Download Early Estimates of the Velocity of Light

Early
of
Estimates
Velocity
of
By CARL B.
the
Light
BOYER
HE astronomical methods by which OLE ROEMERand JAMESBRADLEY
demonstratedthe finite velocity of light are familiar portions of the
scientific tradition. With respect to the early estimates of the speed of
to
which these methods led, however, there is in the history of science
light
an astonishing degree of uncertainty and inconsistency. It is the intention
here to point out the numerical values proposed by ROEMER and BRADLEY
and by their contemporaries and successors, indicating incidentally the
probable origin of the present state of confusion in this connection.'
Speculation as to whether light is propagated in time or is transmitted
instantaneously appears to have arisen as a part of ancient scientific investigation. However, the philosophical and mathematical methods of Greek
science were inadequate either to demonstrate the fact of the finite velocity
of light, or, a fortiori, to furnish an estimate for this speed. Consequently
orthodox scientific thought for almost two thousand years following ARISTOTLE
maintained that light is transmitted instantaneously.
It was during the seventeenth century of our era that an increasing enthusiasm for the experimental method led to renewed suggestions that the
velocity of light might be measurably finite. GALILEOin this connection
went so far as to carry out what he hoped might be an experimentumcrucis
in the Baconian sense. His famous effort to detect a delay in the transmission
of light signals between two observers failed when conducted over a distance
of less than a mile.2 GALILEOsaid that this indicated that the propagation
was extraordinarily rapid or momentary. He felt that if the experiment
should fail also for observers separated by a distance of two or three miles,
then one might "safely conclude that the propagation of light is instantaneous."3
1
As originally written the scope of this article was somewhat more comprehensive and included a
brief summary of the historical background o6 ROEMER'S
discovery and of the reception with which it
met on the part of his contemporaries. Mr. I BERNARDCOHENthen apprised me of his far more extensive account of the work of ROEMER
contained in an article, "The First Determination of the Velocity
of Light," Isis, XXXI (1940), 327-79, which was about to appear. Mr. COHENkindly allowed me to
read the proof sheets of this article so that I might rewrite my own work in the light of his. This made it
possible for me to avoid an excessive duplication of such material as he had already presented and at the
same time to take advantage of certain suggestions contained in his valuable paper.
2 GALILEOGALILEI, Dialogues
Concerning Two New Sciences (Trans. by HENRY CREWand ALFONSO
DE SALVIO,New York, 1914), pp. 42-43.
3 Ibid., pp. 43-44.
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Early Estimates of the Velocity of Light
If one assumes that about a thirtieth of a second is the minimum time
interval distinguishable by the unaided eye, then the experiment of GALILEO
could at best be said to have established for the velocity of light a lower limit
of the order of some sixty mi. per sec.4 The negative result thus indicated
that if the velocity of light was finite, it was far greater than that of sound,
or than any with which scientists of the time were familiar. DESCARTES recognized, nevertheless, that it was possible that a measurable interval of time
of propagation might be obtained if the distance were made sufficiently
great. Accordingly, instead of GALILEO'S terrestrial space interval he proposed an astronomical distance-that between the moon and the earth. If
light were propagated in time, he said, eclipses of the moon would be visible
on the earth later than the calculated times at which the moon, earth, and
sun are exactly collinear. Inasmuch as no such delay was to be detected,
DESCARTESproceeded to compute a lower bound for the velocity of light.
Supposing the distance of the moon to be at least fifty earth radii of 600
leagues, then if light were to traverse half a league in "one twenty-fourth of
an artery beat," he calculated that it would take 5,000 beats, or at least an
hour, to cover the distance from the earth to the moon and back again.
However, he asserted that no delay even of half a minute was to be observed
in the occurrence of eclipses.5 DESCARTES concluded from this that the in-
finitely great velocity of light was established. In fact so confident was he in
this that he declared himself willing to stake his entire reputation as a
philosopher upon the instantaneity of light.6
DESCARTESdid not indicate how the times of collinearity were to be de-
termined with accuracy independently of observations based upon the
transmission of light. HOOKEasserted that even if light took "full two minutes" to pass from the moon to the earth, he knew no means of discovering
this fact.7 However, if one may assume with DESCARTES that a difference of
half a minute between the calculated and observed times could have been
detected, this would establish for the velocity of light a lower limit of about
15,000 mi. per sec., upon the basis of figures for the lunar distance then current.8
4 The text of Saggi di naturali
esperienzefatte nell'Accademia del Cimento (2nd ed., Firenze, 1691),
p. CCLXV, says, "Noi in lontananza d'un miglio (che per l'andar d'un lume, e la venuta dell'altro vuol
dir due) non ve l'abbiamo saputa ritrovare." However, the index to this work carries the entry, "Luce
corre un spazio di 6. miglia senza tempo osservabile. pag. 265." This latter would imply a lower limit about
three times as great as that of GALILEO.
5 (Euvres de Descartes (ed. by CHARLES
ADAMand PAULTANNERY,12 vols. and supplement, Paris,
6 Ibid., cf. also (Euvres, VI, 97 ff.; XI, 98; I, 308.
1897-1913), I, 307-12.
7 ROBERTHOOKE,
Micrographia, comprising vol. XIII of R. T. GUNTHER, Early Science in Oxford
(13 vols., Oxford, 1923-38). See p. 56.
8 For these figures see LUDWIGGUENTHER,
"Die Bestimmungen der Entfernungen der Sonne und des
Mondes von der Erde und deren Parallaxen einst und jetzt," Himmel und Erde, XX (1908), 69-80, 11828.
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Carl B. Boyer
The failure of the efforts of GALILEO
and DESCARTESto detect a retardation in the transmission of light was not regarded by all of their contemporaries as definitive, and the question of the velocity of light was still an
open one when in 1671 ROEMER
joined PICARDand CASSINIand with them
made observations at Paris of the eclipses of the satellites of Jupiter. It is
well known that as the result of these observations ROEMERmade the important discovery that the "second inequality" in the recurrence of the
eclipses of the first satellite could be explained upon the hypothesis that
light is propagated with a finite and determinable velocity. Moreover, his
work furnished not only a lower bound for this speed of transmission, but
provided the first definite estimate of its order of magnitude. The method of
ROEMERhas been often described and is familiar to every student of the
history of science, but with respect to the numerical value which resulted
in this connection there is in the literature of the subject a striking want of
consistency. Books on the history of science and thought-on astronomy,
physics, optics-ascribe
to ROEMERan almost incredible variety of figures,
ranging from 120,000 to 200,000 mi. per sec.,9 or from 193,120 to 327,000 km.
per sec.10The erroneous value 192,000 mi. per sec., or its equivalent in other
units of measurement, is so frequently imputed to ROEMERthat it threatens
to become traditional. This erroneous figure appears in THOMAS PRESTON'S
classic, The Theory of Light;l1 R. W. WOOD,Physical Optics;l2 Sir G. G.
STOKESOn Light;l D. M. TURNER,The Book of Scientific Discovery;14H. B.
LEMON, Fr7om Galileo to Cosmic Rays;'" W. C. D. DAMPIER-WHETHAM, A
History of Science;"6 and F. R. MOULTON,"The Velocity of Light.""7 This
figure appears also in J. W. DRAPER, A Text-Book of Natural Philosophy,l8
but the value 198,000 mi. per sec. is attributed to ROEMERby DRAPER in
History of the Intellectual Developmentof Europe.19The velocity 192,500 mi.
per sec. is ascribed to ROEMERby RICHARDPOTTER,An Elementary Treatise
on Optics,20 and by JOHN TYNDALL,Light and Electricity;21 190,000 mi. per
sec. is imputed to him by H. BUCKLEY,A Short History of Physics,22 and by
R. J. HARVEY-GIBSON,
Two Thousand Years of Science.23 These values are
roughly equivalent to the "remarkably precise value of 3.0 X1010 cm./sec."
9 See A. WOLF,A History of Science, Technology,and Philosophy in the 16th and 17th Centuries (New
York, 1935), p. 259, for the smaller figure; F. BRAY,Light (2nd ed., reprinted, London, 1939), p. 185,
for the larger.
10 See A. WOLF,loc. cit., for the smaller figure; for the larger see N. A. BOUTARIC, "La vitesse de la
lumiere et les theories de l'ether," Revue scientifique, LXIII (1925), 134-41, in particular, p. 136.
13London, 1892, p. 8.
11London, 1890,
12New ed., New York, 1911, p. 17.
p. 10.
16New York, 1931, p. 416.
14London, 1933,
15Chicago, 1934, p. 401.
p. 92.
17Scientific Monthly, XLVIII (1939), 481-84. See p. 481.
183rd ed., New York, 1848, p. 176.
19Revised ed., 2 vols., New York, 1876. See II, 299.
20 2 vols., London, 1851. See I, 4.
22 London, 1927, p. 64.
21 New York, 1871, p. 20.
232nd ed., revised by A. W. TITHERLY,New York, 1931, p. 55.
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Early Estimates of the Velocity of Light
27
ascribed to ROEMERby A. C. HARDYand F. H. PERRIN, The Principles of
Optics,24as well as by L. DARMSTAEDTER,Handbuch zur Geschichte der
Naturwissenschaften und der Technik,25 R. H. BLOCHMANN, Licht und
Wdrme,26and G. S. MONK, Light.27
Most Continental works express the result in geographical miles, and here
the figure 42,000 mi. per sec.-about 193,000 English statute miles per second-is unwarrantedly given as ROEMER'Sby J. C. POGGENDORFF, Geschichte
der Physik;28 AUGUSTHELLER, Geschichte der Physik;29 FERDINAND MONTET,
Precis d'histoire des sciences;30HUGOSPRINGER,"Die Lichttheorie in ihrer
ERNST MACH, Compendium der Physik;32
geschichtlichen Entwicklung";31
and in La science, published by LAROUssE.33 FERD. ROSENBERGER, Die
Geschichteder Physik,34has ascribed to ROEMER the round figure 40,000 mi.
per sec., but E. GERLAND,Wdrme und Licht,35 and E. HOPPE, Geschichte der
Optik,36have imputed to ROEMERa spurious degree of accuracy by ascribing
to him the values 41,936 and 41,965 mi. per sec. respectively.
A few of the figures given are strikingly lower than those commonly attributed to ROEMER. The figure 120,000 mi. per sec. or 193,120 km. per sec.
of A. WOLFhas already been cited above; L. B. LOEB and A. S. ADAMS, The
Developmentof Physical Thought,37put it at 914,000 km. per sec.; and F. S.
TAYLOR,The March of Mind,38places it as "too low by about 40 per cent."
On the Continent three figures, almost identical and about equal to 133,000
mi. per sec., appear in leagues per second: MACH, Die Prinzipien der physikalischen Optik,39places it at 48,203 leagues per second; RUDOLF
WOLF, Geschichte der Astronomie,40 makes this 48,203 1/3; ALEX. WERNICKE, "Die
Entdeckung der endlichen Lichtgeschwindigkeit durch OLAF ROEMER,"4'
puts it at 48,203 377/1141.
Most of the discrepancies in such values as those cited above are unmethod based upon more
doubtedly the result of calculations by ROEMER'S
in
his 1676 paper published
is
that
precise modern observations.42The truth
in the Journal des Sgavans ROEMER did not propose a definite value for the
speed of light, beyond his introductory remark that light requires less than
24 1st ed., 4th
impression, New York and London, 1932, p. 9.
25 2nd
ed., Berlin, 1908, p. 143.
27
113.
New
and
236-37.
York
1937,
London,
1902,
p.
Stuttgart,
pp.
28
29 2
vols., Stuttgart, 1882-84. See II, 211.
Leipzig, 1879, pp. 653-57.
30
136.
Bale,
Geneve,
1915,
p.
Lyon,
31
Programmdes k. k. Obergymnasiumsder Benediktiner zu Seitenstetten,XLI-XLII (1907-8). See 1908,
32 Wien, 1863, pp. 194-95.
332 vols., Paris, 1933-34. See I, 62.
18.
p.
34 2 parts in 1, Braunschweig, 1882-84. See II, 211-12.
35Leipzig, 1883, p. 88.
36
37 New York, 1933, p. 419.
38New York, 1939, p. 155.
Leipzig, 1926, p. 49.
40 Miinchen, 1877,
39Leipzig, 1921, p. 34.
p. 490.
41 Zeitschriftfiir Mathematik und Physik, Historisch-literarischeAbtheilung,XXV (1880), 1-10. See p. 4.
42 See M. E. J. GHEURYDE BRAY, "La vitesse de la lumiere," Ciel et Terre, XLIII (1927), 203-14;
XLIV (1928), 23-29, 107-18, 202-8, 403-10; XLV (1929), 3-11, 82-88, 187-91; XLVI (1930), 216-23;
XLVII (1931), 110-24. See XLIV, 204.
26
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28
Carl B. Boyer
a second of time to traverse a distance of about 3,000 leagues-i.e., a distance
about equal to the diameter of the earth. His estimate for the velocity of
light must be deduced from his conclusion, based on observations of the first
satellite of Jupiter, that light requires about 22 minutes to traverse the orbit
of the earth.43Although ROEMER'S
work is readily accessible, his figure 22
minutes more often is erroneously replaced in the secondary literature in the
history of science by any one of a variety of values. LANCELOT HOGBEN,
Sciencefor the Citizen,44ascribes to ROEMERa value of 16 2/3 minutes; R. A.
HOUSTOUN, A Treatise on Light,45 and PAUL DRUDE, The Theory of Optics,46
give 16 3/5 minutes; P. G. TAIT, Light,47 and EMILE PICARD, "L'evolution
des idees sur la lumiere et l'ceuvre d'ALBERTMICHELSON,"48 place the figure
at 16 1/2 minutes; H. v. MADLER,Geschichte der Himmelskunde,49and
LUDWIG GUENTHER50put it at 16 min. 26 sec.; FELIX AUERBACH, "Ge-
schwindigkeit des Lichts,"51 gives half the figure as 8 min. 18.2 sec.; Sir
WILLIAMBRAGG, The Universe of Light,52 PRESERVEDSMITH, A History of
Modern Culture,53 and H. T. STETSON, "Error in Astronomy,"54 give simply
16 minutes. GEORGE FORBES, "The Velocity of Light,"55 attributes to
ROEMERan estimate of 18 minutes; the figure 14 minutes is found in J. C.
FISCHER,Geschichte der Physik,56 and in A Short History of Science of W. T.
SEDGWICKand H. W. TYLER.57Some authors confuse the time estimates
given for the earth's orbital diameter with those for the radius.58Such inconsistencies as are evident in references to the work of ROEMER appear
likewise in reports on more recent figures for the velocity of light. M. E. J.
GHEURY DE BRAY59has found in the latter connection
that only one in
43For further details on ROEMER'Swork, as well as a facsimile reproduction of his paper, "Demonstration touchant le mouvement de la lumiere trouve par M. ROMERde l'Academie Royale des Sciences,"
which appeared in the Journal des Sgavans for 1676, see COHEN, op. cit. ROEMER'Sarticle appeared also
in Memoires de l'Academie Royale des Sciences depuis 1666 jusqu' a 1699 (hereafter referred to as Anc.
Mem.), X, 575-77. An English translation appeared in the Philosophical Transactions, XII (1677), 89394, and is reproduced in COHEN, op. cit. English translations appear also in A Source Book in Astronomy
and in A Source Book in
SHAPLEYand H. E. HOWARTH,
(New York and London, 1929), ed. by HARLOW
44New York, 1938, p. 317.
Physics (New York and London, 1935), ed. by W. F. MAGIE.
457th ed., London, New York, Toronto, 1938, 120.
p.
46Translated from the German by C. R. MANNand R. A. MILLIKAN,
new impression, London, New
47Edinburgh, 1889, pp. 48-49.
York, Toronto, 1929, p. 115.
48 Institut de France, Academiedes Sciences, Memoires, 2nd series, LXII (1936), 1-35. See p. 3.
50 Op. cit., p. 126, footnote.
492 vols., Braunschweig, 1873. See I, 346.
51In ERNEST GEHRCKE, Handbuch der physikalischen Optik (2 vols., Leipzig, 1926-28), I(1), 73-90.
53 2 vols., New York, 1930-34. See II, 56.
52 London, 1933, p. 206.
See p. 74.
64In JOSEPHJASTROw, The Story of Human Error (New York and London, 1936), pp. 39-63. See p. 54.
65In W. SPOTTISWOODEand others, Science Lectures at South Kensington (2 vols., London, 1878-79),
56 8 vols., Gottingen, 1801-8. See II, 155-56.
II, 212-26. See p. 214.
Revised
H.
W.
TYLER
and R. P. BIGELOW,New York, 1939, p. 322.
by
57
68See BUCKLEY,loc. cit.; also A. GUILLEMIN,Le monde physique (5 vols., Paris, 1881-85), II, 50 n.
69"Published Values of the Velocity of Light," Nature, CXX (1927), 404-5. See also his article, "The
Velocity of Light. History of its Determination from 1849 to 1933," Isis, XXV (1936), 437-48.
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Early Estimates of the Velocity of Light
eleven figures was correctly quoted! Such a state of affairs can not but impress one with the need of exercising caution in the history of science in
citations of numerical values as well as of dates of events.
If one wishes to convert ROEMER'S
figure of 22 minutes for the retardation
of light in crossing the earth's orbit into an estimate of the velocity of light,
it must be recognized that there was at the time considerable uncertainty in
the figures given for the distance of the earth from the sun.60One may reasonably suppose that ROEMERwould have adopted the values resulting from
the work of PICARD, RICHER, and CASSINI, in which ROEMERhimself as-
sisted.61From observations of the parallax of Mars made in 1671 to 1673the very years in which ROEMER was observing the satellites of Jupiter-a
solar distance of 91,600 terrestrial radii was obtained.62This was frequently
more roundly expressed as 22,000 earth radii.63PICARD had in the years just
previous determined the length of one degree on the earth as about 57,060
toises or 69.1 miles, corresponding to a terrestrial diameter of about 2865
leagues of 2282 toises, or a radius of about 3960 miles.64This determination
was adopted by CASSINIwith the understanding that the true length of one
degree might vary from 57,060 toises by 100 toises.65 The distance of the
sun calculated upon this basis would be about 86,000,000 of our present
statute miles. CASSINI, however, said that one commonly took the radius of
the earth as 1500 leagues, so that the sun could be regarded in round figures
as about 33,000,000 leagues away, allowing a million or two leagues difference.66CASSINI'Sround figure is about 91,000,000 miles, computed by taking
one league as equal to 2.762 miles.67 If, now, ROEMER accepted CASSINI'S
round figure, he might have inferred a velocity of light of about 50,000
leagues-or 138,000 miles-per second. If he had based his computation
upon PICARD's degree of 57,060 toises and CASSINI'Ssolar distance of 21,600
earth radii, he would have obtained a value of about 47,100 leagues-or
130,000 miles-per second. It must be remembered that ROEMER'Swork
did not contain such calculations. The emphasis in his paper was upon the
fact of a mora luminis rather than upon the estimate of its value. Long after60See GUENTHER,
Dissertatio academica, praecipua astronomorum
op. cit.; also ALBERTHOLMQUIST,
tentamina circa parallaxin solis, Holmiae, 1746.
61See J. B. DUHAMEL,
Regiae scientiarum academiae historia (2nd ed., Parisiis, 1701), pp. 106-7.
62G. D. CASSINI,Divers ouvragesd'astronomie (Amsterdam, 1736); published as vol. V of Memoires
de l'AcddemieRoyale des Sciences: contenantles ouvragesadoptezpar cetteAcademie avantson renouvellement
en 1699. See pp. 147 f. This is contained also in Anc. Mem., VIII, 115. See also DUHAMEL,op. cit., p. 939.
63 See CASSINI,loc. cit., and DUHAMEL, cit., p. 205.
op.
64JEANPICARD,Ouvragesde
mathematique(Amsterdam, 1736); published as vol. IV of Memoires de
l'Academie Royale des Sciences: contenantles ouvragesadoptez par cette Academie avant son renouvellement
en 1699. See pp. 46-47. See also Anc. Mem., VII(1), 180, or DUHAMEL,op. cit., p. 100.
65 CASSINI,
66Ibid., pp.148-49. See also Anc. Mem., I, 173, and VIII, 116.
op. cit., p. 47.
67See HERCULECAVALLI,Tableaux comparatifs des mesures, poids et monnaies modernes et anciens
(Paris, 1874), p. 32.
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30
Carl B. Boyer
wards FONTENELLE,writing the Histoire de l'Acad6mie Royale des Sciences,
remarked that, "II suit des Observations de M. ROiMER, que la lumiere
dans une seconde de tems fait 48203. lieues communes de France, et 377/1141
parties d'une de ces lieues."68This passage has been seized upon by some later
writers as representing the value given by ROEMERhimself.69Although it
may well represent his general view in this connection, it implies a degree of
accuracy which ROEMERwould most certainly disclaim. He himself conceded,
in correspondence with Huygens and in a note to the Aeademie in 1677, that
uncertainties made impossible an exact determination of the time for light
to traverse the orbit of the earth.70Further observations, including those of
markings of Jupiter, tended, nevertheless, to confirm his estimate of 22
minutes, for they indicated corrections of 12 to 14 minutes for a distance
about equal to one and one-quarter times the radius of the earth's orbit.71
Inasmuch as most of his manuscripts were burned in the Copenhagen fire of
1728, one can not be certain that ROEMERdid not later make a better estimate of the time factor in this connection.72
It is well known that ROEMER'Sconclusion with respect to the finite velocity of light was not generally accepted at the time.73 CASSINIregarded it
as "one of the most beautiful problems of physics,"74 but felt that the evidence was not convincing.75In this he was followed by his nephew and collaborator, J. P. MARALDI,76and by his son JACQUESCASSINI.77HOOKElikewise regarded ROEMER'Swork as inconclusive,78 and FONTENELLE,too, in
1707 renounced with regret the "ingenious and seductive hypothesis of successive propagation."79
68Anc. Mem., I, 215-16.
69See WERNICKE, op. cit.; cf. also R. WOLF,loc. cit., and MACH,Die Prinzipien der physikalischen
Optik, loc. cit. The estimate given by LOEBand ADAMS,loc. cit., is very probably also derived directly
or indirectly from this source.
70More than two centuries later R. A. PROCTOR
(Old and New Astronomy, London, 1892, p. 281) admitted that from observations of Jupiter's satellites one can not obtain very trustworthy results.
71 See CHRISTIAAN
HUYGENS, (Euvres completes (pub. by Societe Hollandaise des Sciences, 19 vols.,
La Haye, 1888-1937), XIX, 432-35; also VIII, 56-58.
72His student, PETERHORREBOW,
who has preserved for us a small part of ROEMER'S work, was
unable to indicate a closer approximation on ROEMER'S
part, and indeed made matters worse in this
respect by suggesting that ROEMERmight have proposed a time of more than 28 minutes (Basis astronomiae, Hauniae, 1735, p. 129).
For attempts to reconstruct a portion of ROEMER'S work see COHEN,op. cit., and KIRSTINE MEYER,
"Om Ole R0mers Opdagelse of Lysets T0ven; avec un resume en frangais," Det Kongelige Danske VidenskabernesSelskabs Skrifter. Series 7. Naturvidenskabeligog Mathematisk Afdeling, XII (1915), 106-45.
73See COHEN,op. cit., for an account of its reception.
74Op. cit., p. 45.
75CASSINI,op. cit., pp. 46, 435-36.
76 See Histoire de l'Academie Royale des Sciences, avec les Memoires de mathematiqueet de physique,
1707, Histoire, pp. 77-81, Memoires, pp. 25-32. Inasmuch as each volume of this work is divided into
two parts with separate pagination, references will hereafter be given as follows: Hist. de l'Acad., 1707,
pp. 77-81, and Mem. de l'Acad., 1707, pp. 25-32. All references are to the Paris edition.
77See infra.
78 ROBERT HOOKE, Posthumous Works (London, 1705), pp. 77-78.
79Hist. de l'Acad., 1707, pp. 77-81.
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Early Estimates of the Velocity of Light
31
ROEMER was not, however, without supporters. HUYGENScited the
"proof" of the finite but extremely great speed of light as an argument
against the corpuscular hypothesis.80 In the opening sections of the Traitt de
la lumiere-presented to the Academie in 1678 but not published until
1690-HUYGENS devoted several pages to the question of the velocity of
light, including a full account of ROEMER'S demonstration.81 Although he
apparently made no independent experimental determination of the speed
of propagation, HUYGENSevinced a greater interest than did ROEMERin
the numerical value of this velocity. The figure 22 minutes which ROEMER
had given as the retardation of light in crossing the earth's orbit HUYGENS
converted into an estimate of the speed of light as compared with that of
sound. Taking the diameter of the earth's orbit as 22,000 terrestrial diameconsidered it as in reality about 24,000 diametersters-although HUYGENS
light would traverse a distance of 1,000 earth diameters per minute or
16 2/3 diameters in a second. Adopting PICARD'Smeasure for this diameter,
HUYGENS found that the indicated velocity was more than 600,000 times
that of sound.82 There seems to be some confusion in secondary sources as
to the figure HUYGENS gave for the velocity of sound. WILLIAMWHEWELL83
and FLORIANCAJORI84place it at 1179 Paris feet per second, but A. WOLF85
puts it at 1097 Paris feet per second. In 1669 HUYGENS himself set the speed
at 1076 Paris feet per second, or about 180 toises per second.86 Although
DUHAMEL reports that CASSINI, PICARD,and ROEMERin 1677 found a velocity of 183 toises per second,87 HUYGENSretained his figure of 180 in his
Traite de la lumiere, and, in fact, continued to use it as late as 1694.88 This
is equivalent to about 1150 English feet per second,89so that his estimate of
the velocity of light is equivalent to about 131,000 mi. per sec.
work NICOLAS
IHARTSOEKER
A few years after the appearance of HUYGENS'
in
his
of
of
a
similar
estimate
the
published
Essay de dioptrique.
speed light
in
this
to
are
not
referred
and HUYGENS
connection, the
Although ROEMER
estimate is most likely based upon their work. From a time of 22 minutes for
deduced
the propagation of light across the orbit of the earth HARTSOEKER
that the speed was more than 110,000,000 toises-about 133,000 miles-per
second.90
Not all of the early estimates of the speed of light obtained by ROEMER'S
method were based upon ROEMER'Sdata. DuHAMEL, ostensibly quoting
from some work by CASSINIwritten in 1675-that
is, before ROEMER'Sdisthe sun to the earth
of
from
for
the
time
the
light
propagation
covery-gave
as 10 or 11 minutes.91 This quotation indicates that CASSINI anticipated
82 Ibid.,
81
Euvres, XIX, 463-69.
(Euvres,X, 613.
p. 469.
2
New
the
Inductive
Sciences
York,
II, 33.
vols.,
1858),
ed.,
(3rd
of
86
84 A
8 Op. cit., p. 286.
Euvres,XIX, 372.
History of Physics (New York, 1906), p. 97.
87 Op.
89 See CAVALLI,
88 Euvres,XIX, 373, 469.
cit., p. 161.
op. cit., for conversion figures.
90 Essay de dioptrique (Paris, 1694), p. 17.
91DUHAMEL, op. cit., p. 148.
8s
83 History
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Carl B. Boyer
32
ROEMERin suggesting that the inequalities of the first satellite of Jupiter
could be explained on the assumption that light travels in time, although he
later abandoned this hypothesis.92 Whether or not this time estimate is
genuinely to be attributed to CASSINI, it was later replaced by him by one
more accurate. In his improved tables of 1693 CASSINIplaced the greatest
correction in the case of the second inequality of the first satellite of Jupiter
at 14 min. 10 sec., and it is this latter estimate-often quoted simply as a
a round 14 minutes-which was dominant in scientific thought before the
appearance of the more accurate one of BRADLEY.93 Although CASSINIdid not
interpret this in terms of the propagation of light, his figure was influential
nevertheless in determining many of the early estimates of the speed of
light.
NEWTON in the first edition of the Principia accepted "almost ten minutes" as the retardation of light from the sun.94In the opening pages of his
Opticks, however, one reads that "it seems that Light is propagated in time,
spending in its passage from the Sun to us about Seven Minutes of Time,"95
and later in the same work this figure is changed to "about seven or eight
minutes"96-a value which appeared also in subsequent editions of the
time estimate may have
Principia.97 It has been suggested98that NEWTON'S
in 1676 which
been made upon the basis of eclipse observations by ROEMER
the latter failed to cite in his paper of that year, ostensibly because he considered them less reliable than the earlier ones. It seems far more probable,
however, that NEWTON'Sfigures were derived, either directly or indirectly,
from those of CASSINI.NEWTON'Sfriend, EDMOND HALLEY,in 1694 published
in the Philosophical Transactions a reduction of CASSINI'Stables of the first
moon of Jupiter to the Julian style and the meridian of London.99Further92 CASSINI'S
supposed anticipation has been generally accepted (see COHEN,op. cit., for further details), but there appears to be room for doubt as to its validity. In the first place, this report by DUHAMEL,
appearing almost a quarter of a century after CASSINI'sreputed statement, represents apparently the
first publication of any such claim. In the interval the discovery was generally attributed to ROEMER.
Secondly, ROEMER'Sreport of 1676 clearly gives the impression that his discovery is something new. It
makes no reference to any anticipation by CASSINI. Thirdly, CASSINIhimself implied the originality of
ROEMER'S
conjecture when in 1693 he wrote, "Monsieur ROMERexpliqua tres-ingenieusement une de
ces inegalitez qu'il avoit observees pendant quelques annees dans le premier satellite, par le mouvement
successif de la lumiere." (CASSINI,op. cit., p. 435, or Anc. M6m., VIII, 391). Would CASSINIhave referred in such language to a mere revival of his own discarded hypothesis? Possibly DUHAMEL was mistaken as to the date of the work from which he said he was quoting CASSINI.Almost two centuries ago
P. C. LEMONNIER (Institutions astronomiques, Paris, 1746, pp. 296, 298 n.), in asserting ROEMER's
"incontestable" priority, rejected this passage of DUHAMEL'SHistoria as "without date and unin93See CASSINI, op. cit., p. 475; also Anc. M6m., VIII, 430-31.
telligible."
94ISAACNEWTON,Philosophiae naturalis principia mathematica (1st ed., reissue, Londini, 1687), Book
95Opticks (London, 1704), Book I, Part I, Def. 2, p. 2.
I, Prop. XCVI, Scholium, p. 231.
96Ibid., Book II, Prop. XI, p. 77.
97See Operaomnia (ed. by SAMUEL
HORSLEY, 5 vols., Londini, 1779-85), II, 258; cf. IV, 176.
98See MEYER, op. cit., pp. 135, 144.
99Philosophical Transactions, XVIII (1694), 237-56.
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Early Estimates of the Velocity of Light
33
more, HALLEYwas an ardent supporter of ROEMER'Shypothesis and sought
to confirm it by independent calculations for the other satellites of Jupiter.100In this connection he seems to have adopted for the time of propagation of light across the earth's orbit the round figure 14 minutes.101JAMES
POUNDlikewise reported some years later in the Philosophical Transactions
that light is "found to proceed in about seven Minutes of time as far as from
the Sun to the Earth."102Upon the basis of the figure 12."5 which HALLEY
accepted for the horizontal parallax of the sun,103this time estimate would
imply a value of some 155,000 mi. per sec. as the velocity of light.
Just as HUYGENShad deduced from ROEMER'Sfigure of 22 minutes that
light was about 600,000 times swifter than sound, so NEWTONin later editions of his Opticksconverted the estimate of 7 or 8 minutes, which he may
have derived from CASSINI directly or through HALLEYor POUND, into an
estimate of the comparative speeds of light and sound.104 Taking the distance
of the sun to be about 70,000,000 miles, he concluded that the velocity of
light was 700,000 times as great as that of sound, which he placed at 1140
English feet per "second minute of time."105This would result in a speed of
something over 150,000 mi. per sec., a figure agreeing roughly with that implied by HALLEY and better than that of HUYGENS, in spite of the poor solar
distance upon which it was based. Had NEWTONhere made use of CASSINI'S
estimate of the distance of the sun, he would have arrived at a value for the
velocity of light close to that accepted at present.
The popularity of NEWTON'Soptical and astronomical works during the
eighteenth century may well account in part for the present confusion with
100Ibid., pp. 239, 254 ff.
101EDMOND HALLEY, Astronomi dum viveret regii tabulae astronomicae (Londini, 1749). This work is
without pagination, the value 14 minutes being cited in the notes (Viri reverendi D. JACOBIBRADLEY,
in has suuas satellitum tabulas notae) introducing the tables of conjunctions of the first satellite.
It has been mistakenly stated (See COHEN,op. cit., p. 355) that HALLEYproposed a time of 8 1/2
minutes as more correct for the retardation of light from the sun. This is probably the result of a misinterpretation of a calculation by HALLEY(Philosophical Transactions, XVIII (1694), p. 256) in which an
observed inequality of 18 1/2 minutes is stated as corresponding to 13 minutes as calculated from
ROEMER'S
estimate and to 8 1/2 according to CASSINI'S tables.
102"New and Accurate Tables for the Ready Computing of the Eclipses of the First Satellite of
Jupiter, by Addition Only," Philosophical Transactions, XXX (1717-19), 1021-34. See p. 1034. In these
tables, purporting to be an improvement of CASSINI'S, POUNDrecalculated the values for the second equation to correspond to a maximum inequality of 14 minutes instead of the 14 min. 10 sec. of CASSINI.
See p. 1030.
103 "Methodus
singularis qua solis parallaxis sive distantia a terra, ope Veneris intra Solem conspiciendae, tuto determinari poterit," Philosophical Transactions, XXIX (1714-16), 454-64. See p. 458.
104Perhaps it is because this work, found in Book III, Query 21, does not appear in the 1704 edition
that it has been stated erroneously by T. J. J. SEE ("Historical Sketch of OLAUSROEMER,"Popular
Astronomy, XI, 1903, pp. 225-38) that the first edition of NEWTON'S
Opticks contains no allusion to the
work of ROEMER.In this connection HARVEY-GIBSON (op. cit., p. 54) has quite incorrectly stated that
"NEWTONmade no attempt at estimating the rate at which light travels. Every one thought that light
105 Operaomnia, IV, 224-25.
was instantaneous."
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Carl B. Boyer
34
respect to ROEMER'Sestimate of the velocity of light. In the Opticks one
reads:
Light is propagated from luminous Bodies in time, and spends about seven or eight minutes
of an hour in passing from the Sun to the Earth.
This was observed first by ROMER, and then by others, by means of the Eclipses of the
Satellites of Jupiter.106
This reference appears to have left the impression that the time figures given
were to be imputed to ROEMERalong with the discovery of the method. A
similar ambiguity is found in SMITH'SOpticks of 1738 where one reads that:
made a noble discovery of a method for determining the velocity of light; by
Mons. ROEMER
which it was concluded and confirmed by long experience that light is shot from the sun to the
earth in 7 or 8 minutes of time.107
In the article "Lumiere" in the Encyclopedie one reads that ROEMERand
NEWTONhave shown beyond a doubt that light takes about seven minutes
to reach the earth.108 In 1772 PRIESTLEY said that CASSINI and ROEMER
concluded "that light was about 14 minutes in crossing the earth's orbit."109
also ascribed the figure 14 minutes to ROEMER, but CONDORCET
DELAMBRE110
set it at 16 to 18 minutes and BAILLYconfused matters still further by asserting that ROEMERfirst placed the figure at 11 minutes, later adopting 14
minutes."'
Throughout the early eighteenth century the figures 7 and 8 minutes given
by NEWTON were cited far more frequently than were the 2 minutes of
ROEMERand the 14 min. 10 sec. of CASSINI.These were coupled with numer-
ous solar distance factors so diverse as to imply velocities of from 100,000 to
more than 200,000 mi. per sec.112
The work of BRADLEY furnished an unexpected confirmation of ROEMER'S
hypothesis and also brought into prominence a new time estimate, but it too
was subject to the equivocal factor of the solar distance. Astronomical aber106
Opticks (1704), Book II, Prop. XI, p. 77.
107ROBERTSMITH,A CompleatSystem of Opticks (Cambridge, 1738), p. 437.
108Encyclopedie, ou dictionnaire raisonne des sciences, des arts et des metiers. (Edition exactement conforme a celle de PELLETin quarto, Berne and Lausanne, 1780), XX, 442.
109JOSEPH PRIESTLEY, The History and Present State of Discoveries Relating to Vision, Light, and
Colours (London, 1772), p. 139.
110J. B. J. DELAMBRE,Astronomie theoriqueet pratique (3 vols., Paris, 1814), III, 496.
111J. A. N. C., marquis de CONDORCET,(Euvres completes (21 vols., Brunswick and Paris, 1804), I,
139-40. J. S. BAILLY,Histoire de l'astronomiemoderne (3 vols., Paris, 1779-85), II, 417, 421 (note a).
112See J. J. SCHEUCHZER,Physica oder Natur-Wissenschafft (2 parts, Zurich, 1729), I, 101, for 7 or
8 minutes and 100,000 mi. per sec. See JACQUESROHAULT,Physica (trans. into Latin by SAMUEL
CLARKE,4th ed., Londini, 1718), p. 186, footnote, for 7 minutes and a distance of 50,000,000 miles. See
A Compendiousand MethodicalAccount of the Principles of Natural Philosophy (London,
BENJ. WORSTER,
A Course of Lectures in Natural Philosophy (2nd ed., London,
HELSHAM,
1722), p. 164, and RICHARD
1743), pp. 287-88, for 7 or 8 minutes and 70,000,000 miles. See [J. A.] abbe NOLLET,Legons de physique
experimentale(vol. V, 4th ed., Paris, 1768), pp. 47-48, for 7 to 8 minutes and 32 to 33 million leagues.
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Early Estimates of the Velocity of Light
35
ration yielded the speed of light relative to that of the earth in its orbit.
The observations of BRADLEY
indicated an angle of aberration of about 20. "2,
from which he computed that the velocity of light is 10,210 times-often
later taken as a round 10,000 times-the earth's orbital speed.113As in the
case of ROEMER,so also here values for the velocity of light have incorrectly
been attributed to BRADLEY. F. BRAY114places his estimate at 193,000 mi.
per sec.; TYNDALL11 puts it at 191,515 mi. per sec.; HopPE116 sets it at 41,200
geographic miles per second. BRADLEY, however, did not set down a figure
for the absolute velocity of light, but his work was significant in that it
afforded a remarkably accurate figure for the retardation of light from the
sun. Whereas the value 11 minutes given by ROEMERwas excessive, the
estimates of between 7 and 8 minutes given by CASSINIand others were too
small. As BRADLEYsaid, his computed figure of 8 min. 12 or 13 sec. was "as
it were a Mean betwixt what had at different times been determined from
the Eclipses of Jupiter's Satellites."117Moreover, this is but some half dozen
seconds less than the value accepted at the present time."8 A corresponding
accuracy with respect to the velocity of light is not, however, to be imputed
to BRADLEY. HALLEYreported that from observations of Mars made in 1719
POUND and his nephew BRADLEYdemonstrated that the sun's parallax was
not more than 12" nor less than 9".119 Such a latitude in the solar distance
would be reflected in a correspondingly great margin of errorin the computed
appears to have
velocity of light. From new observations in 1721 BRADLEY
obtained a mean of 10" 1/3 for the solar parallax,120which would correspond
to a distance of about 79,100,000 miles and a consequent value of 161,000
mi. per sec. for the velocity of light; but BRADLEY did not explicitly suggest
such a figure.
Unfortunately
the accuracy of BRADLEY'S work could not at the time be
fully appreciated. Some astronomers reduced his time estimate to a round
8 minutes and others continued to accept still smaller values for the retardation of light from the sun.
JACQUES CASSINI
in 1740 adopted for the "second
equation of conjunctions" his father's tables of about half a century earlier,
in which the maximum inequality was 14 min. 10 sec.121This time factor,
combined with his estimate of the distance of the sun as 300 times that of
the moon,122would have indicated a speed of light of the order of 170,000
113 "An Account of a New Discovered Motion of the Fixed Stars,"
Philosophical Transactions, XXXV
Miscellaneous Worksand Correspond(1727-28), 637-61. See p. 653. This appears also in JAMESBRADLEY,
ence (Oxford, 1832), pp. 1-15. A facsimile reproduction appears also in connection with an article by
GEORGE
SARTON,"Discovery of the Aberration of Light," Isis, XVI (1931), 233-65.
114Op. cit., p. 186.
116Op. cit., p. 59.
117BRADLEY,
115Op. cit., p. 21.
loc. cit.
118SARTON,op. cit., p. 235.
119BRADLEY, Miscellaneous Works and Correspondence,p. IV.
120Ibid.,
121JACQUES
CASSINI,Tables astronomiques (Paris, 1740), p. 211.
p. 353.
122 Ibid.,
preface, p. x.
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36
Carl B. Boyer
mi. per sec. CASSINI,however, did not so interpret it, but ostensibly shared
his father's view that the table of inequalities had merely empirical significance and did not indicate that light is propagated in time. Other men,
nevertheless, accepted the explanations of ROEMERand BRADLEY, although
discrepancies in estimates of the speed of light continued to be wide. In the
Histoire de l'Academiefor 1737 the velocity is in one connection given simply
as more than 10,000 leagues per second,123but in reporting in the same year
on BRADLEY'S work a speed of more than 4,000,000 leagues per minuteabout 184,000 mi. per sec.-is deduced from CASSINI'Sround 33,000,000
leagues and BRADLEY'S retardation, taken roundly as 8 minutes.124In the
MNmoires for this same year DORTOUSDE MAIRAN placed the velocity of
light "according to the observation of ROEMER" at more than 800,000 times
that of sound,125but EULER at about the same time set it at about 622,000
times as great as that of sound.126EULER was, with the possible exception of
FRANKLIN, the only great scientist of the eighteenth
century who seriously
advanced the wave theory of light. In this connection he carried out calculations127on the density and elasticity of the luminiferous medium as determined by the velocity of light, analogous to those made earlier by NEWTON.128
His computations were based upon the fairly accurate figure of 8 minutes129
for the transmission of light from the sun, but for the solar parallax he
adopted the excessive value 13",with a consequent distance of 311,234,300,000
Paris feet-or about 62,700,000 miles.130Inasmuch as EULER took the velocity of sound to be 1040 Paris feet per second,3l this indicated a velocity of
light about 622,000 times that of sound, or about 131,000 mi. per sec. Thus,
in spite of the accuracy of BRADLEY'S time figure, the speed of light as determined from the data of EULER is about the same as that indicated by the
earlier figures of ROEMERand HUYGENS.
The lack of consistency in estimates of the velocity of light proposed during
the eighteenth century is apparent from numerous sources. MUSSCHENBROEK
in 1731 referred to NEWTON'S Opticksin reporting 14 minutes as the retardation of light in crossing the earth's orbit,132but before the end of the decade
he had adopted BRADLEY'S figure of 8 min. 13 sec. for light from the sun.133
MUSSCHENBROEK accepted a solar distance of 24,000 earth radii of 19,615,782
Paris feet and hence should have arrived at a speed of about 193,000 mi. per
123Hist. de l'Acad., 1737, p. 103.
124Ibid., pp. 76-79.
125 J. D. DEMAIRAN,"Discours sur la propagation du son," MEm.de l'Acad., 1737, pp. 1-58. See p. 36.
126LEONHARD EULER, Opuscula varii argumenti (Berolini, 1746), pp. 193 ff.
127
129EULER, op. cit., p. 195.
128NEWTON,Operaomnia, IV, 224-25.
Op. cit., pp. 196 ff.
130EULER, op. cit., p. 195.
131Ibid., p. 915; cf. pp. 193-94, 207.
132PETRUS VAN MUSSCHENBROEK,Tentamina experimentorum naturalium captorum in academia del
cimento (2 parts, Lugduni Batavorum, 1731), II, 184.
133Essai de physique (trans. from the Flemish by PIERREMASSUET,2 vols., Leyden, 1739), II, 506.
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Early Estimates of the Velocity of Light
37
sec. Instead, however, he calculated in terms of a time factor of only 8 minutes and deduced, with an amazing disregard of the inherent uncertainties,
a speed of 980,809,933 1/3 Paris feet-or about 198,000 miles-per second.134
This figure appeared not only in the numerous editions and translations of
MUSSCHENBROEK'S physical works,135but also in the books of others as late
as 1777.136Another velocity figure popular during the eighteenth century
was that of 164,000 mi. per sec., derived from BRADLEY'S time factor and a
solar distance of 80,000,000 miles. This appeared in the astronomies of
FERGUSON137 and was repeated by others138 as late as 1813. A number of
other figures of about this order appeared about the middle of the eighteenth
century. G. W. KRAFFT,Praelectiones academicaepublicae in physicae,139derived a velocity of 42 earth radii per second-about 166,000 mi. per sec.from BRADLEY'S time factor and a solar distance of 20,618 terrestrial radii.
ETIENNE MONTUCLA,Histoire des mathematiques,l40 employing
a time of
from 8 to 9 minutes and a distance of 22,000 earth radii, estimated the speed
at 43 earth radii per second. This is practically the same as the speed of
170,000 mi. per sec., or 680,000 times that of sound, deduced by B. MARTIN,
Philosophia Britannica: or a New and ComprehensiveSystem of the Newtonian
Philosophy,14lfrom a time of 8 min. 13 sec. and a distance of 82,000,000
miles. R. J. BoscoVICH, Dissertatio de lumine, gave the speed more accurately as more than 180,000 mi. per sec.,142but this was the result of a compensation of errors, deduced as it was from a solar distance of 22,000
terrestrial radii of 4,000 miles and a time factor of only 450 seconds.
The transits of Venus in 1761 and 1769 were observed to imply a solar
distance of from 91,000,000 to 97,000,000 miles,143and as a result the margin
of error in estimates of the speed of light was correspondingly reduced. Nevertheless, although discrepancies in the distance factor had become smaller,
those in the time factor continued to be relatively large. The older figure of
7 minutes derived from the work of CASSINI had not been displaced completely by the better one of BRADLEY. However, whereas estimates of the
134Ibid., p. 509.
135See for
example, Elementa physicae (rev. ed., Lugduni Batavorum, 1741), pp. 356-58; also The Elements of Natural Philosophy (trans. from the Latin by JOHNCOLSON,
2 vols., London, 1744), II, 53-55.
136See J. R. SIGAUD
DELAFOND, Elemens de physique (4 vols., Paris, 1777), IV, 113-14.
137See JAMES FERGUSON, Astronomy explained upon Sir Isaac Newton's
Principles (1st American ed.,
rev. by ROBERTPATTERSON,
Philadelphia, 1806), pp. 109-10.
138 GEORGE
The History of Astronomy (London, 1767), pp. 191, 307, gives this figure and cites
COSTARD,
in this connection. The same figure appears also in TIBERIUS CAVALLO,
FERGUSON
The Elements of Natural or Experimental Philosophy (1st American ed., 2 vols., Philadelphia, 1813), II, 58.
139 3 parts, Tubingae, 1750-54. See III, 80.
140 New ed., 4 vols., Paris, 1799-1802. See II, 580.
141 2nd ed., 3 vols., London, 1759. See II, 273.
142 Romae, 1749,
p. 30. This is in rough agreement with the time and distance factors in his Theory of
Natural Philosophy (Latin-English ed., from the text of the 1st Venetian ed. of 1763, Chicago and London,
143PROCTOR,
1922), pp. 330-33.
op. cit., p. 274.
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38
Carl B. Boyer
velocity of light previously had tended to be too low, those based on the
new values for the distance of the sun almost invariably were too high.
SAMUELHORSLEY,in defending the corpuscular theory against FRANKLIN'S
doubts in view of the prodigious swiftness of propagation, assigned in 1770 a
value of 381,092,323 London yards-or almost 217,000 miles-per second to
the speed of light.144This excessive estimate resulted from his adoption of the
took
figure 7 minutes as the retardation of light from the sun, for HORSLEY
the parallax of the sun as 9", about half a second less than that given by
CASSINI. In this very same year
RICHARD
PRICE placed the delay of light
from the sun at 8.2 minutes,145the result of BRADLEY, which, in terms of a
parallax of 9", would have implied practically the velocity accepted at present. About this time PRIESTLEY accepted a distance of 92,000,000 miles and
a time of 7 minutes,146implying a velocity about that given by HORSLEY.
A few years later a speed of 202,083 mi. per sec. was deduced by GEORGE
ATWOOD,An Analysis of a Course of Lectures on the Principles of Natural
Philosophy,l47from 97,000,000 miles and 8 minutes. G. C. LICHTENBERG,
adopted BRADLEY'S 8 min. 13 sec. and gave
Anfangsgriindeder Naturlehre,148
the velocity as more than 44,336 geographic miles-about 204,000 statute
miles-per second, or more than 975,146 times that of sound. A somewhat
smaller figure of 198,000 mi. per sec. is implied by the 95,173,100 miles and
8 minutes of WILLIAM ENFIELD, Institutes of Natural Philosophy.l49
About this time there appeared several other apparently independent
determinations of the time factor upon which estimates of the velocity of
light depended. BoscoVICHgave a time of 486 seconds which, together with
his solar parallax figure of 8"1/2, implied"15a speed considerably above that
which he had proposed earlier and about that indicated by ENFIELD. In
his popular works on astronomy J. E. BODEadopted 8 min. 7 1/2 sec. as the
retardation of light from the sun, deducing from this a velocity 902,000
times that of sound or 41,000 geographic miles-about 189,000 statute miles
-per second.51 Somewhat later DELAMBRE, upon the basis of a study of
144 "Difficulties in the Newtonian
Theory of Light, Considered and Removed," Philosophical Transactions, LX (1770), 417-40. See pp. 418-19.
145"On the Effect of Aberration of Light on the Time of a Transit of Venus over the Sun," Philosophical
146PRIESTLEY,
Transactions,LX (1770), 536-40. See p. 540.
op. cit., p. 140.
147London, 1784, pp. 243, 251-52.
148 4th ed., Gottingen, 1787, pp. 567-68.
149 London, 1785,
pp. 287, 298-99. The persistence about this time of still lower figures is shown in the
speed of 3,333,000 leagues-about 154,000 miles-per second or 400,000 times that of sound carelessly
given by J. H. POTT,Des El6mens(2 vols., Lausanne, 1782), I, 317.
150See BoscoVIcH, Opera pertinentia ad opticam et astronomiam (5 vols., BASSANI;Venetiis, 1785), V.
429-30, 436-37.
151Kurzgefasste Erlduterungder Sternkunde (2 parts, Berlin, 1778), I, 246-47. This edition places the
velocity of light at 900,000 times that of sound, but later editions replace this with the figure 902,000.
See, e.g., 2nd ed., Berlin, 1793, I, 356. BODE'S time figure quite possibly was calculated from the work
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Early Estimates of the Velocity of Light
39
eclipses of the satellites of Jupiter, gave this time factor as 8 min. 13.2
sec.152This figure, more often taken simply as the 8 min. 13 sec. of BRADLEY
and sometimes falsely ascribed to RoEMER,153 was widely adopted during the
first half of the nineteenth century, and the range of values suggested for
the velocity of light was consequently considerably reduced. In terms of
DELAMBRE'Sestimate of 8.'56 as the most probable solar parallax,154a velocity about 194,000 mi. per sec. is indicated, and estimates tended to cluster
rather closely about this. In English works the values 190,000 mi. per sec.,155
199,500 mi. per sec.,156195,000 mi. per sec.,157and 200,000 mi. per sec.158appeared during the first half of the nineteenth century. In German books the
velocity generally was expressed in round figures as 40,000 geographic miles
-about 184,000 statute miles-per second,159although other values up to
42,000 also appeared.160In France the accepted round figure became 70,000
leagues-about 194,000 miles-per second,161although toward the middle of
the century roughly equivalent figures, such as 77,076 and 79,572, appeared
in leagues of 4,000 meters.162Sometimes the velocity was expressed comparatively in terms of that of sound, with the figure 900,000 times as great
most frequently cited.163
In spite of the fact that the time factor of 8 min. 13 sec. was generally
adopted during the early nineteenth century, estimates of the velocity of
of BRADLEYon the basis of 20", instead of 20." 2, as the angle of aberration. Such a calculation had been
given some years earlier by LEMONNIER
(op. cit., pp. 300-1).
152Histoire de l'astronomie moderne vols., Paris,
(2
1821), II, 653.
153 See the citations to MADLER and GUENTHER
given above.
154Astronomictheoriqueet pratique, II, 507. See also III, 105, 121, for DELAMBRE'Suse of 8 min. 13 sec.
155MARY SOMERVILLE,On the Connectionof the Physical Sciences (from the 7th London ed., New York,
1846), p. 30.
156 DENISON OLMSTED,An Introductionto Natural
Philosophy, vol. II (4th ed., New York, 1840), p. 223.
157JAMES
RENWICK, Familiar Illustrations of Natural Philosophy (New York, 1840), p. 311.
158MARGARETBRYAN, Lectureson Natural Philosophy (London, 1806), p. 217; E. S. FISCHER, Elements
of Natural Philosophy (trans. by JOHN FARRAR, Boston, 1827), p. 230.
159 K. W. G. KASTNER, Grundriss der
Experimentalphysik (2nd ed., 2 vols., Heidelberg, 1820-21),
II, 413-14; ANDREAS BAUMGARTNER,Die Naturlehre (3 vols., Wien, 1824), II, 10; H. W. BRANDES,
Vorlesungeniiber die Naturlehre (3 parts, Leipzig, 1830-32), II, 65-66; C. S. CORNELIUS,Die Naturlehre
(Leipzig, 1849), p. 318.
160 JOH. MULLER, Lehrbuchder
Physik und Meteorologie (2nd ed., 2 vols., Braunschweig, 1844-45), II,
351.
161E. PECLET, Trait6 e6lmentairede physique (2nd ed., 2 vols., Paris, 1832), II, 257; C. DESPRETZ,
Traite elementairede physique (6th ed., Bruxelles, 1840), pp. 361-62; G. LAME,Cours de physique (2nd
ed., 3 vols., Paris, 1840), II, 114.
162For the figure 77,076 see FRANCOIS
ARAGO, (Euvres completes (ed. by M. J. A. BARRAL, 17 vols.,
Paris and Leipzig, 1854-62), XVI, 401-2; for 79,572 see C. S. M. POUILLET,lelmens de physique experimentale (2nd ed., 2 vols., Paris, 1832), II(1), 213-14, and LEON FOUCAULT,Recueil des travaux scientifiques (ed. by C. M. GARIEL, Paris, 1878), p. 187.
163ALEX. BERTRAND,Lettressur la physique (2 vols., Paris and Leipzig, 1824-25), II, 220; also BRANDES,
loc. cit.; KASTNER, loc. cit., gives the figure 750,000 times that of sound.
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Carl B. Boyer
40
light continued to indicate a margin of error of some 5 per cent as a consequence of inaccuracies in determining the solar parallax. This serves to
indicate how great was the need for new terrestrial methods for the determination of this constant, so important in both physics and astronomy.
Whether because of the lack of a satisfactory theory of light or because of
the practical difficulties inherent in the astronomical procedures, very little
interest in the precise determination of the speed of light appears to have
been manifested before about the middle of the nineteenth century. Most
early estimates were given only incidentally and with no claim to accuracy.
This is in striking contrast with the appearance of scores of scientific papers
devoted solely to this subject following the work of FIZEAU and FOUCAULT.
With the perfection of their experimental procedures the very factors which
formerly had operated to make uncertain the estimates of the speed of light
now inversely could themselves be determined far more accurately in terms
of terrestrial measurements of this velocity.
Brooklyn College
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