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 16-2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises;[17]
Huygens was obviously not concerned about the 9% difference between his preferred value for the distance from the Sun to Earth and the one he uses in his calculation. Nor was there any doubt in Huygens' mind as to Rømer's achievement, as he wrote to Colbert (emphasis added):
I have seen recently, with much pleasure, the beautiful discovery of Mr. Romer, to demonstrate that light takes time in propagating, and even to measure this time;[8]
Neither Newton nor Bradley bothered to calculate the speed of light in Earth-based units. The next recorded calculation was probably made by Fontenelle: claiming to work from Rømer's results, the historical account of Rømer's work written some time after 1707 gives a value of 48203 leagues per second.[18] This is 16.826 Earth-diameters (214,636 km) per second.
Doppler method
It has also been suggested that Rømer was measuring a Doppler effect. The original effect discovered by Christian Doppler 166 years later[19] refers to propagating electromagnetic waves. The generalization referred to here is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio c⁄v, where c is the speed of light and v is the Earth's orbital velocity (strictly, the component of the Earth's orbital velocity parallel to the Earth–Jupiter vector), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.[19]
There is no evidence that Rømer thought that he was measuring c⁄v: he gives his result as the time of 22 minutes for light to travel a distance equal to the diameter of Earth's orbit or, equivalently, 11 minutes for light to travel from the Sun to Earth.[2][5] It can be readily shown that the two measurements are equivalent: if we give τ as the time taken for light to cross the radius of an orbit (e.g. from the Sun to Earth) and P as the orbital period (the time for one complete rotation), then
Bradley, who was measuring c⁄v in his studies of aberration in 1729, was well aware of this relation as he converts his results for c⁄v into a value for τ without any comment.[14]
不知道有没有奇怪的符号,撮合着看