36 CH He DIX 
surface of the earth forms an iso-time curve which is a conic section, 
usually an ellipse. The wave front surface is not all conical but is 
partly a sector of a sphere. The spherical part corresponds to the 
wave front of the returning reflected wave incident on the interface 
at a smaller angle than a. The spherical part of the surface fits on to 
the conical part the way a sphere would rest in a cone with vertex 
down. Evidently this surface, partly spherical and partly conical 
may intersect the surface of the earth in a curve that is-partly an 

HiGar 
ellipse and partly a circle. In fact there is a curve, usually an ellipse, 
which is the curve where the cone whose vertex is S’, whose axis is 
S’S, and whose vertex angle is 2a intersects the surface of the earth. 
Inside of this curve the iso-time lines are circles and outside the iso- 
time lines are conic sections. 
Let 8 be the vertex angle of the cone of wave fronts. Then 8/2 
=o9o—a. Hence cos B/2=sin a=Vi/V>. Evidently then the shape 
of the cone, i.e., 8, depends only on V;/V»2 and not on the dip angle #. 
Observe what happens when the dip angle @ increases. First when 
0 =o the axis of the cone is vertical and the iso-time curves are circles. 
As # increases from o to a the conic sections which are ellipses have 
greater and greater eccentricities. When #=a the iso-time curves 
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