STRUCTURE OF THE EARTH HODGSON^ 293 



we fully expect to have better ones as time goes on. The hypotheti- 

 cal, perfect graph tells us the rate at which the nose of the ever 

 widening circle of P waves is radiating outward from the epicenter 

 about the surface of the earth. That is all we ask to know. It is 

 this we crave to apprehend better year by year. 



If we knew the varying velocity with which this surface circle of 

 energy progresses throughout the entire distance range from the 

 epicenter to its antipodes, we should be able to deduce the rate at 

 which the waves travel at various depths within the earth and 

 through what surfaces of discontinuity they pass. We may speak 

 of the nose of surface energy as the trace of the waves and speak 

 of its velocity as the trace velocity or apparent surface velocity in 

 contradistinction to the true wave velocity at any point within the 

 earth. 



The time-distance graph gives the data for determining at any 

 given distance the trace velocity; for we have only to find the rate 

 at which distance varies with time at that particular distance range. 

 For example we can take as our distance say 2,500 miles. We find 

 how long it takes the trace to reach a distance of 2,500 miles by simply 

 reading the ordinate of the graph for this distance. Now we read 

 off the time it takes to go to 2,600 miles. The difference in these 

 gives the time it takes the trace to travel 100 miles at the distance 

 2,500 miles. For those who are used to the process we simply say 

 that the tangent to the time-distance curve at any distance value 

 gives the apparent surface velocity or trace velocity at that distance. 

 Suffice it to note that it may be deduced from the time-distance graph. 



The most difficult part (3f the task set by this discussion now 

 appears: that which the speaker so far "ain't never tried yet." It 

 is hoped, however, that it may prove feasible tO' present, without 

 recourse to technical details, a clear and convincing picture of just 

 how the time-distance graph contains in its very shape the data 

 from which may be deduced the velocity at any given depth within 

 the mantle of the earth. 



Before doing so, it is necessary to take drastic liberties with the 

 earth. We have a time-distance curve for an earth, the cinist of 

 which varies from one point to another. We require for considera- 

 tion a time-distance curve for an earth stripped of its outer crust. 

 We may not be able to do this physically but we can use our knowl- 

 edge of surface structure to cut off a little bit of distance and a little 

 bit of time from each end of every focus-to-station path, obtaining 

 time-distance values for that part of the earth which lies below the 

 crust. 



If you had a timetable showing the actual time it would take you 

 to go, via subway, from Times Square to the surface levels at various 

 subway stations in New York, you would not have a fair appraisal 



