Earthquake-Wave in the Interior of the Earth. 585 



This gives different expressions for f(a) for different 

 ranges of values of a, but by a suitable choice of the expres- 

 sions for S we can find forms of /'(a) for which the integrals 

 can be evaluated. 



Illustrative example. 



Taking Milne's corrected values for the time of transit of 

 the first phase, as given in Prof. Knott's paper*, we must 

 determine S as a function of 6 so as to obtain the following 

 values for the time of transit: — 



9. 



1 

 KS = T. 



9. 



153 



17 



18 



30° 



60° 

 90° 



o-2 



98 



131 



120° 

 150° 

 180° 



A simple expression satisfying these conditions is 



30 



T = RS = 22 



y/"*W 



This formula, however, does not give an integrable form 

 for f(a). For purposes of illustration we shall choose a 

 formula which does not agree quite so well. 



Consider 



Rs=- i+6 -i(Q-. 5 (Q 2 . 



This gives a set of values of S which differ slightly from 

 the observed ones, as will be seen by the following table, in 

 which the times are measured in minutes. 



Arc. 



Milne. 



Formula. 



30° 



5-2 



52 



60° 



9-8 



9-8 



90° 



13-1 



134 



120° 



153 



16 



150° 



17 



176 



180° 



18 



18-2 



* See p. 223. 



