According to Einstein's theory of special relativity, **the speed o...
An extract of a lecture where Feynman explains the importance of Rø...
Ole Christensen Rømer (1644-1710) was a Danish astronomer who is be...
The main doubt is whether the **discovery of the finiteness of the ...
Rømer's work is based on geometric considerations illustrated in fi...
The four Galilean satellites that were used to first determine the ...
Giovanni Domenico Cassini (1625 – 1712) was an Italian mathematicia...
The conclusion did not meet immediate universal acceptance. Other c...
Rømer announced his discovery to the Académie Royale des Sciences o...
Rømer was able to conclude that it took around 22 minutes for light...
Cassini abandoned the hypothesis of the finite velocity of l...
You can learn more about James Bradley's arguments here: [A Letter ...
### Milestones of the estimations of the speed of light:
**1676** ...
Journal of Astronomical History and Heritage, 11(2), 97-105 (2008).
97
CASSINI, RØMER AND THE VELOCITY OF LIGHT
Laurence Bobis
Bibliothèque, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France.
E-mail: Laurence.Bobis@obspm.fr
and
James Lequeux
LERMA, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France.
E-mail: James.Lequeux@obspm.fr
Abstract: The discovery of the finite nature of the velocity of light is usually attributed to Rømer. However, a text at
the Paris Observatory confirms the minority opinion according to which Cassini was first to propose the ‘successive
motion’ of light, while giving a rather correct order of magnitude for the duration of its propagation from the Sun to the
Earth. We examine this question, and discuss why, in spite of the criticisms of Halley, Cassini abandoned this
hypothesis while leaving Rømer free to publish it.
Keywords: velocity of light, satellites of Jupiter, longitude, Jean-Dominique Cassini, Jean Picard, Ole Rømer,
Edmond Halley, James Bradley, Christiaan Huygens.
“The Danish astronomer Olaus Römer (1644-1710) discovered the velocity of propagation of light at
the Paris Observatory in 1676.” Inscription on the north frontage of the Paris Observatory.
1 INTRODUCTION
The discovery of the finite nature of the velocity of
light has been abundantly commented on by many
authors. The general opinion is that it is due to Ole (or
Olaus) Rømer (Figure 1),
1
who published it on 7
December 1676 in the Journal des Sçavans. The paper
by Rømer
(1676), well-written and very clear, shows
that the discovery was made while studying the motion
of the first Galilean satellite of Jupiter, Io (Figure 2).
There is, however, some doubt about this discovery,
which we will now try to dissipate. Before this, let us
examine why the satellites of Jupiter were so actively
observed during the seventeenth century.
Figure 1: Ole Rømer, engraving by J.G. Wolffgang (1735).
Rømer appears here in full glory. After his return to Denmark,
around 1681, he became Mayor and head of the police of
Copenhagen, and also head of the State Council of the Realm
(Library of the Paris Observatory).
Figure 2: Rømer’s drawing in his article of the Journal des
Sçavans. The Sun is in A, Jupiter in B with its shadow cone,
and the drawing is in the reference system Sun-Jupiter. Two
positions of the Earth, L and K, are represented at the times of
two emersions of the first satellite out of Jupiter’s shadow; in
D, the Earth moved away from Jupiter between these two
observations, and the second one seems late because of the
extra time required for the light to propagate. Conversely,
immersions of the satellite in the shadow, in C, seem
increasingly early when the Earth moves from a non-labelled
point to G (Library of the Paris Observatory).
Immediately after he discovered the four main
satellites of Jupiter, Galileo proposed that their motion
could be used as a natural clock. In 1692 Jean-
Dominique Cassini (Figure 3) wrote:
It is not by curiosity alone that the most famous
astronomers of the present century have observed with
so much care the planet Jupiter; they mainly did it in
order to obtain an exact knowledge of longitudes, on
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
98
which the perfection of geography and navigation
depends. They estimated that one would have a fast and
secure way to determine longitudes, if one could find in
the sky some rapid phenomenon which could be
observed at the same time from very distant points on
the Earth. This being assumed, comparing with each
other the times of observations done simultaneously in
different locations distant from each other from the East
to the West, it would be easy to know by how much one
of these places is more to the East than the other; which
indicates their difference in longitude. (Cassini, 1692: 1-
2; our translation)
Figure 3: Jean-Dominique Cassini, by Lépold Durangel (1879),
from an old engraving. The Paris Observatory is on the
background, with one of the long refracting telescopes used by
Cassini, placed here by mistake on the roof of the building
(Library of the Paris Observatory).
The eclipses of the Jovian satellites thus allowed
clocks in different locations to be synchronized. Mea-
suring with clocks synchronized in this way the times
of meridian transit of the Sun or of the same star at
each location, one obtains by subtraction the difference
of longitude of these places after small well-known
corrections are made. Prior to this, lunar eclipses were
used, but as Cassini (ibid.) noted, “… these eclipses
are not frequent enough, and they are so difficult to
observe that one has not found in this way the longi-
tudes of many places.” Improvements in instruments
allowed easy observations of Jupiter’s satellites, at
the very time when Cassini (Figure 3) took over the
leadership of the Paris Observatory (which was
founded in 1667 by the French Academy of Sciences).
Cassini (1692: 2-3; our translation) continues:
This only became possible in 1668, when Mr. Cassini
published ephemerides from these satellites, and the
method to calculate their eclipses. Since that time, one
has performed at the Observatory a large number of
observations, together with astronomers of the Academy
sent especially by order of the King in all parts of the
world, and with other astronomers with whom mail was
exchanged; and by the means of these observations one
found in the longitudes indicated on all maps a large
quantity of errors which have been corrected for.
This was obviously of prime importance, so that Ber-
nard le Bouyer de Fontenelle (1657–1757) was able to
write:
Were there no other use of astronomy than that drawn
from Jupiter’s satellites, it would justify well enough
these huge calculations, these diligent and scrupulous
observations, this large ensemble of instruments built
with so much care; [and] this superb building [the Paris
Observatory] raised for our science. (Fontenelle, 1740:
3; our translation).
In another text, Cassini (1693a) gives an historical
account of the attempts to use Jupiter’s satellites for
longitude determination. One can find there the names
of Galileo, Peiresc and Kepler, as well as lesser-known
astronomers. Cassini claimed that it was possible to
reach an accuracy of 15 seconds in the determination
of the time of immersion or emersion of a satellite. A
study by Suzanne Débarbat (1978) shows that this
figure is somewhat optimistic: differences between the
observers could reach half a minute, even for the
eclipses of Io. But the accuracy of the observations of
Jupiter’s satellites was sufficient to show the irregu-
larities in their motions, some of which were well
understood and taken into account in the ephemerides,
while others were not. It is in this context of system-
atic research that the discovery of the finite nature of
the velocity of light occurred.
2
2 THE DISCOVERY
Amidst the numerous texts which describe and com-
ment on the discovery of the finite velocity of light, the
poorly-known one by Urbain J.-J. Le Verrier (1811–
1877), written in 1862 on the occasion of the first
accurate measurement of this velocity by Léon Fou-
cault (1819–1868), appears to us of particular interest.
Le Verrier (1862) reminds us that the astronomer Jean
Picard (1620–1682) was sent to Denmark in 1671 to
measure the longitude difference between the old
observatory of Tycho Brahe and the Paris Observa-
tory, and that he was helped by a young man named
Rømer, who “… showed such great abilities for
astronomical works that Picard took him back to
France where he became one of the most active mem-
bers of the Observatory.”
A letter from Cassini to Picard dated 3 October 1671
provides further information:
M. Carcani will see that M. Colbert [the Prime Minister
of France] knows how strongly you insist on the reward
due to M
r
. Bartholin for his work on the observations of
Tycho, and will take care that the money is sent to him,
as well as the fee due to the young man you recommand
and who worked with you at Uranibourg, so that he can
come to Paris. He will certainly do this rapidly so that
no time is lost. (Cassini, 1671; our translation).
Erasmus Bartholin (1625–1698) was a famous physi-
cist and astronomer from Copenhagen, and the young
man was obviously Rømer. Colbert granted them
2,000 livres, as reported in another letter from Cassini
to Picard dated 10 October. But let us continue with
Le Verrier’s text:
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
99
This is Rœmer’s discovery. Its extreme simplicity does
not decrease its value. The contemporaries have first
dismissed it; later, they attempted to divert a part of the
merit to Cassini. It seems that in this respect the
scientific habits are the same today as they were in that
time ... When one considers the origins of a discovery, it
is rare not to find some obscurity ... Should we ask
ourselves if Rœmer is the sole author of the discovery
of the velocity of light, in agreement with the only
tradition of our time? (Le Verrier, 1862; our translation).
3 THE ROLE AND THE RESERVATIONS OF
CASSINI
As remarked by Le Verrier (ibid.), the history of the
discovery of the finite velocity of light is not entirely
clear. Let us examine the chronology, which is of
importance as in the case of many discoveries.
The minutes of the Académie Royale des Sciences
are incomplete for the year of the discovery, between
18 July and 14 November 1676. The missing content
can however be reconstructed, thanks to indirect
sources that cite or copy it. Jean-Baptiste Du Hamel
(1624–1706), Secretary of the Academy from its
creation to 1697, reproduces in 1698 in his Histoire de
l’Académie in Latin a text that he considers important
and little known (Du Hamel, 1698: 143-146). Here is
an English translation of what he wrote, based on a
somewhat later manuscript that was translated into
French:
The different configurations of Jupiter’s satellites being
of great importance for Astronomy and Geography, Mr
Cassini found it adequate to warn astronomers on 22
August by means of a public announcement about the
way they will appear during the next year, in order to
determine accurately their motions.
But because one cannot find copies of this report
anymore and since it is very short, we thought it
opportune to reproduce it here. Selected observations of
Jupiter’s satellites made by the Academy during the past
five years have displayed a new inequality common to
all of these satellites, and which is of such importance
that it could cause the prediction of their eclipses to be
in error by up to a quarter of an hour. For example, the
emersion of the first satellite on 16 November occurs
about 10 minutes later than according to the calculation
based on emersions observed immediately after the
opposition of Jupiter. (Du Hamel, s.d.).
If one had doubts about the correctness of the trans-
cription he gives next, another document which proves
that Du Hamel is entirely reliable. Joseph Nicolas
Delisle (1688–1768) and his collaborators collated
before 1738 the minutes of the Academy (including the
now missing ones) when preparing an ambitious, but
never written, book on the history of astronomy. Their
collation, which is literal, can be found in a manuscript
register (Figure 4) conserved in the Library of the Paris
Observatory (Anonymous 1, s.d.). Here is our trans-
lation of their text:
Inequality of Jupiter’s satellites, by M. Cassini. 22
August 1676
The selected observations of the satellites of Jupiter
decided by the Academy five years ago yielded a new
prostapheresis [irregularity of motion],
3
the same for all
the satellites, which is so important that it could give an
error up to a quarter of an hour in the prediction of the
eclipses; thus, for example, the next emersion of the
first satellite on 16 November will occur about 10
minutes later than predicted by the calculation, which
usually derives from the emersions which occurred
immediately after the opposition of Jupiter and the Sun
in the months of July or August.
This irregularity is related to a variation in the visible
diameter of Jupiter, or to the distance of Jupiter from
the Earth, and it seems to come from the fact that light
arrives from the satellites with a delay such that it takes
ten or eleven minutes [to cross] a distance equal to the
half-diameter of the annual orbit. [our italics].
But the difficulty with this element would make the
calculation very intricate if one could not find at the
same time a method to build tables in which the true
times of the eclipses of any satellite are obtained only
from its mean motion and from a single prostapheric
table, without help from other tables.
This table will contain the inequality of the days or the
true motion of the Sun [i.e. the inequality due to the
eccentricity of the Earth’s orbit], the eccentric motion of
Jupiter [i.e. the inequality due to the eccentricity of the
orbit of Jupiter] and this new, not previously detected,
inequality. This sort of table will surpass all those in
use until now thanks to its shortness, to the ease of its
use and to the extent of the data.
Figure 4: The manuscript of the text of Cassini of 22 August
1676. It is written on two pages, joined together here. It is very
probably from the hand of Delisle (Library of the Paris
Observatory).
The discovery of this manuscript—where the
mentioned date is beyond any question because the
excerpts of the Minutes of the Academy were copied in
chronological order—solves definitively a date
problem raised by the version of Du Hamel. In effect,
the page setting of his book could raise a doubt about
the date of the discovery to which it related.
4
On his
side, Pedersen (1978) supposes that Du Hamel’s mem-
ory was failing when he reproduced this text at the age
of 75, and that his citation concerns Rømer rather than
Cassini. The manuscript collation negates this hypoth-
esis. The first written account of the discovery is thus
undeniably by Cassini.
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
100
It is not known if the 16 November emersion for
which a delay was predicted with respect to ephem-
erides was actually observed or not. However, another
one had been observed on 9 November, with a delay of
10 minutes (Anonymous 2, 1676).
After the Minutes of the Academy are resumed, one
reads for 21 November 1676:
Römer read to the Company an account where he shows
that the motion of light is not instantaneous, which he
demonstrated by the inequalities in the immersions and
emersions of the first satellite of Jupiter. He will confer
with Messieurs Cassini and Picard in order to insert this
report in the first Journal. (Our translation).
The mentioned account is from an article to be
submitted to the Journal des Sçavans, which was
published on 7 December 1676, as we have seen.
However, Cassini soon raised objections about the
hypothesis of the “… successive propagation of light
…”, and he attempted to raise other possibilities to
explain an inequality that he did not clearly find in the
eclipses of the other satellites:
Saturday 28 November, the Company being assembled
... the immersions and emersions of the first satellite of
Jupiter were again discussed, and the fact that the sum
of immersions is shorter than the time of emersions, and
it was considered relevant that Mr Cassini gives in
writing the reasons he proposed, and Mons
r
Römer will
answer.
[The following Saturday, 5 December] Mons
r
Cassini
read his observations on the inequalities of the motions
of the satellites of Jupiter. (Minutes of the Academy of
Sciences, 1676; our translation).
The objections of Cassini can be found in a later text
(Cassini, 1693a: 391; our translation):
[After correcting for the known inequalities] … there
remain other inequalities in the motions of Jupiter’s
satellites, that differ from each other. When con-
structing my first tables, the motion of the fourth
satellite looked to me more equal than those of all the
others, and the first satellite seemed to approach the
equality of the fourth. I noticed that in the second and
the third there were more important inequalities, and I
confessed that in the ephemerides I used some empirical
equations which I derived from the observations [see
later], whose causes I could not yet discover. Monsieur
Romer explained very ingeniously one of these in-
equalities that he observed for several years in the first
satellite by the successive motion of light, which needs
more time to come from Jupiter to the Earth when it is
more distant than when it is closer; but he did not
examine if this hypothesis would suit the other satel-
lites, which would require the same time inequality.
Cassini (1693b: 47; our translation) also writes:
The Academy did indeed notice in the series of these
observations that the time for a considerable number of
immersions of the same satellite is appreciably shorter
than for the same number of emersions, something
which can be accounted for by the hypothesis of the
successive motion of light: but this was not enough to
convince the Academy that the motion of the light is
indeed successive, because one cannot be certain that
this time inequality is not produced by the eccentricity
of the [orbit of the] satellite, or by irregularities in its
motion, or by some other cause not yet understood, that
might become clear in the future.
Thus Cassini abandoned the hypothesis of the finite
velocity of light, because of irregularities in the motion
of Jupiter’s satellites that he could not understand.
However, he had the intuitive feeling that some of
them could result from the interaction between the
satellites (but did he know of Newton’s Principia?).
5
Rømer’s idea was accepted with enthusiasm by
Christiaan Huygens (1629–1695), who had temp-
orarily left Paris for the Netherlands in June 1676 and
discovered them through the excellent English
translation (by Halley?) of the Journal des Sçavans
paper, which was published on 25 July 1677 in the
Philosophical Transactions of the Royal Society
(Rømer, 1677). Actually, Huygens needed a finite
velocity for light in order to account for reflection and
refraction in his undulatory theory (Costabel, 1978;
Verdet, 1978), and he was very pleased with Rømer’s
theory.
6
In his Traité de la Lumière of 1690, which
was written in 1678 (after he returned to France) and
was shown to his colleagues at the Royal Academy of
Science, in particular the “… famous Messieurs,
Cassini, Romer and De la Hire …”, Huygens repro-
duces the demonstration of Rømer, “… waiting for him
to give every element for its confirmation.” (Huygens,
1690: 467). Then he calculates the velocity of light
from Cassini’s and Rømer’s data, and finds it
… more than 600,000 times larger than that of sound,
which is not at all the same thing as being instan-
taneous, since there is the same difference as between
something finite and something infinite … (Huygens,
1690: 469).
In modern units, he found 230,000 km/s. Note that
Huygens was the first scientist to give a numerical
value for this velocity (Wróblewski,
1985); neither
Cassini nor Rømer had attempted this, probably
because they considered that the velocity was incon-
ceivably large. There is in the Histoire de l’Académie
Royale des Sciences for 1676 (on page 215) a figure
for the velocity of light of “… 48,203 lieues communes
of France [per second] …”,
7
but one should realize that
this text was only printed in 1733. The context
suggests that it was written by Fontenelle some time
after 1707.
4 WHY DID CASSINI PERSIST WITH HIS OPINION?
Cassini had doubts about the explanation of some
astronomical phenomena several years before 1676.
His certainties began to be shaken as early as 1671, on
the matter of an apparent displacement of Polaris with
respect to the North Celestial Pole, which he dis-
covered.
8
This displacement was real, but neither
Cassini nor Picard nor Jean Richer (1630–1696), who
also observed it, could understand the cause, which
was aberration. What is important for us here is that,
probably for the first time in his career, Cassini was in
doubt: would it ever be possible to do better than
Tycho Brahe, who reached an accuracy of the order of
one minute of arc in his observations?
This position of doubt was also his when he
discussed the delays in the eclipses of Jupiter’s
satellites. His carefulness explains why he proposed
several hypotheses on the same footing: either the
delays were due to the finite velocity of light, or they
came from other causes, like a variation in the
diameter of Jupiter. The possibility of such a variation
looks absurd to us, but in Cassini’s time it was not,
since nothing was known about the physical nature of
the planets. Cassini himself discovered variable spots
on Jupiter, and he thought that he saw dark zones on
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
101
the satellites which made their apparent diameter
variable.
9
Cassini’s doubts about the hypothesis of the finite
velocity of light are those of an experienced scientist:
as claimed by Fontenelle (1707: 79), “… an hypothe-
sis must account for everything.” Giacomo Filippo
Maraldi I (1665–1729), Cassini’s nephew who also
worked at the Paris Observatory, writes: “In order for
an hypothesis to be accepted, it is not enough that it
agrees with some observations, it must also be con-
sistent with the other phenomena.” (Maraldi, 1707:
32). If one was unable to find the expected delays or
advances in the eclipses of the other satellites of
Jupiter, masked by irregularities that could only be
seen without understanding them, one had to abandon
their explication in terms of the successive motion of
light. Maraldi also considered rightly that the eccen-
tricity of the orbit of Jupiter, which is rather large,
should affect by several minutes the delays or ad-
vances of the eclipses if they were due to the finite
velocity of light, but he claimed in 1707 (ibid.) that he
had not seen this effect (which however was found
later!). Backed up by this new argument, Cassini stuck
to his position until the end of his life. Conversely,
Rømer threw himself without hesitation into promoting
the hypothesis of the finite velocity of light. One
should remember that his article was published with
the agreement of Cassini and Picard, who let him take
sole responsibility for this.
Rømer never made public a refutation of Cassini’s
arguments against the successive motion of light.
However, this can be found in a letter in Latin that he
wrote to Huygens on 30 September 1677, where (at
Huygens’ request) he provided details of the discovery
(Huygens, 1888-1950, t. 8: 32-35). From this letter, it
seems that Picard shared Cassini’s doubts. Rømer
gives four reasons which, according to him, explain
why the advances or delays due to the finite velocity of
light cannot be seen clearly in the three external Galil-
ean satellites: their immersions and emersions are less
frequent than for the first satellite; their motions are
slower so that the timing of these events is less
accurate; the uncertainties in the inclinations and nodes
of their orbits might also give errors of several minutes
for eclipses occurring obliquely in the shadow; and
finally:
It is certain that these satellites exhibit irregularities that
are not yet determined, either due to eccentricity [of
their orbits] or to some other cause, which produce
discrepancies between observations and the theories of
D. Cassini of time intervals two or three times larger
than the one we are looking for and determine from the
first satellite. (Huygens, ibid.; our translation).
This is not really an explanation, since Rømer, like
Cassini and Picard, did not understand the reason for
these discrepancies. Yet in another part of the letter,
Rømer demonstrates in a most convincing way that no
other cause than the finite velocity of light can account
for the delays or advances in the eclipses of the first
satellite.
In spite of Cassini’s views, the idea of the finite
velocity of light made its way into France and else-
where. If Maraldi I did not take the velocity of light
into account in his tables, the Swedish astronomer Pehr
Wilhelm Wargentin (1717–1783) did in his Tabulae
pro calculandis eclipsibus satellitum Jovis. Calculated
in 1741, these were the best Jovian satellite tables
available at the time (Wargentin, 1746). These tables,
and to a lesser extent those of Giovanni Domenico
Maraldi (1709–1788, a nephew of Maraldi I), were
used by Jean-Sylvain Bailly (see Condorcet, 1763),
Joseph-Louis Lagrange (1766) and Pierre-Simon La-
place (1788) in support of their theory of the motion of
Jupiter’s satellites.
5 HALLEY’S CRITICISMS
The English astronomer Edmond Halley (1656–1742)
is well known for having shown that the comet to
which his name has been given reappears regularly
every 76 years or so. Halley (Figure 5) knew Cassini
very well, and visited him at the Paris Observatory
during the first months of 1681.
10
Halley was thus
very aware of the work carried out at the Observatory
on the satellites of Jupiter. In 1694, he published an
adaptation for London of Cassini’s new ephemerides
for Jupiter’s satellites (Halley, 1694). He acknow-
ledged that they were rather exact, but he made im-
portant criticisms.
Figure 5: Edmond Halley (after Wikipedia Commons).
Halley’s text of is very interesting. He adopts as
‘most ingenious’ Rømer’s hypothesis, acknowledges
Cassini’s opposition, then gives details about the way
the latter constructed his new tables. Maraldi I
explained why Cassini did not take the eccentricity of
Jupiter’s orbit into account, “… which would occasion
a much greater difference than the Inequality of Jupiter
and the Earth’s Motion, both of which are accounted in
these Tables with great Skill and Address.” Cassini
introduced an inequality in the orbital motion of the
first satellite, assuming that the eclipses occurred 14m
10s earlier when Jupiter was in opposition that when it
was in conjunction (we do not understand why Cassini
choose this value, which is too small); which corre-
sponds to an inequality of 2º in the orbital longitude of
the satellite as seen from Jupiter. Halley (ibid.) con-
tinues:
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
102
But what is most strange, he affirms that the same
Inequality of two Degrees in the Motion, is likewise
found in the other Satellites, requiring a much greater
time, as above two Hours in the fourth Satellite: which
if it appeared by Observation, would overthrow Mon-
sieur Romer’s Hypothesis entirely ... [so] Monsieur
Cassini has, by his Praecepta Calculis ... supposed that
the Minutes thereof to be increased in the same pro-
portion; as instead of 14′. 10″. in the First, to be 28′.
27″. in the Second, 57′. 22″. in the Third, and no less
than 2h. 14′. 7″. in the Fourth; whereas if this second
Inequality did proceed from the successive propagation
of Light, this Æquation ought to be the same in all of
them, which Monsieur Cassini says was wanting to be
shown, to perfect Monsieur Romer’s Demonstration;
wherefore he has rejected it as ill founded. But there is
good cause to believe that his motive thereto, is that he
has thought not proper to discover.
11
From the letter of Rømer to Huygens cited above, we
can understand why Cassini used this ‘most strange’
trick when building the ephemerides for the external
satellites: he had observed for them inequalities “…
two or three times larger …” than for Io.
Halley then attempted to confirm the hypothesis of
the finite velocity of light. Analysing various observa-
tions, some of which were made by Cassini, he showed
that the inequalities for the third and the fourth satel-
lites are much smaller than considered by Cassini, and
were compatible with the idea of the successive propa-
gation of light. Halley finally noted that Cassini’s
tables, printed in Paris by the Royal Printing Office,
were full of mistakes “… which yet ought not in the
least to be attributed to the Excellent Author, but rather
to the Negligence of those employed by him.”
Therefore, in spite of his admiration and respect for
Cassini, Halley did not hesitate to strongly criticize his
stubbornness in rejecting the idea of the finite velocity
of light, and also the strange recipes he used to build
the tables of the second, third and fourth satellites of
Jupiter—which were fortunately much less observed
than the first satellite.
6 CONCLUDING REMARKS
A text by Fontenelle (1707), the successor of Du
Hamel as the Secretary of the Academy, summarizes
the facts quite correctly, and we now see that there is
no reason to contest it as has been done by several
commentators (including Le Verrier):
The observations of Jupiter’s satellites made by the
Academy from 1670 to 1675 lead to the discovery in
their motion of an inequality not previously known ...
M. Cassini and M. Roëmer, then a member of the
Academy, after scrutinizing this anomaly, found that it
depended of the distance of Jupiter from the Earth …
They called it the second inequality ... A very ingenious
conjecture on the cause of this inequality first came to
the mind of the two astronomers. They imagined that
the motion of light was not instantaneous as all previous
philosophers believed, but that it took some time to
spread ... M. Cassini proposed this idea in a writing
published in August 1674 [actually 1676, for Fontenelle
was fooled by the page setting of Du Hamel’s book and
made a further careless mistake], to announce to astron-
omers the second inequality he had discovered in the
satellites of Jupiter. To gain their confidence, he pre-
dicted that this inequality would cause a delay of 10
minutes, with respect to the calculations, for an emer-
sion of the first satellite due for the following 16 Nov-
ember.
But M. de Cassini did not remain convinced for long
that the successive propagation of light produced this
second inequlity, while conversely M. Roëmer stuck to
this hypothesis, and maintained it with such strength
and subtlety that it became his own, and that a large
number of skilled philosophers took it from him.
Indeed, it was worthy of inspiring some sort of passion
in a high-spirited man. Why should light be able to
cross space instantaneously, but not a piece of marble
[i.e. a material object]? The motion of the most subtle
body can only be faster than that of a heavier and more
massive object, but it cannot be instantaneous either ...
If one wishes that the motion of light be not a real
change of place, an effective transport, but a simple
pressure of some subtle matter, an undulation, sound is
another one but it does not spread in an instant.
Moreover, the 14 minutes that light takes to cross the
diameter of the Earth’s orbit, i.e. 66 millions of lieues,
makes it pleasantly easy to perform calculations on this
motion, to compare it to that of sound, to build upon it
elevated and subtle speculations, and all this persuades
in favour of the hypothesis. (Our translation).
12
However, convinced by the arguments of Maraldi I
published in the same volume, Fontenelle concluded
that
… we must abandon, although perhaps with regret, the
ingenious and attractive hypothesis of the successive
propagation of light, or at least the only certain evidence
that we thought we had for it, because a missed proof
does not make a thing impossible. (ibid.).
As we have seen, the English astronomers were
much less reluctant to adopt the hypothesis. In France,
one would have to wait until 1728, the date of the
discovery of aberration by James Bradley, to see
scientists convinced that the propagation of light was
not instantaneous. Bradley (1728) understood that
… [if] Light was propagated in an Instant, then there
should be no Difference between the real and visible
Place of an Object … [and that] if Light was propagated
in Time, the apparent place of a fixt Object would not
be the same when the Eye is at Rest, as when it is
moving in any other Direction, than that of the Line
passing through the Eye and Object; and that, when the
Eye is moving in different Directions, the apparent
place of the Object would be different …
This is aberration. Bradley realized that his discovery
confirmed at the same time the finite velocity of light
and the revolution of the Earth around the Sun (the
first observational proof of the hypothesis of Coper-
nicus). He admitted, however, that since no one had
yet succeeded in observing the annual parallax of the
stars, which also resulted from the revolution of the
Earth,
… the Anti-Copernicians have still room to object
against the Motion of the Earth; and they may have
(if they please) a much greater Objection against the
Hypothesis, by which I have endeavoured to solve the
fore-mentioned Phænomena; by denying the progressive
Motion of Light, as well as that of the Earth. But I do
not apprehend, that either of these Postulates will be
denied by the Generality of the Astronomers and
Philosophers of the present Age. (ibid.).
But let us come back to our question: who discovered
the finite velocity of light? If we take literally the text
of 22 August 1676, then it was Cassini. This is also
affirmed by Jean Étienne Montucla (1758: 579) who
wrote:
One generally attributes to Roemer the merit of having
found an explanation both likely and ingenious of this
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
103
phenomenon. But this is mistaken; one can see in a
writing by Cassini, published in August 1675 [actually
1676], that this astronomer was the first author.
However, perhaps Cassini wrote on behalf of his
team, which included Picard, Rømer and perhaps even
Richer and Philippe de La Hire (1640–1718). This
becomes a most convincing hypothesis when one reads
the minutes of the Academy and considers the working
methods at the Paris Observatory: it may be that the
discovery was collective, and was due to both Cassini
and Rømer, as suggested by Fontenelle (we should
remember that Cassini was still alive when Fontenelle
was writing his ‘history’, and that they both attend-
ed Academy meetings every Saturday). In any case,
Cassini cannot be dismissed for this discovery, as
proposed by some commentators, and we must ac-
knowledge his eminent contribution to the solution “…
of one of the most beautiful problems in physics.”
(Cassini, 1693b: 46). He behaved like an open-minded
scientist, who left to others the possibility of promoting
ideas opposite to his own beliefs; but he also showed
some stubbornness when refusing to adopt the idea of
the finite velocity of light, in spite of Halley’s demon-
stration—which he could hardly ignore.
Even if the discovery of aberration solved in a de-
finitive way the problem of the velocity of light, the
situation surrounding the ephemerides of Jupiter’s
satellites remained unsatisfactory until the time of La-
grange and Laplace, in spite of the efforts of Wargen-
tin and of Maraldi II. Empirical terms were still
introduced in order to account for the observations in
the best possible way. The ephemerides remained in
use for determining longitudes until the end of the
eighteenth century, because they were precise enough
in the short-term to give time, hence longitude, within
a few minutes: this only required a single eclipse
observation, without need for comparison with a
simultaneous observation in Paris. But this was only
possible on land; observations of Jupiter’s satellites
made at sea were impossible in practice because of the
motions of the ships. In this case, the solution finally
came with the construction of precise marine chrono-
meters by John Harrison (1693–1776) in England
between 1737 and 1773. Good marine chronometers
were also built in France by clock-makers like Ferdin-
and Berthoud (1727–1807), Duroy and Jean-André
Lepaute (1709–1789), and were tested ashore and at
sea by astronomers. By 1800, longitude could be
determined within a fraction of a degree on voyages of
one or two months’ duration.
7 NOTES
1. Rømer’s name is also spelt Römer, Roemer, Rœmer
and even Romer.
2. The observations used in the discovery are collected
in a manuscript by Rømer which was written two
years later.
3. Astronomers used to call prostapheresis (modern
equivalent: equation of centre) the difference be-
tween the mean and the true position of the Sun, of
a planet or of a satellite.
4. Du Hamel inserts the text in question in page 145 of
his book, in a chapter entitled “De rebus Astro-
nomicis anni 1675” (beginning on page 143). In
the margin of page 144 we find the mention ‘Ann.
1675’, but at the end of the chapter, on page 146, it
becomes ‘Ann. 1675 & 76’. It is clear, when
reading the chapter, that the text dated 22 August is
from the same year as the publication by Rømer,
i.e. 1676, but some commentators confused the
dates: for example, Montucla (1758) attributes the
text to August 1675 and Fontenelle (1707) to
August 1674.
5. Indeed, Cassini writes in an unpublished project for
an ‘Abrégé d’Astronomie’ preserved in the Library
of the Paris Observatory:
The observations show that aside from the known in-
equalities there are others which are larger in the
second and the third satellite, and smaller in the first
and the fourth. They clearly change their distances
from Jupiter and anticipate or delay conjunctions and
eclipses.
Reason demands that there are three others similar to
those of the Moon, and more difficult to disantangle,
because one of them results from the equilibrium of all
satellites together, which is continuously changing and
produces effects on each satellite. Experience shows
however that the sum of these inequalities is not large
and that they do not prevent a prediction of the
conjunctions and eclipses with approximately the same
accuracy as for the predictions of those of the Sun and
of the Moon. (Cassini, MS B4[2]; our translation).
6. On 14 October 1677 Huygens (Oeuvres Complètes,
1888-1950, t. 8: 36-37; our translation) wrote to
Colbert, the Prime Minister of France:
I have seen recently with much pleasure the beautiful
invention [sic] of Mr. Romer, to demonstrate that light
takes time to propagate, and even to measure this time;
this is a very important discovery, worthy of a con-
firmation by the Royal Observatory. As to myself,
this demonstration suits me more especially as, in
what I am writing about Dioptics, I supposed the same
thing about light, and demonstrated with it the
properties of refraction, and recently those of the
Iceland Cristal.
7. These ‘lieues de 25 au degré’ measure 4,444 metres,
so the velocity of light is calculated as 214,000
km/s, a figure somewhat smaller than that derived
by Huygens and much smaller than the current
value of 299,792.458 km/s.
8. Here is what Cassini observed, as documented in
letters to Picard, written in Italian, and preserved in
the Library of the Paris Observatory (Ms B4[3]).
On 24 October 1671, Cassini wrote:
I already told you about the difference I found for the
largest elevation of the Pole Star observed last fall,
with respect to the present one ... I plan to set up a
fixed telescope in order to see if this difference arises
from the thing itself, or from the observation. (Our
translation of the French translation Ms A4[2]).
The “largest elevation” was the elevation of the
Pole Star above the horizon at culmination. If it
varied, this was because the Pole Star was getting
closer or further from the North Celestial Pole.
Picard wrote Cassini on 13 November 1671 that he
had also seen this variation:
I can say that, unless the observations I have made last
summer during several following evenings are wrong,
the Pole Star must presently be at a distance from the
Pole of 2° 28′ 30″ instead of 2° 28′ 10″. Whatever it
may be, I have not much difficulty to imagine that the
axis of diurnal motion of the Earth, by changing its
parallelism [sic], might experience some periodical
agitation or libration. This would be enough to
account for these kinds of anomalies. (Our trans-
lation).
Laurence Bobis and James Lequeux Cassini, Rømer and the Velocity of Light
104
Cassini asked more questions of himself, before
writing to Picard on 14 January 1672:
I have found the largest elevation of the Pole Star
similar to that last fall ... I examine if the differences ...
could arise from the quality of the air, altered by the
exhausts and the smoke from the city above which the
visual rays propagate. [Note that Paris Observatory
was located to the south of the city.] (Our translation).
He then writes Picard again on 11 February:
The confrontation of the observations of the distance
of the Pole Star to the Pole, made by you, by M.
Richer and by myself, shows that the difference of the
instruments, or our estimate, or the difference in the
quality of the air, or all these things together do not
allow an exactness better than a quarter or a third of a
minute of time [probably of a degree]. (Our trans-
lation).
9. Du Hamel (1698: 27) comments on Cassini’s
observations as follows:
There are some parts in the satellites that do not reflect
light so that they are larger than they look. This is
confirmed by the shadow of the fourth satellite [on the
disk of Jupiter] because it sometimes looked more
extended than the satellite itself. And because these
kinds of spots do not always show up, and sometimes
the satellites in the same situation with respect to
Jupiter and the Sun do not always appear with the
same magnitude, M
r
Cassini believes that one may
conclude that they rotate around their axis or that they
suffer some physical changes which cause sometimes
their spots to appear then to disappear, as it happens
on Jupiter. One might also conjecture that there is a
kind of atmosphere around the first satellite, from the
fact that Mr Cassini sometimes could not see its
shadow on Jupiter when it was crossing its disk. (Our
translation).
10. Indeed, it is Cassini who suggested to Halley that
some comets should appear periodically (see Cook,
1998: 115).
11. This sentence is somewhat obscure, but there is
little doubt that Halley accuses Cassini of insin-
cerity.
12. Cassini indeed adopted 14m 10s for his new tables
instead of the 20 to 22 minutes announced before.
The actual value is 16m 28s.
8 REFERENCES
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la lumière trouvé par M. Römer de l’Académie Royale des
Sciences. Journal des Sçavans, 233-236.
*Rømer O., 1677. A demonstration concerning the motion of
light, communicated from Paris, in the Journal des
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(The translation is probably by Halley, who was then the
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– C.N.R.S.). Pp. 169-178.
Wargentin, P.W., 1746. Tabulae pro calculandis eclipsibus
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After studies at the Ecole des Chartes, Laurence
Bobis obtained the title of "Conservateur des
bibiothèques" in 1990 and obtained a Ph.D. in
1997. She worked at the National Library for three
years, then at the Ministery of Cutlure and in a big
public library. Since 2000 she has headed the
library of the Paris Observatory which is exception-
ally rich in historical manuscripts, periodicals and
books; she is also responsible for the conservation
of the historical astronomical instruments. She
authored several books, and organised with James
Lequeux three important scientific exhibitions on
Lèon Foucault, François Arago and on the velocity
of light.
Dr James Lequeux started research in radio
astronomy in 1954 as a young student, and after a
long military service obtained his Ph.D. in 1962.
He and Jean-Louis Steinberg produced the first
French text book on radio astronomy in 1960. After
a career in radio astronomy and in various fields of
astrophysics, his post-retirement interests turned to
history, and his 2005 book, l’Univers Dévoilé, is a
history of astronomy from 1910 to the present day.
He published a scientific biography of Arago in
2008 and is finishing a biography of Le Verrier.
James is now affiliated with the LERMA Depart-
ment at the Paris Observatory.
Physicist Brian Cox explaining how the first measurements fo the speed of light were made by Rømer: [watch Brian Cox explanation here](https://www.youtube.com/watch?v=DMKE5YGLnmc)
An extract of a lecture where Feynman explains the importance of Rømer's measurement: [Feynman talking about Rømer's discovery](https://youtu.be/b9F8Wn4vf5Y?t=204)
You can learn more about James Bradley's arguments here: [A Letter from James to Edmond Halley giving an Account of a new discovered Motion of the Fix'd Stars](https://ia601601.us.archive.org/24/items/jstor-27900373/27900373.pdf)
The four Galilean satellites that were used to first determine the speed of light are: Io, Europa, Ganymede and Callisto (in order outwards from Jupiter). Their orbits are approximately coplanar with the orbit of Jupiter and, as a result, they are subject to eclipses when they pass behind the planet.
The conclusion did not meet immediate universal acceptance. Other contemporary scientists like Cassini, Kepler, Hooke and Descartes believed that light travelled instantaneously. However, many other prominent figures such as Newton, Halley, Flamsteed and Huygens accepted Rømer’s findings. In 1729, James Bradley announced the discovery of the aberration of light, and the matter was well and truly settled. You can learn more about his discovery here: [Aberration of light
](https://en.wikipedia.org/wiki/Aberration_of_light)
Ole Christensen Rømer (1644-1710) was a Danish astronomer who is best know for establishing that the velocity of light is finite. He based his conclusions on nine years (1668-76) of observations of the Galilean satellites of Jupiter, made at Uraniborg and Paris, and communicated it to the Académie Royale des Sciences in Paris in 1676.
*Rømer at work in his house with his instrument **the Machina Domestica.***
Cassini abandoned the hypothesis of the finite velocity of light because he noticed that the other three Galilean moons did not seem to show the same effect as seen for Io. He believed that there were other irregularities which could not be explained by Rømer's theory. Rømer replied that it was much more difficult to accurately observe the eclipses of the other moons. The dispute between the two went on and both firmly kept their positions. Rømer claimed that he had discovered a simple solution to an important practical problem, while Cassini rejected the theory because it could not explain all the observations.
The main doubt is whether the **discovery of the finiteness of the speed of light** should be attributed to **Ole Rømer** or to **Giovanni Cassini**. Rømer worked under the directorship of Cassini at the Observatoire de Paris from 1672 to 1681.
Giovanni Domenico Cassini (1625 – 1712) was an Italian mathematician, astronomer, astrologer and engineer. Cassini is know for discovering four satellites of the planet Saturn (Iapetus, Rhea, Tethys and Dione) and noting the division of the rings of Saturn, the Cassini Division was named after him. He also observed and published surface markings on Mars, determined the rotation periods of Mars and Jupiter. He helped establish the Paris Observatory under Louis XIV of France, which opened in 1671 and he remained the director of the Observatory for the rest of his career until his death in 1712.
*An engraving of the Paris Observatory during Cassini's time.*
### Milestones of the estimations of the speed of light:
**1676** - Olaus Roemer, Jupiter's satellites: 214,000,000 m/s
**1726** - James Bradley, Stellar Aberration: 301,000,000 m/s
**1849** - Armand Fizeau, Toothed Wheel: 315,000,000 m/s
**1862** - Leon Foucault, Rotating Mirror: 298,000,000 m/s
**1879** - Albert Michelson, Rotating Mirror: 299,910,000 m/s
**1907** - Rosa, Dorsay, Electromagnetic constants: 299,788,000 m/s
**1926** - Albert Michelson, Rotating Mirror: 299,796,000 m/s
**1947** - Essen, Gorden-Smith, Cavity Resonator: 299,792,000 m/s
**1958** - K. D. Froome Radio Interferometer: 299,792,500 m/s
**1973** - Evanson et al, Lasers: 299,792,457 m/s
**1983** - International System of Units, Adopted Value: 299,792,458 m/s
Rømer announced his discovery to the Académie Royale des Sciences on the 21st of November of 1676. His discovery was reported in Journal des Sçavans on the 7th of December of 1676 and translated in the Philosophical Transactions the following year.
- Journal des Sçavants: [Démonstration touchant le mouvement de la lumière](http://fermatslibrary.com/s/demonstration-touchant-le-mouvement-de-la-lumiere)
- Philosophical Transactions: [A Demonstration concerning the Motion of Light](http://fermatslibrary.com/s/demonstration-concerning-the-motion-of-light)
This paper and private letters to Huygens are all the documents that exist about Rømer's discovery.
Rømer's work is based on geometric considerations illustrated in figure below. A represents the Sun and B Jupiter. The circle EFGHLK represents the Earth’s orbit. The circle around Jupiter represents the orbit of Io. Io is eclipsed at C and leaves the shadow and reappears at D. The point L is close represents the moment, at which time the distance between the planets is increasing at its greatest rate. Let's suppose that the Earth at L and Io is at D. After some 42.5 hours the Earth has moved to point K and Io has completed a revolution around Jupiter. If light has a finite speed then the second emergence at D will appear late when compared to the first one du to the increase distace from the Earth to Jupiter: $ LD < KD $. The same observation is valid for points F and G where the situation is reversed and immersions of Io into the shadow of Jupiter at point C appear early: $ GC < FC $.
Rømer was able to conclude that it took around 22 minutes for light to cross the diameter of Earth’s orbit around the Sun. Christiaan Huygens later converted this to more commonplace numbers, showing that by Rømer’s estimation, light traveled at about $230,000$ kilometres per second. This figure is a little off (about 27% off) the real value of the speed of light that we know today to be $299,792,458$ metres per second.
According to Einstein's theory of special relativity, **the speed of light is finite** and represents the maximum speed at which all matter and information in the Universe can travel. Nothing in the Universe can travel faster than light, which travels at **$299\,792\,458$ metres per second** in the vacuum.
Interestingly **until the 17th century, the scientific establishment believed that the speed of light was infinite**. René Descartes argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, he concluded the speed of light was infinite.
It was only in 1676, Ole Rømer and Giovanni Cassini were the first to bring forth some proof of the finiteness of the speed backed by their observations of the orbits of Jupiter's moons. This paper describes the discovery, debate and first estimation of the speed of light.