parabola

If the load travels the reverse way, the shearing force at the head of the train is given by the ordinates of the dotted parabola.

This parabola is the curve of maximum moments for a travelling load uniform per ft. run.

Now, except for very short bridges and very unequal loads, a parabola can be found which includes the curve of maximum moments.

Let we be the load per ft. run which would produce the maximum moments represented by this parabola.

The planet would then have moved in a parabola, or an hyperbola, curves not returning into themselves.