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In Fizeau's cog experiment to determine the speed of light, how would he have had a way to accurately determine the number of rotations per second of the cog, given the experiment was conducted in 1850?

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  • $\begingroup$ In one version one compares the the pitch of the sound with that of a tuning fork of known frequency. That's probably good to a few parts in $10^4$. This is just one method, of course, for the real historic experiment you have to study the writings of Fizeau and those who reported on his work. $\endgroup$
    – CuriousOne
    Jun 21, 2016 at 19:46
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    $\begingroup$ Don't underestimate the power of simple mechanical systems for this purpose just because you are used to seeing electronic employed in modern systems. This was an era of sophistication in geared system. While I don't know what was done, one could use a worm gear to drive a counter off the shaft with a hundred or more to one step-down. $\endgroup$ Jun 21, 2016 at 20:16

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Fizeau in his paper page 92 wrote the following (rough translation) with regard to his experimental set up:

The first telescope was placed in the belvedere of a house [an architectural structure sited to take advantage of a scenic view] in Suresnes , the second on the hill of Montmartre, a distance of approximately 8633 meters

The disk with seven hundred and twenty teeth was mounted on a wheel driven by weights and built by Mr. Froment; a counter could measure the speed of rotation. The light was produced by a lamp arranged to produce a very bright light source


La première lunette était placée dans le belvédère d'une maison située à Suresnes, la seconde sur la hauteur de Montmartre, à une distance approximative de 8633 mètres.

Le disque portant sept cent vingt dents était monté sur un rouage mû par des poids et construit par M. Froment; un compteur permettait de mesurer la vitesse de rotation. La lumière était empruntée a une lampe disposée de manière à offrir une source de lumière très-vive.

and that was it.

Fizeau promised to write a further paper but never did.

So perhaps your question does not have a definitive answer?

Update The clue (from @EmilioPisanty) about the final resting place of Fizeau's apparatus has enabled me to find this video which indicates that the speed of revolution of the toothed wheel was found by using known gear ratios, a counter of revolutions and a timing device.

enter image description here

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    $\begingroup$ As I recall, the Musée des Arts et Métiers in Paris has the original apparatus, and it had some fancy way to turn the rotations into sound using some kind of whistle, which was then tuned using tuning forks. Possibly there were multiple versions of the experiment, though? Either way, maybe it's worth having a deeper dig? $\endgroup$ Mar 2, 2017 at 17:03
  • $\begingroup$ @EmilioPisanty I think this would work well and could be simple. The cogs on the main wheel would be too high-pitched to be useful, but you could put a wheel with 16 teeth on the same shaft and get (about) concert A. It is easily possible to compare frequencies in that range to ~0.1Hz by ear, and quite stable frequency sources (tuning forks!) existed. $\endgroup$
    – user107153
    Mar 2, 2017 at 18:00
  • $\begingroup$ A publication by Jan Frercks which I have just come across may be of interest? Creativity and Technology in Experimentation:Fizeau’s Terrestrial Determination of the Speed of Light $\endgroup$
    – Farcher
    Aug 14, 2023 at 9:46

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