Since the time of Galileo, the relativity of motion has been a central issue in physics. But how does it apply to light? At the end of the 18th century, a Newtonian theory of the propagation of light, a natural extension of Newton’s Principia, was developed but quickly forgotten. A series of works completed the Principia with the formulation of a Galilean relativistic optics of moving bodies and the discovery of the analog of the Doppler-Fizeau effect some 60 years before Doppler, as well as many other effects and ideas that are a fascinating preamble to Einstein’s special and general relativity.

1.
Isaac
Newton
,
Philosophiae Naturalis Principia Mathematica
(London, 1687), in
I. Bernard
Cohen
and
Anne
Whitman
,
Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. A New Translation
(
Univ. of California
, Berkeley,
1999
).
2.
Alan E.
Shapiro
,
Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reflection
(
Cambridge U. P.
, Cambridge,
1993
), p.
218
; and
Jean
Eisenstaedt
, “
L’optique balistique newtonienne à l’épreuve des satellites de Jupiter
,”
Arch. Hist. Exact Sci.
50
,
117
156
(
1996
).
3.
Isaac
Newton
,
Opticks
(1704) (
Dover
, New York,
1952
).
4.
Reference 1, p.
622
.
5.
Reference 1, p.
626
.
6.
Reference 1, pp.
622
629
.
7.
Alexis-Claude
Clairaut
, “
Sur les explications Cartésiennes et Newtoniennes de la Réfraction de la Lumière
,”
Académie Royale des Sciences (Paris), Mémoires pour
1739
,
259
275
(
1741
).
8.
Jean
Eisenstaedt
,
Avant Einstein Relativité, Lumière, Gravitation
(
Seuil
, Paris,
2005
);
Jean
Eisenstaedt
, “
Light and relativity, a previously unknown eighteenth-century manuscript by Robert Blair (1748–1828)
,”
Ann. Sci.
62
,
347
376
(
2005
).
9.
Olaüs
Rœmer
, “
A demonstration concerning the motion of light, communicated from Paris, in the Journal des Savants, and here made English
,”
Philos. Trans. R. Soc. London
12
,
893
894
(
1677
).
10.
James
Bradley
, “
A letter from the Reverend Mr. James Bradley to Dr. Edmund Halley giving an account of a new discovered motion of the fix’d stars
,”
Philos. Trans. R. Soc. London
35
,
637
661
(
1728
).
11.
John
Michell
, “
On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose, by the Rev. John Michell, B. D. F. R. S. In a letter to Henry Cavendish, Esq. F. R. S. and A. S.
,”
Philos. Trans. R. Soc. London
74
,
35
57
(
1784
).
12.
See
Jed Z.
Buchwald
,
The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century
(
Univ. of Chicago
, Chicago,
1989
), pp.
111
233
.
13.
Einstein to Freundlich, August 1913; quoted in
Jean
Eisenstaedt
, “
De l’influence de la gravitation sur la propagation de la lumière en théorie newtonienne. L’archéologie des trous noirs
,”
Arch. Hist. Exact Sci.
42
,
315
386
(
1991
).
14.
See
Russell
McCormmach
, “
John Michell and Henry Cavendish: Weighing the stars
,”
Br. J. Hist. Sci.
4
,
126
155
(
1968
).
15.
Reference 11, p.
37
.
16.
It is clear that neither the concept of energy nor its conservation appear in the Principia; see
I. Bernard
Cohen
and
Anne
Whitman
, Ref. 1, pp.
119
123
. In this somewhat ahistorical approach I chose a modern view of the field and used a modern notation as well as translated concepts.
17.
See, for example, in
Herbert
Goldstein
,
Classical Mechanics
(
Addison-Wesley
, London,
1980
).
18.
Reference 11, p. 42. Michell has given a geometrical derivation of it and Laplace gives an algebraic one but without quoting Michell. Pierre-Simon Laplace, “
Beweis des Satzes, dass die anziehende Kraft bey einem Weltkörper so gross seyn könne, dass das Licht davon nicht ausströmen kann
,”
Allgemeine Geographische Ephemeriden, F. von Zach, Weimar
,
4
,
1
6
(
1799
).
19.
Pierre-Simon
Laplace
,
Exposition du Systême du Monde
(
Imprimerie du Cercle-Social
, Paris,
1796
), Vol.
2
, pp.
304
306
.
20.
See
Gary
Gibbons
, “
The man who invented black holes
,”
New Sci.
82
,
1101
(
1979
);
Simon
Schaffer
, “
John Michell and black holes
,”
J. Hist. Astron.
10
,
42
43
(
1979
); and
Jean
Eisenstaedt
in Ref. 13. The history of general relativity and especially black holes is given in Jean Eisenstaedt,
The Curious History of Relativity
.
How Einstein’s Theory of Gravity was Lost and Found Again
, translated by Arturo Sangalli (
Princeton U. P.
, Princeton, NJ,
2006
).
21.
Reference 11, p.
42
.
22.
Johann G.
von Soldner
, “
Ueber die Ablenkung eines Lichtstrals von seiner geradlinigen Bewegung, durch die Attraktion eines Weltkörpers, an welchem er nahe vorbei geht
,”
Astronomisches Jahrbuch für das Jahr
1804
,
161
172
(
1801
).
For more on the Newtonian light-deflection see
Stanley L.
Jaki
, “
Johann Georg von Soldner and the gravitational bending of light, with an English translation of his essay on it published in 1801
,”
Found. Phys.
8
,
927
950
(
1978
).
23.
See
Clifford M.
Will
, “
Henry Cavendish, Johann von Soldner, and the deflection of light
,”
Am. J. Phys.
56
,
413
415
(
1988
).
24.
Albert
Einstein
, “
Die Grundlage der allgemeinen Relativitätstheorie
,”
Ann. Phys.
49
,
769
822
(
1916
); translated as
“The foundation of the general theory of relativity,” in
The Principle of Relativity
, edited by
H. A.
Lorentz
 et al (
Dover
, New York,
1923
), pp.
111
164
.
Frank W.
Dyson
,
Arthur S.
Eddington
, and
Charles
Davidson
, “
A determination of the deflection of light by the Sun’s gravitational field from observations made at the total eclipse of May 29, 1919
,”
Philos. Trans. R. Soc. London
220
,
291
333
(
1920
).
25.
Robert
Blair
, “
A proposal for ascertaining by experiments whether the velocity of light be affected by the motion of the body from which it is emitted or reflected; and for applying instruments for deciding the question to several optical and astronomical enquiries
,” Royal Society Manuscript L & P, VIII, 182 (1786). Blair’s paper manuscript remained unpublished.
26.
Dominique François
Jean Arago
, “
Mémoire sur la vitesse de la lumière, lu à la première Classe de l’Institut le 10 décembre 1810
,”
Acad. Sci., Paris, C. R.
36
,
38
49
(
1853
).
27.

A frequency-shift always accompanies a shift in refraction and conversely.

28.
Reference 25, p.
10
.
29.
The use of an achromatic prism was then general and problematic in order to observe a “Doppler” effect. On this question, see Ref. 8, pp.
360
362
.
30.
Reference 26, p.
53
.
31.
John
Michell
, “
An Inquiry into the probable Parallax and Magnitude of the fixed Stars, from the Quantity of Light which they afford us, and the particular circumstances of their Situation. By the Rev. John Michell, B. D. F. R. S.
,”
Philos. Trans. R. Soc. London
57
,
234
264
(
1767
).
32.
Reference 11, pp.
52
53
.
33.
This derivation is only implicit in Ref. 11.
34.
Albert
Einstein
, “
Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen
,”
Jahrb. Radioakt. Elektron.
4
,
411
462
(
1907
), see pp. 458–459.
35.
Reference 11, pp.
52
57
;
see also Ref. 14, pp.
148
149
.
36.
Walter S.
Adams
, “
The relativity displacement of the spectral lines in the companion of Sirius
,”
Nati. Acad. Sci. Proc.
11
,
382
387
(
1925
).
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