218 BELL SYSTEM TECHNICAL JOURNAL 



oscillation. For an electron in the earth's magnetic field (assumed 

 to have a value of 1/2 gauss) this resonant frequency is 1.4 X 10' cycles, 

 corresponding to a wave length of 214 meters.' We thus ha\e an 

 indication that some at least of the phenomena of transmission at 

 the lower wave lengths may be explained by taking into account the 

 action of the earth's magnetic field upon electrons present in the 

 earth's atmosphere and acted upon by the electric field of the wave. 

 This frequency occurs at appro.ximately the position in the spectrum 

 at which the peculiar effects already mentioned occur. The next 

 resonant frequency which would be encountered would be due to the 



e 1 



hydrogen ion which has a ratio, — , equal to 7^777; that of the electron. 



ni 1 oUU 



The resonant frequency of this ion is only 800 cycles and certainly 

 can have no sharply selective effect in the propagation of electro- 

 magnetic waves over the earth. We have, therefore, worked out the 

 consequences of the assumption that we ha\'e in the upper atmos- 

 phere two controlling factors influencing the propagation of electro- 

 magnetic wav-es in the radio range, namely, free electrons and ions 

 together with the earth's magnetic field. The electrons will be 

 dominant in their effects in the neighborhood of the resonant frequency 

 and perhaps above, while the heavy ions will affect the wave at all 

 freciuencies and, if much more numerous, may be controlling at 

 frequencies other than the critical one. In working out this theory 

 it is assumed that there are present in the earth's atmosphere free 

 electrons and ions. At high altitudes these are capable, on the 

 average, of %-ibrating under the influence of the electromagnetic 

 field through several complete oscillations before encountering other 

 ions or neutral atoms. At low altitudes this assumption will not 

 hold, the collisions being so numerous that the importance of tiie 

 resistance term in the equations of motion becomes much greater. 

 In either case the ions ha\'e no restoring forces of dielectric type. 

 The motion of the electron or ion constitutes a convection current 

 which reacts upon the electromagnetic wa\e and changes the \i'l()rit\- 



^ This frequency does not depend upon ifu' direction of the field, and is practically 

 constant over the earth's surface. 



f)n March 7, after this paper had been written, the February 15 issue of the Pro- 

 ceedings of the Physical Scxiety of 1-ondon arrived in New York. In this journal 

 there was a discussion on ionization in the atmosphere in which Prof. K. V. .Appleton 

 suggested, in an appendix, that the earth's magnetic field acting upon electrons 

 would change the velocity of a wave and produce rotation. A calculation of the 

 critical frequency was given in which, however, only the horizontal com|X)nent 

 of the earth's field was used, resulting in an incorrect value for the critical frequency, 

 namely less than half the actual value. If the complete equations are written 

 down it is evident at once that the total field is involved in the critical frequency, 

 no matter what may be the direction of propagation. 



