Sir William Rowan Hamilton (1805-1865): Mathematical Papers

This collection consists of the mathematical papers of Sir William Rowan Hamilton published during his lifetime, transcribed and edited by David R. Wilkins. With one exception, these papers are available here in an edition based on the original published text. (The exception is the paper Remarques de M. Hamilton, Directeur de l'Observatoire de Dublin, sur un Mémoire de M. Plana inséré dans le Tome VII de la Correspondance Math.)

Hamilton's mathematical papers have also been re-published in the four volumes of The Mathematical Papers of Sir William Rowan Hamilton, edited for the Royal Irish Academy by J. L. Synge, A. W. Conway, A. J. McConnell, H. Halberstam, R. E. Ingram and B. K. P. Scaife, and published by Cambridge University Press. (Volume 4 was published by Cambridge University Press in December 2000.) These volumes also include a substantial quantity of previously unpublished papers and manuscripts of Hamilton.

The following are the papers of Sir William Rowan Hamilton available here:

• Theory of Systems of Rays
  (Transactions of the Royal Irish Academy, 15 (1828), pp. 69-174)
• Supplement to an Essay on the Theory of Systems of Rays
  (Transactions of the Royal Irish Academy, 16, part 1 (1830), pp. 4-62)
• On the Error of a received Principle of Analysis, respecting Functions which vanish with their Variables
  (Transactions of the Royal Irish Academy, 16, part 1 (1830), pp. 63-64)
• Second Supplement to an Essay on the Theory of Systems of Rays
  (Transactions of the Royal Irish Academy, 16, part 2 (1831), pp. 93-125)
• Note to a Paper on the Error of a received Principle of Analysis
  (Transactions of the Royal Irish Academy, 16, part 2 (1831), pp. 129-130)
• On a View of Mathematical Optics
  (British Association Report 1832, 2nd edition published 1835, pp. 545-547)
• On some Results of the View of a Characteristic Function in Optics
  (British Association Report 1833, published 1834, pp. 360-370)
• On a New Method of investigating the relations of Surfaces to their Normals, with results respecting the Curvatures of Ellipsoids
  (Dublin University Review (1833), pp. 653-654)
• On the Effect of Aberration in prismatic Interference
  (Philosophical Magazine, 2 (1833), pp. 191-194)
• On the undulatory Time of Passage of Light through a Prism
  (Philosophical Magazine, 2 (1833), pp. 284-287)
• Note on Mr. Potter's Reply
  (Philosophical Magazine, 2 (1833), p. 371)
• On a General Method of expressing the Paths of Light and of the Planets by the Coefficients of a Characteristic Function
  (Dublin University Review (1833), pp. 795-826)
• On the Application to Dynamics of a General Mathematical Method previously applied to Optics
  (British Association Report 1834, published 1835, pp. 513-518)
• On Conjugate Functions, or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr Graves respecting the Existence of Two independent Integers in the complete expression of an Imaginary Logarithm
  (British Association Report 1834, published 1835, pp. 519-523)
• 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, part II for 1834, pp. 247-308)
• Remarques de M. Hamilton, Directeur de l'Observatoire de Dublin, sur un Mémoire de M. Plana inséré dans le Tome VII de la Correspondance Math. (Extrait d'une Lettre)
  (Correspondance Mathématique, 8 (1834), pp. 27-30)
• Second Essay on a General Method in Dynamics
  (Philosophical Transactions of the Royal Society, part I for 1835, pp. 95-144)
• Inquiry into the Validity of a Method recently proposed by George B. Jerrard, Esq. for Transforming and Resolving Equations of Elevated Degrees
  (British Association Report 1836, published 1837, pp. 295-348)
• Calculus of Principal Relations
  (British Association Report 1836, published 1837, part 2, pp. 41-44)
• Theorems respecting Algebraic Elimination, connected with the Question of resolving in finite Terms the Equation of the Fifth Degree
  (Philosophical Magazine, 8 (1836), pp. 538-543 and 9 (1836), pp. 28-32)
• Third Supplement to an Essay on the Theory of Systems of Rays
  (Transactions of the Royal Irish Academy, 17 (1837), pp. 1-144)
• On Differences and Differentials of Functions of Zero
  (Transactions of the Royal Irish Academy, 17 (1837), pp. 235-236)
• Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time.
  (Transactions of the Royal Irish Academy, 17 (1837), pp. 293-422)
• On the Propagation of Light in Vacuo
  (British Association Report 1838, published 1839, part 2, pp. 2-6)
• On the Propagation of Light in Crystals
  (British Association Report 1838, published 1839, part 2, 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
  (Transactions of the Royal Irish Academy, 18 (1839), pp. 171-259)
• Investigations respecting Equations of of Fifth Degree
  (Proceedings of the Royal Irish Academy, 1 (1841), pp. 76-80)
• Researches on the Dynamics of Light
  (Proceedings of the Royal Irish Academy, 1 (1841), pp. 245, 267-270)
• Researches respecting Vibration connected with the Theory of Light
  (Proceedings of the Royal Irish Academy, 1 (1841), pp. 341-349)
• On Fluctuating Functions [Abstract]
  (Proceedings of the Royal Irish Academy, 1 (1841), pp. 475-477)
• 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, 19 (1841), pp. 289-294)
• On a Mode of deducing the Equation of Fresnel's Wave
  (Philosophical Magazine, 19 (1841), pp. 381-383)
• On certain discontinuous Integrals, connected with the Development of the Radical which represents the Reciprocal of the Distance between two Points
  (Philosophical Magazine, 20 (1842), pp. 288-294)
• On a Theorem in the Calculus of Differences
  (British Association Report 1843, published 1844, part 2, pp. 2-3)
• On some investigations connected with the Calculus of Probabilities
  (British Association Report 1843, published 1844, part 2, pp. 3-4)
• On Fluctuating Functions
  (Transactions of the Royal Irish Academy, 19 (1843), pp. 264-321)
• On Equations of the Fifth Degree: and especially on a certain System of Expressions connected with those Equations, which Professor Badano has lately proposed
  (Transactions of the Royal Irish Academy, 19 (1843), pp. 329-376)
• 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, 23 (1843), pp. 360-367)
• On the Composition of Forces
  (Proceedings of the Royal Irish Academy, 2 (1844), pp. 166-170)
• On a Method proposed by Professor Badano for the Solution of Algebraic Equations
  (Proceedings of the Royal Irish Academy, 2 (1844), pp. 275-276)
• On the Calculus of Probabilities
  (Proceedings of the Royal Irish Academy, 2 (1844), pp. 420-422)
• On a new Species of Imaginary Quantities connected with a theory of Quaternions
  (Proceedings of the Royal Irish Academy, 2 (1844), pp. 424-434)
• On Quaternions, or on a new System of Imaginaries in Algebra
  (Philosophical Magazine, 25 (1844), pp. 10-13, 241-246, 489-495; 26 (1845), pp. 220-24; 29 (1846), pp. 26-31, 113-122, 326-328; 30 (1847), pp. 458-461; 31 (1847) pp. 214-219, 278-293, 511-519; 32 (1848), pp. 367-374; 33 (1848), pp. 58-60; 34 (1849), pp. 294-297, 340-343, 425-439; 35 (1849) pp. 133-137, 200-204; 36 (1850) pp. 305-306)
• On a Theory of Quaternions
  (British Association Report 1844, published 1845, part 2, p. 2)
• On Symbolical Geometry
  (Cambridge and Dublin Mathematical Journal, 1 (1846), pp. 45-57, 137-154, 256-263; 2 (1947), pp. 47-52, 130-133, 204-209; 3 (1848), pp. 68-86, 220-225; 4 (1849), pp. 84-89, 105-118)
• On Quaternions
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 1-16)
• Illustrations from Geometry of the Theory of Algebraic Quaternions
  (Proceedings of the Royal Irish Academy, 3 (1847), Appendix, pp. xxxii-xxxvi)
• A Theorem on Spherical Quadrilaterals and Spherical Conics
  (Proceedings of the Royal Irish Academy, 3 (1847), p. 109)
• On the Application of the Method of Quaternions to some Dynamical Questions
  (Proceedings of the Royal Irish Academy, 3 (1847), Appendix, pp. xxxvi-l)
• Additional Applications of the Theory of Algebraic Quaternions
  (Proceedings of the Royal Irish Academy, 3 (1847), Appendix, pp. li-lx)
• On a proof of Pascal's Theorem by means of Quaternions; and on some other connected Subjects
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 273-292)
• On Theorems of Central Forces
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 308-309)
• The Hodograph, or a new Method of expressing in symbolical Language the Newtonian Law of Attraction
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 344-353)
• On a theorem of Hodographic Isochronism
  (Proceedings of the Royal Irish Academy, 3 (1847), p. 417)
• On a theorem of Anthodographic Isochronism
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 465-466)
• On the Application of the Calculus of Quaternions to the Theory of the Moon
  (Proceedings of the Royal Irish Academy, 3 (1847), pp. 507-521)
• Researches respecting Quaternions: First Series
  (Transactions of the Royal Irish Academy, 21 (1848), pp. 199-296)
• Exercises in Quaternions
  (Cambridge and Dublin Mathematical Journal, 4 (1849), pp. 161-168)
• On additional Applications of Quaternions to Surfaces of the Second Order
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 14-19)
• On Quaternions and the Rotation of a Solid Body
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 38-56)
• On the Application of Quaternions to the Determination of the Distance of any recently discovered Comet or Planet from the Earth
  (Proceedings of the Royal Irish Academy, 4 (1850), p. 75)
• On the Double Mode of Generation of an Ellipsoid
  (Proceedings of the Royal Irish Academy, 4 (1850), p. 173)
• Additional Theorems respecting certain Reciprocal Surfaces
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 192-193)
• On Theorems relating to Surfaces, obtained by the Method of Quaternions
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 306-308)
• On an Equation of the Ellipsoid
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 324-325)
• On the Inscription of certain ``Gauche'' Polygons in Surfaces of the Second Degree
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 325-326)
• On the Construction of the Ellipsoid by two Sliding Spheres
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 341-342)
• On a Theorem respecting Ellipsoids, obtained by the Method of Quaternions
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 349-350)
• On some Results obtained by the Quaternion Analysis respecting the inscription of ``gauche'' Polygons in Surfaces of the Second Order
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 380-387)
• On ``Gauche'' Polygons in Central Surfaces of the Second Order
  (Proceedings of the Royal Irish Academy, 4 (1850), pp. 541-557)
• On Continued Fractions in Quaternions
  (Philosophical Magazine, 3 (1852), pp. 371-373; 4 (1852), p. 303; 5 (1853), pp. 117-118, 236-238, 321-326)
• A Generalization of Pascal's Theorem
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 100-101)
• On the Nature and Properties of the Aconic Function of Six Vectors
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 177-186)
• On the Connection of Quaternions with Continued Fractions and Quadratic Equations
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 219-221, 299-301)
• On the Geometrical Interpretation of some Results obtained by calculation with Biquaternions
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 388-390)
• On the Geometrical Demonstration of some Theorems obtained by means of the Quaternion Analysis
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 407-415)
• A Theorem concerning Polygonic Syngraphy
  (Proceedings of the Royal Irish Academy, 5 (1853), pp. 474-475)
• On some Extensions of Quaternions
  (Philosophical Magazine, 7 (1854), pp. 492-499; 8 (1854), pp. 125-137, 261-269; 9 (1855), pp. 46-51, 280-290)
• Memorandum respecting a new System of Roots of Unity
  (Philosophical Magazine, 12 (1856), p. 446)
• On the Calculation of the Numerical Values of a certain class of Multiple and Definite Integrals
  (Philosophical Magazine, 14 (1857), pp. 375-382)
• On the Integrations of certain Equations
  (Proceedings of the Royal Irish Academy, 6 (1858), pp. 62-63)
• On the celebrated Theorem of Dupin
  (Proceedings of the Royal Irish Academy, 6 (1858), pp. 86-88)
• On some Extensions of Quaternions
  (Proceedings of the Royal Irish Academy, 6 (1858), pp. 114-115)
• On the Solution of the Equation of Laplace's Functions
  (Proceedings of the Royal Irish Academy, 6 (1858), pp. 181-185)
• Account of the Icosian Calculus
  (Proceedings of the Royal Irish Academy, 6 (1858), pp. 415-416)
• On some Quaternion Equations connected with Fresnel's wave surface
  (Proceedings of the Royal Irish Academy, 7 (1862), pp. 122-124, 163)
• On Anharmonic Co-ordinates
  (Proceedings of the Royal Irish Academy, 7 (1862), pp. 286-289, 329, 350-354)
• On Geometrical Nets in Space
  (Proceedings of the Royal Irish Academy, 7 (1862), pp. 532-582)
• Quaternion Proof of a Theorem of Reciprocity of Curves in Space
  (British Association Report 1862, published 1863, part 2, p. 4)
• Elementary Proof, that Eight Perimeters, of the Regular inscribed Polygon of Twenty Sides, exceed Twenty-five Diameters of the Circle
  (Philosophical Magazine, 23 (1862), pp. 267-269)
• 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, 24 (1862), pp. 127-128)
• On a New and General Method of Inverting a Linear and Quaternion Function of a Quaternion
  (Proceedings of the Royal Irish Academy, 8 (1864), pp. 182-183)
• On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear Operation in Quaternions
  (Proceedings of the Royal Irish Academy, 8 (1864), pp. 190-191)
• On ``Gauche'' Curves of the Third Degree
  (Proceedings of the Royal Irish Academy, 8 (1864), pp. 331-334)
• On a General Centre of Applied Forces
  (Proceedings of the Royal Irish Academy, 8 (1864), p. 394)
• On Röber's Construction of the Heptagon
  (Philosophical Magazine, 27 (1864), pp. 124-132)
• On a Theorem related to the Binomial Coefficients
  (Proceedings of the Royal Irish Academy, 9 (1867), pp. 297-302)
• On a New System of Two General Equations of Curvature
  (Proceedings of the Royal Irish Academy, 9 (1867), pp. 302-305)

Links:

• Sir William Rowan Hamilton (1805-1865)
• History of Mathematics