The Mathematical Papers of Sir William Rowan Hamilton

, by William Rowan Hamilton , Edited by B. K. P. Scaife

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ISBN: 9780521592161 | 052159216X
Cover: Hardcover
Copyright: 2/5/2001

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This fourth and final volume of The Collected Papers of Sir William Rowan Hamilton (1805–1865) contains three previously unpublished and important manuscripts, namely Systems of Rays and two lengthy letters to de Morgan (on definite integrals) and Hart (on anharmonic coordinates). In addition the volume contains reprinted papers on geometry, analysis, astronomy, probability and finite differences, as well as a collection of papers on various topics. A cumulative index for all four volumes is provided, as well as a CD containing all four volumes of the Collected Papers.

Preface

PART I. MANUSCRIPTS

Systems of Rays. Part Third

(31)

Two Letters to Augustus de Morgan (1858)

(145)

Letter to Hart on Anharmonic Coordinates (1860)

179

(597)

PART II. GEOMETRY

On Symbolical Geometry (1846-49)

[Cambridge and Dublin Mathematical Journal, 1, 45--57, 137--154, 256--263 (1846); 2, 47--52, 130--133, 204--209 (1847); 3, 68--84, 220--225 (1848); 4, 84--89, 105--118 (1849).]

431

(70)

On some new applications of Quaternios to Geometry (1849)

[British Association Report 1849, Part II., p. 1.]

501

(1)

On Polygons inscribed on a Surface of the Second Order (1850)

[British Association Report 1850, Part II., p. 2.]

502

(1)

Symbolical Extensions of Quaternions; and Geometrical Applications of Quaternions (1855)

[Proceddings of the Royal Irish Academy 6, 250, 260, 311, (1858).]

503

(1)

On a General Expression by Quaternions for Cones of the Third Order (1857)

[Proceedings of the Royal Irish Academy 6, 506, 512 (1858).]

504

(1)

On a certain harmonic property of the envelope of the chord connecting two corresponding points of the Hessian of a Cubic Cone (1857)

[Proceedings of the Royal Irish Academy 6, 524 (1858).]

505

(1)

On some applications of Quaternions to Cones of the Third Degree (1857)

[British Association Report 1857, Part II., p. 3.]

506

(1)

On Anharmonic Co-ordinates (1860)

[Proccedings of the Royal Irish Academy 7, 286--289, 329, 350--354 (1862).]

507

(9)

On Geometrical Nets in Space (1861)

[Proccedings of the Royal Irish Academy 7, 532--582 (1862).]

516

(45)

On Geometrical Nets in Space (1861)

[British Association Report 1861, Part II., p. 4.]

561

(1)

Elementary Proof that Eight Perimeters of the Regular inscribed Polygon of Twenty Sides exceed Twenty-five Diameters of the Circle (1862)

[Philosophical Magazine (4S), 23, 267-269 (1862).]

562

(2)

On the Locus of the Osculating Circle to a Curve in Space (1863)

[Proceedings of the Royal Irish Academy 8, 394 (1864).]

564

(1)

On the Eight Imaginary Umbilical Generatrices of a Central Surface of the Second Order (1864)

[Proceedings of the Royal Irish Academy 8, 471 (1864).]

565

(1)

On Rober's Construction of the Heptagon (1864)

[Philosophical Magazine (4S), 27, 124-132 (1864).]

566

(8)

On a New System of Two General Equations of Curvature (1865)

[Proceedings of the Royal Irish Academy 9, 302-305 (1867).]

574

(7)

PART III. ANALYSIS

On the Error of a received Principle of Analysis, respecting Functions which vanish with their Variables (1830)

[Transactions of the Royal Irish Academy 16, 63-64 (1831).]

581

(2)

Note on a Paper on the Error of a received Principle of Analysis (1831)

[Transactions of the Royal Irish Academy 16, 129-130 (1831).]

583

(1)

On Fluctuating Functions (1840)

[Proceedings of the Royal Irish Academy 1, 475-477 (1841).]

584

(2)

On Fluctuating Functions (1840)

[Transactions of the Royal Irish Academy 19, 264-321 (1843).]

586

(45)

Supplementary Remarks on Fluctuating Functions (1842)

[Proceedings of the Royal Irish Academy 2, 232-238 (1844). (Identical with pp. 317-321 of No. XXII.)]

631

(1)

New Demonstration of Fourier's theorem (1841)

[Proceedings of the Royal Irish Academy 2, 129 (1844).]

632

(1)

On certain discontinuous Integrals connected with the Development of the Radical which represents the Reciprocal distance between two Points (1842)

[Philosophical Magazine (3S), 20, 288-294 (1842).]

633

(7)

On a mode of expressing Fluctuating or Arbitrary Functions by mathematical formulae (1842)

[British Association Report 1842, Part II., p. 10.]

640

(1)

On an Expression for the Numbers of Bernoulli by means of a Definite Integral, and on some connected Processes of Summation and Integration (1843)

[Philosophical Magazine (3S), 13, 360-367 (1843).]

641

(6)

On the Integrations of certain Equations (1854)

[Proceedings of the Royal Irish Academy 6, 62-63 (1858).]

647

(2)

On the Solution of the Equation of Laplace's Functions (1855)

[Proceedings of the Royal Irish Academy 6, 181-185 (1858).]

649

(4)

On the Calculation of Numerical Values of a certain class of Multiple and Definite Integrals (1857)

[Philosophical Magazine (4S), 14, 375-382 (1857).]

653

(10)

PART IV. ASTRONOMY

Introductory Lecture on Astronomy (1832)

[Dublin University Review 1, 72-85 (1833).]

663

(10)

The Comet (1832)

[Dublin Penny Journal. 207, 208 (December 1832); and 223, 224 (January 1833).]

673

(3)

Review of Arago's work, ``The Comet'', translated by Colonel Charles Gold, London, 1833 (1833)

Dublin University Review 1, 365-372 (1833).]

676

(5)

On the Day of the Vernal Equinox at the time of the Council of Nice (1842)

[Proceedings of the Royal Irish Academy 2, 249-250 (1844).]

681

(1)

On approximating to the calculation of Eclipses (1844)

[Proceedings of the Royal Irish Academy 2, 597 (1844).]

682

(1)

On the New Planet. Metis (1848)

[Proceedings of the Royal Irish Academy 4, 169 (1850).]

683

(1)

Remarks, chiefly Astronomical, on what is known as the Problem of Hipparchus (1855)

[Hermathena (Dublin) 4, 480-506 (1883).]

684

(17)

PART V: PROBABILITY AND FINTTE DIFFERENCES

On Differences and Differentials of Functions of Zero (1831)

[Transactions of the Royal Irish Academy 17, 235-236 (1830). Translation in Quetelet's Correspondance Mathematique et Physique 8, 235-237 (1834).]

701

(2)

On a Theorem in the Calculus of Differences (1843)

[British Association Report 1843, Part II., pp. 2-3.]

703

(2)

On the Calculus of Probabilities (1843)

[Proceedings of the Royal Irish Academy 2, 420-422 (1844).]

705

(2)

On some investigations connected with the Calculus of Probabilities (1843)

[British Association Report 1843. Part II., pp. 3-4.]

707

(4)

PART VI. MISCELLANEOUS

On the double refraction of light according to the principles of Fresnel (Review of two scientific memoirs of James MacCullagh B.A.) (1830)

[National Magazine 1, pp. 145-149. Dublin. August 1830.]

711

(5)

Address as Secretary of the Dublin Meeting of the British Association (1835)

[British Association Report 1835, pp. xli-lvi.]

716

(12)

On a new theory of Logologues: also On a new theory of varying orbits; and Explanation of the method of investigation pursued by Mr G.B. Jerrard for accomplishing the solution of equations of the fifth and of higher degrees (1835)

[British Association Report 1835, Part II., p.7.]

728

(1)

New Application of the Calculus of Principal relations; and Exposition of Mr. Turner's theorem respecting the series of odd numbers, and the cubes and other powers of the natural numbers (1837)

[British Association Report 1837, Part II., p. 1.]

729

(1)

Inaugural Address as President of the Royal Irish Academy (1838)

[Proceedings of the Royal Irish Academy 1, 107-120 (1841).]

730

(9)

Address as President of the Royal Irish Academy on Professor Mac-Cullagh's Paper on the Laws of Crystalline Reflexion and Refraction (1838)

[Proceedings of the Royal Irish Academy 1, 212-221 (1841).]

739

(6)

Notice of a singular appearance of the clouds observed on the 16th of December, 1838 (1839)

[Proceedings of the Royal Irish Academy 1, 249 (1841).]

745

(1)

Address as President of the Royal Irish Academy on Dr. Apjohn's researches on the Specific Heat of Gases (1839)

[Proceedings of the Royal Irish Academy 1, 276-284 (1841).]

746

(6)

Address as President of the Royal Irish Academy on Mr. Petrie's Paper on the History and Antiquities of Tara Hill (1839)

[Proceedings of the Royal Irish Academy 1, 350-354 (1841).]

752

(3)

On Dr. Robinson's Table of Mean Refractions (1843)

[Proceedings of the Royal Irish Academy 2, 400-401 (1844).]

755

(1)

Address as President of the Royal Irish Academy on Dr. Kane's Researches on the Natural of Ammonia (1839)

[Proceedings of the Royal Irish Academy 2, 411-419 (1844).]

756

(6)

Sir W. Rowan Hamiltion on the Elementary Conceptions of Mathematics (Seven Letters to Viscount Adare (March and April, 1835))

[Hermathena (Dublin) 3, 469-489 (1879).]

762

(11)

Address to Academy of Sir W.R. Hamilton on Retiring from the Presidency (1846)

[Proceedings of the Royal Irish Academy 3, 199-201 (1846).]

773

(2)

Obituary Notice of Sir W.R. Hamilton (1865)

[Proceedings of the Royal Irish Academy 9, 383 (1867).]

775

(1)

List of the works of Sir William Rowan Hamilton in approximate Chronological order

776

(19)

Index for this volume

795

(6)

Combined index for all four volumes

801

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The Mathematical Papers of Sir William Rowan Hamilton

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