. Elements of geology : a text-book for colleges and for the general reader. Geology. EARTHQUAKES. 115 perpendicular to the surface at a, and become more inclined until it finally becomes parallel with the surface at an infinite distance. The velocity of its transit will be infinite at a, and then gradually decrease until, if we regard the surface as a plane surface, at an infinite distance it reaches its limit, which is the velocity of the spherical wave. Between these two extremes of infinity at a, and the velocity of the spherical wave at infinite distance, the velocity of the surface-wave
. Elements of geology : a text-book for colleges and for the general reader. Geology. EARTHQUAKES. 115 perpendicular to the surface at a, and become more inclined until it finally becomes parallel with the surface at an infinite distance. The velocity of its transit will be infinite at a, and then gradually decrease until, if we regard the surface as a plane surface, at an infinite distance it reaches its limit, which is the velocity of the spherical wave. Between these two extremes of infinity at a, and the velocity of the spherical wave at infinite distance, the velocity of the surface-wave varies in- versely as the cosine, or directly as the secant, of the angle of emergence x b a, x c a, etc. For, if a a, b b, c c, d d, etc. (Fig. 96), be successive positions of the spherical wave, then the radii x a, x b, x c, would be the direction both of propagation and of vibration. Now, when the wave-front is at by while the spherical wave moves from V to c, the surface-wave would move from b to c; when the spherical wave moves from c' to d, the sur- face-wave moves from c to d, etc. If, therefore, b c, c d, etc., be taken very small, so that b b' c, c c' d, may be considered right-angled tri- angles, then in every position the surface-wave moves along the hypote- nuse, while the spherical wave moves along the base of the small tri- angles b V c, c d d, etc. Letting v = velocity of the spherical wave, and v' that of the surface-wave, and E the angle of emergence (x ba, x c «, etc., Fig. 96), we have the proportion—v : v' : : 1 : sec. E, and v'= v. sec. E, or if v is constant v' a sec. E. Therefore, at a, the point of first emergence, E being a right angle and sec. E = infinity, v' = infinity. At an infinite distance from a the angle E becomes 0, and the secant. Fig. 97. = 1, and v'= v. 1 = v. That is, at the point of first emergence the ve- locity of the surf ace-wave is infinite ; from this point it decreases as the secant of the angle of emergence decreases, until fin
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectgeology, bookyear1892
