A = [y(PJ + s'Trn e '"(I - P_)^]p'v^ 



(66) 



A = C2(Pm)p'v^ 



The dissipated energy according to (64) and (32) is 



.2_.2 _ _,. ._2_ _4al .2r(l-p^).a/a(l)^ 



A(l) 



D = 2M(l)ir''g6'' = 2M(p^)7r''g —^ e "^ "^ (6?) 



where a means the amplitude of the increasing p(l)-wave, a(l) its 

 maximum value given by (63) and 



A(l) = 1^ v^ (68) 



the wave length. With 



a^ = A(l)n e"^ = A(l)n . (69) 



(67) can be written 



2 2r(l-B ) -.^ m 



-3-^ M(p Je "^ A(l)n (70) 



n - fw^„ -r — 5 M(p„)e 



Since C = v and p(l) = 1, equation (65) takes the form 



i-gpva fl = C2(pjp'v3 - STT^g -^ M(p^)e^JaT5^^"^ni^^ (71) 



according to (66) and (70). By division with p'v^ and considering 

 (68) we get 



1 n? rio 2g%6 )a^ -^(l-p„)a 



2 , 2 '^ dx "a'^'m' , 7 

 p'v p'v' 



or 



dx = p^ ^^ (73) 



P'^ 2g-3M(p„) p r !.„ T 



^2(Pm^ rf- a^expf -^ (1 - pj a 



p'v' [ irv n . 



With regard to the later numerical calculation, it is more convenient 



93 



