How fully this interesting theoretical result has been confirmed is well shown in Mr. Oldham's recent and very valuable investigation on the propagation of earthquake-motion to great distances.[87] A study of the records of the Indian earthquake revealed the existence of three series of waves, the first two consisting in all probability of longitudinal and transversal waves travelling through the body of the earth, and the third of undulations spreading over its surface (pp. 282-285). Extending his inquiries to ten other earthquakes originating in six different centres, Mr. Oldham distinguishes the same three phases in their movements; the third phase being the most constantly recorded, the second less so, while the first phase is the most frequently absent. With the exception of a few very divergent records, the initial times of these phases and the maximum epoch of the third phase are plotted on the accompanying diagram (Fig. 80), in which distances from the epicentre in degrees of arc are represented along the horizontal line and the time-interval in minutes along the perpendicular line. The dots near the two lower curves refer to the records of the heavily weighted Italian instruments, and the crosses to those of the light horizontal pendulums, which respond somewhat irregularly to the motion of the first two phases (p. 282). In the third phase, there is less divergence between the indications of the two classes of instruments, and dots are used in each case for the initial, and crosses for the maximum epoch. [Illustration: FIG. 80.--Time-curves of principal epochs of earthquake-waves of distant origin. (_Oldham._)] Of the smoothed curves drawn between these series of points, those marked A, B, and C represent the time-curves of the beginnings of the first, second, and third phases respectively, while D is the time-curve for the maximum of the third phase. The concavity of the two lower lines towards the horizontal base-line shows that the surface-velocity of the corresponding waves increases rapidly with the distance, far more so than would be possible with rectilinear motion. The rates at which these waves travel through the earth therefore increase with the depth, and the wave-paths must in consequence be curved lines convex towards the centre of the earth. If the time-curves A and B were continued backwards to the origin, their inclinations at that point to the horizontal line give the initial velocities of the corresponding waves, which prove to be about 5 and 3 kms. per sec. respectively. Now, according to recent experiments made by Mr. H. Nagaoka on the elastic constants of rocks,[88] the mean velocity of seven archaean rocks is 5.1 kms. per sec. for the longitudinal waves, and 2.8 kms. per sec. for the transversal waves--values which agree so closely with those obtained for the first two series of earthquake-waves as to leave little doubt with regard to their character.