Th e di s pe rs iQn prope rti es of a n a nisotropi c me dium, s uc h as the ionos phere in prese nce of the earth 's magne ti c fi e ld , are c onve nie ntly re prese nte d by the variations of the refractiv e index with th e direc tio n of propagati on. It is s hown tha t, fo r a numbe r of cases of prac ti cal inte rest, th e vari ati on of the ind ex n with th e angle 0 tak es a s pec ial form whi c h can b e e xpressed by a graphi cal co ns tru c ti o n; th e res ult n is re ad on a circ ula r scale, c aU ed the ind ex c ircle, a t the points where it is inte rsec ted by a s tra ight line whi c h de pe nd s in a simpl e mann e r o n the direc tio n of propagati o n o. The sa me co ns tru cti on a ppli es whe n the wave is e vanesce nt a nd th e n it giv es the imagin ar y valu e of th e refra c tive ind ex or extin ction ind ex.Th e range of appli cati on of t hi s co ns truc tio n includ es th e Apple ton-H a rtree equ ati on, its ge neralization for a ny numbe r of io ns , th e hydro magne tic wa ves in a me dium with finite co mpress ibiljty, a nd th e va ri ous a pp rox.im ati ons corres po ndin g to limiting or transiti onal cases -As trom wa ves, uni axial medi a, a nd Booker's h ydrom agn eti c approxim a tion . It could also be a ppli ed to magneti zed ferrites.For mos t a ppli ca ti ons th e inde x c ircle re prese ntati on ca n take th e pl ace of th e di s pe rsio n s urface. Th e milln features of thi s s urface-the numbe r of s hee ts, wh e th e r th e y are real o r im agin ar y, and th e directi on of th e asy mptotes -a re all di s pla yed on th e ind ex c ircl e. If th e need ari ses, it is easy to trace th e di s p e rs ion s urface a nd 1.0 foUow its de form a ti o ns as th e para mete rs of the me dium a re vari e d .