42 Ceo DIX: 
Critical Point Curves: As is well known, for points very near to 
the shot point the impulses that come over direct paths come sooner 
than the refracted impulses. As we go out farther and farther from 
the shot point the travel times for the direct impulse and the refracted 
impulse come closer together until at some point, Q, they coincide, 
i.e., Q is a point such that the direct impulse and the refracted impulse 
from S arrive simultaneously. As we vary the direction out from the 
shot point, Q traces out the locus that we are concerned with here. 


FIG. 5 
As in the preceding section our construction is here geometrical. 
Fig. 5 shows a section of the construction. In Fig. 5 the line LL’ is 
parallel to the refracted wave fronts. Each refracted ray reaches the 
surface JJ’ at the time it would have reached that same point J;’ had 
it started from the foot of the perpendicular to LL’ drawn from this 
point Jy’, ie., SRi/o+RiRy!/v24+ Ry'Ty'/0,= S'"Ty'/01. So we have 
reduced the problem to the problem of finding the point Q on JI’ 
such that the distance SQ is equal to the distance from Q to LL’. In 
the plan of the figure (Fig. 5) we have drawn the parabola QRiQ’ 
with focus at S and directrix LL’. 
286 
