LAMINATED TRANSMISSION" LINES. II 



111) I 



(iii) /(O n linear function. Let 



m = 2^-1, ^ ^ g 1, 



(5.-)!) 



so that /(^) is a linear fuiR'tiou \-anini;- tVoni — 1 at $ = lo +1 at 

 ^ = 1. Then equation (532) becomes 



d-w/d^' + [(A + iC) - 2iC^]w{^) = 0, 

 which, by tlie change of variable 



2iCl^ - (A + iC) 



(552) 



(553) 



(2(7)2/3 



is transformed into Stokes' equation, 



d'^w/dr- + TW = 0. (554) 



The general solution of this e(iuation may be written in the form 



w = Ah.ir) + M.>(r), (555) 



where h\ and hi are the pair of independent solutions of Stokes' equation 

 which have been tabulated for complex arguments by the Computation 

 Lal)oratoiy of Harvard University. ^^ (The solution may also be ex- 



C =100 



Fig. 26 — Real and imaginary parts of the first eigenfunction, Wi = u\ -\- ivi 

 for the nonuniform stack of PMg. 25. 



" Tables of the Modified Hankel Functions of Order One-Third and of Their Deriv- 

 atives, Harvard University Press, Cambridge, Mass., 1945. 



