Chapter IV: Part 4

Gravitation. _Scientific American Supplement_, July 6 and
13, 1918.

An excellent popular explanation by the leading British
disciple of Einstein.

EINSTEIN, A.

Time, Space, and Gravitation. _Science_, Garrison, 1920,
Jan. 3, n.s., vol. 51, p. 8-10.

My Theory. _Living Age._ Boston, 1920, vol. 304, p. 41-3,
Jan. 3.

FLAMMARION, CAMILLE.

Lumen. New York: Dodd, Mead and Co., 1897.

Contains nothing about Einstein but presents the relativity
of time in fantastic form.
KEYSER, C. J.

Concerning the Figure and the Dimensions of the Universe
of Space. _Science_, June 13, 1913.

LODGE, SIR OLIVER.

The New Theory of Gravity. _Nineteenth Century_, Dec.,
1919.

The Ether versus Relativity. _Fortnightly Review_, Jan.,
1920.

Admirable article by a courteous opponent.

POINCARÉ, HENRI.

Science and Method; also contained in The Foundations
of Science. New York: The Science Press, 1913.

RUSSELL, BERTRAND.

The Relativity Theory of Gravitation. _English Review_,
Dec., 1919.

A clear explanation by one of the foremost of British
philosophers.

THOMSON, J.

Deflection of Light by Gravitation and the Einstein
Theory of Relativity. _Scientific Monthly_, Garrison, N. Y.,
1920, vol. 10, p. 79-85, Jan.

VARIOUS WRITERS.

The Fourth Dimension Simply Explained. New York:
Munn and Co., 1910.

The essays submitted for a prize offered by the _Scientific_
_American_. Twenty-two mathematicians try their best to
justify the title and if they do not succeed it is not their
fault.

WETZEL, REINHARD A.

The New Relativity in Physics. _Science_, New York,
1913. New ser., vol. 38, pp. 466-474.

Explains the relativity of time with diagrams and references
to the literature.

Other articles of general interest may be found in:

_Science_: July 16, 1909; May 20, 1910; June 20, 1913;
April 24, 1914; Dec. 5, 1919.

_Scientific American Supplement_: April 7, 1917; Dec. 17,
1910.

London _Nation_: Nov. 14 and Dec. 27, 1919.

London _Times_: Nov. 8, 18, and 25, Dec. 4 and 19,
1919.

London _Nature_: Almost every number in Nov., Dec., 1919,
Jan., Feb., 1920.

New York _Times_: Nov. 7 and 16, Dec. 21, 1919.

New York _Sun_: Nov. 10, 1919.

_The New Republic_: Jan. 21, 1920.

_For the mathematical reader_:

EINSTEIN, ALBERT.

Bases physiques d’une théorie de la gravitation. Société
Astronomique de France. _Bulletin_, Paris, 1917, Tome 31,
pp. 407-411.

Die formale Grundlage der allgemeinen Relativitätstheorie.
Königlich Preussischen Akademie der Wissenschaften.
_Sitzungsberichte_, Berlin, 1904 (Juli-Dez.), pp.
1030-1085.

Die Grundlagen der allgemeinen. Relativitätstheorie. _Annalen_
_der Physik_, Leipzig, 1916, Band 49, Folge 4, p. 769.

Ist die Trägheit eines Korpers von seinem Energieinhalt
abhängig? _Annalen der Physik_, Leipzig, 1905, Band 18,
Folge 4, pp. 639-644.

Lichtgeschwindigkeit und Statik des Gravitätionsfeldes.
_Annalen der Physik_, Leipzig, 1912, Band 38, Folge 4, pp.
355-369.

Prinzipielles zur allgemeinen Relativitätstheorie. _Annalen_
_der Physik_, Leipzig, 1918, Band 55, Folge 4, pp. 241-244.

Uber das Relativitätsprinzip und die aus demselben
gezogenen Folgerungen. _Jahrbuch der Radioaktivität und_
_Elektronik_, Leipzig, 1908, Band 4, pp. 411-462.

Uber den Einfluss der Schwerkraft auf die Ausbreitung
des Lichtes. _Annalen der Physik_, Lypzig, 1911. Band 35,
pp. 898-908.

Uber die Möglichkeit einer neuen Prüfung des Relativitätsprinzips.
_Annalen der Physik_, Leipzig, 1907, Band 23,
pp. 197-208.

Uber die vom Relativitätsprinzip geforderte Trägheit der
Energie. _Annalen der Physik_, Leipzig, 1907, Band 23,
Folge 4, pp. 371-384.

Uber einen die Erzeugung und Verwandlung des Lichtes
betreffendes heuristischen Gesichtspunkt. _Annalen der_
_Physik_, Leipzig, 1905, Band 17, Folge 4, pp. 132-148.

Zum gegenwärtigen Stande des Gravitätionsproblems.
_Physikalische Zeitschrift_, Leipzig, 1913, Band 14, pp. 1249-1266.

Zum Relativitäts Problem. _Scientia_, Bologna, 1914, vol.
15, pp. 337-48.

Zur Elektrodynamik bewegter Korper. _Annalen der_
_Physik_, Leipzig, 1905, Band 17, Folge 4, pp. 891-921.

Zur Theorie der Lichterzeugung und Lichtabsorption.
_Annalen der Physik_, Leipzig, 1906, Band 20, Folge 4, pp.
199-206.

Spielen Gravitationsfelder im Aufbau der materiellen
Elementarteilchen eine wesentliche Rolle? _Sitz. Preuss._
_Akad. Wiss._, April 10, 1919.

EINSTEIN, ALBERT, and MARCEL GROSSMAN.

Entwurf einer verallgemeinerten Relativitätstheorie und
einer Theorie der Gravitation. _Zeitschrift für Mathematik_
_und Physik_, Leipzig, 1914, Band 62, pp. 225-261.

EINSTEIN, LORENTZ and MINKOWSKI.

Relativitätsprinzip, Das. Eine Sammlung von Abhandlungen.
Mit Anmerkungen von A. Sommerfeld und Vorwort
von O. Blumenthal. Leipzig: B. G. Teubner, 1913,
89 p. (_Fortschritte der mathematischen Wissenschaften in_
_Monographien_, Heft 2.)

A reprint of these three famous fundamental papers.

ABRAHAM, M.

Die neue Mechanik. _Scientia_, Bologna, 1914, vol. 15,
pp. 8-27.

Nochmals Relativität und Gravitation. Bemerkungen zu A.
Einsteins Erwiderung. _Annalen der Physik_, Leipzig, 1912,
Folge 4, vol. 39, pp. 444-448.

BACKLUND, A. V.

Zusammenstellung einer Theorie der klassischen Dynamik
und der neuen Gravitätionstheorie von Einstein. _Arkiv för_
_mathematik, astronomie, och fysik_, Stockholm, 1919, Band
14, no. 11, 64 seite.

BATEMAN, H.

General Relativity Theory. _Phil. Mag._, Feb., 1909, vol.
37.

Applies the theory to life and mind.

BRILLOUIN, MARCEL.

Propos Sceptiques au Sujet du Principe de Relativité.
_Scientia_, Bologna, 1913, vol. 13, pp. 10-26.

BROSE, HENRY L.

Einstein’s Theory of Relativity (non-math. form). Lecture
published in pamphlet by B. H. Blackwell. Noted in
_English Mechanic_, Dec. 19, 1919.

CARMICHAEL, ROBERT DANIEL.

The Theory of Relativity. _Mathematical Monographs_,
no. 12. New York: John Wiley, 1913.

COBB, CHARLES W.

Relativity. _Journal of Philosophy, Psychology, and Scientific_
_Method_, Jan. 18, 1917.

CONWAY, A. W.

Relativity. _Edin. Math. Tracts_, no. 3, London, 1913.

CROMMELIN, A. C. D.

Results of the Total Solar Eclipse of May 29 and the
Relativity Theory. _Science_, vol. 50, pp. 518-520. _Sci. Amer._
_Supp._, Dec. 6, 1919.

CUNNINGHAM, E.

Report on the Relativity Theory of Gravitation. London,
Green, 1915.

DEZUANI, ARMANDO.

Equilibrio relativo ed equazioni gravitazionali di Einstein
nel caso stazionario. _Il nuovo cimento_, Pisa, 1919, vol. 18,
pp. 5-25, July, 1919.

DONDER, T. DE.

Gravitational Tensors of Einstein’s Theory. _Science Abstracts_,
April 30, 1919.

DROSTE, J.

The Field of Moving Centers in Einstein’s Theory of
Gravitation. Koninklijke Akademie van Wetenschappen.
_Proceedings_, Amsterdam, 1916, vol. 19, pp. 447-475.

The Field of a Single Center in Einstein’s Theory of
Gravitation and the Motion of a Particle in that Field.
Koninklijke Akademie van Wetenschappen. _Proceedings_,
Amsterdam, 1916, vol. 19, pp. 197-218.

EDDINGTON, A. S.

Report on the Relativity Theory of Gravitation. London:
Fleetway Press, 1918. 91 p.

The only account of Einstein’s latest theory in English.

EDDINGTON, A. S., and OTHERS.

The Deflection of Light by Gravitation and the Einstein
Theory of Relativity. The Report of the British Eclipse
Expedition to the Royal Society. _Scientific Monthly_, Jan.,
1920.

GROSSMAN, MARCEL.

Définitions, méthodes et problèmes mathématiques relatifs
à la théorie de la gravitation. _Archives des Sciences_
_Physiques et Naturelles_, Genève, Jan.-Juin, 1914, 4 période,
Tome 37, pp. 13-19.

GUILLAUME, E.

Theory of Relativity. _Archives des Sciences_, Dec., 1918,
vol. 46.

HUMM, R. J.

Energy Equations of General Theory of Relativity. _Annalen_
_der Physik_, 1919, vol. 58.

HUNTINGTON, EDWARD V.

A new approach to the theory of relativity. Festschrift
Heinrich Weber. Leipzig, 1912, pp. 147-169.

ISHIWARA, JUN.

Zur relativistischen Theorie der Gravitation. Tohoku Imperial
University. _Science_ reports, ser. 1, Sendai, Japan,
vol. 4, pp. 111-160.

KAFKA, H.

Tensor Analysis. _Annalen der Physik_, 1919, vol. 58, pp.
1-54.

KOTTLER, FRIEDRICH.

Uber die physikalischen Grundlagen der einsteinschen
Gravitätionstheorie. _Annalen der Physik_, Leipzig, 1918,
Band 56, Folge 4, pp. 408-462.
LARMOR, J.

Essence of Physical Relativity. _Nat. Acad. Sci. Proc._,
vol. 4, Nov., 1918.

LAUE, RD. M.

Das Relativitätsprinzip. Braunschweig, 1911. 208 p.

LECORNU, LÉON.

La Mécanique. Paris: Flammarion, 1909.

LORENTZ, H. A.

Considerations élémentaires sur le principe de relativité.
_Revue générale des sciences_, Paris, 1914. Tome 25, pp.
179-186.

La gravitation. _Scientia._ Bologna, 1914, vol. 6, pp. 28-59.

Das Relativitätsprinzip. 1914.

La Gravitation. _Scientia_, Bologna, 1914, vol. 16, pp. 28-59.

On Einstein’s theory of gravitation. Koninklijke Akademie
van Wetenschappen. _Proceedings_, Amsterdam, 1917-18,
vol. 19, pp. 1341-1369; vol. 20, pp. 2-34.

On Hamilton’s principle in Einstein’s theory of gravitation.
Koninklijke Akademie van Wetenschappen. _Proceedings_,
Amsterdam, 1917, vol. 19, pp. 751-765.

LUNN, ARTHUR C.

Some functional equations in the theory of relativity.
American Mathematical Society. _Bulletin_, Lancaster, Pa.,
1919, vol. 26, pp. 26-34.

MICHELSON, A. A., and MORLEY, E. W.

The Relative Motion of the Earth and the Luminiferous
Ether. _American Journal of Science_, 1887, vol. 34, p. 333.

See also: _Astro-Physical Journal_, vol. 37, pp. 100-193.
The report of the crucial experiments that upset the idea
of a stationary ether.

MINKOWSKI, HERMANN.

Relativitätsprinzip. _Jahresbericht der Deutschen Mathematiker-Vereinigung._
Leipzig, 1915, Band, 24, pp. 1241-1244.

NORDSTRÖM, GUNNAR.

Einstein’s theory of gravitation and Herglotz’s mechanics
of continua. Koninklijke Akademie van Wetenschappen.
_Proceedings_, Amsterdam, 1917, vol. 19.

NORDSTRÖM, G.

On the Energy of the Gravitation Field in Einstein’s
Theory. Koninklijke Akademie van Wetenschappen. _Proceedings_,
Amsterdam, 1918, vol. 20, pp. 1238-1245.

PALATINI, A.

La Teoria di Relatività nel suo Sviluppo Storieo. _Scientia_,
Nov. and Dec., 1919 (in Italian and French).

PLANCK, MAX.

Zur Dynamik bewegter Systeme. Königlich Preussischen
Akademie der Wissenschaften. _Sitzungberichte_, Berlin, 1907,
pp. 542-570.

His theory.

PETZOLDT, J.

Does the Relativity Theory Exclude the Reality of Space
and Time? _Deutsche Phys. Gesell._, Dec. 30, 1918.

RITZ, W.

La gravitation. _Scientia_, Bologna, 1909, vol. 5, pp. 152-165.

RUFUS, CARL.

Relativity in astronomy. _Popular Astronomy_, Northfield,
Minn., 1918, vol. 26, pp. 160-165.

SILBERSTEIN, L.

The Theory of Relativity. London: Macmillan, 1914,
92 p.

SITTER, W. DE.

On Einstein’s theory of gravitation, and its astronomical
consequences. Royal Astronomical Society. _Monthly Notices_,
London, 1915-18, vol. 76, pp. 699-728; vol. 77, pp.
155-184; vol. 78, pp. 3-28.

On the relativity of rotation in Einstein’s theory.
Koninklijke Akademie van Wetenschappen. _Proceedings_,
Amsterdam, 1917, vol. 19, pp. 527-532.

On the relativity of inertia. Remarks concerning Einstein’s
latest hypothesis. Koninklijke Akademie van Wetenschappen.
_Proceedings_, Amsterdam, 1917, vol. 19, pp.
1217-1255.

Planetary motion and the motion of the moon according
to Einstein’s theory. Koninklijke Akademie van Wetenschappen.
_Proceedings_, Amsterdam, 1916, vol. 19, pp. 367-381.

Further Remarks on the Solutions of the Field-equations
of Einstein’s Theory of Gravitation. Koninklijke Akademie
van Wetenschappen. _Proceedings_, Amsterdam, 1918, vol. 20,
pp. 1309-1312.

ST. JOHN, CHARLES EDWARD.

The principle of generalized relativity and the displacement
of the Fraunhofer lines toward the red. Carnegie
Institution of Washington. _Contributions of the Mount_
_Wilson Solar Observatory_, Washington, vol. 7, no. 138.

TRESLIN, J.

The equations of the theory of electrons in a gravitation
field of Einstein deduced from a variation principle.
Koninklijke Akademie van Wetenschappen. _Proceedings_,
Amsterdam, 1917, Band 19, pp. 892-896.

TUNZELMAN, G. W. DE.

Relativity Theory. _Science Progress_, 1919, vol. 13.

WEYL, H.

Eine neue Erweiterung der Relativitätstheorie. _Annalen_
_der Physik_, 1919, vol. 59, pp. 100-123.

Raum, Zeit, Materie. Springer. 1918.

Zur Gravitätionstheorie. _Annalen der Physik_, 1917, vol.
54, pp. 117-145.

WILSON, EDWIN BIDWELL.

Generalized coördinates, relativity, and gravitation. _Astrophysical_
_Journal_, Chicago, 1917, vol. 45, pp. 244-253.

WILSON, WILLIAM.

Relativity and gravitation. Physical Society of London.
_Proceedings_, London, 1919, vol. 31, pp. 69-77.

WILSON and LEWIS.

The Time-Space Manifold. _Proceedings of the American_
_Academy of Arts and Sciences_, Nov., 1912, vol. 48, pp. 389-506.

THANKS

Most of the mathematical references cited above have been borrowed bodily from the book list prepared by Miss Mary E. Todd of the Science Room of the New York Public Library and published in the _Library Journal_. As soon as the Einstein craze struck New York these books were placed on a long table and it has been difficult to find a seat at this table, day or evening, ever since. At Cambridge University when Professor Eddington lectured on the Einstein theory the students waiting for the opening of the hall doors formed a cue extending half-way across Trinity Great Court. It is unusual in any university to have “standing room only” at a lecture on mathematical physics.

About half of the present volume appeared in _The Independent_ of November 29, December 7, 13, and 20, 1919, and I am indebted to Hamilton Holt, the editor, and to Karl V. S. Howland, the publisher of that magazine, for the privilege of reprinting them in book form. I am further grateful to several professors of physics, mathematics, astronomy and philosophy who have been kind enough to criticize and correct this material, but since it would not be fair to hold them responsible for my personal views and unconventional language I shall have to express my thanks to them in private.

INDEX

Bergson, Henri, 47, 51, 52

Carlyle, iv

Curvature of space, 26, 35, 38, 96

Eclipse observations, 2, 65, 72

Einstein, Albert
Postulates of, 13, 83, 111
Theory of time, 109
Theory of gravitation, 39, 58, 76, 80, 86, 93, 96, 109
Life of, 78
Works of, 116, 117

Equivalence, principle of, 14, 83, 86

Ether, 8, 11, 88, 106

Flammarion, Camille, 40

Flatland, 35, 57

Fourth dimension, 24, 34, 49

Gravitation, 68, 74, 77, 80, 86, 90

Laws, natural, 102, 109

Light, deflection of ray, 11, 62, 79, 85

Light, pressure of, 67, 93

Lodge, Sir Oliver, 2, 68, 75, 87, 88

Lorentz, 22, 111, 112, 118

Macdonald, George, 34

Maxwell, Clerk, 67, 111, 112

Mercury, orbit of, 14, 66

Michelson and Morley experiment, 11, 21, 22, 85

Minkowski, iv, 18

Mirror, images, 18

Motion picture illustrations, 31, 44, 46, 50, 53

Newton, 15, 23, 39, 66, 76, 79, 87, 90, 95

Non-Euclidean geometry, 30, 48, 57, 112

Planck, 98, 121

Poincaré, H., 88, 107

Relativity of measurements, 15, 20, 26

Relativity of motion, 4, 8, 15, 23

Relativity of time, 15, 24, 47, 51

Slade, 58, 60

Spectrum, shifting of lines of, 14, 77, 85

Theories, reception of new, 98, 101

Theory of relativity, 2, 15

Thomson, Sir Joseph, 3, 93, 94, 95

Time as fourth dimension, 30, 32, 49

Time, reversal of, 41, 44

Wells, H. G., 32, 34, 40, 52

Zöllner, 58, 60

=TRANSCRIBER’S NOTES=

Simple typographical errors have been silently corrected; unbalanced quotation marks were remedied when the change was obvious, and otherwise left unbalanced.

Punctuation and spelling were made consistent when a predominant preference was found in the original book; otherwise they were not changed.

Inconsistent hyphens left as printed.