Wave-Motion in an Elastic Solid. 

 With ft thus determined, (48) gives ft as follows, 



a ,2 



2ft{t) Uq . t 

 i v ' ± sm coi 



Q) 



493 



D4). 



For f, ?;, £ by (19) we now have 



7) = B(>, <)«y 



f = B(r, t)» 



where (compare § 9 above) 



TV a ir^A)^^ 2 )l, 3,-^,(0 > 2 fe)-i ) 



lft (01 



+5i[^ft) + ^fe)] > 



(56). 



*! = £ 



>— 



§ 19. The wave-lengths of tbe equivoluminal and rotational 



waves are respectively and . Jb or values or r very 



great in comparison with the greater of these, the second 

 members of (55) become reduced approximately to the terms 

 involving i\ and F 2 - These terms represent respectively a 

 train of equivoluminal waves, or waves of transverse vibration, 

 and a train of irrotational waves, or waves of longitudinal 

 vibration ; and the amplitude of each wave as it travels 

 outwards varies inversely as r. 



§ 20. For the case of an incompressible solid we have 

 v = go , which by (53) gives 



&W „ • , 



■>- = — £hq sm cot 



(57); 



and by (55) we have, for r very great, 

 7j == — %hg sm cot -— 



f = —%hq sin o>£ 



:58), 



which fully specify, for great distances from the origin, the 

 wave-motion produced by a rigid globe of radius q, kept 

 moving to and fro according- to the formula h sinco£. 

 [To be continued.] 



