WAVE PROPAGATION 547 



''=mQ''''"'''-ik{d'''"^''+- 



r cos B r^ cos 56 , r^ cos 96 



3 32.52.7 ' 32.52.72.92.11 ■ 



r^ cos 36 r'' cos 76 , r'^ cos 116 



0-3 



32.5 32.52.72.9 ' 32.52.72.92.112.13 

 1 1\ 1 



-(l+2-+3+i-8^)34D(^)^^"^^^ + 



= j52 approximately, 



-(l+2- + 3-+4-+5--ra)4l.(2T -=«*'+ • ■ • ■ 



= ^54 approximately. 

 o 



It is to be regretted that the foregoing formulas appear so com- 

 plicated. The series, however, are very rapidly convergent and for 

 r^2 only the two leading terms of each series need be retained. For 

 r^l, only the leading terms are of importance. 



For the important range r^l/4, 



P = ^ ^rcos6 + :^ cos26fo.6728 + log-)+:^6sin 26, (34) 



(2= -0.0386 + ^ log fy") H ^rcos6. (35) 



For r>5 the following asymptotic expansions, derivable from (29) 

 by rep^eated partial integrations, are to be employed. 



1 cos 6 cos 26 1 cos 36 3 cos 56 .^ . 



^_1 cos 6 1 cos 36 3 cos 56 .„„s 



