# What was James Bradley's calculation to calculate the speed of light?

Looking into the history of how the speed of light came to be determined, to what we know it to be today, James Bradley is often mentioned. He was credited with the discovery of the aberration of light and having used the aberration of light to calculate the speed of light. There are many online sources that confirm this, though the year of discovery and calculated speed of light differs here and there.

I've read through Bradley's "A Letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr.Edmond Halley Astronom. Reg. &c. Giving an Account of a New Discovered Motion of the Fix'd Stars" published in "Philisophical Transaction vol 35" which explains his findings of the aberration of light but makes no mention of calculating the speed of light.

How did James Bradley calculate the speed of light and what publication of his shows these calculation?

• – HDE 226868 Jan 3 '16 at 22:39
• You read the right paper. It starts at page 648 and culminates in the calculation of at a value of 10210 times Earth's orbital velocity near the top of page 653. – David Hammen Jan 4 '16 at 0:22
• This question would probably be a better suited at the History of Science and Mathematics Stackexchange site, hsm.stackexchange.com. – David Hammen Jan 4 '16 at 0:24
• Let me guess he talks to constellations for proof that Earth indeed orbits Sun, then when his calculation didn't agree with textbook he have decided to throw in a constant. Typical! – user6760 Jan 4 '16 at 4:45

Despite many online sources crediting James Bradley with having calculated the speed of light to a 295.000 km/sec (britannica) or 301.000 km/sec (wikipedia), a small nuance ought to be added. Like Ole Romer before him in 1676, James Bradley calculated the speed of light relative to something else but both never provided a value in Earth-based units.

He wrote,

This therefore being 20’’,2, AC will be to AB that is the Velocity of Light to the Velocity of the Eye (which in this Case may be supposed the same as the Velocity of the Earth's annual Motion in its Orbit) as 10210 to One from whence it would follow that Light moves or is propagated as far as from the Sun to the Earth in 8’ 12’’.

(source)

The calculation to get to the ratio of 10210 is,

size of a radian (206265’’) / angle of aberration (20’’,2)


This ratio also holds for the speed of light to the speed of the earth. Not sure though exactly how britannica and wikipedia arrive at their respective values.