40 



PROFESSOR HORACE I, A Ml? OX THE PROPAGATION OF 



regards the horizontal displacement </, the minor tremor will consist of a single 

 to-and-fro oscillation about the epoch anr, followed after an interval by a somewhat 

 similar oscillation about the epoch bis, with almost complete quiescence between. As 

 regards the vertical displacement, there will be a to-and-fro oscillation about the epoch 

 ats, then a period of comparative quiescence, and finally a gradually increasing 

 negative displacement (with a slight irregularity at the epoch bis) leading up to the 

 main shock, after which there is a gradually decreasing positive displacement. 



The expression for the horizontal displacement </ may be treated in a different 

 manner. Transforming (169) we have 



q = ~ a ^f o R (* - CBT cosh u) du - ~- ("' 0U (0). 3 f R (t - OTS cosh u) du.dd 



H 3 f* 



= - - R (t cis cosh u) du 



TT/JL OWJO 



+ ,f f" W (0) + U (0)} . TR (t - 0zs cosh u) du.dO . (171). 

 iro/iwJa Jo 



A rough sketch of the graph of 0U'(0) + U(6) is easily made, and the function 







R (t Q-ss cosh u) du 



is, in such a case as (165), one-signed, but its integral with respect to does not 

 converge when the lower limit is large and negative. The method therefore fails to 



V 



Fig. 10, 



