Fig. 12.—Vertical section of Cathedral Church at Potenza. (Mallet.)[ToList]
Objection to Mallet's Method.—The weakest point in Mallet's method is probably his assumption that the wave-paths are straight lines extending outward from the focus. Even if the depth of the focus is not more than a few miles, the waves must traverse rocks of varying density and elasticity, and, at every bounding surface, they must undergo refraction. If the rocks are so constituted that the velocity of the earth-waves in them increases with the depth, then the wave-paths must be bent continually outwards from the vertical, so that the angle of emergence at the surface may be considerably less than it would have been with a constant velocity throughout. In this case, the actual depth will be greater, perhaps much greater, than the calculated depth. For instance, if the angle of emergence at Potenza were diminished only 5° by refraction, the calculated depth of the focus would be too small by 1¾ miles.
Fig. 13.—Diagram of wave-paths at seismic vertical of Neopolitan earthquake. (Mallet.)[ToList]
Mallet's Estimate of the Depth of the Focus.—Mallet measured the angle of emergence at twenty-six places, the mean angle (i.e. the mean of the greatest and least observed angles) varying from 72° at Vietri di Potenza and 70° degrees at Pertosa, which are about two miles from the calculated epicentre, to 11½° at Salerno, distant about 40 miles. Fig. 13 reproduces part of the diagram on which he plotted the mean angle of emergence at different places. The horizontal line represents the level of the sea, and the vertical line one passing through the epicentre and focus, called by Mallet the "seismic vertical." The lines on the left-hand side represent the commencing wave-paths (assumed straight) to the observing stations situated to the westward of the meridian through the epicentre, those on the right-hand side corresponding to places to the eastward of the same meridian. Small horizontal marks are added to indicate the depth in miles below the level of the sea.
It will be seen, from this diagram, that all the wave-paths start from the seismic vertical at depths between three and nine miles; but the points of departure are clustered thickly within a portion, the length of which is about 3½ miles and the mean depth about 6½ miles. So great was Mallet's confidence in these calculations that he assigns the diverging origin of the wave-paths to different points of the focus, and thus concludes that, while the mean depth of the focus was about 6½ miles, its dimensions in a vertical direction did not exceed 3½ miles.
How far Mallet's results should be accepted as correct, it is difficult to say in our ignorance of the constitution of the earth's interior. There can be no doubt that the focus was of considerable size, and that, in consequence, the wave-paths would diverge from different points of it. But that each wave-path should actually intersect the focus, and so enable its magnitude to be determined, would surely involve an approach to some law connecting the direction of a wave-path with the depth of its own origin, and no such law seems to be ascertainable. Nor can the limitation of these apparent origins between certain depths be held to argue that the focus, or any part of it, was equally confined, for the wave-paths would to a great extent be similarly refracted. I fear that the only conclusions that we can with safety draw from Mallet's admirable work are that his figures indicate the order of magnitude both of the vertical dimensions and of the mean depth of the focus.