The existence of the second phase was noticed for the first time by Mr. Oldham in the records of the Indian earthquake, but he has since detected it in those of other shocks. He believes, in common with most seismologists, that the first phase corresponds to waves of elastic compression, or longitudinal waves, travelling through the body of the earth; and the second phase he attributes to waves of elastic distortion, or transversal waves, travelling in the same way, in which the particles move at right angles to the direction in which the wave travels, thus causing a slight tilting of the surface. It is probable that the waves of both phases move along curved, rather than straight, lines through the earth, that the curves are concave towards the surface, and that the velocity of the waves increases with the depth of their path below the surface. On the other hand, the surface-velocity of the first undulations of the third phase is practically constant for all distances from the epicentre, and, in the case of the Indian earthquake, it agrees almost exactly with that obtained for the velocity within the disturbed area, and as far as Bombay. It is therefore difficult to resist the conclusion that the third phase consists of undulations which travel along the surface of the earth. Diverging in two dimensions only, they fade away much more slowly than the vibrations of the other two phases. We may thus imagine these surface-undulations speeding outwards from the epicentre in ever-widening circles until they have passed over a quarter-circumference of the earth, when they should begin to converge towards the antipodes. Here they should cross each other, and again spread out as circular waves, once more in their course passing the same observatories where they were first recorded, but in the opposite order. It has been reserved for the most violent earthquake of modern times to verify this interesting conclusion. Faint, but decided, are the traces of the second crossing. At Edinburgh, they occur at 2.6 P.M., at about the same time at Shide, at Leghorn 2.10, Catania 2.12-3/4, while at Ischia there are several movements between 2 and 3 P.M. At Rocca di Papa, near Rome, the time is slightly earlier, but the undulations, like those at the first crossing, have a complete period of about 20 seconds. The distances traversed by the waves are more than 20,000, instead of less than 5000 miles; but the mean velocity with which they travelled is almost exactly the same as at first--namely, 2.95 kilometres per second. EARTH-FISSURES, SAND-VENTS, ETC.