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the least depending on the dashed parts of the N{z) curve of Fig. ZA 

 or indicating anything whatever about those parts except that they 

 do not rise above the ordinate Ne. 



Now if the signal and the echo traveled fro and to with the speed c, 

 the delay T of the echo multiplied by \c would be the height of the 

 ceiling. This, however, is not the case, since the signal-speed depends 

 on N. We must therefore denote the product \cT by another symbol 

 h' , and make an inquiry into the probable dependence of h' on /, 

 taking into account our vague knowledge as to the dependence of 

 signal-speed on N. 



ALTITUDE 



FREQUENCY 



Fig. 3 — A. The "curve of inference": conjectural dependence of number N of 

 electrons per unit volume on true altitude h. B. The "curve of data": dependence 

 of virtual altitude h' of ceiling (one-half the delay of the echo, multiplied by c) on 

 frequency /, 



It is easily seen that h' must be greater (or at least no less) than h, 

 and that the excess of h' over h must be larger, the farther the signal 

 travels through regions where N is almost but not quite equal to Nc. 

 The {h' ,f) curve must therefore lie above the {h,f) curve, and farthest 

 above it in the immediate neighborhood of the gap on both sides. 

 There will still be an E-branch and an F-branch, but the upturns 

 toward the right-hand ends of these branches will be exaggerated, and 

 an upturn running to the left will be introduced into the left-hand end 

 of the F-branch. It is conceivable that these upturns may become 

 so large, that the {h',f) curve will appear to show a peak where the 

 {h,f) curve would show a gap. 



With the remark that h' is known as "virtual altitude," "virtual 

 height," "equivalent height," or "efifective height," I turn now to 

 examples of the characteristic {h',f) curves of the ionosphere. 



