442 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1908. 



paths with accuracy through the depths of the earth. How is that 

 possible? I must attempt to give you at least an approximate idea 

 of it. 



If the precursors remained at the surface of the earth, the velocity 

 with which they are there propagated would have to remain the same 

 at all distances from the focus. Now, this is not the case. On the 

 contrary we note that the velocity of their propagation increases the 

 farther we remove from the focus and the closer we approach to the 

 opposite point. We are thus led to the conclusion that these waves 

 must find paths of more rapid propagation in the depths of the earth. 

 By studying the manner of their propagation along the surface it is 

 possible, by means of mathematics, not only to calculate their paths 

 in the interior of the earth but also to ascertain the velocity of their 

 propagation along those paths. It is a beautiful illustration of the 

 power of mathematics that all this can be done without any appeal to 

 unsafe hypothetical assumptions. We are merely concerned with 

 reliable deductions from the observations themselves. The more ac- 

 curately we are able, by the aid of the seismologic stations, to record 

 the rate of propagation of the waves on the surface of the earth in 

 point of time, the more accurately are we able to trace the paths and 

 the velocity of the earthc{uake waves in the interior of the earth. At 

 this moment there are probabl}^ 100 seismologic stations in existence, 

 with instruments which constantly record the earthquakes. Quite a 

 number of these stations possess instruments so fine and so carefully 

 watched that the arrival of earthquake waves can be recorded with 

 precision to within one or two seconds. Thus even at this day, when 

 we can look back over hardly more than ten jenrs of more intense 

 work, we possess a mass of records that we are able to use for reliable 

 deductions. And what do we find? I hope that you will feel some 

 astonishment when I announce the results, and to share with me to 

 some degree the investigator's jo}^, when I address you as the repre- 

 sentative of geophysics. 



It is found that to a depth of about 1,500 kilometers the velocity 

 both of the first and of the second precursors steadily increases, to 

 become suddenly almost constant from that point onward. It is 

 probable that there is a gradual increase in velocity even beyond that 

 point; but this is so slight that existing observations do not as yet 

 permit any definite conclusion regarding it. This statement is valid 

 to a depth of about 3,000 kilometers, that is to say, about halfway be- 

 tween the surface and the center of the earth. Existing observations 

 do not permit us to carry our inferences farther into the interior. 

 But I think even this is a respectable achievement, and, moreover, 

 we have every hope of farther advance and eventually reaching the 

 center. 



