[Since this second instalment of my paper was read to the Society my attention has been called to a remarkable investigation by Hertz; in which the circumstances of collision of two elastic spheres are fully worked out, under the special limitations that both are smooth, and that their deformations are exceedingly small. This forms a mere episode in the paper, which is devoted mainly to the statical form of the problem of deformation; as, for instance, the case of the ordinary apparatus for the production of Newton's rings. But it contains a definite numerical result; giving for the duration of impact between two iron spheres of 50mm diameter, which encounter one another directly with a relative speed of 10mm per second, the value 0s·00038. This seems to be the earliest reckoning of the time of collision. The experimental verification of Hertz' formulæ was undertaken with success by Schneebeli, who obtained results in close accordance with them. His mode of measuring the duration of impact was defective, though ingenious.