The quantity represented by ∫vds, or its equivalent ∫v2dt, in any case of the motion of a particle, is known to possess important dynamical relations. The accidental discovery of a singularly simple geometrical representation of this quantity in the case of planetary motion led me to inquire whether the method involved might not be easily generalized. This note contains a sketch of some of the results of a hurried investigation of the point.

Graphical representations of the action in some common cases of motion readily suggest themselves.