Scientific Papers of Josiah Willard Gibbs, Volume 2

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Volume 1

Scientific Papers of Josiah Willard Gibbs, Volume 2 (1906)
by Josiah Willard Gibbs

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1890402Scientific Papers of Josiah Willard Gibbs, Volume 21906Josiah Willard Gibbs

THE

SCIENTIFIC PAPERS

OF

J. WILLARD GIBBS, Ph.D., LL.D.

FORMERLY PROFESSOR OF MATHEMATICAL PHYSICS IN YALE UNIVERSITY

IN TWO VOLUMES

VOL. II

DYNAMICS

VECTOR ANALYSIS AND MULTIPLE ALGEBRA

ELECTROMAGNETIC THEORY OF LIGHT

ETC.

LONGMANS, GREEN, AND CO.

39 PATERNOSTER ROW, LONDON

NEW YORK AND BOMBAY

1906

PREFATORY NOTE.

The present volume contains all the published papers of Professor J. Willard Gibbs except those upon Thermodynamics, which are placed in Volume I. of this collection.

In a few cases slight corrections had been made by the author in his own copies of the papers. These changes, together with the correction of obvious misprints in the originals, have been incorporated in the present edition without comment. Where for the sake of clearness it has seemed desirable to insert a word or two in a footnote or in the text itself, the addition has been indicated by enclosing it within square brackets [ ], a sign which is otherwise used only in the formulæ.

HENRY ANDREWS BUMSTEAD.

RALPH GIBBS VAN NAME.

Yale University,

New Haven,

October, 1906.

CONTENTS OF VOLUME II.
DYNAMICS.
Page
I. On the Fundamental Formulae of Dynamics, [Amer. Jour. Math., vol. ii, pp. 49–64, 1879.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		1
II. On the Fundamental Formula of Statistical Mechanics with Applications to Astronomy and Thermodynamics. (Abstract), [Proc. Amer. Assoc., vol. xxxiii, pp. 57, 58, 1884.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		16
VECTOR ANALYSIS AND MULTIPLE ALGEBRA.
III. Elements of Vector Analysis, Arranged for the Use of Students in Physics, [Not published. Printed, New Haven, pp. 1–36, 1881; pp. 37–83, 1884.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		17
IV. On Multiple Algebra. Vice-President's Address before the American Association for the Advancement of Science, [Proc. Amer. Assoc., vol. xxxv, pp. 37–66, 1886.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		91
V. On the Determination of Elliptic Orbits from Three Complete Observations, [Mem. Nat. Acad. Sci., vol. iv, part 2, pp. 79–104, 1889.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		118
VI. On the Use of the Vector Method in the Determination of Orbits. Letter to the Editor of Klinkerfues' "Thoretische Astronomie", [Hitherto unpublished.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		149
VII. On the Rôle of Quaternions in the Algebra of Vectors, [Nature, vol. xliii, pp. 511–513, 1891.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		155
VIII. Quaternions and the "Ausdehnungslehre", [Nature, vol. xliv, pp. 79–82, 1891.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		161
IX. Quaternions and the Algebra of Vectors, [Nature, vol. xlvii, pp. 463, 464, 1893.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		169
X. Quaternions and Vector Analysis, [Nature, vol. xlvii, pp. 364–367, 1893.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		173
THE ELECTROMAGNETIC THEORY OF LIGHT.
XI. On Double Refraction and the Dispersion of Colors in Perfectly Transparent Media, [Amer. Jour. Sci., ser. 3, vol. xxiii, pp. 262–275, 1882.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		182
XII. On Double Refraction in Perfectly Transparent Media which Exhibit the Phenomena of Circular Polarization, [Amer. Jour. Sci., ser. 3, vol. xxiii, pp. 460–476, 1882.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		195
XIII. On the General Equations of Monochromatic Light in Media of Every Degree of Transparency, [Amer. Jour. Sci., ser. 3, vol. xxv, pp. 107–118, 1883.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		211
XIV. A Comparison of the Elastic and the Electrical Theories of Light with Respect to the Law of Double Refraction and the Dispersion of Colors, [Amer. Jour. Sci., ser. 3, vol. xxxv, pp. 476–475, 1888.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		223
XV. A Comparison of the Electric Theory of Light and Sir William Thomson's Theory of a Quasi-labile Ether, [Amer. Jour. Sci., ser. 3, vol. xxxvii, pp. 129–144, 1889.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		232
MISCELLANEOUS PAPERS.
XVI. Reviews of Newcomb and Michelson's "Velocity of Light in Air and Refracting Media" and of Ketteler's "Theoretische Optik", [Amer. Jour. Sci., ser. 3, vol. xxxi, pp. 62–67, 1886.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		247
XVII. On the Velocity of Light as Determined by Foucault's Revolving Mirror, [Nature, vol. xxxiii, p. 582, 1886.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		253
XVIII. Velocity of Propagation of Electrostatic Force, [Nature, vol. liii, p. 509, 1896.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		255
XIX. Fourier's Series, [Nature, vol. lix, pp. 200 and 606, 1898–99.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		258
XX. Rudolf Julius Emanuel Clausius, [Proc. Amer. Acad., new series, vol. xvi, pp. 458–465, 1889.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		261
XXI. Hubert Anson Newton, [Amer. Jour. Sci., ser. 4, vol. iii, pp. 359–376, 1897.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		268