ANALYSIS OF THE IONOSPHERE 467 



Characteristic Curves of the Ionosphere: the (h',f) Curves 



Now that we have the concept of a signal ascending until it reaches 

 the ceiling where N = Nc, we will consider first the to-be-expected 

 relation between true height of ceiling and frequency of signal, then 

 the relation between delay of echo and frequency of signal. By 

 following this order we pass from the unobservable to the observed, 

 which is the reverse of the customary way, but nevertheless has its 

 advantages. Let z stand for height over ground when used as inde- 

 pendent variable, with N depending on it; h for the height of the 

 mirror or ceiling for signals, when expressed as a function of the signal- 

 frequency /. 



Take first the oversimplified model of the ionosphere appearing in 

 Fig. 1 : N having the values Ne over one range of heights and 

 Nf (> Ne) over another range at a higher elevation, and the value 

 zero elsewhere. It is evident that the {h,f) curve for such an iono- 

 sphere would consist of two horizontal lines or "b ranches," extending 

 respectively from abscissa to abscissa /e = 'vNE^hrm and from 

 abscissa/^ to abscissa /f = '^Npe'^/Trm respectively. The latter would 

 lie higher than the former; there would be a jump or gap between 

 the branches. The names "£-branch" and "F-branch" for these 

 last are obvious, and so is the usage "penetration-frequency of the 

 E (or F) layer" iov Je or fp; "critical frequency" is also used. 



Next we approach closer to the truth by supposing that N rises 

 continuously with increase of z across the £-layer and also across the 

 F-layer, Ne and Nf now representing the highest iV-values found in 

 the respective layers. The two branches of the (h,f) curve would 

 then be no longer horizontal, but slanting or probably curving upwards 

 toward the right. 



In the foregoing paragraph it was tacitly assumed that TV still 

 vanishes between the layers; but now let us approach still closer to 

 the truth by postulating the sort of dependence of iV on z shown in 

 Fig. 3A. Here N drops with further increase of height after the 

 "crown" of the -E-layer is reached, but it does not fall to zero. It 

 might, however, just as well fall to zero so far as reflections are con- 

 cerned, for the signals which could be reflected from these regions 

 never reach them. Regarding the curve of Fig. 3A as a sequence of 

 hills and valleys, we see that the valleys contribute no echoes. The 

 £)-branch of the (h,f) curve refers to the left-hand side of the first 

 hill; the F-branch refers to the left-hand side of the second hill, and 

 not even to all of that, but only to the portion which rises above the 

 first hill. Thus Fig. 3B, with its upturning branches and its gap, 

 represents the {h,f) curve for the ionosphere of Fig. 3A, without in 



