So the question still stands...Why 540? Why did the ASAE in April of 1927 decide that the PTO rotational speed was to be 536 +/- 10 rpm?
Yes, that is the question? Why?
I believe the early engine speed comment has merit and could be a good starting point for the ASAE logic.
One might think so, but what would the connection be? These old engines were used for a flat belt connection to the powered equipment. How does that relate to a shaft connection?
I have seen photos of a belt pulley on the rear of tractors. If it was driven by the PTO with a one-to-one ratio right-angle gearbox then having it turn at the same speed at the old engines might make some sense. Were the first PTOs used for belt connections rather than a shaft connection?