1919] on The Propagation of Earthquake Waves 441 



record was obtained could be estimated with fair accuracy ; and 

 hence a comparison of the records obtained at different stations of 

 the disturbances due to the same earthquake led to the determination 

 of the position of the epicentre and of the approximate position of 

 the earthquake origin. 



With more accurate instruments of the Galitzin type, which may 

 be regarded as the finished product evolved from the various types 

 of instrument constructed by different investigators, it is possible 

 under certain conditions to determine the position of the epicentre 

 from the record of one set of seismometers at a given station. The 

 steady accumulation of observations has led to a gradual improve- 

 ment of our knowledge of the times of transmission of the two types 

 of earthquake wave over arcs of different size. It is usual to call 

 these types of wave the Primary wave and the Secondary wave, both 

 being believed to be elastic waves through the body of the earth. 

 If, as is probable, the Primary is the compressional wave, and the 

 Secondary the distortional wave, their velocities of propagation are 

 given by the expressions — 



V' T -^ Vf 



p 



where Jc is the incompressibility or resistance to change of volume, 

 71 the rigidity or resistance to change of form of the material of the 

 earth, and p the density. Thus the Primary wave must obviously 

 outrun the Secondary, since its speed of propagation is the greater. 

 If the speed of propagation did not change from point to point 

 within the earth the rays would be straight lines, just as the ordinary 

 and extraordinary rays in a piece of Iceland spar or other doubly 

 refracting crystal are straight within the crystal. In such a case the 

 rays would be chords to the sphere, and it would be a simple matter 

 to calculate the speeds of propagation. But a little calculation soon 

 shows that the rays cannot be straight ; and the question naturally 

 arises. What is their form ? 



There are several mathematical ways of attacking this problem, 

 which has exercised the attention of several investigators. The 

 most elegant way is to treat it by Hamilton's general method applied 

 to the problem 'of the brachistochrone, or path of shortest time from 

 point to point — that is, with no assumption as to the manner in 

 which .the speed of the disturbance varies with depth below the 

 earth's surface, find expressions for the form of the ray and for the 

 time taken when the disturbance passes from one surface point to 

 another. Now, the only data of observation we have are the times 

 of transit over arcual distances up to about 110° or 120°. Beyond 

 this distance the characteristic form of the record is no longer 

 distinguishable, and no certain conclusions can be deduced from its 

 appearance. 



2 H 2 



