Accelerated motion of Encke's comet; its periods continually diminish–It describes a spiral, and will ultimately fall into the sun–Hypothesis of a resisting medium; how does the resistance of a medium increase the rapidity of motion?–The nature of this supposed medium, according to Arago, Encke, and Plana–Objections of M. Faye; the acceleration of motion explained by the tangential component of the repulsive force.

In our account of the periodic comet of Encke we gave, together with the dates of its successive apparitions, the durations of the revolutions comprised between these dates. If the reader will turn back to the table on p. III he will readily perceive that these durations are unequal, and that the period is continually decreasing, and has suffered a diminution of a little more than two days, or exactly of 2.06 days. As the table includes twenty-two revolutions of the comet it is at most a diminution in each revolution of two hours twenty-two minutes, a quantity small in itself, but which, incessantly accumulating, is capable of producing changes of very great importance in the course of time.

The discovery of this acceleration is due to the astronomer whose name the comet bears.