Henry Ernest Dudeney/Modern Puzzles/222 - A Mechanical Paradox

Modern Puzzles by Henry Ernest Dudeney: $222$

A remarkable mechanical paradox, invented by James Ferguson about the year $1751$, ought to be known by everyone, but, unfortunately, it is not.

It was contrived by him as a challenge to a sceptical watchmaker during a metaphysical controversy.

"Suppose," Ferguson said, "I make one wheel as thick as three others and cut teeth in them all,

and then put the three wheels all loose upon one axis and set the thick wheel to turn them,

so that its teeth may take into those of the three thin ones.

Now, if I turn the thick wheel round, how must it turn the others?"

The watchmaker replied that it was obvious that all three must be turned the contrary way.

Then Ferguson produced his simple machine, which anyone can make in a few hours,

showing that, turning the thick wheel which way you would,

one of the thin wheels revolved in the same way, the second the contrary way, and the third remained stationary.

Although the watchmaker took the machine away for careful examination, he failed to detect the cause of the strange paradox.

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