The following text is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Speed of Light", page 447, topic "Michelson Method":
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Michelson and his co-workers made a series of similar experiments. The first determination was made in $1879$ with an octagonal [$8$] rotating mirror. The latest in the series was underway at the time of the death of Michelson and was completed in $1935$ by Pease and Pearson. This experiment used a rotating mirror with $32$ faces.
The following text is from the "Air & Space" article - The Pipeline That Measured the Speed of Light:
On each run, a “sun bright” beam from an arc lamp bouncing off a $16$-sided whirling mirror completed five round trips. To clock elapsed time, Michelson adjusted the mirror’s rotation until the returning beam met the next mirrored face exactly.
The first thing I noticed once I read about this experiment from different sources was - the number of reflecting surfaces in the rotating mirror is in multiples of $8$. Is this a coincidence or are there any valid reasons behind this?
I think Michelson method of determining the speed of light is different from the Michelson Morley experiment. So, I had to use the query
michelson speed of light -morley as my initial results were populated with the second experiment which has a similar name.