_The difference in time of the arrival of two disturbances._—In the various calculations which have been made to determine an origin based on the assumption of a known or of a constant velocity, we have only dealt with a single wave, which may have been a disturbance in the earth or in the water. A factor which has not yet been employed in this investigation is the difference in time between the arrival of two disturbances; one propagated, for instance, through the earth, and the other, for example, through the ocean. The difference in the times of the arrival of two waves of this description is a quantity which is so often recorded that it is well not to pass it by unnoticed. To the waves mentioned we might also add sound waves, which so frequently accompany destructive earthquakes, and, in some localities, as, for instance, in Kameishi, in North Japan, are also commonly associated with earthquakes of but small intensity. It was by observing the difference in time between the shaking and the sound in different localities that Signor Abella was enabled to come to definite conclusions regarding the origin of the disturbances which affected the province of Neuva Viscoya in the Philippines, in 1881; the places where the interval of time was short, or the places where the two phenomena were almost simultaneous, being, in all probability, nearer to the origin than when the intervals were comparatively large. I myself applied the method with considerable success when seeking for the origin of the Iquique earthquake of 1877. The assumptions made in that particular instance were, first, that the velocity of the disturbance through the earth was known, and, secondly, that the velocity with which a sea wave was propagated was also known. A method similar to the above was first suggested by Hopkins. It depended on the differences of velocity with which normal and transversal waves are propagated.[85] _Seebach’s method._—To determine the true velocity of an earthquake, the time of the first shock, and the depth of the centre. [Illustration: FIG. 32.] Let the straight line M, _m__{1}, _m__{2}, _m__{3} represent the surface of the earth shaken by an earthquake. For small earthquakes, to consider the surface of the earth as a plane will not lead to serious errors. If an earthquake originates at C, then to reach the surface at M it traverses a distance _h_ in the time _t_. To reach the surface at M_{1} it traverses a distance _h_ + _x__{1} in a time _t__{2}. If _v_ equals the velocity of propagation, _h_ _h_ + _x__{1} then _t_ = ———, _t_{1}_ = —————————————, _v_ _v_ _h_ + _x__{2} _t_{2}_ = —————————————, &c. _v_