A solut ion is given to the problem of r epresentin g the complex proper ties of ionospheri c cha racteristics on a worldwide scale, including their diurnal variation, by num eri cal analysis of ionospher ic data as t h ey a re obtained fr om a n etwork of so undin g statio ns, wit hout prior han d operations. The problem is co mpli cated by t wo bas ic diffi culties : (1) t he da ta ar e affected by noise (ran do m fiuctuation) an d (2) t he stations ar e irreg ularl y posit ion ed in t h e two s pace dim ens ions. The seco nd diffi culty is over co me by a gener al met hod for constructing fun ctions orthogonal relative to the dist ri bution of t he sta t ions . S pccial filterin g p ro cesses a re employed for t hc optimum separation of noise fr om real p hys ical var iat ions . The en d produ ct of t he a na lys is is a table of numerical coeffi cie nts de finin g a fun ction r (A, 0, I) of t hr ec variables, latit ud e (i--) , longitude (0) and ti me (I) , w hich can be used to compute t he io nospheri c characte ristic at a ny des ir ed location or instant of t ime. The method a pplies to a ny io nospheri c characte ristic; however, a s a means of illus tration we use in t h e p resent p a p er only t he characterist ic, monthly med ian of t he F2-laye r cri t ical fr eq uency (fo F,).December 1957 96 stations.
Pulse trains with periods of the order of a minute occur in the natural VLF signals emitted in the exosphere. Composed of otherwise ordinary VLF emissions, the long‐period pulses always rise in frequency. At magnetically conjugate points the long‐period pulse signals are received simultaneously. The period of the pulsation events exhibits a latitude dependence, becoming longer at higher latitudes. On the basis of available data, a hypothesis associating hydromagnetic waves with emitting particles is offered to account for the observed properties of the pulsations.
SC' lecL ive travc lin g-wave nmplificatiol1 in t he o u ter ionosphere is postulated to explain vpr•.v-l o w-frequ e ll c.v emiss io,)s, fI class of ve ry Jow-fr equency (1 to 30 kilocycles p er second) nal ura l n o i~e. B ya na logy willl Lhc mechanis m of Lrave lin g w a ve tubes, low-level ambient nOise In Lho ou Le r lo no phe l'e is a mplified in streams of in coming ioni zed solar p a rticles at f requ e nclcs for whICh the stream a nd wave veloc it ies a rc equal. R equired velocities a re in t he r~n ge 0.01 t o 0.1 c (where c is the velocity of ligh t). Streams with densities of the o rde r of one electron p er cub ic centimeter would provide s nffici ent energy. Phenomena w hi ch can be explain ed quaiJ tatl vely by t h e theo r'y arc the hi ss, quas i-constant tones, dawn chorus and r elated tranSlCnts, a nd very long train s of whis t ler echoes. A quantitative example shows how t he theory can reproduce t he genera l form of certain characteristic di s cr~te spectra " hooks" of e mi ss ion s, and how t his leads to de fi nite values of par t icle velOC ity and a Jaw for t he di stribution of elec tron density in t he outer ionos pllerc .
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