208 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



If we set 



C{ = c' sin K cos w 



C — c sm K sin co 



Cf = c' cos K 

 we find 



Mc) - /.(c) = _- c, + -^ c, + -^ (c, - c) + - ^^ c, 



, 1 d'/l(c) ,2 , 1 d%{c) , / ,2 , d^c) r t 



, a'/i(c) ,, , . , a'/i(c) ,w . , 



With the formulas given, integration over co is elementary. We find 



g « .(0 m 1 - 1 I + 1 {^ (o' cos . - 0) 

 \\c) t{c') t(c)J t{c) \ dc^ 



All coefficients are to be evaluated only to the lowest non-vanishing order 

 .in M/m. From the equations (41) and (42) we get 



c' cos K — c ;^ (M/m) c(l — cos x) 

 c'^ sin^ K ^ {M/mfc sin^ x 



The first term in ^ is simplified further by introduction of the parameter 

 a used in the dimensional analysis of Section ID. According to that 

 section we have that 



^-4^ = -1 + a (69) 



a inc 



We can generalize the original definition for any t{c) by the above 

 equation, where a is now a function of c. Eliminating also the tempo- 



