Early in my research into the Bessler mystery, I came across an article written by George Biddel Airy. It was published in the Cambridge Philisophical Transactions in the mid 1800s, and I found it at my local university library. It is entitled On Certain conditions under which a Perpetual Motion is possible, and appears to be the only known rigorous mathematical proof of the theoretical possiblity of perpetual motion.
The historical record shows that Johann Bessler might have happened upon the secret after working for some time as a pipe organ apprentice. It is interesting to note that Airy's conclusions were based on the work of Robert Willis. Willis was studying the human voice organ and did experiments with air passing over inclined plates.
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Other links:
Airy's Escapement