# The Naked Scientists Forum

### Author Topic: How did Maxwell compute the speed of light?  (Read 14242 times)

#### don kingsley

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##### How did Maxwell compute the speed of light?
« on: 04/07/2008 09:34:04 »
don kingsley  asked the Naked Scientists:

Since you asked for any science questions, here is one that bothers
me...  How did Maxwell compute the speed of light?

Don Kingsley, Hastings Ne, USA

What do you think?

#### JP

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##### How did Maxwell compute the speed of light?
« Reply #1 on: 04/07/2008 12:59:07 »
This is how I learned the story in physics courses:

When scientists (other than Maxwell) were originally looking at electric and magnetic fields generated by charges (in a vacuum), they came up with some equations to predict the strength and direction of these fields.  It turned out that some constants were required in the equations to get the field strengths right.

Maxwell came along and (in addition to fixing one equation), he put them together and realized that combining the equations resulted in two "wave equation" which predicted that the electric and magnetic fields were waves.  All waves travel with a certain speed, and it just so happened that the constants in these equations grouped together to give precisely the speed of light.  This was a huge revelation since everyone thought those constants were just there in order to get the electric/magnetic field strengths right!  Maxwell was then able to combine this new idea of electromagnetic waves with the old idea that light was a wave in order to say that light was electromagnetic waves and give its speed accurately.

#### Alan McDougall

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##### How did Maxwell compute the speed of light?
« Reply #2 on: 04/07/2008 17:04:28 »
There were others who came before Maxwell who came up with remarkably accurate conclusions

Although Galileo was the first person of record to try to determine the speed of light, he was not successful. His experiments took place over terrestrial distances and the timing methods available to him were far to crude to make a successful determination given such distances and the very great speed of light.

It was the Danish astronomer, Olaus Roemer, who, in 1676, first successfully measured the speed of light. His method was based on observations of the eclipses of the moons of Jupiter (by Jupiter).

Roemer's estimate for the speed of light was 140,000 miles/second, which is remarkably good considering the method employed.

Michelson Measures the Speed of Light
On returning to Annapolis from the cruise, Michelson was commissioned Ensign, and in 1875 became an instructor in physics and chemistry at the Naval Academy, under Lieutenant Commander William Sampson. Michelson met Mrs. Sampson's niece, Margaret Heminway, daughter of a very successful Wall Street tycoon, who had built himself a granite castle in New Rochelle, NY. Michelson married Margaret in an Episcopal service in New Rochelle in 1877.
At work, lecture demonstrations had just been introduced at Annapolis. Sampson suggested that it would be a good demonstration to measure the speed of light by Foucault's method. Michelson soon realized, on putting together the apparatus, that he could redesign it for much greater accuracy, but that would need money well beyond that available in the teaching demonstration budget. He went and talked with his father in law, who agreed to put up \$2,000. Instead of Foucault's 60 feet to the far mirror,

Michelson had about 2,000 feet along the bank of the Severn, a distance he measured to one tenth of an inch. He invested in very high quality lenses and mirrors to focus and reflect the beam. His final result was 186,355 miles per second, with possible error of 30 miles per second or so.

This was twenty times more accurate than Foucault, made the New York Times, and Michelson was famous while still in his twenties. In fact, this was accepted as the most accurate measurement of the speed of light for the next forty years, at which point Michelson measured it again

#### quantdec

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##### How did Maxwell compute the speed of light?
« Reply #3 on: 31/07/2008 23:15:06 »
This question came up independently on the RiskAnal list server today.  I thought it might be pertinent here to share a portion of the answer I posted.

In his 1864 paper, "A Dynamical Theory of the Electromagnetic Field" (Phil. Trans. of the Roy. Soc. London; available on the Web at newbielink:http://en.wikipedia.org/wiki/Image:A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf [nonactive] ), sections (96), and (97), Maxwell cites experiments of Weber & Kohlrausch (1857), Fizeau (1849), and Foucault (1862).  The first were "electromagnetic experiments" while the last two measured the speed of light.  Maxwell refers to Foucault's estimate as the "more accurate" of the two and indeed it is within one percent of the truth.  It was "obtained by determining the angle through which a revolving mirror turned, while the light reflected from it went and returned along a measured course."  I recall reading of this experiment in modern physics textbooks, perhaps the Feynman lectures.

Maxwell cites a fourth value for "the velocity of light in the space surrounding the earth, deduced from the coefficient of aberration and the received value of the radius of the earth's orbit."  All four values are within 5% of the correct one and they bracket it.  Immediately following these comments, Maxwell draws his famous conclusion:

"The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."

#### Alan McDougall

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##### How did Maxwell compute the speed of light?
« Reply #4 on: 01/08/2008 00:58:31 »
Maxwell was a colossal genius as great as Einstein in my book.Many of Einsteins ideas were the result of what Maxell had done before him. Of course there were many others

Regards

Alan

#### The Naked Scientists Forum

##### How did Maxwell compute the speed of light?
« Reply #4 on: 01/08/2008 00:58:31 »