TREMOltS OVER THE SURFACE OF AN ELASTIC SOLID. 35 



f | 2 fe ^' c 8h " d % - 2 K sil1 (* w cosh w ) ~ 2 ^$ f " Jri* e~* w cos " " d 

 J- Jb (f) J*.b (f) 



- 2P I ^^^ ~ ^')^ t : a-^acothu Jf 



L F 



where H aud K are the numerical quantities defined by (68) and (71). Substituting 

 in (149) we have 



TT / \ i - 7 



- - . H . K, (K.) + I) 



, 



where the notation ol the various BKSSKL'S Functions is as in Art. 2. 

 Superposing the system of free waves in which 



f/ = ^ . H . J\ (KCT), ?; = '' - . K . J (/era) .... (154), 



Z^, ^/A 



we obtain, finally, on inserting the time-factor, 



* -H-^M^ + 



Since these expressions are made up entirely of diverging waves, they constitute 

 the complete solution of the problem where a periodic normal force He** is applied to 

 the surface at the origin. 



An alternative form of (156), which puts in evidence that part of the vertical 

 disturbance which is most important at a great distance from the origin, is obtained 

 from (75). Attending only to the "singular" term, we find 



r* i'~ffiL 



^ F (\ e iwcosl1 " d = 2iV/eK . cos (/era cosh u) + &c. . . (157), 

 and therefore, from (149), 



(158). 



Adding in the system (154) we have altogether 



g = - ~ . H . D! (/era) 0* + &c., v> = J R . K . D (/era) <* + &c. ( 159). 



F 2 



