The notion of the phase in an anisotropic and inhomogeneous medium is introduced (Equation 3).
The doppler effect is found by deriving after the time (Equation 4) and the corresponding relative frequency difference is given (Equation 5).
For cylindrical coordinates, the anisotropy being neglected Bouger's refraction law (Equation 6) is valid for a stratification along the radial axis. Under these two hypotheses the relative doppler effect takes a simplified aspect (Equation 8). The integral over the height yet present in this expression occurs also in the expression for the angular difference between the endpoints of the path (Equation 9a). By comparison an expression for the Doppler effect is found which contains no integral and describes the doppler effect as a function of the angle of incidence (Equation 10a).
The relation between the profile and the angle of incidence is established (Equation 11).
With the Sellmeier dispersion formula (Equation 12) the expression can be simplified by introducing the electron content (Equation 11b and Equation 13). Developing for week refraction (Equation 14 and Equation 15) a final approximative equation is obtained (Equation 16) where the cinematic and the refraction influence appear separately.
The reduction method of mass uses integration of the doppler shift/time curve and allows to determine the electron content in the hypothesis that the horizontal variation is linear (Equation 21).
Orders of magnitude of the Doppler effect are indicated and the main recording methods described. An example is given in Figure 3.
The equation for the differential doppler effect is established (Equation 22).
In the cylindrical case treated above the ionospheric influence alone appears in the difference (Equation 23).
Approximations for high frequencies are given, they lead to an expression for the electron content (Equations 25).
The phase difference by comparison of two frequencies is established (Equation 26), which is another way to obtain information on the electron content.
Another determination uses the time variation at the point of closest approach (Equation 27).
The ratio between differential and direct effect gives another determination method (Equation 29).
The particular case of harmonic frequencies is treated (Equation 30).
Formulae for the relative phase allow the beat pulsation to be described (Equation 33).
The particular case of vertical rocket sounding is considered (Equation 35) and discussed,
as well as the technical realisations.
An example is given (Figure 7).
Polarisation conditions in a magnetized plasma are discussed
and the Faraday-Effect is explained.
The Faraday rotation Ω is established from the phase difference (Equations 39–41).
The angle of incidence is computed (Equation 42).
From the general dispersion formula (Equation 43) suitable approximations are developed (Equations 44, 46, 47) and expressions for Ω are found from them (Equations 45, 48, 49).
The case of transverse conditions must be considered separately (Figure 8 and Equation 50).
The magnetic field of the earth plays an important role, it is described by a dipole field (Figure 9 and 10, Equations 51–53).
After a description of observational techniques
the fading frequency is established (Equations 55–58), examples in Figures 14 and 15.
The range of fading numbers is discussed (Figures 16–19).
Perturbations of the records occur by multiway propagation, the stronger cases are scintillations (Figures 17–20).
The difficulties arising at the interpretation of Faraday records are noted.
the most important is the indetermination of the absolute number of rotations. Five different experimental methods (α — ɛ) are indicated and discussed.
Heuristic methods using supposed regularities are critically reviewed
the advantage of coherent evaluation is stated (compare Figure 23 — incoherent — and Figure 24 — coherent -)
The use of model profiles is recommended and the parameter γ defined (ratio of total electron content to content of the inner ionosphere).
Possible interference by satellite spin is discussed.