Next it was observed that the paths of the waves drawn on the surface, although generally intersecting in a point, did not do so absolutely, but along a line passing through the main focus some 7½ miles in length. This, coupled with the observations of sounds, led to the supposition that the centre of disturbance, considered horizontally, originated along a curved line passing through the chief focus and the various intersections of the wave paths. The last phenomena brought forward to assist in the solution of this interesting problem were a study of the tremulous movements that preceded and followed the shock, and their relation to the sound phenomena. If the earthquake originated by the formation of a fissure, after the rending has gone on for a certain time the focal cavity is enlarged to a certain extent, and the great shock takes place. This would be followed by concluding tremulous waves. A succession of phenomena like those accompanied the shock about which Mallet writes. By observations such as these, coupled with what has been said about the maximum and mean depths of the focal cavity, Mallet came to the conclusion that the focal cavity was a fissure, the rending open of which produced the earthquake. The vertical dimensions of this cavity were not more than 5·3 miles, but were probably limited to three miles. From the intersection of the wave paths upon the surface and the observed emergences, this fissure followed horizontally a curve of double flexure, about nine geographical miles in length. The area of this fissure was twenty-seven geographical miles. The time of rending it open in Apennine limestone would be about 7½ seconds, which should be the same as the period during which tremors were felt. The time actually recorded was six or eight seconds. Briefly, this is, then, the line of reasoning which was followed by Mallet in an investigation the results of which are as interesting as they are startling. Since the line of investigation has been opened, and the existence of new problems has been indicated, other investigators, although not exactly following Mallet’s method in all their details, have, when endeavouring to attain the same ends, employed similar weapons. Thus, for example, Seebach, when determining the depth and nature of the origin of the earthquake of Middle Germany, reasoned somewhat as follows:— Had the origin been more or less of a spherical cavity, then the region of most violent disturbance upon the surface would, according to a theorem we have already mentioned, have been upon or near a circle of about 8·8 miles in radius round the _epicentrum_. This region, however, was found by observation to lie along a curved band about forty miles in length, altogether on one side of the _epicentrum_. To explain this anomaly Seebach followed Mallet, and assumed that the origin was not a spherical cavity, but a fissure.