When Light Slowed Down for Olaf R/omer
                 ______________________________________

                          Timothy Paul Smith
                      University of New Hampshire
                          tim.smith@unh.edu

                      (received: October 25, 1995)
           (first printed - Vol. 2, No. 4 - November 1995)
 
	One of the major revolutions of physics in the twentieth century 
has been the introduction of special relativity.  It arises from the 
counter-intuitive premise that the speed of light is constant in all 
references frames. Three hundred thousand kilometers each second, no 
matter if I am at rest, or flying by on the tail of a comet, or 
piggy-backed on a TeV proton.  It upsets and angers us.  When solids are 
contracted, time dilated and nothing is simultaneous. That the speed of 
light is constant in all references frames is not obvious to me in my 
everyday life.  In fact that light has a finite speed is not obvious 
either.
 
	Hero of Alexandria (1st-century) tells us that of course the 
speed of light is infinite.  To prove this he tells us to go outside on 
a clear and starry night with our eyes closed.  Turn our face towards 
the sky and open our eyes.  We instantly see stars.
	Now this may seem like an absurd `proof' to us until we realize 
that most of the theories of light at that time were really more 
interested in explaining sight.  Hero subscribed essentially to the 
theory of Pythagoras (c 580- c 500 bc). We see things by `touching' them 
with our `eye-ray' (my word). Sight originates at our eyes, propagates 
to the object, and returns to our eyes.  Thus sight, and therefore 
light, is modeled on the sense of touch.
 
	This was not the only theory of light in antiquity.  The Atomist 
described light as motes which started out at the object and propagated 
to the observe;
 
	The images must cross tremendous space
	In time almost dimensionless. This happens
	Because they need only the slightest push,
	...
	In the first shine of starlight, see the stars
	Respond that very instant, radiant
				- Lucretius [1]
 
 
	Perhaps I should not put too much emphasis on the writings of 
antiquity.  What could they say when such concepts as infinity and 
infinitesimal were not developed into the Calculus concepts we presently 
use?
 
	The theory of eye-rays was put to rest by an Arabic physicist 
and mathematician named Alhazen, about the year 10000,  but the speed of 
light, finite or infinite, remained veiled in its rapidity.
 
	Galileo Galilei (1564-1642) considered it but a simple problem 
to solve, in principle.  In his book "Dialogues Concerning Two New 
Sciences" (1638) he proposed:
 
	  SIMPLICIO: Everyday experience shows that the propagation
	of light is instantaneous; for when we see a piece of
	artillery fired, at great distance, the flash reaches
	our eyes without lapse of time; but the sound reaches
	the ear only after a noticeable interval.
	  SAGREDO: Well, Simplicio, the only thing I am to infer
	from this familiar bit of experience is that sound, in
	reaching our ear, travels more slowly than light; it
	does not inform me whether the coming of the light is
	instantaneous or whether, although extremely rapid, it
	still occupies time. An observation of this kind tells
	us nothing more than one in which it is claimed that
	"As soon as the sun reaches the horizon its light
	reaches our eyes"; but who will assure me that these
	rays had not reached this limit earlier than they
	reached our vision?
	  SALVIATI: The small conclusiveness of these and other
	similar observations once led me to devise a method by
	which one might accurately ascertain whether illumination,
	i.e., the propagation of light, is really instantaneous.
	The fact that the speed of sound is as high as it is,
	assures us that the motion of light cannot fail to be
	extraordinarily swift. The experiment which I devised
	was as follows:
	  Let each of two persons take a light contained in a
	lantern, or other receptacle, such that by the
	interposition of the hand, the one can shut off or admit
	the light to the vision of the other. Next let them stand
	opposite each other at a distance of a few cubits and
	practice until they acquire such skill in uncovering and
	occulting their lights that the instant one sees the light
	of his companion he will uncover his own. After a few trials
	the response will be so prompt that without sensible error
	the uncovering of one light is immediately followed by the
	uncovering of the other, so as soon as one exposes his light
	he will instantly see that of the other. Having acquired skill
	at this short distance let the two experimenters, equipped as
	before, take up positions separated by a distance of two or
	three miles and let them perform the same experiment at night,
	noting carefully whether the exposures and occultations occur
	in the same manner as at short distances; if they do, we may
	safely conclude that the propagation of light is instantaneous;
	but if time is required at a distance of three miles which,
	considering the going of one light and the coming of the other,
	really amounts to six, then the delay ought to be easily
	observable. If the experiment is to be made at still greater
	distances, say eight or ten miles, telescopes may be employed,
	each observer adjusting one for himself at the place where he
	is to make the experiment at night; then although the lights
	are not large and are therefore invisible to the naked eye at
	so great a distance, they can readily be covered and uncovered
	since by aid of the telescopes, once adjusted and fixed, they
	will become easily visible.
	  SAGREDO: This experiment strikes me as a clever and reliable
	invention. But tell us what you conclude from the results.
	  SALVIATI: In fact I have tried the experiment only at a short
	distance, less than a mile, from which I have not been able
	to ascertain with certainty whether the appearance of the
	opposite light was instantaneous or not; but if not
	instantaneous it is extraordinarily rapid - I should call
	it momentary; and for the present I should compare it to
	motion which we see in the lightning flash between clouds
	eight or ten miles distant from us.
 
				- Galileo Galilei [2]
 
 
	Whereas Galileo thought that the only aspect of the speed of 
light which needed to be addressed was measuring, at the same Descartes 
(1596-1650) tells us "I confess that I know nothing of Philosophy, if 
the Light of the Sun is not transmitted to our Eyes in an instant" [3]
 
		------====+++====------
 
	In all introductory astronomy textbooks we are told that the 
speed of light was measured in 1676. But I want to stay with Galileo for 
the present.
 
	On the night of January 7, 1610 Galileo turned his telescope to 
Jupiter and noted the planet in front of three fixed stars. He sketched 
in his notebook;
 
                 *   *   O   *               (Jan.  7, 1610)
 
Coincidentally, the next night he trained his telescope once again on 
Jupiter, and this time saw;
 
                         O  * * *            (Jan.  8, 1610)
 
He concluded that Jupiter had moved to the left (east),  which he knew 
it should not be doing.  He also thought that the "fixed stars" appeared 
to be a bit closer to each other then on the previous night.  January 
9-th was cloudy.  On the 10-th he observed;
 
                   *  *  O                   (Jan. 10, 1610)
 
and concluded that Jupiter blocked one of the "stars".  He was now truly 
intrigued.  In his sketches he tried to indicate the magnitude of the 
"stars"
 
                  X   *  O                   (Jan. 11, 1610)
 
                   *   . O    *              (Jan. 12, 1610)
 
The third "star" appeared out from behind Jupiter at about 3 o'clock in 
the morning.  Finally he spotted four;
 
                     *   O * *  *            (Jan. 13, 1610)
 
	That same year Galileo realized not only where the "stars" 
really moons of Jupiter, but also here was a clock in the heavens which 
everyone one earth could see.  He knew that this meant you could measure 
longitude!
 
		------====+++====------
 
	The whole idea of using eclipses to measure longitude is an old 
one, usually attributed to Hero of Alexandria [4] (again!). If an 
observer in Alexandria and Rome where to both note the instant they 
observed a lunar eclipse in local time, then later compared notes they 
would find that their observations varied by over an hour (1h 10m), 
which would mean about 17-degrees of longitude.  Hero already knew how 
to measure latitude,  and the distance around the earth,  thus he could 
calculate the distance between Alexandria and Rome.
	I will note that (depending on the latitude) on error of ten 
minutes leads to an error of about 150 miles.  So how good are the 
clocks of antiquity?
 
		------====+++====------
 
	Galileo's moons of Jupiter were being eclipsed every day or so. 
If he could construct a table predicting the times of eclipses as viewed 
from his observatory, a navigator anywhere in the world could calculate 
their longitude accurately and frequently.  So for several years Galileo 
took data on Jupiter's moons, but was never able to construct his table 
with any great predictive power,  and finally gave up the project.
 
	In 1668 Giovanni Domenico Cassini (1625-1712) published his 
tables of the eclipses of the moons of Jupiter, and on the strength of 
that opus he was invited by Louis XIV to continue his observations at 
the observatory in Paris.  A few years later the Danish astronomer Olaus 
R/omer joined him,  and in 1675 R/omer proposed that the discrepancy in 
time were due to the finite velocity of the speed of light.  In fact he 
calculated that it took fourteen minutes for light to cross the diameter 
of the earths orbit.
	The observation sounds so straight forward.  First measure the 
period of orbit of one of the moons of Jupiter.  To do that just count 
the number of orbits in an extended period of time,  say ten years,  
then divide the time by the number of orbits.  Now on a day when the 
earth is close to Jupiter predict the time of an eclipse six months 
later.  If you then measure the time of the eclipse six months later you 
will observe a sixteen and a half minute delay (R/omer originally 
reported fourteen minutes).
 
 
(Io) (Jupiter)          (Earth)     (Sun)             [at time 0]
         | <-- light 0 --> |
 
 
(Io) (Jupiter)                      (Sun)       (Earth) [at time 6]
         | <--------------- light+6 -------------> |
         | <-- light 0 --> | <--- light across --->|
                                the earths orbit
 
	R/omer went on to calculate the speed of light as 140,000 
miles/sec. = 225,000 km/s.  Modern measurements yield 186,000 miles/sec 
= 300,000 km/s.  The problem in R/omer's day was not the timing (the 14 
minutes was soon corrected),  but the distance.  The distance to the Sun 
was not well known.
 
		------====+++====------
 
 
	The data seems so clear, the signature so evident,  but that is 
from our 300+ year vantage point.  Newton wrote in the first edition 
(1686) of Principia:
 
	Namq; Lucem successive propagari & spatio quasi
	decem minutorum primorum a Sole as Terram venire,
	jam constat per Phaenomena Satellitum *Jovis*,
	Observationibus diversorum Astronomorum confirmata.
 
				- Newton (1686) [5]
 
	[ For it is now certain from the phenomena of Jupiter's
	satellites, confirmed by the observations of different
	astronomers, that light is propagated in succession, and
	requires about seven or eight minutes to travel from the
	sun to the earth]
				- Newton (1725) [6]
 
 
Yet when Cassini published his  tables of eclipses in 1693 he refused to 
use the "equation of light".  Instead there was a stream of `classical' 
corrections;  the eccentricities of the orbits,  the incline of the 
planes of the orbits, and so forth.  The problem was that the equation 
of light did not explain all of the data:
 
	It appears then, that we must renounce, though perhaps
	with regret, the ingenious and seductive hypothesis of
	the successive propagation of light . . . . . How little
	prevents us from falling into great errors! If Jupiter
	had but one satellite, or if the eccentricity had been
	less, and these two things are very possible, we should
	have concluded with the the utmost confidence that light
	traversed the annual orbit of the earth in 14 minutes.
 
				- Fontenelle [7]
 
	The problem for the equation of light correction is that it did 
not explain all the data. It only explained the deviation in the 
"principle moon" (Io), the other moons were not periodic with a simple 
speed of light correction factor.
 
	Farther observations seemed to be filled with all types of 
problematic details. In 1693 Cassini measured the inclination of the 
orbits of all the moons at 2-deg 55-min.  In 1707 Maraldi found that the 
incline of the second moon was 3-deg 33-min!  This is one of those 
things which are not suppose to change.  The times of the eclipses of 
some of the moons varied by as much as an hour!  It appeared as if 
predictability in the orbits had broken down.
 
	In retrospect we quickly realize that the problem was that this 
is a few-but-not-two body problem,  which can not really be calculated 
with circles and close orbits.  This too was becoming apparent in the 
first half of the eighteenth century.  Bradley recognized that the 
discrepancies might be due to the mutual attraction of the moon,
 
	While we carefully attend to future observations, by
	means of which the theory of the satellites may be
	established,*'a posteriori*, let us hope that some
	rival of the great Newton, relying upon sure and tried
	principle of gravitation, will achieve the noble task
	of investigating *'a priori* the effects of their
	mutual attraction
 
				- Bradley [8]
 
 
	Still, the theory of R/omer did eventually prevail,  and this 
first measurement of the speed of light became part of our textbooks.
 
		------====+++====------
 
	When I started this study I expected to find a great resistance 
to Olaus R/omer on the grounds that a finite velocity of light might 
have been unthinkable.  But instead I found it was resisted on the 
perfectly valid point that it didn't explain the discrepancies in *all* 
of the data.  To paraphrase Fontenelle; If there had been but one moon, 
they would have accepted the speed of light much sooner.
 
	The other thing which struck me is the practical application of 
science which drove this study,  the search  for a tool to measure 
longitude.  Hero, Galileo, Cassini and even R/omer were trying to 
calibrate this time piece in the sky.  The speed of light seems like 
such an abstract or at least esoteric measurement,  it is had to imagine 
a sea-captain relying upon its measurement to steer clear of Scylla and 
Charybdis!
 
		------====+++====------
 
[1] Lucretius, "On The Nature Of Things".
 
[2] Galileo Galilei, "Dialogues Concerning Two New Sciences" (1638).
 
[3] Rene Descartes,  "XVII Letter of the III Volume ", quoted by
	Francois-Marie Voltaire, "The Elements of Newton's Philosophy ", p 9-10 (1738).

[4] Hero of Alexandria, "Dioptra".
 
[5] Isaac Newton, "Principia" (1686).
 
[6] Isaac Newton, "Principia" third edition (1725).
 
[7] Bernard Le Bovier Fontenelle (1657-1757),
	"M'em. Acad. des Sciences, Hist." p. 80
 
[8] James Bradley (1693-1762).