100 Geometrical Problems
- ANOTHER WHEEL PARADOX
Two cyclists were resting on a railway bridge somewhere in Sussex, when a
railway train went by.
"That's a London train, going to Brighton," said Henderson.
"Most of it is," replied Banks, "but parts of it are going direct towards
London."
"What on earth are you talking about?"
"I say that if a train is going from London to Brighton, then parts of that
train are all the time going in the opposite direction-from Brighton to
London."
"You seriously tell me that while I am cycling from Croydon to Eastbourne,
parts of my machine are flying back to Croydon?"
"Steady on, old man," said Banks calmly. "I said nothing about bicycles.
My statement was confined to railway trains."
Henderson thought it was a mere catch and suggested the smoke or steam
of the engine, but his friend pointed out that there might be a strong wind in
the direction. the train was going. Then he tried "the thoughts of the passen-
gers," but here there was no evidence, and these would hardly be parts of the
train! At last he gave it up. Can the reader explain this curious paradox?- A MECHANICAL PARADOX
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 skeptical 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 pro-
duced his simple machine, which anybody can make in a few hours, showing
that, turning the thick wheel which way you would, one of the thin wheels re-
volved the same way, the second the contrary way, and the third remained
[. Ferguson was an eccentnc self-educated Scottish astronomer of the 18th-century, well known
in his day as the "Peasant-Boy Phtlosopher." For a biographtcal sketch, see The Encyclopaedia
Britannica, 11th edition.-M. G.]