In 1937 Ba il ey a nd M a rtyn proposed a t heo!"y of ionos pheric cross mod ulat ion a lo n/, !: the following lin es. lla di at io n em.itted by th e di stu rbing tra nsmi tte r is stro ngly abso l bed in a r ('gion of the io nos phere where the wanted wave is refracted a nd attenuated. Abso rption of the dist urbin g r a diati o n raises th e temperature of t he ionosp here. If the a mplitud<, of the d isturbing radi at ion va ri es with time, so wi ll the r es ultin g te mperature in crease

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... a nd h en ce the attenuation s ufTered by the wa nted wav c. In th e simpl est ex perim e ntal a rran gem ent the wa nted wave is ini t iall.v unmod ul ated a nd th e di sturbin g nLdiat io n is modul ated at a definit e a udi o fr equ e ncy. In trave rsin g t he io nosphere, the wa nted wave becom es modul ated at the fr eque ncy of the di sturbing ra di ation a nd also at twice this fr equ ellcy. The Ba il ey-M a rt.v n t heo ry ma kes three qu a ntitati ve p redi ctions co nce rn in g the tra ns-fC' rr ed modul at ion . The firs t concc rns its dependence o n th e power of the di st urbin g radiat io n, :l nd in voh'es on ly the ass ump t io n j' hat t he dTcct is s ma ll l' no ug h to wa rrant it lin eari z('d d escription. The rema inin g two p rC'd icti o ns co ncc rn the depend encc of t Il(' tran sferr ed modulation a nd its phase lag on the modu lat io n frequ ency. TI1l'se p redi ct io ns in vo lve the ad ditiona l ass umpt io n of a unique r ela tion, vali d fo r all values of the modul at io n fr equ e ncv, betw('C'n t1w m ean tll('rm al energy a nd the mean co lli s io n frequen c.v of t hC' electro ns. A r elat io n of thi s kind can e xi st, however, o nl y for mod ulation fr eq uencies mu ch less t ha n 150 cis . Since t he expC' rimental r a nge of m odu la t ion fr eq ue ncies ex t cnds to nea rl y 1500 cis, t he fo und a tions of the Bailey-M a rt y n t heo ry n eed to be reco nsidered. Thi s p a p er desc ribc's a mi croscopi c theor y of io nos pheri c cross modulat io n . The velocity-distribu t io n fun ctio ll for the electrons e nters explicitl y in to t he theor y; it is determin ed b y a differentia l C'q uat ion whose form dep ends on the modula t io n fr eq ue ncy. Kn owin g the di st ri but io n fun ct io n, one can calcul at c the a bsorpti on coefficie nt . The fo rm of the predi cted a bso rpti o n coefficient depe nds on t he ass um cd form of the elec tron-mo lec ule in teract io n I a \\" . By num eri cal mct hods, we have calcul ated t he tra nsferred modu lat io n a nd i t s ph as(' lag as fun ctio ns of modulatIOn fr equ e ncy for a few simplC' inte ract io n la ws. The calc ul at io ns sho w t ha t the effects of depa rtul"C's fro m it maxwe lli a n ve locit y di st ri bution a re indeed sig nifi cant. The predi ctio ns a re se ns it ive to t he ass um ed fo rm of t he eIPct ro nmolec ul e coll is io n la \\". Alt hou g h t he prese nt theo r." is sti ll hi g hl y idealih ed, t he res ults o btained s ll ggC'st t hat furtlH'l" theoret ical a nd ex perim ental refinements co uld lead to a n experim e ntal detC'rmin at ioll of the electro n-m olec ul e inter action la w in the D r egio n .