ANALYSIS OF THE IONOSPHERE 477 



beginning to study the distribution of A^^ in the horizontal plane, 

 e.g. by using obliquely-sent as well as vertically-emitted signals. 



Now we turn briefly to a difficulty affecting not the relation between 

 h' and h, but the relation between Nc and/ presented as equation (5). 

 This equation was based on the tacit assumption that the electric 

 force on a single electron is the same as though there were no other 

 electrons at all in the ionosphere. The assumption has been doubted, 

 and quite a polemic has ranged about it. The question is in fact a 

 special case of one of the most pestiferous questions of all mathematical 

 physics, occurring for instance in the theory of magnetized bodies 

 and of bodies polarized electrically: when a great many similar atoms 

 side by side are exposed together to an external field, how is the force 

 suffered by any one of them modified by the presence of its equally- 

 affected neighbors? One strongly-held position is, that there is such 

 a modification which manifests itself in a factor 3/2, to be multiplied 

 into the right-hand member of equation (5). A test experiment has 

 been devised, and the early results have favored this theory. The 

 presence or absence of this factor alters in equal proportion all the 

 ordinates, but does not modify in the least the trend of the N{z) 

 curve; but the student specially interested in numerical values of N 

 must discover, from each paper wherein such are given, which formula 

 was used in computing them. 



After uttering all these warnings about the theory underlying the 

 (TV, z) curves, I will risk a few statements about the curves themselves. 



The shape of the {N, z) curve, when the sun is low in the sky and 

 there is no crinkle in the {h'f) curve, is roughly that of Fig. ZA. If 

 the sun is within some 40° of the zenith and the crinkle is present in 

 the {h'f) curve, the theory indicates not that the 7^-peak of Fig. ZA 

 has split into two, but rather that a bulge has appeared on the left- 

 hand side of the i^-peak. The letters Fi and F^ are then applied to 

 the bulge and the peak, respectively. If the shape of the {h' ,f) curve 

 indicates yet another layer between E and Fi, it appears as a small 

 hump in the valley between the peaks of Fig. 2>A . 



As for the iV-values, those of most interest are those corresponding 

 to the crests of the peaks; or to define them better by staying closer 

 to the data, they are the ones corresponding to the points on {h'f) 

 curves which adjoin the gaps or lie at the tops of the crinkles. These 

 may be called the values corresponding to the "crowns" of the 

 several layers. 



At Huancayo in the Peruvian Andes, at a typical summer noon, 

 N has the values 1.8-10^ - 3.3 lO^ - 1-10« at the crowns of the 

 layers £, Fi, Fz: so says Berkner. At Slough near London, at noon 



