[Solution]

No. LIX.—ADVANCING BACKWARDS

Here is a most curious and interesting question:—When an engine is drawing a train at full speed from York to London, what part of the train at any given moment is moving towards York?

At any time, when the engine is drawing a train at full speed from York to London, that part of the flange of each wheel which is for the moment at its lowest is actually moving backwards towards York.

For any point, such as A, on the circumference of the tyre, describes in running along a series of curves, as shown by full lines in the diagram; and any point, B, on the outer edge of the flange, follows a path shown by the dotted curves.

If these lines are followed round with a pencil in the direction of the arrows, it will be found that the point on the flange actually moves backwards as it passes below the track, while the point A, as it completes each curve, is at rest for the instant on the track, just before it starts afresh. The speed of the train does not affect these very curious facts.

No. LX.—THE FIFTEEN BRIDGES

In the subjoined diagram A and B represent two islands, round which a river runs as is indicated, with fifteen connecting bridges, that lead from the islands to the river’s banks.