160 



MR. It. D. OLDHAM ON THE PKOI'AC. ATIOX OF 

 Third Phase; maximum. 



Here, if we exclude the results of the Turkestan earthquake of 1897, there is a 

 most striking concordance in the rates of transmission at all distances between GO and 

 120 degrees of arc. The lesser velocity in the case of the smaller arc will be con- 

 sidered further on ; here it will be enough to say that in itself this cannot be regarded 

 as an indication" of a progressive increase of apparent rate of propagation with distance, 

 such as was observed in the case of the first and second phases. 



4. Before proceeding further with this investigation it will be necessary to hark 

 back and consider some general principles involved. 



Firstly, the rate of propagation may, as is well known, mean one of two things, 

 either (l) the apparent rate of propagation as measured at the surface of the earth, 

 or (2) the true rate of propagation as measured along the actual wave path. These 

 velocities, whose distinction is well recognised and for which distinct symbols are 

 always employed, must, however, be further subdivided, and for the present purpose 

 the four following values recognised : 



v = the apparent rate of propagation at any given point on the surface. This 

 is what is commonly meant by apparent rate of propagation. 



v a = the apparent average rate of propagation as between two points on the 

 surface of the earth. The only average which appears to be of any 

 value is that referred to the origin. It is this value which has been 

 given in the tabular statements above as the rate. 



V = the true rate of propagation at any given point of the wave path. 



V a = the true average rate of propagation, obtained by dividing the distance, 

 measured along the wave path, by the time interval. 



In the special case of waves propagated along the surface with a uniform velocity 

 these four values are identical ; if wave motion is propagated at a uniform speed and 

 along rectilineal paths through the earth the values of V and V a will be identical but 

 different from v and <:, which will also differ from each other. In any other case the 

 four quantities must necessarily be different. 



