irish Academy
Proceedings, IV., 1850, pp. 541556.

*On Polygons inscribed on a Surface of the Second Order:
British Association Report, 1850, part II.,
p. 2.

On Continued Fractions in Quaternions: Philosophical
Magazine, III., 1852, pp. 371373; IV.,
1852, p. 303; V., 1853, pp. 117, 118, 236238,
321326.

*On a Proof from Quaternions of the celebrated Theorem of
JOACHIMSTHAL [communicated January 27, 1851]:
Irish Academy Proceedings, V., 71.

A generalization of PASCAL'S Theorem
[communicated March 16, 1851]: Irish Academy
Proceedings, V., 1853, pp. 100, 101.

On the nature and properties of the Aconic Function of six
Vectors [communicated June 23, 1851]: Irish
Academy Proceedings, V., 1853, pp. 177186.

On the connexion of Quaternions with Continued Fractions, and
Quadratic Equations [communicated December 8, 1851,
and May 24, 1852]: Irish Academy Proceedings,
V., 1853, pp. 219221, 299301.

*On Biquaternions: British Association Report, 1852,
Part II., p. 2.

On the Geometrical Interpretation of some results obtained by
calculation with Biquaternions [February 28, 1853]: Irish
Academy Proceedings, V., 1853, pp. 388390.

On the Geometrical Demonstration of some theorems by means of the
Quaternion analysis [communicated April 11, 1853]:
Irish Academy Proceedings, V., 1853,
pp. 407415.

*Theorem concerning Polygonic Syngraphy
[communicated June 13, 1853]: Irish Academy
Proceedings, V., 1853, pp. 474, 475.

*LECTURES ON QUATERNIONS:
Dublin, Hodges and Smith,
1853, pp. (64), lxxii., 736. [Supra Vol. ii.,
pp. 679685.]

*On the Integration of certain Equations [communicated
February 27, 1854]: Irish Academy Proceedings,
VI., 1858, pp. 62, 63.

On the celebrated Theorem of DUPIN
[communicated May 8, 1854]: Irish Academy
Procedings, VI., 1858, pp. 8688.

On some Extensions of Quaternions [communicated June 26,
1854]: Irish Academy Proceedings, VI., 1858,
pp. 114, 115.

On some Extensions of Quaternions: Philosophical
Magazine, VII., 1854, pp. 492499; VIII,
1854, pp. 125137, 261269; IX., 1855, pp. 4651,
280290.

*On an Extension of Quaternions: British Association
Report, 1854, Part II., p. 1.

On the Solution of the Equation of LAPLACE'S Functions
[communicated February 26, 1855]: Irish Academy
Proceedings, VI., pp. 181185.

*Symbolical Extensions of Quaternions; and Geometrical
Applications of Quaternions [communicated June 11,
1855]: Irish Academy Proceedings, VI., 1858, p. 250, 260, 311.

*On the conception of the Anharmonic Quaternion, and on its
application to the Theory of Involution in Space: British
Association Report, 1855, Part II., p. 7.

Memorandum respecting a new System of Roots of Unity [The Icosian
Calculus]: Philosophical Magazine, XII., 1856,
p. 446.

*Account of the ICOSIAN CALCULUS [communicated
November 10, 1856]: Irish Academy Proceedings,
VI., 1858, pp. 415, 416. [See also Irish
Academy Proceedings [February 9, 1857], VI., 1858,
p. 462.]

On a General Expression by Quaternions for Cones of the Third
Order [communicated May 11, 1857]: Irish Academy
Proceedings, VI., 1858, p. 506. See also Irish
Academy Proceedings [May 25, 1857], VI., 1858, p. 512.

*On a certain harmonic property of the envelope of the chord
connecting two corresponding points of the Hessian of a Cubic
Cone [communicated June 22, 1857] Irish Academy
Proceedings, VI., 1858, p. 524.

*On some applications of Quaternions to Cones of the Third
Degree: British Association Report, 1857,
Part II., p. 3.

*On the Icosian Calculus: British Association Report,
1857, Part II., p. 3.

On the Calculation of the Numerical Values of a certain class of
MULTIPLE AND DEFINITE INTEGRALS: Philosophical
Magazine, XIV., November 1857, pp. 375382.

On some Quaternion Equations connected with FRESNEL'S
wave surface for biaxal crystals [communicated
February 28, 1859 and May 9, 1859]: Irish
Academy Proceedings, VII., 1862, pp. 122124, 163.

On some Quaternion Equations connected with FRESNEL'S
wavesurface for biaxal crystals: British Association
Report, 1859, Part II., p. 248.

On some Quaternion Equations connected with FRESNEL'S
wavesurface for biaxal crystals: Natural History
Review, VI., 1859, pp. 240242, 365.
*[The Natural History Review and Quarterly Journal of
Science was published under the editorship of W. H. Harvey
and Samuel Haughton, Vol. i.vii. London and Dublin,
18541860.]

*On ANHARMONIC COORDINATES [communicated
April 9, 1860; May 28, 1860; June 25, 1860]: Irish
Academy Proceedings, VII., 1862, pp. 286289, 329,
350354.

On Anharmonic CoOrdinates: Natural History Review,
VII., 1860, pp. 242246, 325327, 506509.

*On GEOMETRICAL NETS IN SPACE [communicated
June 24, 1861]: Irish Academy Proceedings,
VII., 1862, pp. 532582.

*On Geometrical Nets in Space: British Association
Report, 1861, Part II., p. 4.

Quaternion Proof of a Theorem of Reciprocity of Curves in Space:
British Association Report, 1862, Part II.,
p. 4.

Elementary Proof that Eight Perimeters of the Regular inscribed
Polygon of Twenty Sides exceed Twentyfive Diameters of the
Circle: Philosophical Magazine, XXIII., 1862,
pp. 267269.

On a New and General Method of Inverting a Linear and Quaternion
Function of a Quaternion [communicated June 9, 1862]:
Irish Academy Proceedings, VIII., 1864,
pp. 182, 183.

On the Existence of a Symbolic and Biquadratic Equation, which is
satisfied by the Symbol of Linear Operation in Quaternions
[communicated June 23, 1862]: Irish Academy
Proceedings, VIII., 1864, pp. 190, 191.

On the Existence of a Symbolic and Biquadratic Equation, which is
satisfied by the Symbol of Linear or Distributive Operation on a
Quaternion: Philosophical Magazine, XXIV.,
1862, pp. 127, 128.

On ``Gauche'' Curves of the Third Degree [communicated
April 27, 1863]: Irish Academy Proceedings,
VIII., 1864, pp. 331334.

On a General Centre of Applied Forces [communicated
(May 25), June 22, 1863]: Irish Academy Proceedings,
VIII, 1864, p. 394.

*On the Locus of the Osculating Circle to a Curve in Space
[communicated June 22, 1863]: Irish Academy
Proceedings, VIII., 1864, p. 394.

*On the Eight Imaginary Umbilical Generatrices of a Central
Surface of the Second Order [communicated January 11,
1864]: Irish Academy Proceedings, VIII., 1864,
p. 471.

On RÖBER'S CONSTRUCTION OF THE HEPTAGON:
Philosophical Magazine, 4th Series, XXVII.,
February 1864, pp. 124132.

*NOTE, appended to a Paper by the Rev. Charles
Graves; On a Theorem related to the Binomial Coefficients
[communicated June 26, 1865]: Irish Academy
Proceedings, IX, 1867, pp. 297302.

On a New System of Two General Equations of Curvature, including
as easy consequences a new form of the Joint Differential
Equation of the Two Lines of Curvature, with a new Proof of their
General Rectangularity; and also a new Quadratic for the Joint
Determination of the Two Radii of Curvature: all deduced by
GAUSS'S Second Method, for discussing generally the
Properties of a Surface; and the latter being verified by a
Comparison of Expressions for what is called by him the Measure
of Curvature [communicated June 26, 1865]: Irish
Academy Proceedings, IX., 1867, pp. 302305.
POSTHUMOUS PUBLICATIONS

ELEMENTS OF QUATERNIONS. London: Longmans, Green, &
Co., Octavo, pp. ilix, 1762.

[ELEMENTE DER QUATERNIONEN. Deutsch von
DR. PAUL GLAN, Docent für Physik an der
Universität Berlin. Zwei Bände. Johann Ambrosius Barth,
Leipzig, 188284. I Band, pp. xxiv, 746, gr. 8°.
(Theorie der Qu.); II Band, pp. lxxiii, 436, gr. 8°.
(Anwendungen.)]

On the Elementary Conceptions of Mathematics. Seven Letters to
Viscount Adare (March and April, 1835): Hermathena,
Vol. III., pp. 469489. Dublin, 1883.

Remarks, chiefly Astronomical, on what is known as the Problem of
Hipparchus [1855]: Hermathena, Vol. IV.,
pp. 480506. Dublin, 1883.
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 Manuscriptbooks. All these
remains are, or shortly will be, deposited for reference in the
Manuscript Room of the Library of Trinity College, Dublin:

A criticism on the work of Scheffler, entitled Der
SituationsKalkul. 1856.

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.

Two Letters to Professor De Morgan on Multiple and Definite
Integrals. 96 folio pages. 1858. Vid. supra, p. 95.

Letter (with Postscript) to Andrew S. Hart, LL. D., S.F.T.C.D.,
on Anharmonic Coordinates. 280 folio pages. 1864.
Vid. supra, p. 123, also Note to p. 124.

`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.

`Gauss's Measure of Curvature of a Surface.' 2 pages,
11 articles. 1864. Vid. supra, p. 201.

`Intersections of Normals to Quadrics.' 74 pages, 262
articles, 1864. Vid p. supra, 201.

`Locus of the Vertex of a Quadric Cone having Sixpoint
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:

Allegret: Essai sur le calcul des Quaternions. Paris,
1862.

Tait: An Elementary Treatise on Quaternions. Oxford,
1867; second edition, 1873; a German translation by von Scherff,
1880, and a French translation by Plarr, 18821884.

Kelland and Tait: Introduction to Quaternions. London,
1873; second edition, 1882.

Hoüel: Eléments de la théorie des
Quaternions. Paris, 1874.

K. W. Unverzagt: Theorie der goniometrischen und
longimetrischen Quaternionen. Wiesbaden, 1876. 312 pp.

Laisant: Introduction à la méthode des
Quaternions. Paris, 1881.

Graefe: Vorlesungen über die Theorie der
Quaternionen.

Dillner (in Upsala): Versuch einer neuen Entwicklung der
Hamilton'schen Methode, genannt, ``Calculus der Quaternionen.''
(An article in the Mathematische Annalen,
XI. Band. Leipzig, 1877).

Peirce (Professor Benjamin): Linear Associative Algebra
(American Journal of Mathematics, Vol. IV.,
1881).
[The author of this Paper in a note, p. 105, makes
objection to Quaternions on the ground of the treatment of
imaginaries. A reply to this objection may, I believe, be
gathered from what will be found stated by Sir William Hamilton
in pages 578, 579 of Vol. II., and pages 84, 85 of
Vol. III. of this work, as well as passim in
the Correspondence with Professor De Morgan.  R. P. G.]
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:

Mathematische Annalen, XII., 1877, pp. 375386:
Hermann Grassmann: Der Ort der Hamilton'schen
Quaternionen in der Ausdehnungslehre.

Zeitschrift für Mathematik und Physik, Teubner,
Leipzig, criticises certain works on Quaternions in the
Literaturzeitung at the end of each volume as
follows:
 XII. Band, 1867, p. 61:

Hankel, Vorlesungen über die complexen Zahlen, und
ihre Functionen I. Theil: Theorie der complexen
Zahlensysteme. Leipzig, 1861.
 XXII. Band, 1877, p. 83 of the
Historischliterarische Abtheilung:

Unverzagt's Work mentioned above by Professor Tait.
 XXIII. Band, 1878, p. 191 of the
Historischliterarische Abtheilung:
 Unverzagt: Der Winkel als Grundlage mathematischer
Untersuchungen, 18778.
 XXIV. Band, 1879, p. 197 of the
Historischliterarische Abtheilung:

Odstrcil: Kurze Anleitung zum Rechnen mit den
Hamilton'schen Quaternionen, 1879.

Archiv der Mathematik und Physik. Leipzig, Koch.
 LXIX. Band, 1867, pp. 118.

Graefe: Einige Sätze über abwickelbare
Flächen abgeleitet mit Hülfe der Quaternionen.

Americal Journal of Mathematics, Johns Hopkins
University, Baltimore.
 II. 1879, pp. 205210:
 W. I. Stringham:
The Quaternion Formulæ for Quantification of Curves,
Surfaces, and Solids, and for Barycentres.
 IV. 1881.
 Beside Prof. Peirce's article:
Linear Associative Algebra, included in Prof. Tait's
list, this volume contains Prof. W. I. Stringham's article,
Determination of the Finite Quaternion Groups,
pp. 345357.
 VI. 1884. pp. 113:

E. W. Hyde:
Calculus of Direction and Position; and pp. 270286:
J. J. Sylvester: Lectures on the Principles of Universal
Algebra.

VII. 1885. pp. 294326:

Arthur Buchheim: A Memoir on Biquaternions.

American Academy of Arts and Sciences: Proceedings,
January 9, 1878: Lowell: Surfaces of the Second Order as
treated by Quaternions (28 pages octavo).

Giornale di Matematiche, diretto dal Prof. G.
Battaglini; Pellerano, Napoli.
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:

Laisant: Applications mécaniques du calcul des
quaternions. Paris, 1877.

Bellavitis: Calcolo dei Quaternioni di Hamilton e sua
relazione con il metodo delle equipollenze, 1858, published in
the Atti della Societa Ital. d. Scienze, Ser. 2,
Tom. i, p. 126.

Prof. Legnazzi: Aggiunte illustrative alla
commemorazione del prof. conte Guisti Bellavitis, Padova, 1881.
Chapter IV. (pp. 181227) deals with Quaternions.
Clifford, Mathematical Papers (Macmillan, London, 1882)
contains towards the close exercises on Quaternions.
[In the Introduction by Prof. Henry J. Stephen Smith,
at pp. lxiilxvi., 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 classroom.'']
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
fisicomatematicas, Catedratico di matematicas superiores en la
Universidad Nacional di Buenos Ayres, &c.; Buenos Ayres, 1887.