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ANNUAL EEPORT SMITHSONIAN INSTITUTION, 19 39 



this way find the angle of emergence of the rays at all distances, pro- 

 vided they do not dip into the core and become deflected. Up to more 

 than half the distance around the earth from the epicenter chosen, 

 we can deduce the angle of emergence of the rays. 



As we saw in the refraction method, a ray passing from a stratum 

 of lower velocity to one of higher velocity is bent toward the surface. 

 If the true velocity increases at successively deeper levels the ray 

 will be bent more and more until it is at right angles to the radius. 

 This is its deepest point. It then traverses the second half of its 

 path, which is the mirror image of the first half; and it emerges 



FiGUEB 8. — Velocity-depth curve by Witte, 1932, based on Jeffreys' P curve. 



at the surface (of the stripped earth let us remember) at the same 

 angle of emergence with which it started. That is to say, the ray is 

 symmetrical about its center radius through the vertex. (Se© fig. 7.) 

 Clearly the amount of bending to which the ray is subjected is 

 the sum of all the effects within its path ; and the angle of emergence 

 of the ray at any given distance is determined by the velocity at 

 every depth through which the ray passed. If we could set up a 

 mathematical expression giving the value of the radius to the vertex 

 Tv and the velocity Y at that vertex, of any chosen ray defined by its 

 epicentral distance of emergence, in terms of the emergence angle 

 for that epicentral distance, we could get one value of a true veloc- 



