EARTHQUAKE MOTION TO GREAT DISTANCE Mil 



The earliest suggestion that the' propagation of earthquake movement was along 

 curved, ami not straight, wave paths is contained in a paper hy Dr. A. SCHMIDT,* of 

 Stuttgart, in which he |x>inted out that the assumption, made hy all previous investi- 

 gators, of a constant rate of propagation and a rectilinear wave path, was an improb- 

 ahle one. The very different conditions of temperature and pressure in the interior 

 of tin- earth cannot be without influence in modifying the elasticity and consequently 

 tlir rate of propagation, and an investigation of the observed rates of propagation of 

 certain earthquakes indicates that this modification result* in an incresise of the rate 

 of propagation with the depth below the surface. 



The problem has been investigated mathematically by M. P. KuD2Ki,t for the OMB 

 of a spherical body, such as the earth. He shows that the wave path which would 

 be straight in the case of a homogeneous solid, or one in which the rate of trans- 

 mission was constant for all distances from the centre, would l>e convex towards the 

 centre if the velocity of transmission increased as the distance from the centre 

 diminished, that is as the depth below the surface increased, and concave towards the 

 centre if the opposite were the case. He then investigates the form of the wave paths 

 on the assumption that the velocity of propagation is a constant function of the 

 radial distance from the centre. 



On this supposition he finds that the wave paths would form a series of curves 

 intersecting at the focus, the upward path to the surface forming part of the same 

 curve with the path of the wave motion which starts downwards from the focus in 

 the opposite direction. Each of these curves is symmetrical on either side of a 

 radius, drawn from the centre of the earth, which intersects the curve at the point 

 where it approaches nearest to the centre of the earth, and where it is tangent to a 

 circle drawn round this centre. A limiting condition is found where this radius passes 

 through the focus; in this case the curves are symmetrical on either side of the focus, 

 and the circle on which this group of curves intersects the surface of the sphere is 

 taken as the limit between an inner and an outer area. 



Turning from the wave paths and the variations in V, or the true velocity, he then 

 deals with the variations of v, or the apparent velocity at the surface. This is 

 infinite at the seismic vertical, and decreases outwards till the limit of the inner area 

 is reached, where it has its minimum value. Passing from this inner area into the 

 outer area, the value of v increases once more, and becomes infinite at the antipodes 

 of the seismic vertical. 



It is only the value of i which is investigated, but it is obvious that the value of 

 V., or the apparent average velocity of transmission from the centre, must be subject 

 to similar variations. It can never be infinite, but within the inner area it will 



* " YVellenlieweguiig mid Erdbeben. Ein Beitrag zur Dynamik tier Erdhehen." 'Jahresheft Ver. f. 

 \;uerl;m<l. Naturk. ill Wiirttemberg,' vol. 44, 1888, pp. 248-270. 



t " Ueber die scheinbare Geschwindigkeit dor Verbreitung der Erdbeben " (German translation of paper 

 in Polish, published by the Academy of Krakan). GKKI.AXD'S Bcitriige z. Geophysik, 1 vol. 3, 1888, 

 pp. 485-518. 



VOL. CXCIV. A. Y 



