Oi.**. 1^ 



f^W ' 



413 



(A-13) 



Orx 1^ ■=. =— • (A-LV) 



The substitution of these expressions into (A-9) and (A-IO) gives Eqs. (l) 

 and (2) of Part I. 



To complete the derivation, we must find explicit expressions for 

 flc, and fl| . Introducing the radial displacement ix« r- r^ we may write 



(It) -- fe-C'^lfp^ (A-15) 





, (A-16) 



in which the partial differentiations with respect to »• and t: are under- 

 stood to be performed at constant "t and r , respectively. Operating on ic 

 by (A-15) and (A-l6) we obtain after some manipulation 







(A-17) 



(A-18) 



where 





,x 





% 



