ANALYSIS OF THE IONOSPHERE 465 



ionosphere in Fig. 1, and considering the lower frequencies, we have 

 the non-ionized lower atmosphere and the £-layer for these media. 

 The paths of the waves are drawn accordingly. Now I further recall 

 that total reflection occurs for all values of the angle of incidence i 

 greater than that given by the equation : 



sin i = c-jur. (3) 



Thus we see that for any frequency whatever, total reflection must 

 occur when the waves impinge with sufficient obliqueness upon the 

 ionosphere; but (so long as cju does not sink to zero) total reflection 

 will not occur if the waves rise vertically, or in a direction sufficiently 

 near to the vertical. 



The waves thus penetrate or are reflected back from the ionosphere, 

 according as their angle of incidence thereon is less or greater than a 

 certain critical value. Here is the explanation of what is called 

 "skip-distance": the sky-wave is perceived beyond a certain distance 

 from the source, but not within that certain distance.^ 



But all this seems to have nothing to do with the usual conditions 

 of experiment, in which, as I intimated, the signals are sent up verti- 

 cally! It is indeed a fact that in optics, no case is known in which 

 total reflection occurs at vertical incidence. Yet equations (2) and 

 (3) predict that if ever c^ju^ should vanish, total reflection would 

 extend even to vertical incidence. Now there is nothing mathemati- 

 cally impossible or physically unplausible about the condition for the 

 vanishment of c^ju^, which is simply that / should be equal to fc 

 given thus: 



fc- = Neyirm (4) 



or alternatively that TV should be equal to Nc given thus: 



iV. = TTw/Ve-. (5) 



Here we have the basic formula of the analysis of the ionosphere; 

 for it is assumed that vertically-rising waves or signals of any frequency 

 / climb until they reach the lowest level at which N is equal to Nc, 

 and there they find their mirror or their ceiling, and are converted 

 into echoes which return. Equation (5) is the formula for the "mirror- 

 density" for signals of frequency c, to which I above referred. 



It sounds all right to say that dju^ is zero when N = Nc, and 

 negative when N > Nc] but it is disconcerting to notice that this 



^ Notice incidentally that owing to the curvature of the earth and its overhanging 

 ionosphere, the angle of incidence can never rise to 90°; it follows that waves of 

 frequency beyond a certain value (ordinarily around 30 mc.) never suffer total 

 reflection. 



