PARIS, March 28: For centuries, children have performed a small conjuring trick: getting a “magic” egg to stand up on a table.

The egg is hard-boiled, and when it is spun on its side, it rises vertically to stand on its end.

But how does this work?

Scientists at the University of Cambridge and at Keio University, Japan, say they have now figured out the phenomenon.

The big factor is friction, they reported in Thursday’s issue of Nature, the British science journal.

When an egg is spun on its side, its axis of symmetry — a line stretching between the eggs’ two tips — starts off by being horizontal.

Friction with the table top forces the egg to rise up in a series of little jerks, and this shifts the axis of symmetry somewhat towards the vertical.

With the egg standing up a tiny bit, gyroscopic forces then intervene.

These gradually convert the horizontal energy into a spin around the axis of symmetry. Hey presto — like a child’s top or gyroscope, the egg stands on its tip, rotating around its own axis.

Mathematician Keith Moffatt told AFP that he and Yutaka Shimomura of Keio University of Yokohoma, who was on a visiting fellowship to Cambridge, worked on the puzzle in their spare time.

After six months, they cracked it.

The horribly complex equations cover two pages, with factors including angular momentum, frictional force, angular velocity, axis of symmetry and gyroscopic balance.

To simplify things, Moffatt offered this rhyme:

“Place a hard-boiled egg on a table,

And spin it as fast as you’re able;

It will stand on one end

With vectorial blend

Of precession and spin that’s quite stable.”

The trick does not work on raw eggs, because the viscous fluid in the shell absorbs and dissipates the energy.

“By the time the whole thing is spinning up to speed, you’ve lost a lot of energy and not a lot remains to get it up on its end,” he said.

Similarly, a surface that offers no friction, or too much of it, fails to provide the kick start that makes the egg lift up and thus trigger the gyroscopic force.

Moffatt said he had been obsessed with the egg problem for a couple of years before Shimomura came along.

He confided that he had driven his wife to despair because he raided the refrigerator so often in search of eggs to experiment on.

Asked whether he thought the research would have any practical or commercial use, he said, “You never know with these things. I suppose it will find an application but I don’t know of any.

“I just thought it was a nice, amusing problem, especially at Easter time, when people are rolling eggs, and that’s really why we did it.”—AFP