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This part concerns t he heigh t-gain differe ntial equation in order to obtain a series Jor t he complete solu t ion wh ich star t wi t h t hc extended VV. Ie B. approximation discussed in part 1. The coefficients of t his eq uat ion depend for each mode a mongst other t hings on the parameters Aj fixi ng t he r efr active-index pro file. H owever, t he explicit dependence on these para mcLers can only be given in terms of expansions wi t h respect to (koa)-2/3 (koa = circumferencc of t he earth divided by t he wavelength). I n t urn these expansions are derived with t he a id of other ones for t he co mplex t urning poin t co nnected with t he heigh t -gain differential equation. The final expa nsion for t he solu tion of t he differential eq uation is substituted in t he boundary condit ion at t he ear t h 's surface. This leads to correspondin g expansions, with reo pect to (koa)-2/3, of t he quantity 111(a), and Il ext of the eigenvalu es I themsel yes.

On the theory of wave propagation through a concentrically stratified troposphere with a smooth profile. Part II. Expansions of the rigorous solution