Christiaan Huygens Presents Ole Rømer's Proof that the Speed of Light Is Finite
This is my second post on the Traité de la lumière1 [Treatise on Light], published in 1690 by Christiaan Huygens (1629-1695). The first post was
In this post, I will focus on Huygens’s presentation of the work undertaken by the Danish astronomer Ole Rømer (1644-1710, also written Römer or Roemer) to demonstrate that the speed of light is finite. This post should be seen as a continuation of my previous post, Galileo Galilei, Isaac Beeckman and René Descartes Discuss the Speed of Light.
In 1672, Rømer moved to France, and started to work under Giovanni Cassini (1625-1712), the director of the Royal Observatory. Rømer was also named tutor to the Dauphin, Louis XIV’s son and successor-to-be, who died before inheriting the throne. In 1676, Rømer correctly predicted that the eclipse of Io, Jupiter’s closest moon, by Jupiter would take place some 10 minutes late, based on the assumption of a finite speed of light. Despite his accurate prediction, Rømer’s hypothesis was not accepted by Cassini. Huygens, on the other hand, was one of the earliest supporters of Rømer.
For Huygens, Rømer’s proof supported his theory of a mechanical propagation of light waves through a sea of aether particles, said propagation needing to take time. Hence, in his Treatise on Light, Huygens presented the proof, which Rømer himself never published.
The presentation begins with the following diagram:
Below is Huygens’s explanation of the diagram:
For this he [Rømer] makes use of the Eclipses suffered by the little planets which revolve around Jupiter, and which often enter his shadow: and see what is his reasoning. Let A be the Sun, BCDE the annual orbit of the Earth, F Jupiter, GN the orbit of the nearest of his Satellites, for it is this one which is more apt for this investigation than any of the other three, because of the quickness of its revolution. Let G be this Satellite entering into the shadow of Jupiter, H the same Satellite emerging from the shadow. [p.8]
The “little planets which revolve around Jupiter” would now be called “Jupiter’s moons”. The “nearest of his Satellites” is the moon Io. Two orbits are described: first, that of the Earth, around the Sun at A, passing successively through the points B, C, L, D, E and K; second, that of Io, around Jupiter at F, passing successively through the points G, H and N. When Io passes between G and H, it is eclipsed by Jupiter, hence not visible from Earth. We call G the immersion and H the emergence2.
Huygens continues:
Let it be then supposed, the Earth being at B some time before the last quadrature, that one has seen the said Satellite emerge from the shadow; it must needs be, if the Earth remains at the same place, that, after 42 1/2 hours, one would again see a similar emergence, because that is the time in which it makes the round of its orbit, and when it would come again into opposition to the Sun. And if the Earth, for instance, were to remain always at B during 30 revolutions of this Satellite, one would see it again emerge from the shadow after 30 times 42 1/2 hours. But the Earth having been carried along during this time to C, increasing thus its distance from Jupiter, it follows that if Light requires time for its passage the illumination of the little planet will be perceived later at C than it would have been at B, and that there must be added to this time of 30 times 42 1/2 hours that which the Light has required to traverse the space MC, the difference of the spaces CH, BH. Similarly at the other quadrature when the earth has come to E from D while approaching toward Jupiter, the immersions of the Satellite ought to be observed at E earlier than they would have been seen if the Earth had remained at D. [pp.8-9]
When the Earth is moving away from Jupiter, as when the Earth moves from B to C, it is the emergences that are observed. Similarly, when the Earth is moving towards Jupiter, as when the Earth moves from D to E, it is the immersions that are observed. The period of the orbit of Io is known to be 42 1/2 hours. If, while the Earth is moving from B to C, Io revolves 30 times around Jupiter, then if the speed of light is finite, then the time in passing from B to C will be greater than 30 times 42 1/2 hours. Similarly, should Io revolve n times around Jupiter in passing from D to E, the time elapsed will be less than n times 42 1/2 hours.
Huygens continues:
Now in quantities of observations of these Eclipses, made during ten consecutive years, these differences have been found to be very considerable, such as ten minutes and more; and from them it has been concluded that in order to traverse the whole diameter of the annual orbit KL, which is double the distance from here to the sun, Light requires about 22 minutes of time.
The movement of Jupiter in his orbit while the Earth passed from B to C, or from D to E, is included in this calculation; and this makes it evident that one cannot attribute the retardation of these illuminations or the anticipation of the eclipses, either to any irregularity occurring in the movement of the little planet or to its eccentricity. [p.9]
So Rømer conducted observations for more than ten years, and was able to calculate that the time for light to pass from K from L, i.e., the diameter of Earth’s orbit, is 22 minutes.
Huygens concludes:
If one considers the vast size of the diameter KL, which according to me is some 24 thousand diameters of the Earth, one will acknowledge the extreme velocity of Light. For, supposing that KL is no more than 22 thousand of these diameters, it appears that being traversed in 22 minutes this makes the speed a thousand diameters in one minute, that is is 2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises; since the diameter of the Earth contains 2,865 leagues, reckoned at 25 to the degree, and each league is 2,282 Toises, according to the exact measurement which Mr. Picard made by order of the King in 1669. But Sound, as I have said above, only travels 180 toises in the same time of one second: hence the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite. Now the successive movement of Light being confirmed in this way, it follows, as I have said, that it spreads by spherical waves, like the movement of Sound. [pp.9-10, my emphasis]
A toise is about 1.949 meters. So by these calculations, the speed of sound is about 350 m/s, while the speed of light is at least 210’000’000 m/s. Today’s value for the speed of sound at 343 m/s at 20ºC3, very close to the value used by Huygens. As for the speed of light, today’s value is 299’792’458 m/s in vacuo4, some 43% more than the value given by Huygens; equivalently, the value Huygens calculated was some 30% less than the correct value, but the order of magnitude is correct.
What is most important, as wrote Huygens, is that “there is all the difference between a finite thing and infinite”. For the purpose of his Treatise on Light, what was crucial was that the speed of light be finite, as it would allow Huygens to explain the propagation of light as the movement of waves through the aether. That will be the subject of my next post.
If you wish to donate to support my work, please use the Buy Me a Coffee app.
Christiaan Huygens. Treatise on Light. In which are explained the causes of that which occurs in Reflexion, & in Refraction. And particularly in the strange Refraction of Iceland Crystal. Rendered into English By Silvanus P. Thompson. New York: Dover, 1962. First published by Macmillan and Company, Limited, in 1912.
I like Huygen’s idea of a finite speed of light, but I wondered, is its propagation finite? If our telescopes are seeing light that is billions of light years old, and the light is still going, is there an infiniteness to its propagation? Maybe light is both finite and infinite? Or as John Milton described it poetically, an ‘eternal, co-eternal beam’?