No hard evidence to cite (yet...I'm still looking) but IIRC, the reasoning behind pto rpms ending up @ 540 aren't nearly as complicated as some replies indicate.
What I remember hearing was, first tractor equipped with pto had an engine operating speed of around 1600rpm. Pto final gearing was arbitrarily decided to be 1/3rd of engine speed.
"It just happened to work out that way".
540rpm was closest "even number" to first workable pto's speed, hence 540 was settled upon as industry standard.
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