The problem is evidently beyond our present powers of solution, and its interest is therefore mainly historical. All the known methods are vitiated by our ignorance of the refractive powers of the rocks traversed by the earth-waves. But, even if this ignorance could be replaced by knowledge, most of the methods suggested are open to objection. Falb's method, depending on the time-interval between the initial epochs of the sound and shock, is of more than doubtful value. Dutton's, based on the rate of change of surface-intensity, is difficult to apply, and in any case gives only an inferior limit to the depth. Time-observations have been employed, especially in New Zealand; but the uncertainty in selecting throughout the same phase of the movement, and the large errors in the estimated depth resulting from small errors in the time-records, are at present most serious objections. There remains the method devised by Mallet, and, though he claimed for it an exaggerated accuracy, it still, in my opinion, holds the field against all its successors. When carefully applied, as it has been by Mallet himself, by Johnston-Lavis and Mercalli, we probably obtain at least some conception of the depth of the seismic focus. Professor Omori and Mr. K. Hirata have recently[80] lessened the chief difficulty in the application of Mallet's method. They have deduced the angle of emergence from the vertical and horizontal components of the motion as registered by seismographs, instead of from the inclination of fissures in damaged walls. In two recent earthquakes recorded at Miyako in Japan, they find the angle of emergence to be 7.2° and 9° respectively, the corresponding depths of the foci being 5.6 and 9.3 miles. These are probably the most accurate estimates that we possess, and it will be noted that they differ little from the mean values obtained for the Neapolitan, Andalusian, and Riviera earthquakes--namely, 6.6, 7.6, and 10.8 miles. NATURE OF THE SHOCK In one respect, the earthquakes described above fail to represent the progress of modern seismology. They furnish no diagrams made by accurately constructed seismographs within their disturbed areas. The curve reproduced in Fig. 36, as already pointed out, is no exception to this statement. For another reason, the records that were obtained in Japan of the earthquake of 1891 are trustworthy for little more than the short-period initial vibrations; for, owing to the passage of the surface-waves, visible in and near the meizoseismal area, the Japanese seismographs registered the tilting of the ground rather than the elastic vibrations that traversed the earth's crust.