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?
Answer
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.
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