Earthquake- Wave in the Interior of the Earth. 531 

 is given uniquely by the formula * 



Substituting for t, s, and a we get 



1 dx _2rj _rf p yf(ot)d et n ,. 



X df) it drjj n a? Va?—rf 



This may be reduced to a simpler form by observing that 



Thus we have the formula f 



Id* 2 ± p /(«>fc 



* Maxime Bocber, 'An Introduction to the Study of Integral Equations,' 



P- 9. . 



f This formula may be obtained directly by writing equation (6) in 



the form 



w-i'X'-M ■»■(?)*!■ 



Now Hankel has shown that if 



£(!)=£ J (a£;aF(a)rfa; 



consequently, 



£ Sin (°g) ± =f jj J (|a)/ («.)*, = *(£). 



Again, applying Fourier's formula 



H(fl-£rin(fe)Gfo)dfc 



