STRUCTURE OF THE EARTH — HODGSON 295 



stripped of all lack of uniformity throughout any concentric shell; 

 that we can find the trace velocity at any distance from the tangent 

 to such a curve; and that we can determine the true velocity at 

 the very surface of our stripped earth by application of the re- 

 fraction method described for surface conditions. We have also, 

 in effect, moved the origin from some point within the earth — the 

 focus — to a point exactly in the surface of our stripped earth. Our 

 amended time-distance graph begins at zero-zero — at the origin of 

 coordinates. We may choose any point on the surface of our stripped 

 earth and image an earthquake focus there. Proceeding to some 

 distance about the surface of the stripped earth, we come to a point 



Figure 7. — The Herglotz-Wiechert method applied for any chosen epicentral distance 

 E8 yields the value of the vertex radius rv and ttie true velocity of the earthquake 

 waves V at that depth. 



where the conditions of figure 6 obtain. Here two separate rays 

 from the focus, E, emerge at the hypothetical surface of the stripped 

 earth. It is assumed that they are chosen so that the second ray 

 reaches B just one second after the first ray reaches A. Thus the 

 distance AB is a measure of the trace velocity; for it is the distance 

 traveled by the trace in 1 second. We draw the line AC perpendic- 

 ular to CB; thus the distance CB is a measure of the true velocity at 

 the surface ; for it is the distance traveled by the wave along the ray 

 CB in 1 second. Now if we know the sides AB and CB of a right- 

 angled triangle we can measure the angle of emergence, e, which is 

 equal to angle CAB. We know the trace velocity from the amended 

 graph and the true velocity from the refraction method so we can in 



