PHYSICS OF THE IONOSPHERE1

G. R. Mimno, Cambridge, Massachusetts, USA

E. The Nature of the Accelerating Field

Although the elementary theory set forth in Section D does connect a certain number of interesting elementary facts, we shall nevertheless need a more careful mathematical treatment of the phenomenon in order to explain the frequently observed effect of double refraction. As a preliminary step toward considering a more complete theory, we shall first study several fundamental postulates concerning the forces by which the motion of electrons is determined.

Fabry[^60] drew attention to the fact that free electrons scatter radio waves extremely strongly, since at these comparatively low frequencies one should expect the phases to combine. In the case of free electrons set in motion by a light wave, however, only the intensities are added. We must therefore expect a small resultant change in a beam of light, although it is possible that slight astrophysical effects might be detected. When, however, we attempt to calculate the scattering of radio waves caused by the motion of electrons, we immediately encounter a serious difficulty concerning the nature of the accelerating field. In the ionosphere, besides free electrons, there are present in large numbers positive ions and neutral molecules. In the elementary treatment of the phenomenon given above, and in the theoretical works that appeared first, a simple electric field averaged over space was used in calculating the motion of the electrons, without any special critical examination of the question. When we study the change in the dielectric constant as a result of the presence between the plates of a capacitor of ordinary neutral atoms, we know that this “line of force” must be corrected by the Lorentz “polarization” term, which takes account of the actual corpuscular distribution of matter. We often visualize an individual atom or molecule separately as an object enclosed in an approximately spherical shell, upon which the field acts,

formed by charges induced on the walls of the shell. This physical picture can be used to calculate the “polarization” Lorentz term, although several other mathematical methods lead to the very same expression. The formula obtained by these routes was checked experimentally on the dielectric constants of ordinary materials, and good quantitative agreement was obtained.

Subsequently Hartree \(^{61-63}\) used this Lorentz correction term in several mathematical works on wave scattering in stratified media and noted the fact that this term had been omitted by Goldstein \(^{64}\) and other authors. The corrected expression was used in several papers by Eppleton \(^{65-67}\); the resulting “Eppleton–Hartree formula” for the dielectric constant of a birefringent medium was widely applied in calculations by Taylor \(^{68}\) and many others. The numerical correction is large; it changes the value of the electron density computed from measurements of the frequency of wave penetration by fifty percent. The equations themselves will be given later.

In 1933 Tonks \(^{6,70}\) called into question the correctness of Hartree’s derivation and expressed the conviction that the polarization term may be omitted, except in those cases where “there is some detailed arrangement of negative charges relative to positive ones.” This objection of Tonks was supported by Norton \(^{71}\), who asserted that it is permissible to use the field averaged over space, since the electron moves over a distance that is large in comparison with its extent, and over a time that is small in comparison with the period of the wave.

Although the works of Tonks and Norton contained strong theoretical argumentation, no immediate agreement was reached as to the merits of the various points of view that had been put forward. Hartree \(^{72}\) pointed to two unjustified assumptions in the argument proposed by Tonks, and to one such assumption in his own earlier derivations. This important and pressing question remained unresolved. In self-defense, several experimental physicists made it a practice to publish two series of calculation results, leaving the reader to choose between them for himself.

In 1934 Darwin published a preliminary communication \(^{73}\) indicating that the Lorentz term should not be taken into account. In December 1934 he gave an extensive and complete re-examination \(^{74}\) of the whole problem, which, apparently, resolves the question definitively. In his latest paper Darwin notes that the given problem is entirely definite and that it can be solved completely without resorting to experiment. The principal work on this subject had been done more than fifty years earlier. Here a purely classical treatment is quite sufficient, although one may also use the methods of quantum mechanics without changing the result-

data. This problem, which at first sight seems simple, is exceptionally treacherous. Since the mean field is very small in comparison with the fields existing at individual points of the medium, the computed value is very strongly affected by an insignificant change in the method used to estimate the mean. Darwin first considers the various methods that had been used previously. By means of arguments “just as fully convincing as many of those accepted in theoretical physics,” one can confirm either of two formulae that are entirely contradictory to one another. Although a re-examination of these older points of view does not give a completely clear answer to the question, the totality of the facts justifies omitting the Lorentz term in calculating the force acting on an electron in the presence of positive ions or neutral atoms and molecules. Since atoms cannot penetrate one another, only the external fields of other atoms act on an individual atom. This restriction does not apply to a free electron, and in determining the force one should use the simple spatial average.

Darwin, however, obtains a more decisive formulation of the problem with the help of an entirely new method, which avoids the unpleasant ambiguities connected with a closer analysis of the internal electric fields in matter, and indicates the conditions for recognizing substances requiring two types of formula. Applying the equations of dynamics in Hamiltonian form, one can form the electric moment of a small volume of the medium; the size of the region is then such that retardation of the waves may be neglected. The conditions under which the polarization term may be omitted are fulfilled in the ionosphere and in metals. In the study of the properties of metals the theory finds support in quantitative experimental facts; it therefore appears that it provides a reliable basis also for the exact calculation of the properties of the ionosphere.

F. Other forces acting on electrons

Having discussed the question of the nature of the electric field produced by the incident wave, we can then consider several additional factors that may affect the motion of the scattering electrons. The frictional force due to collisions, and the deflecting force produced by the Earth’s magnetic field, will be treated mathematically in Section G. The perturbing forces arising as a result of interference of signals will be described in Section S. In addition to these effects, we must investigate the hypothetical “quasi-elastic” or “relaxation” force, which entered the literature as a result of laboratory experiments undertaken to study the properties of ionized gases.

In 1913 Zalpeter\(^{75,26}\) developed equations for the refraction of electric waves in an ionized gas. Although Zalpeter’s derivation was analogous to the treatment of the question previously given by Eccles\(^{24}\), it included a more detailed consideration of friction in

the ionization density increases, the resulting capacitance assumes a large negative value, and then suddenly changes it to a large positive value. Although this critical behavior is exclusively a property of the electrical circuit itself, the effect is strikingly similar to a resonant change in the properties of an ionized gas.

Although Appleton considers Gotton’s “quasi-resonance” to be entirely false, he nevertheless confirms certain experimental observations made by Tonks ^94, which indicate the existence of a second “resonant” point obtained at low values of the current strength in the tube. Appleton, however, believes that Tonks and Langmuir are wrong when they describe this effect as “plasma resonance.” He prefers to regard it as “sheath resonance,” occurring at the plasma boundary, since “it can be shown that a restoring force will act on an electron oscillating away from the main discharge in the sheath, and it will thus possess its own frequency of oscillation.” Despite the fact that sheath resonance is of importance in the theory of discharge tubes, it can evidently be neglected in the ionosphere.

In France the concept of “quasi-elastic” forces still receives strong support at the National Laboratory of Radioelectricity. Gotton ^95, the director of the laboratory, recently published an interesting paper summarizing the French experiments; so far, however, Appleton’s quantitative data have apparently not been refuted by them.

If, as a result of this, we reject the idea of “quasi-resonance” in the plasma, we can nevertheless still search for real resonant frequencies due to the internal oscillations of large molecules. In 1934 Ziegler ^96 summarized the theories and measurements of the dielectric constant and concluded that there are no satisfactory facts indicating such an effect in the ultra-high-frequency radio spectrum extending from 100 cm to 10 cm. However, at a wavelength of 1.1 cm, Cleeton and Williams ^97 demonstrated an absorption effect due to ammonia molecules. Investigations of this kind will undoubtedly develop, but molecular resonance may be neglected, since the matter concerns the ionosphere.

G. Equations of motion of electrons

Theoretical investigations, confirmed by direct experimental checks, indicate that the Earth’s magnetic field is responsible for the phenomena of double refraction that are often encountered in commercial radio transmission and in ionospheric research. The accuracy of the experiments is sufficient to verify the known quantitative facts concerning the variation of magnetic-field intensity with latitude, and to provide means for determining its variation with height within the limits of the Earth’s atmosphere.

In the special cases of propagation along the magnetic field and propagation perpendicular to the magnetic field, this effect was studied in 1926 by Appleton and Barnett \(^{98}\) and, independently of them, by Nichols and Schelleng \(^{99}\). Below \(70\text{--}80\) km the electrons undergo collisions with gas molecules so often that the effect of the magnetic field is relatively insignificant here. Above this critical height the collision frequency is lower than the rotational frequency about the terrestrial field. Therefore the induction in the direction of the field differs appreciably from the induction at right angles to the field, and the plane of polarization rotates. The Faraday effect and the Kerr effect depend on the wavelength. So long as investigations were limited to the two special cases mentioned above, one could use the equations previously applied by Voigt \(^{100}\), Drude \(^{101}\), and Lorentz \(^{102}\) in studying the propagation of optical waves in the field of a magnet.

Appleton \(^{103}\) and many other authors soon extended the equations of magnetoionic double refraction so as to include the general case of wave propagation at an arbitrary angle to the direction of \(H\). The form of the final expressions for the indices of refraction depends strongly on the choice of the directions of the coordinate axes and on the nature of the abbreviations used to reduce the complicated expressions to a compact and convenient form. Although the corresponding exposition can already be found in the scientific literature of several different countries, the importance of the effect justifies repeating the derivation in general outline in the present review. Since in numerical calculations the form of Lorentz’s equations belonging to Appleton \(^{104}\) has been widely used, I shall adopt his notation and choice of axes, but shall omit the Lorentz correction term for the reasons set forth in section E. The reader may also wish to study the derivations of the equations given in a somewhat different form by Försterling and Lassen \(^{105}\), Bailey and Trine \(^{106}\), and Pierce \(^{107}\).

Considering the propagation of a plane wave along the \(x\)-axis and choosing our coordinate system so that there is no component of the terrestrial magnetic field along the \(y\)-axis, we shall denote the \(x\)- and \(z\)-components of this field respectively by the symbols \(H_L\) and \(H_T\).

For Maxwell’s field equations (expressed in Lorentz units) we may write:

\[ \operatorname{rot} H=\frac{1}{c}\left(\frac{\partial E}{\partial t}+j\right), \tag{1} \]

\[ \operatorname{rot} E=-\frac{1}{c}\frac{\partial H}{\partial t}, \tag{2} \]

where \(E\) and \(H\) are the electric and magnetic field strengths of the plane wave; \(j\) is the convection-current density. We therefore have:

\[ j=\frac{dP}{dt}, \tag{3} \]

where \(P\) is the polarization at some point of the field,

In expanded form Maxwell’s equations take the form:

\[ [[unclear: partial displayed equation]] \]

Combining (20) with (14) and eliminating \(E_y, E_z, P_y\), and \(P_z\), we obtain:

\[ \gamma_L^2 = \left\{(\alpha+i\beta)-\frac{1}{c^2q^2-1}\right\} \left\{(\alpha+i\beta)-\frac{\gamma_T^2}{1+\alpha+i\beta} -\frac{1}{c^2q^2-1}\right\}, \tag{21} \]

whence:

\[ c^2q^2 = 1+ \frac{2}{ 2(\alpha+i\beta)-\dfrac{\gamma_T^2}{1+\alpha+i\beta} \pm \left[ \dfrac{\gamma_T^4}{(1+\alpha+i\beta)^2} +4\gamma_L^2 \right]^{1/2} }. \tag{22} \]

In order to make it more convenient to analyze this equation, we write:

\[ p_0^2=4\pi\frac{Ne^2}{m},\qquad p_L=\frac{eH_L}{mc},\qquad p_T=\frac{eH_T}{mc}, \]

where \(e, H_L\), and \(H_T\) will now be expressed in electrostatic units. Thus,

\[ \alpha=-\frac{p^2}{p_0^2},\qquad \beta=\frac{pg}{p_0^2m}, \]

\[ \gamma_L=\frac{pp_L}{p_0^2},\qquad \gamma_T=\frac{pp_T}{p_0^2}. \]

Making the substitution, we obtain:

\[ c^2q^2 = \left(\mu-\frac{ick}{p}\right)^2 = \]

\[ = 1- \frac{2p_0^2}{ 2\left(p^2-\dfrac{ipg}{m}\right) -\dfrac{p^2p_T^2}{p^2-p_0^2-\dfrac{ipg}{m}} \pm \left[ \dfrac{p^4p_T^4}{\left(p^2-p_0^2-\dfrac{ipg}{m}\right)^2} +4p^2p_L^2 \right]^{1/2} }. \tag{23} \]

In general, therefore, the ray treatment of the problem shows that we must expect the existence of two different indices of refraction and two corresponding types of wave propagation through an ionized medium. To find the polarization belonging to each of these types of wave propagation, we may use the auxiliary equation

\[ \frac{H_y}{H_z} = \frac{i\gamma_L}{ \dfrac{1}{c^2q^2-1}-(\alpha+i\beta) }, \tag{24} \]

obtained as a result of substituting (10) into (14).

If we had included the Lorentz correction term, then instead of equation (23) we would have obtained the following:

\[ \frac{2p_0^2}{ 2\left(p^2+\frac{1}{3}p_0^2-\frac{ipg}{m}\right) -\frac{p^2p_T^2}{p^2-\frac{2}{3}p_0^2-\frac{ipg}{m}} \pm \left[ \frac{p^4p_T^4}{\left(p^2-\frac{2}{3}p_0^2-\frac{ipg}{m}\right)^2} +4p^2p_L^2 \right]^{1/2} } \tag{23'} \]

If one neglects the insignificant additional change that arises when the coefficient of friction \(g\) is expressed in terms of the collision frequency \(\nu\), then we may note that equation (23′), in its essential features, is the Appleton–Hartree formula, which was widely used in numerical calculations by Taylor \(^{108}\) and many others. For the reasons mentioned in section E, we now prefer equation (23), which is equivalent to the simpler Appleton formula \(^{104}\).

Equations analogous to those derived above have been widely used in the theory of the ionosphere and have likewise been broadly confirmed by experiments. We shall consider their significance in further detail in a number of the following sections. It would, however, be wrong to suppose that the magneto-ionic theory of the ionosphere has received universal acceptance or that it represents the only possible attempt to solve this problem. Therefore, before beginning the analysis of this theory, I shall give several references representing those points of view that are not covered by the preceding derivations.

A competing theory, proposed by Eckersley \(^{109,110}\), attracted considerable attention. Eckersley asserts that magneto-optical effects are of great importance only at night and, perhaps, for exceptionally long waves during the day. He believes that daytime transmission is determined primarily by absorption phenomena, which in turn depend on whether the frequency of the radio wave is higher or lower than the mean collision frequency of the electrons. Somewhat earlier, Menzel \(^{111}\) compared Eckersley’s hypothesis with the theory set forth here and gave an interesting critique of the theories of Lassen, Nagaoka, Pedersen, Breit and Chapman, and of Pickard’s experiments.

The question of the correctness of the ray method of analyzing an electric wave has been discussed by many authors. Eckersley \(^{112–114}\) expresses the wish to replace the approximate treatment of the phase integral, which constitutes a formal analogy with quantum theory and uses the methods of Bohr and Sommerfeld. He considers the ray method unsuitable for long waves. Hartree \(^{63}\) finds that the conditions of applicability of the ray method are not fully satisfied, but that the correction introduced by the wave method is insignificant. Epstein \(^{115,116}\) justifies the use of geometrical optics, since there is no noticeable reflection here, unless the conditions are such as correspond to total reflection. He believes that a rectilinear ray can be correctly traced along

to the ray method and that this refracted ray carries the principal part of the energy.

In conclusion we may also briefly refer to the theory, based on the idea of “subelectrons,” proposed by Bagchi \(^{117}\), and to the theory, assuming diffusion by small clouds of electrons, put forward by Pont and Rocard \(^{118}\). Neither of these theories, apparently, has attracted much attention in the general literature.

H. Analysis of Magnetic Double Refraction

The elementary theory set forth in Section D shows that we may expect the following: a radio wave directed vertically upward undergoes total internal reflection on reaching the level at which the electron density is just sufficient to reduce the refractive index of the medium to zero. We derived there a simple relation connecting the refractive index with the electron density and with the angular frequency of the wave.

In Section G we undertook a more detailed investigation of the problem, taking into account the changes introduced by terrestrial magnetism. As a result of this we obtained, for the refractive index, a more detailed formula [equation (23)], containing, in addition to the quantities mentioned earlier, the longitudinal and tangential components of the earth’s magnetic field. Our improved equation indicates that, for given electron density, wave frequency, and direction of propagation, there correspond two different numerical values of the complex refractive index. We thus arrive at the conclusion that the ionosphere is a doubly refracting medium, and that we should expect two types of propagation of radio waves in ionized regions.

In general we find that a radio wave emitted by a transmitting antenna in the form of a single ray, on passing through ionized layers, will split into an ordinary and an extraordinary ray. These rays will follow different paths, penetrate to different levels, and return to the earth at different times. If both waves happen to return to one and the same point at approximately one and the same time, they combine and give a resultant signal in the receiving antenna. Under such conditions the resultant wave often undergoes a rapid change of intensity and polarization, which is the result of the slightest changes in the path of one ray or the other. Under other conditions one of these two rays may be lost owing to its absorption or penetration beyond the limits of the ionized layer, or else may be so delayed that we can clearly distinguish it as a separate echo when it finally returns to the earth.

Until quite recently, practically all direct measurements of the properties of the ionosphere were made with the aid of transmitting and receiving stations situated comparatively not far from one another.

one another, so that the “reflection” of waves by the layers of the ionosphere occurred at normal incidence of the waves.

Under such conditions, experiments of two main types were often carried out. In experiments with “variable frequency,” the angular frequency of the wave being tested is varied over a wide interval; the corresponding sequence of echoes, obtained at the receiving point, is recorded automatically or noted by an observer watching the screen of a cathode-ray oscillograph. In this way it is often possible to obtain two “critical frequencies.” One of these “critical frequencies” is the highest frequency at which the extraordinary ray will be “reflected” by the electron concentration that is maximal in the given layer during the experiment. The other “critical frequency” is the highest frequency that will allow the ordinary ray to return to the earth under these same conditions. Evidently each of the “critical frequencies,” carefully measured by direct experiment, has precisely the value sufficient to reduce to zero the refractive index for the corresponding type of wave propagation at that point of the layer where the electron density is greatest. For higher frequencies the corresponding refractive indices do not decrease to zero at any point of the layer, and one of the rays, or both constituent rays, will penetrate into the higher layers of the atmosphere or pass out into interstellar space. If we may suppose that the analysis of the phenomenon given in Section G is valid, then from our measurements of the critical frequency it would be possible to calculate the electron density and the intensity of the earth’s magnetic field. Since the whole experiment takes only a very short time, the electron density remains fairly constant during it.

Experiments with “constant frequency,” on the contrary, are long-duration experiments intended for the study of normal and anomalous variations of the electron density. In studying the \(F\)-region, the transmitter is assigned such a frequency as normally would not reveal, at vertical incidence, reflections from this layer during the early morning hours (say, 3492.5 kilocycles). During the period of sunrise the electron density increases as a result of the absorption of ultraviolet rays. Eventually the electron density becomes so great that it reduces to zero the refractive index for the extraordinary ray (in the numerical example just mentioned). The exact time of the first arrival of this type of echo can be recorded automatically. Some 30 minutes later a further increase in the electron density suddenly permits the “reflection” of the ordinary ray as well. Similar phenomena occur in the reverse order when the electron density slowly decreases during the late evening hours. From day to day there are, of course, considerable variations; however, using automatic instruments, one can obtain statistical data sufficient for studying the rates of increase and

decrease of ionization. Continuous measurements of this kind are also extremely useful for accumulating precise data on the influence exerted on the propagation of radio waves by magnetic storms, sunspots, and other geophysical phenomena. These two types of experiments mutually supplement one another.

Obviously, in interpreting the data of experiments of either type, it will be of interest to study the variation, with angular frequency and with electron density, of the refractive index, and to elucidate the character of the polarization corresponding to each of the two refractive indices. We shall be especially interested in those conditions which are just sufficient for the refractive index to be reduced to zero. The equations derived in Section G will therefore be analyzed precisely from this last point of view. Such an analysis was given by Goldstein \(^{64}\), Ratcliffe \(^{119}\), Taylor \(^{108}\), and others. The results obtained by the various authors are equivalent, apart from certain quantitative differences arising from the retention or omission of the Lorentz correction term considered by us earlier. Ratcliffe’s treatment is especially successful in that he gives special attention to the progressive changes which accompany changes in the relative directions of the wave normal and the terrestrial magnetic field. The following exposition was suggested by his paper, although the notation here has been somewhat changed and the treatment itself has, of necessity, been greatly shortened.

Fig. 7. Polarization of radio waves
(Fig. 1, Wireless Engineer, 10, 355, 1933).

Since differences in terminology have caused certain misunderstandings \(^{120,121}\) concerning the true polarization of downward-traveling radio waves, we must familiarize ourselves with the direction of the coordinate axes and with the convention regarding signs with particular care.

Let us consider, as in Section G, a radio wave propagating in the positive direction of the \(x\)-axis (Fig. 7); its own magnetic field is situated entirely in the \(yz\)-plane. The Earth’s magnetic field is represented by a vector in the \(xz\)-plane with a longitudinal component \(H_L\) along the positive direction of the \(x\)-axis and a tangential component \(H_T\) along the positive direction of the \(z\)-axis. In an ionized medium the wave may be resolved into two parts, represented by two ellipses in the \(yz\)-plane. The dotted ellipse represents the “right-polarized ray,” since its magnetic component \(H_y\) reaches its maximum positive מאַקסimum

values, leading by \(90^\circ\) the electric component \(H_z\). The magnetic vector of this ray therefore rotates clockwise, if viewed in the direction of propagation of the wave. Since for a solid ellipse we obtain the reverse, it represents “left-hand polarization.”

In the present section we shall neglect friction due to collisions and omit all terms containing the coefficient of friction \(g\). With this simplification we can rewrite equation (23) in the following form:

\[ c^2 q^2=\left(\mu-\frac{jck}{\omega}\right)^2 = \]

\[ =1-\frac{ 2\frac{\omega_0^2}{\omega^2}\left(1-\frac{\omega_0^2}{\omega^2}\right) }{ 2\left(1-\frac{\omega_0^2}{\omega^2}\right) -\frac{\omega_T^2}{\omega^2} \mp \left[ \frac{\omega_T^4}{\omega^4} + \frac{4\omega_L^2}{\omega^2\left(1-\frac{\omega_0^2}{\omega^2}\right)^2} \right]^{1/2} }, \]

where

\[ \omega_0^2=\frac{4\pi N e^2}{m} \]

\[ \omega_L=\frac{H_L e}{mc} \]

\[ \omega_T=\frac{H_T e}{mc} \]

We shall also use the notations

\[ \omega_1=\frac{He}{mc}, \quad Y=\frac{\lambda}{\lambda_1}, \]

\[ X=\frac{\omega_0^2}{\omega^2} \]

(note that \(X\) and \(Y\) are certain ratios and do not coincide with the spatial variables \(x\) and \(y\)),

\[ \lambda_1=\frac{2\pi c}{\omega_1}, \]

\(\theta\)—the orientation of \(H\), measured relative to the direction of propagation of the wave. At a point where the Earth’s magnetic field is approximately equal to \(0.5\) CGSM, the numerical value of \(\lambda_1\) is about \(200\) m. The corresponding frequency is the resonant frequency produced by the rotation of free electrons about magnetic lines of force. By analogy with optical problems, one naturally expects here significant differences in the properties of the medium above and below this critical region. The resonance, however, is not sharply expressed, since the intensity of the magnetic field varies greatly with latitude and since in practice, owing to friction, damping will occur. Let us first consider the special case when \(\lambda=100\) m, since this will illustrate the typical conditions encountered in the transmission of high-frequency radio waves. The corresponding curves, representing the dependence of \(\mu^2\) on \(X\), were calculated and plotted by Ratcliffe (Fig. 8) for three different orientations of the direction of wave propagation relative to the Earth’s magnetic field.

Let us note that the abscissa \(X\) is directly proportional to the ionization density \(N\). The shaded areas embrace a family of curves that may be drawn for any of the intermediate orientations lying between the longitudinal and transverse directions of propagation. We may quite arbitrarily choose the curve for 45 degrees as a typical representative of this group. Taking the lower sign in equation (23), we obtain a solid curve passing through the point \((0,1)\). Although the form of this curve depends on the intensity of the magnetic field, we may note that \(H\) does not affect the position of the point at which \(\mu^2\) becomes zero. Consequently the designation “ordinary ray” is assigned to the corresponding type of wave propagation. Taking, instead, the upper sign in equation (23), we obtain the curve for the “extraordinary ray.” This curve has one point at infinity and intersects the horizontal axis at two points: \(X=1-Y\) and \(X=1+Y\). The position of these zero points depends, evidently, on the value of the quantity \(H\), but not on its direction.

Fig. 8. Variation of the refractive index with ion density \(\left(Y=\frac{1}{2}\right)\)

(Fig. 9, Wireless Engineer, 10, 359, 1933).

Examining equation (23), it can be shown that the ordinary ray is polarized left-handed circularly \(\left(\dfrac{H_z}{H_y}<0\right)\) for values \(X<1\); it is linearly polarized for \(X=1\) and right-handed circularly polarized for \(X>1\). The extraordinary ray is right-handed circularly polarized for \(X<1\), linearly polarized for \(X=1\), and left-handed circularly polarized for \(X>1\) (let us note that these results are based on the assumption that \(H\) has a positive component in the direction of wave propagation, as is the case for waves traveling downward in the northern hemisphere. In the southern hemisphere the polarization will everywhere be reversed. In the limiting case of strictly transverse propagation, both waves are plane-polarized at right angles to one another).

Let us now apply these results to the practical problems of transmission on short radio waves and to the problems of experimental study of the ionosphere. A radio wave directed vertically upward, upon reaching the ionosphere, is split into ordinary and extraordinary components. These two components continue

can propagate upward through a region of increasing electron density. In the end they may reach a level where there is a sufficiently large electron density capable of reducing to zero the refractive index of the extraordinary ray \((X = 1 - Y)\). This ray then undergoes total internal reflection, while the ordinary ray must rise to a greater height in search of a region with a noticeably greater electron density, such that \(X = 1\). If the layer is sharply defined, the difference in paths may be too small for it to be measured by ordinary means, and the reflected signals will therefore be closely superposed on one another. During sunrise and late in the evening, however, the difference in paths is often large and the two echoes are easily distinguishable. It frequently happens that the extraordinary ray for a wavelength of \(86\ \mathrm{m}\) undergoes reflection at vertical incidence throughout the entire night, while no trace whatever of the ordinary ray can be detected.

Fig. 9. Change of the refractive index with ion density \((Y = 2)\)
(Fig. 10, Wireless Engineer, 10, 360, 1933).

The second zero point for the extraordinary ray at \(X = 1 + Y\) probably cannot be detected experimentally, since practically all the energy of the ray has already been lost during reflection at \(X = 1 - Y\) and as a result of collisional friction. Theoretically, even in the case of “complete” internal reflection, a small amount of energy nevertheless penetrates into the external region, but it becomes imperceptible already at distances of the order of a wavelength. Thus the zero points at \(X = 1 - Y\) and at \(X = 1\) are the points that can most directly be connected with experiment.

In the case of oblique incidence the results are qualitatively the same. The extraordinary and ordinary rays rise to different heights, since their refractive indices must become small, but need not decrease to zero. The electron density may be sufficient to return one or both components to the Earth at distant points, but insufficient to produce reflection of either ray at small angles of incidence. Let us now consider the behavior of waves that are appreciably longer than \(200\ \mathrm{m}\). Fig. 9 presents the results of Ratcliffe’s study of the propagation of waves of wavelength \(400\ \mathrm{m}\) \((Y = 2)\). The limiting curves are constructed

again for the limiting cases of transverse and longitudinal propagation, while the intermediate curve is for the case \(\theta = 30^\circ\); the shaded areas show the transition region.

It is obvious that the ordinary and extraordinary rays have here exchanged their roles, and the extraordinary ray now gives the echo that traverses the longer path and is reflected from the denser region. Although the extraordinary ray, when it passes through the level where \(X = 1\), evidently changes its polarization to the opposite one, in the lower layers of the earth’s atmosphere, where it can be studied experimentally, it is again polarized to the right. The ordinary ray retains its left-hand polarization (both statements refer to waves traveling downward, in the northern hemisphere).

In conclusion we may briefly mention several characteristic experiments that illustrate the methods used in studying the double refraction of the ionosphere. The construction of a typical polarimeter receiver for studying the nature of downward-traveling waves was described by Ratcliffe and White\(^{122,123}\). Martin and Green\(^{124,125}\), in order to determine the polarization of downward-traveling waves in the southern hemisphere, used measurements with systems of three antennas. Their results differ from those obtained by analogous measurements in the northern hemisphere, and the differences between the two are correctly predicted by the ordinary magneto-ionic theory.

Berkner and Wells\(^{126,127}\) compared the critical frequencies measured in Washington, in Colombia, and in Huancayo, Peru, and concluded that the results are in general agreement with the known differences in the intensity of the magnetic field. Appleton\(^{128}\) and Chapman\(^{129}\) believe that, by means of night-time measurements of critical frequencies, it is now possible to make a careful determination of the intensity of the magnetic field as a function of latitude. The preliminary results are in agreement with the theory.

Although the normal component of the high-frequency echo having the smaller delay is the extraordinary ray, Appleton and Builder\(^{67}\) found that the group delay in the lower layer, in the case when the experimental frequency is somewhat higher than the penetration frequency for the lower layer, can cause a reversal of the position. This reversal is caused by the fact that the ordinary ray has a higher group velocity.

Using exceptionally good experimental technique (an oscillograph), Handel and Plendl\(^{130}\) carried out a detailed investigation of the distortion of a radio signal (selective interference of the sidebands) caused by double refraction in the ionosphere.

Green and Builder\(^{131}\) explained and interpreted the observations of Hollingsworth, Naismith, and Namba on the rotation of the plane of polarization of long radio waves.

I. Friction as a Result of Collisions

The effect of friction arising as a result of collisions has been considered to some extent by many authors; however, no definite quantitative mathematical treatment of the phenomenon has yet been...

until now has still not received general recognition. I shall therefore confine this discussion to a brief qualitative review, with references to some typical calculations that have been undertaken by various groups of investigators—one may try to approach this problem from many different sides. Thus, we may be interested in the nature of molecular or atomic collisions, or in losses due to friction, which may limit the useful transition region, or else in selective absorption, which changes the polarization of the “reflected” wave.

Halbert132,133 published a number of interesting papers devoted to the question of the absorption of radio waves in the upper layers of the atmosphere. Considering collisions of electrons and molecules, he derives a simple formula for the attenuation of waves and believes that the measured values can provide information about the density of electrons and molecules at great heights.

Yokoyama and Nakai134 find that, in the case of long-wave transmission, the attenuation observed at very high latitudes during the daytime in the direction from east to west is decidedly greater than the attenuation in the direction from north to south. However, the agreement between the experimental measurements and the various theories proposed in connection with this is still by no means very good.

Kreider135 investigates the absorption in a dielectric of a train of waves of finite length and finds that the absorption constant depends on the depth of penetration of the waves into the medium, on the frequency, and on the length of the train. The absorption proves to be smaller than that given by classical optics for frequencies close to resonance. The theory was tested by experiments on ethyl alcohol.

Assuming that the quantity of motion of an electron changes at each collision and that the velocity attained between collisions is small compared with the random velocity of thermal motion, Childs136,137 calculates theoretically the conductivity of a gas and finds that this quantity is of the same order as the observed conductivity. He comes to the conclusion that the kinetic theory of gases is suitable for calculations connected with the ionosphere.

Using the Appleton–Hartree formula in a form analogous to that derived in Section G (but with explicit use of the Lorentz polarization term and of the Lorentz estimate of the coefficient of friction through the collision frequency), Taylor68 calculates dispersion curves for four radio frequencies and four values of the collision frequency. The introduction of the friction term eliminates from the dispersion curves, presented in Section H, the infinite singularities, but it does not affect their general form or the conclusions drawn from them. Nevertheless, this makes it possible to obtain a considerable amount of additional information (an analogous, but less complete, treatment of the question had earlier been given by other authors). At broadcast frequencies in the northern hemisphere the extraordinary ray is greatly weakened as a result of attenuation and absorption. The ordinary ray, however, despite the fact that it penetrates more deeply into the iono-

sphere and experiences a large delay, returns in the end with an amplitude larger than that of the extraordinary ray. We therefore find that, in the case of broadcast waves traveling downward, left polarization normally predominates. But if the electron density falls below the critical value and only the extraordinary ray remains, then the polarization suddenly changes to right-hand. These changes were observed experimentally by Appleton and Builder^67, by White^138, and by others, and, apparently, this part of the theory of friction as a result of collisions is in complete agreement with experiment.

From our present point of view it is somewhat unfortunate that Taylor, in his calculations, also took into account the Lorentz polarization term. Although most of Taylor’s results are qualitatively, undoubtedly, correct, the importance of the subject would seem to justify repeating the quantitative side of the work in accordance with the revision of the problem that was carried out by Darwin. In addition to the effects of polarization, Taylor finds, at the critical collision frequency, a transition from quasi-transverse to quasi-longitudinal propagation of the waves. Considering, besides the refractive indices, the attenuation constants, she also concludes that the lower boundary of the lower layer must be optically sharp.

On the basis of observations of long waves at short distance, Naismith^139, ^140 finds that the most intense downward-going wave is obtained in the direction from north to south; he therefore supposes that, for the propagation of waves in this direction over a great distance, correspondingly less energy will be required. He also finds that magnetic storms strengthen the field of a long wave at short distances, but weaken it at large distances.

J. Complete analysis by means of conformal mapping

Bailey^141 and Martyn^142 have recently developed an interesting graphical method for obtaining quantitative solutions of the Appleton–Hartree formula (or analogous equations) for the complex refractive index of the ionosphere, fully taking into account both the damping caused by friction as a result of collisions and the effect of the earth’s magnetic field.

Although this new attempt to solve the problem deserves special mention in a separate section of this report, it does not, however, seem necessary to us to give here any detailed description of the special geometrical devices involved. The new method is a direct application of the methods of conformal mapping^148 and is described in detail in two recent papers^141, ^142, which can be obtained in practically all scientific libraries. “The two maps required for determining, respectively, the polarization and the refractive index are easily drawn, since only circles, ellipses, and parabolas occur in them.”

Martin^142 carried out a graphical analysis for five typical wavelengths (from 100 to 20,000 m), three collision frequencies (\(10^4\), \(10^5\), \(10^6\) per sec.), also in order to cover the region of practical importance in the problem of radio-wave propagation, and for directions making three angles, \(0\), \(40\), and \(90^\circ\), with the magnetic field. In general, his results confirm and supplement the conclusions set forth in Sections H and I of the present survey. A detailed analysis of the limiting values of the polarization obtained for low electron densities shows that Martin’s results differ substantially from those of Taylor^68, although at the same time they are in agreement with the conclusions of Bailey and Green^106. Since Taylor and Martin studied the same basic equation (the Appleton–Hartree formula with the Lorentz polarization term taken into account), the difference is evidently due to a minor analytical discrepancy which can undoubtedly be eliminated. In view of the fact that Martin speaks in a footnote of the controversial character of the Lorentz polarization term, we may hope that he will soon give consideration to the changes of a quantitative character which would result from dropping this term.

K. The “fine structure” of the ionosphere

In making a survey of the experimental facts (Section C), we noted the existence of two principal “reflecting” regions, usually denoted by the symbols \(E\) and \(F\). Analyzing the effect of the earth’s magnetic field (Section H), we came to the conclusion that in each region two types of wave propagation should be expected. The echo picked up by the receiver is usually complicated, moreover, by the existence of “multiple” reflections, consisting of waves which have been “reflected” repeatedly from one or several layers and from the earth (in our own measurements, when the attenuation was very weak, we observed up to 18 such repeated reflections).

In addition to these well-known effects, many observers have noted, however, the presence also of such echoes as can be explained only by assuming that the \(F\)-layer in the daytime is usually divided into two parts, and that additional reflections may sometimes be produced by small concentrations of electrons above, between, or below the principal \(E\) and \(F\) regions. The analysis of echoes proves to be almost as complicated as the analysis of spectra, and in order to describe the “fine structure” of any radio echo, special symbols are evidently needed. Since the best measurements have been made by a relatively small number of groups of experimenters, the influence of geographical differences is still not fully clear, and the literature on the “fine structure” of the ionosphere is still somewhat contradictory. Further difficulties arise from differences in the terminology and notation used in different countries. Nevertheless, references to several experimental works on the stratification of the ionosphere may be of some interest. Wherever this

if possible, I shall use the symbols adopted as a result of the international agreement at the London congress of URSI in 1934, although in the current periodical literature other designations are also often used.

As early as 1916, Levenstein[^144], considering the propagation of radio waves in the atmosphere, expressed the conviction that “measurements of the intensity of light made at sunset reveal three distinct discontinuities when the last rays of the sun become tangent to layers of air at altitudes of 11, 75, and 220 km.” We are still not yet in a position to determine whether or not the “discontinuities” noted by Levenstein at 75 and 220 km are closely connected with the ionized $E$ and $F$ regions; however, additional observations of this character might prove very valuable.

Using his original experimental methods (studying natural “fading” and producing artificial interference variations at the receiving point by slowly changing the transmitter frequency), Appleton and his collaborators[^145,^148] established the existence of two “reflecting” regions and assigned them the symbols $E$ and $F$. These letters were chosen, apparently, in order to provide such designations as could later be extended to higher and lower “layers.” Appleton also established facts indicating the existence of an absorbing layer located below the $E$ layer.

During the same period of time, Breit, Tuve, and Dahl[^58,^149] developed a method for observing pulses (transmission of a very short radio signal and measurement of the echo delay time) and obtained the “heights” of layers extending from 85 to 220 km.

In honor of Appleton’s numerous contributions to the study of the ionosphere, other English authors often call the $F$ layer the “Appleton layer,” while retaining the name “Kennelly–Heaviside layer” for the $E$ layer, which probably played an important role in transmission on long waves used in Marconi’s first transatlantic experiments. (Kennelly originally postulated the existence of more than one reflecting level, whereas Heaviside had in mind only a single layer.) In general, however, the expression “Kennelly–Heaviside region” was used as a synonym for the layer “ionosphere,” since the use of proper names as names for individual parts of the ionosphere would, it seems, cause still greater confusion.

After the existence of the two principal layers had apparently already been well established, Goubau and Zenneck[^150] published a work in which they attributed all reflections to a single lower layer. Their work was reviewed in English by Howe[^151], and soon after this there followed the articles of Eccles[^152], Schafer and Goodall[^153], Gilliland, Kenrick, and Norton[^154], indicating the presence of unquestionable experimental evidence in favor of the existence of at least two ionized layers.

Let us now consider some of the facts concerning the secondary layers, which we mentioned earlier. In order to interpret the data on radio transmission obtained in 1927–1928 in China, Ids ¹⁵⁵ put forward the supposition that there exists a low-lying region with slight ionization. He estimated the height of this layer at 10 km. Recent experiments made by Coulomb ²⁷⁸ appear to confirm the existence of such a C-layer.

In 1927 and 1928 Appleton ¹⁴⁷, Haisang ¹⁵⁶ and Goldstein ⁶⁴ obtained indications of the existence of a certain absorbing region somewhat below the E-layer. This (partly hypothetical) region is now called the “ozone layer” or the D-layer. In general, the existence of this layer may be inferred from indirect facts, although Appleton ¹⁵⁷, Goubau ¹⁵⁸ and some other authors report weak reflections observed by them. Estimates of the height of this region range from 30 to 65 km. Goldstein believes that it reaches the height of the Lindemann–Dobson temperature inversion. Lugeon ¹⁵⁹, ¹⁶⁰ finds over France a layer at 50 km. Additional observations were reported by Bonch-Bruevich ¹⁶¹ and Sillittoe ¹⁶²; however, Kirby and Judson ¹⁶³ assert that if the absence of refraction above 5000 kilocycles in summer around noon is due to absorption, then absorption does not occur chiefly below the E-layer.

Fig. 10. M—reflection.

In 1933, Schafer and Goodall ¹⁶⁴ reported an “intermediate layer” at a height of 150 km and denoted it provisionally by the letter M. Their observations were soon confirmed by Appleton ¹⁶⁵ and Ratcliffe and White ¹⁶⁶, ¹⁶⁷. The use of the letter M to denote the layer appears, however, somewhat unfortunate, since it disrupts the established alphabetical sequence and since this same letter is used in England as the graphic representation of a quite special type of ray path, following a zigzag, as illustrated in Fig. 10.

If my interpretation of the recent recommendation of the URSI is correct, then the principal E-layer should now be denoted by E₁, and the “intermediate” layer by E₂.

In the E-region there are, however, additional complications. In addition to normal daytime ionization (caused, probably, by simple ultraviolet absorption), practically all observers have noted frequent “anomalous,” “sporadic,” or “nighttime” reflections at approximately the same height. In order to distinguish this

random, shifting reflection from the regular daytime effect, Ratcliffe and White\(^{167}\) propose using the lowercase letter \(e\) to denote this sporadic phenomenon. In the present review I shall use the term “anomalous \(E\)-reflection” to designate this nocturnal reflection.

The critical frequency that is just sufficient for the ray to penetrate into the \(E_1\)-layer is denoted by the symbol \(f_{E_1}\). If the resolving power of the experimental arrangement is sufficiently great, then the two components of the critical frequency \(f_{E_1}^{0}\) and \(f_{E_1}^{x}\), corresponding to the ordinary and extraordinary rays, can be separated. (Magnetoionic splitting of the \(E\)-layer was observed in our own experiments, although this effect is considerably more noticeable in the \(F\)-region owing to the smaller gradients of electron density encountered at higher levels.)

Similar indications of the existence of substratification have also been obtained for the \(F\)-region. Kerby, Berkner, and Stuart\(^{168}\) note the existence of an \(F_1\)-layer somewhat below the principal \(F_2\)-layer. The boundary between these layers becomes indistinct in winter and at night, but it can often be distinguished in summer during the daytime. Appleton\(^{169}\) confirms this observation. On the basis of the character of the curve graphically representing the dependence of ion density on height, he considers that the \(F_1\)-region is something like a projection or protuberance on the lower side of the main \(F_2\)-region. It is quite possible that both types of reflection appear simultaneously. Indeed Henderson\(^{170}\) has drawn attention to cases of anomalous echoes from high levels, which occur when the \(E\)-region is ionized considerably more strongly than the \(F\)-region.

When the experimental frequency is gradually increased, the \(F_1\)-region becomes completely penetrable, and then, in the end, the \(F_2\)-reflections also disappear. In the latter case, however, we do not have entirely clear indications of a sudden decrease in group velocity, which in a definite way marks the penetration frequencies for the lower layers. Reflections often disappear rather gradually, without any noticeable increase in the equivalent height. Moreover, since \(F_2\) is probably the most strongly reflecting shell, we cannot detect its penetration by means of powerful echoes obtained from points situated beyond it. The indirect confirmation supplied by observations of the skip zone seems to agree entirely with the usual assumption that the boundedness of the number of free electrons determines the short-wave limit for radio transmission with the participation of the ionosphere, and that waves of very high frequency therefore escape into interstellar space. Some authors\(^{168,171}\), however, suppose that very short waves simply penetrate into the \(F_2\)-region until they are completely absorbed. Our own measurements support the hypothesis of “complete penetration,” but the question still cannot be regarded as finally settled.

The effect of magnetoionic double refraction can easily

observed in the \(F\)-region. Consequently the symbols \(F_1^0, F_1^x, F_2^0, F_2^x\) are needed to describe the complete series of first-order reflections. The results are in complete agreement with the magneto-ionic theory of double refraction set forth in Sections H and I. Several types of polarimeters were used in the measurements. Some statistical results will be given in Section O.

Although no strong and constant reflections from points more distant than the \(F_2\) region have usually been observed, there are nevertheless many indications of the existence of weak or intermittent, or diffuse, or accidental radio echoes. In our very earliest measurements, made with simple mechanical oscillographs, strong radio echoes were often obtained from points more than 1500 km away; however, these echoes usually disappeared within fractions of a second. Similar effects are easily demonstrated by projecting the received echo onto the screen of a cathode-ray oscillograph. Taylor and Young\(^{172,173}\) and Kukk and Megel\(^{174,175}\) noted anomalous echoes at points lying within the normal “skip zone”; these echoes are probably due to the scattering phenomena discussed below in Section R. Working under conditions of maximum sensitivity with our own continuously and automatically recording apparatus\(^{176,178}\), we discovered two types of extremely weak but systematic reflections\(^{179}\), arriving from points 600–1800 km from the transmitter. These echoes sometimes remain for several hours, comparatively constant in their strength and position. The direction from which such echoes arrive is still unknown.

Hollingworth\(^{180,181}\) finds indirect evidence in favor of the idea that 30-meter waves are sometimes trapped between the \(E\) and \(F\) regions and propagate over great distances precisely by this path. Similar ideas were expressed by Janko\(^{182}\).

To establish the relation between the “apparent height” and the “true height” in the \(F\)-region, we shall probably need more refined simultaneous measurements using different ray paths. Considerations concerning the “true height” were expressed by Schelleng\(^{183}\), Kenrick and Yen\(^{184}\), Ranzi\(^{185}\), and many others.

In 1927 Hals observed strong echoes which were apparently reflected from regions lying far beyond the limits of the earth’s atmosphere, since the returning signal could be recognized by ear and the corresponding delay time measured with an ordinary stopwatch. Hals’s observations were repeated and confirmed by Størmer\(^{186–189}\) and Van der Pol\(^{190}\). Størmer believes that these reflections are due to distant clouds of moving electrons which, owing to their motion in the presence of the earth’s magnetic field, form a converging mirror of toroidal shape. Van der Pol states that the enormous delay time of the signal (30 sec. and more) is simply the result of an abnormally low group velocity, and believes that reflec-

... does not take place in the ionosphere. Pedersen \(^{191}\) disputes this opinion, pointing out that abnormally low group velocities would be accompanied by exceptionally strong damping. Although the original observations appear trustworthy, recent attempts to reproduce echoes of this type have not been successful. These echoes can probably be heard only during an especially favorable part of the sunspot cycle.

L. Why does stratification exist?

Knowing the nature and intensity of solar radiation and knowing the composition, absorption coefficients, and motion of the earth’s atmosphere, it would seem possible to give a complete interpretation of the stratification observed in the atmosphere. Unfortunately, as Chapman \(^{192, 193}\) has recently pointed out, the existing tables of values of atmospheric pressure, temperature, density, and composition for altitudes considerably above 30 km are, to a large extent, speculative. At best, they merely illustrate conclusions derived from various hypotheses.

Extensive new quantitative data obtained from measurements of the ionosphere should therefore play an important role in extending our knowledge of the atmosphere and of the incident radiation. Do winds exist at great heights in the atmosphere? What is the degree of dissociation of the constituent parts of the atmosphere? Does hydrogen predominate at great heights, or is it entirely absent there? How far is ozone transported by winds? A full analysis of such questions would extend over the whole field of meteorology. It is therefore impossible, in the present scope, to do more than name a limited number of references that may be used as points of departure in investigating the theoretical foundations of ionospheric stratification. The current literature is in many respects contradictory, although it is often useful for questions concerning the planning of new experiments.

Chapman \(^{194}\) gave a theoretical analysis of the problem, which covers:

1. Absorption of ionizing radiation.
2. Absorption of non-ionizing radiation, such as that which leads to the formation of ozone.
3. Treatment of dissociating radiation, where the products of dissociation recombine according to the simple law:

\[ \frac{dn}{dt}=I-\alpha n^2 . \]

Chapman obtains expressions for the density of the products of dissociation as functions of height, time of day, latitude, and season (time of year). Appleton \(^{195}\) finds that the measured values of ionization density show diurnal variations similar to those obtained by Chapman in studying ionization produced by monochromatic radiation.

In a theoretical review Hulburt^196,197 compares radio determinations of electron density with values obtained from magnetic theories and by other available means. He also discusses the meaning of the measured values of the “recombination” rate in the \(E\) and \(F\) regions, asserting that ionic recombination takes place in the \(E\)-region. Hulburt believes that the decrease in the density of free electrons in the \(F\)-region can be explained by the attachment of electrons to oxygen molecules. He considers that the \(F_2\)-region owes its existence to ionic winds flowing outward from heated regions located near the terrestrial equator.

Appleton, however, states that Hulburt confused the main \(F_2\) region, which was discovered in 1926, with the additional \(F_1\) layer, which was discovered in 1933. He further asserts that Hulburt is wrong in considering that the \(E\)-region consists chiefly of ions of molecular mass. Chapman^199 finds that true recombination is of greater importance than the attachment of electrons to neutral particles (both in the \(F\)-region and in the \(E\)-region). Eckersley^200 also gives numerical data confirming this point of view.

Lassen^201 asserts that the effect of free electrons is insignificant in comparison with the effect of hydrogen ions, whereas Conroy^202 finds no hydrogen at any altitude. In doing so he compares data obtained from observations of meteors, spectra of auroras, and refraction of sound waves in the stratosphere. The dissociation of oxygen was considered in detail by Kryuchkov.^203 Nagaoka^204 believes that the formation of the upper layer is due to the ionization of helium.

In addition, Nagaoka attributes certain differences between east-to-west transmission and west-to-east transmission to an asymmetry of the layer. This question was also investigated by Nakai.^205 Namba^206–209 gives a general theory of the development of the ionosphere and attempts to calculate the influence of the height of the sun on the properties of the layer. Various hypotheses concerning the nature of the incident radiation were analyzed by Chapman^210 in his extensive theoretical work devoted to magnetic storms. Elias^211 assumes the existence of a constant ionization produced by corpuscular radiation from the sun, plus a temporary diurnal ionization due to the wave radiation of the sun. Suess^212 notes that the electric charge of the Earth (as measurements up to a height of 10 km show) would decrease by 90% within ten minutes if it were not replenished by some unknown means. He postulates the possible slow death of the Earth’s positive charge and discusses the difficulties connected with the hypothesis of a flux of electrons emitted by the sun. Suess proposes a new scheme of electrodynamics. Various other authors believe, however, that the electric charge of the Earth is maintained in equilibrium by constant thunderstorm activity over large, statically active areas of the Earth’s surface.

G. R. MIMNO

M. Tidal Effects in the Ionosphere

By measuring the strength of the signal sent by distant radio stations, some observers have obtained indirect evidence indicating the existence of a lunar tidal effect in the ionosphere. Stetson \(^{213,214}\) has recently given a review of several experiments and described his own observations. The signal intensity apparently decreases when the moon passes through the observer’s meridian. The cause of the tidal effect and the nature of the disturbance arising in the ionosphere still remain somewhat obscure. The ordinary gravitational tide in the atmosphere is very small.

Using the experimental data of Gilliland \(^{215}\), Vrieland \(^{216}\) finds indications of a decrease in the height of the layer at the time of full moon. Observations of the layer height are not yet sufficiently extensive to enable us to choose between the lunar cycle and the period of rotation of sunspots with the accompanying changes of magnetic character. Breckel \(^{217}\) suggests that Stetson’s conclusions apply only to relatively long waves, and believes that the effect reverses in the region of 3500–4000 kc of the radio spectrum. Various additional observations have been made by Pickard \(^{218}\), Stoye \(^{219}\), Wensel \(^{220}\), and Shennol \(^{221}\), but general agreement has not yet been reached, and direct measurements of the height of the layer over a long period of time are evidently necessary.

Stetson \(^{214}\) also studied certain systematic discrepancies between the radio time signals transmitted from the Greenwich Observatory and the time signals transmitted from the Naval Observatory in Washington. He finds that these discrepancies depend on the hour angle of the moon and reach values of 0.03 sec. As a preliminary hypothesis it may be assumed that this variation is due to the tidal deformation of the earth’s crust, which can change the distance between the two observatories by as much as \(\pm 32\) feet. This deformation is unexpectedly large. From the same numerical data he calculates the transmission time of a radio signal across the Atlantic Ocean and finds that it is approximately 0.04 sec. This transmission time also reveals systematic variations of the order of 0.01 sec, which may presumably be ascribed to tidal effects in the ionosphere. Although the possible correlation between discrepancies in the time signals and the lunar hour angle is of undoubted interest, I feel that this numerical analysis is somewhat weakened by the basic assumption according to which “the radio wave traverses both paths across the Atlantic Ocean in an equal interval of time.” Since the results suggest that the effective velocity of the signal for the principal level is less than half the speed of light, it is evident that the properties of the transmitting medium must here be carefully taken into account, and it is possible that the west–east, east–west asymmetry mentioned above may lead to the basic assumption proving incorrect. Moreover, the paths emplo-

ing rays probably depend in part on the corresponding characteristics of the transmitting and receiving antennas. In view of the fact that the transmission time is apparently of the same order as the observed discrepancies, it seems somewhat risky to treat the condition of symmetry as a self-evident fact.

N. Sunspots, Magnetic Indices, and Auroras

The existence of a close connection between sunspots, magnetic disturbances, auroras, and radio reception is generally recognized, although the details of the mechanism linking these phenomena are still little understood. The technical literature covering this phase of radio transmission is especially extensive.

A large amount of data on the field intensity of distant radio stations has been collected by Austin \(^{222,\,2,\,3}\), Pickard \(^{224–227}\), and many others. If these data are traced by years, months, or weeks, then the connection between radio reception and Wolf’s sunspot number appears unquestionable. In general, transmission becomes worse when the number of sunspots increases; however, the magnitude and even the direction of the change depend to some extent on the wavelengths employed. Plendl \(^{228}\) and Mögel \(^{229}\) find that in short-wave transmission between definite geographical points the optimum wavelength, as a result of a decrease in the mean ionization density, may be increased even by \(30\%\), which apparently occurs during a sunspot minimum. Austin \(^{230}\), Yokoyama and Nakai \(^{231}\) find a closer connection with the Sun for short waves than for long waves, although Abbott \(^{232}\) believes that the seven periodicities in the values of the solar constant are also reflected in data on the propagation of long waves.

However, no good day-to-day correlation is found between the intensity of the radio field and the passage of definite groups of sunspots through the central part of the Sun, although at the same time radio data do follow the diurnal changes of the Earth’s magnetic field. It is quite possible that sunspots are not the direct cause of the disturbances occurring on Earth, but merely a symptom of more deeply seated solar perturbations. If corpuscular radiation causes changes in ionization, then it is also possible that these rays, after being emitted by the Sun, do not follow simple radial paths.

Reviews of earlier experiments devoted to the study of the connection between radio transmission and sunspots were given by Menn \(^{233}\) and Stetson \(^{234}\). Recent observations of transatlantic signals were published by Judson \(^{235}\). Gunn \(^{236}\) and Larmor \(^{237}\) considered the magnetic fields of sunspots, while Dauvillier \(^{238}\) investigated the question of the possibility of deformation of the ionosphere under the pressure of solar radiation.

Measurements of radio-field intensity, despite the fact that they can readily be performed with a minimum of apparatus, do not give direct indications concerning the ionization density at various points of the ionosphere,

depend on the wavelengths used in the investigations and on the geographical position of the transmitter and receiver; in this, some signals become stronger, others weaker, since magnetic conditions and the numbers of sunspots change.

In recent years we have therefore begun to carry out continuous daily registration of actual reflections obtained from various levels of the ionosphere. Such an experiment requires very perfect automatic apparatus, but in return it gives direct information about ionization densities. We have already obtained a sufficiently large number of records of reflections, making it possible to carry out their preliminary comparison with the magnetic data available.

Fig. 11.

The 86-meter signal, sent vertically upward, usually penetrates through the \(E\)-layer without producing a reflection, but sometimes the ionization in this region exceeds the critical value, and then the corresponding echo is recorded photographically. On those days when the average ionization of the \(E\) region is high, we can expect to record such an echo during a relatively large fraction of the 24-hour period.

In Fig. 11 we have graphically represented the total duration of these \(E\)-reflections in hours per day. In constructing these curves, we arbitrarily classified \(E\)-reflections for \(86\ \mathrm{m}\) as “anomalous” when they begin between 9 o’clock in the afternoon and the moment of sunrise. Obviously, the cause of these “anomalous” reflections is not the simple uniform ionization that arises from absorption of ultraviolet light. All the remaining \(E\)-reflections are described as “normal.” The curve of the “normal” reflection reveals decisive agreement with the magnetic index (the values of which were plotted downward, since the correlation here is inverse). The numerical value of the correlation coefficient is equal to \(37\%\). Large values of the magnetic index indicate days characterized by strong oscillations of the Earth’s magnetic field. These

indices are the mean values obtained from the data of 48 magnetic observatories by van Dijk. They are published in “Caractère Magnétique des Jours” and in “Terrestrial Magnetism and Atmospheric Electricity.” “Anomalous night reflections” do not reveal such a sharply expressed correlation with magnetic conditions (the numerical value of the correlation coefficient here is 15).

In general it appears that in those cases when magnetic conditions are disturbed, the probability of daytime \(E\)-reflections decreases.

Fig. 12.

This indicates a decrease, under such conditions, of the mean ionization or an increase in absorption. The first hypothesis finds strong support in the observations of the \(E_1\)-layer presented in Fig. 12.

When the mean ionization is low, we should expect the morning sunlight to act on the \(F\)-region for a comparatively long time before it creates an ion density sufficiently large to reflect 86-meter waves at normal incidence. The onset of reflections during the period of sunrise should therefore be delayed. Under analogous conditions, the gradual decrease of ionization after sunset should interrupt reflections from the \(F_1\)-layer at a comparatively early hour of the evening. The “critical instants of time,” when \(F_1\)-reflections begin and cease, can usually be determined exactly for the extraordinary and ordinary rays. In these critical periods, rapid changes of the group velocity cause corresponding changes

of the observed equivalent height of the reflecting surface, and therefore it is convenient to speak of a “rising” \(F_1\)-layer in the evening hours and of a “descending” \(F_1\)-layer at the time of sunrise. The critical moments of time correspond to the attainment of definite critical densities in the ionized region.

With the method of graphical representation adopted in Fig. 12, all four upper curves should rise whenever the mean ionization is low. Obviously this occurs when the magnetic state is disturbed. In order to show the general tendency, we have plotted the ionospheric data and the values of the magnetic index, taking as a basis the means for each ten days. Similar correlations can be obtained by plotting the data directly for individual days as well; however, excessive detail in the graph would entail a certain lack of clarity, unless the horizontal axis of the graph were considerably extended. From Fig. 11 and Fig. 12 we obtain two separate statistical indications of a decrease in the mean atmospheric ionization on days when magnetic variations occur. This raises interesting theoretical problems. Obviously, we cannot accept the naive idea of large clouds of electrons violently ejected from the sun during the eruption of sunspots—clouds of electrons that can cause aurorae, magnetic variations, and an immediate increase of atmospheric ionization. Moreover, this detailed analysis of changes from day to day must in the end be reconciled with reliable individual observations^169,239, which show that the mean annual ionization is greatest at the maximum of the sunspot cycle. In order to obtain further information experimentally, it seems desirable to continue the recording of radio echoes over a long period of time. At present we have at our disposal the results of automatic recording covering about 10,000 hours, but this covers only a limited fraction of the solar cycle.

Among experimenters there apparently exists unanimity of opinion regarding the effect of aurorae on radio transmission in northern latitudes. Reports on this subject, essentially similar, have been published by Wagner^240, Gelbronner^241, Odjilvy^242, Satton^243, and many others. A marked decrease in signal strength occurs simultaneously with the beginning of an aurora visible nearby. This effect is especially noticeable in transmission on short waves and is often so serious that it completely cuts off the signals. Echoes disappear in such a way as to suggest complete absorption. At more distant points there occurs a less strong effect, generally of the same nature, although there are some indications of the existence of a noticeable time lag between the aurora and the ensuing weakening of the signals. A visible aurora is accompanied by simultaneous strong oscillations of the Earth’s magnetic field. Dellinger^244 asserts that this is preceded by rapid changes in the direction of arrival and in the intensity of the signals.

Dauvillier \(^{245,246}\) divides the phenomena of aurorae into two distinct phases. He asserts that the initial cosmic effect, which often lasts a very short time, is followed by a relatively slow development of phosphorescence, due to the excitation of ionization and the formation of ozone. He observes luminous clouds of ions in rapid motion at approximately an altitude of \(200\) km and believes that the existence of this ionic “wind” is due to large electromagnetic forces. “Wind velocities” of the order of tens of kilometers per second are encountered.

The nature of the principal cosmic effect still remains somewhat unclear, although Størmer \(^{247,248}\) has shown that the observed patterns of aurorae (“draperies”) can be naturally explained by considering a family of trajectories of electrons arriving at the Earth.

Broglie \(^{249–251}\) reproduced some of the phenomena of northern lights by demonstrating Størmer’s hypothesis of electron rays on a small model of the Earth. His experimental technique is especially interesting. Dostal \(^{252}\), on the basis of Størmer’s theory of aurorae and the associated theory of the long-delayed echo, calculated the density of the space electric charge in the incident electron ray; he maintains that this charge is insufficient to cause direct reflection of 30-meter radio waves.

Vegard \(^{253}\) has recently made a survey of extensive studies of the spectrum of aurorae. He comes to the conclusion that the electric rays producing the aurora may apparently be regarded as a mixture of electrons and ordinary matter, existing mainly in the form of positive ions precipitating toward the Earth from the solar corona. The supposition has also been put forward \(^{254}\) that the matter of the corona consists to a considerable extent of oxygen. If the mean charge of the beam of rays is negative and numerically small, then “we can explain the large angular distance between the auroral zone and the point of the magnetic axis.”

Larmor \(^{255}\) also expressed considerations concerning the cause of aurorae and their influence on terrestrial ionization. He notes that “the fact that a very small density of ions completely destroys the optical elasticity of space for long waves points to the cause which preserves ionized gaseous clouds of astronomical dimensions, for example within stars, from rapid general disintegration or scattering.”

O. Magnetic Storms and Meteor Showers

Most of the ordinary variations of the magnetic index have the character and duration of small long-period oscillations of the Earth’s magnetic field. Sometimes, however, the Earth experiences a sudden disturbance of such great intensity that it deserves the name of a “magnetic storm.” In exceptional cases magnetic storms completely interrupt both wire communication and radio communication. Fortunately, these intense disturbances are short-lived.

With regard to magnetic storms (from eight consecutive cases256) it is known that they recur at approximately 27-day intervals. It is usually thought that this is connected with the rotation of the Sun; however, it still cannot be asserted with confidence that a storm is connected with a particular visible sunspot or with any other visible form of solar anomaly. In individual cases, magnetic storms of exceptional strength were indeed accompanied by certain groups of sunspots of unusual size. Skellett257 gives preliminary indirect statistical evidence in favor of the view that “the presence of some area whose activity can be observed with the aid of a spectrohelioscope is a necessary, though not sufficient, condition for radio disturbances.” There are also probable indications of a lag (of the order of one day) between the passage of an active region of the Sun’s surface and the appearance of the corresponding terrestrial effects. More complete data on the action of the Sun are needed here.

Dellinger258 recently described a “cosmic phenomenon” which, in four cases in 1935, caused brief interruptions of long-distance short-wave communication. Such interruptions of communication were observed over the entire illuminated half of the terrestrial globe and were separated from one another by approximately 54 days (twice the period of rotation of the central zone of the Sun). We had the good fortune to obtain records259 of the true height of the layer during extremely turbulent periods accompanying three successive small magnetic storms. It seems quite certain260 that such turbulence would have been sufficient to produce the effect described by Dellinger. If the apparent doubled period of 54 days is not subsequently confirmed, then it seems preferable to assume that brief intermediate disturbances at points corresponding to a period of 27 days may have escaped observation. This, it would seem, could easily have happened if the most active or the most sensitive radio channels were, at the critical moment, on the unilluminated side of the Earth.

Many observers have reported indications of ionization changes connected with meteor showers. The available statistical data, however, are not yet sufficiently decisive, and some of the results of individual experiments may be attributed to chance. Some astronomers believe that the energy of the heaviest of the known meteor showers is insufficient to produce the observed change in ionization, unless we assume that the visible meteors are accompanied by very large quantities of meteoritic dust. In Fig. 11 we have indicated the time of appearance of some periodic meteor showers; however, no clear correlation is observed in our data.

Supposed correlations with records of commercial transmission were reported by Nagaoka261, Kuekom262, and Pickard263. Skel-

finds a lowering of the height of the \(E\)-layer and, in support of his point of view, gives calculations of ionization. Minohara and Ito\(^{266}\) assert that meteors greatly increase the number of radio echoes. Schaefer and Goodall\(^{267}\) are somewhat more cautious, but they too find some grounds for supposing that meteors cause a noticeable increase in ionization. Interesting theoretical works were published by Lindemann\(^{268}\), Maris\(^{269}\), Mascart\(^{270}\), Millman\(^{271}\), and Malmzer\(^{272}\).

Visual observation of the motion of meteor trails has indicated the existence, at great heights in the upper layers of the atmosphere, of winds. This phase of the subject was considered by Halbert\(^{273}\).

P. Thunderstorms and Barometric Effects

A large part of the changes of a meteorological character by which everyday weather is determined occurs within the lower 10 km of the Earth’s atmosphere. The ionization observed in this region, even under quite exceptional conditions, is relatively small, and one therefore cannot expect any appreciable absorption or ionic refraction of radio waves here. Nevertheless, there is a considerable number of reliable facts indicating that the weather observed at the surface of the Earth is in some way connected with the propagation of radio waves.

In the “quasi-optical” region, below 10 m, with an appropriate distribution of the temperature gradient and the humidity gradient, ordinary optical mirages are often observed. As was already mentioned in section C, distant transmitting stations, situated one or two degrees below our optical horizon, were sometimes received in Cambridge with phenomenal strength. The transmission path was probably confined to the troposphere, and the slight atmospheric refraction did not depend on the existence of ionization.

In the range of wavelengths above 10 m, however, general agreement has not yet been reached concerning the explanation of the observed effects. Bureau\(^{274}\) believes that “the chief role here is played by the ionized layers of the upper region of the atmosphere; however, under certain conditions, a slight change may decide in favor of one of two possible and different paths along these layers. This change may be the result of phenomena occurring in the troposphere, which would then become arbiters of wave propagation and would decide the fate of the wave.” Although this point of view could explain the changes in signal intensity sometimes noticed at sea after crossing the boundaries of air masses, it could hardly account for the numerous reports of actual changes in the height of the \(E\)-layer and in electron density that accompany barometric changes. Ranzi\(^{275}\) finds a large increase in the ionization of the \(E\)-layer after sunset, when a decrease of pressure occurs at the place of observation or to the north of it. Ratcliffe\(^{276}\) agrees with Ranzi’s observations and asserts that a large rain-...

cloud. Martin\(^{27}\) reports a close connection between the ionization density of the \(E\)-layer and atmospheric pressure at the Earth's surface from 12 to 36 hours later. Colwell\(^{276}\) claims an accuracy of 85 to 90% for weather forecasts based on data from the reception of broadcasting stations. Fox\(^{276}\) finds that changes in signal strength depend on the atmospheric pressure along the transmission path.

Thunderstorms produce an effect that appears even stronger. In Fig. 13 we have shown the reflection conditions before, during, and after local thunderstorms that occurred in Cambridge at the point of transmission and reception. The curve of the “height of the \(F\)-layer” is the average obtained from the records of 22 thunderstorms. During this period there were ten more

Fig. 13.

thunderstorms which, in constructing the average, were, however, omitted either because of insufficient data or because they occurred at a time when the \(F\)-layer was strongly disturbed by the normal diurnal cycle or by magnetic storms. The apparent increase in the “height” of the \(F\)-layer at the beginning of the thunderstorm could be attributed to a decrease in the group velocity in the lower-lying regions through which the signal must pass.

Since reflections from the \(E\)-layer at vertical incidence for waves of length 86 m are less frequent than reflections from the \(F\)-layer, the curve of the height of the \(E\)-layer represents the average obtained from three thunderstorms that occurred when reflections from the \(E\)-layer were present. In full agreement with the curve for the \(F\)-layer, our observations for the \(E\)-layer reveal a maximum delay of the echo at the time the thunderstorm began. The curves in Fig. 13 also show that a thunderstorm that has begun reduces the probability of sporadic \(E\)-reflections occurring. However, if such reflections nevertheless occur at this time, an abnormally high intensity is found in the increase of the echo-train length (i.e., the number of multiple reflections). This could be the result of a general increase of ionization in the upper layers of the atmosphere, often penetrating downward into the “absorbing” \(D\)-region,

but sometimes not noticeably affecting levels below the $E$-layer. C. Wilson et al.^280 suggested that the enormous electric fields of thunderclouds may produce penetrating radiation, which could cause ionization at a considerable distance from the center of the thunderstorm. In order to decide whether this hypothetical radiation actually exists, and to determine its nature, additional experimental data are needed.

Fig. 14.

Despite the fact that our few individual observations made in New England appear to indicate an increase in the height of the $E$-layer when a thunderstorm is developing, it is possible that under other meteorological conditions other effects will be observed. Ratcliffe^281 describes a thunderstorm which apparently produced a noticeable temporary lowering of the $E$-layer.

Q. Local clouds in the ionosphere

In Section K we mentioned the fact that the ion density in the $E$-region does not decrease uniformly and gradually after sunset, as the simple recombination hypothesis would have suggested. Numerous observers have noted high nocturnal ionization^282 and the extremely sudden appearance of strong night reflections from the $E$-layer^283, which, it seems, are not connected with local thunderstorms or with general magnetic disturbances^284.

Often the ion densities reached suddenly in such cases exceed the greatest densities attained during the day[^285].

Our detailed analysis of the predominance of reflections from the \(E\)-layer for \(86\) m in New England is presented in Fig. 14. The ordinate in \(10\%\) indicates that \(E\)-reflections were present in one tenth of all observed cases. It may be noted that the values for daytime are low in winter and high in summer. The decrease in the hours around noon is probably due to absorption in the underlying \(D\)-region. (In agreement with this hypothesis it may be noted that reflections from the \(F_1\)-layer are likewise less frequent at noon than before and after noon.) The probability of observing reflections from the \(E\)-layer for waves of length \(86\) m has a maximum in mid-summer, but there is also an additional maximum in mid-winter. This winter maximum is produced chiefly by night ionization. In the daytime curve, very shortly before sunrise there is a small maximum. This occurs both in summer and in winter, and was observed over the course of two successive years.

We have not been able to find a satisfactory explanation of this effect for the time before sunrise.

The sudden and frequent appearance of very strong reflections of short duration could be due to an extremely strong instantaneous increase in the activity of some corpuscular ionizing agent capable of acting over a large area on the unilluminated side of the Earth. Equally, it could be due to a dense moving cloud of ions with comparatively sharp boundaries and of limited extent, which happened to pass over the area where the experiments are being carried out. Our own preliminary experiments, conducted simultaneously in Cambridge and in Worcester, seem to confirm the second hypothesis. In these experiments measurable time differences are found (of the order of one minute), consistently indicating the progressive motion of such a cloud over the distance of 40 miles separating the indicated points.

If it should prove possible to confirm these preliminary indications, they might become indications of great importance in connection with the protection of life and property. The first radio beacons on air-communication lines were subject to serious errors caused by reflection of an undesirable “sky wave.” This situation was greatly improved by changing the antenna design, which reduced the energy radiated upward. Nevertheless, even an antenna of an improved system must to some extent radiate upward, and, at least, we think that sudden reflections from small dense local clouds of ions may sometimes cause unavoidable local deviations of short duration in an isolated “spot” within the beacon’s region of action. Airline pilots mention such “dead spots.” Reports of recent catastrophes show that experienced pilots sometimes, without any visible cause, lose

orientation when their beacon gives a satisfactory signal at distant ground stations and properly guides flight on other parts of that same route.

Unfortunately this experiment was completely interrupted for a period of about three years by the strikingly casuistical objection, unexpectedly advanced by the Federal Communications Commission[^286]. In order to finish the greatly protracted argument, which simply came down to the precise interpretation of the phraseology of the Radio Act, we were now compelled to seek a special act of Congress certifying the usefulness of the automatic instruments needed for our investigations. No scientific objections to their usefulness were ever raised, since it is acknowledged that our methods are in all respects in agreement with normal engineering practice.

Further evidence of the unfortunate absence of government support in fundamental research is seen in the distribution of frequencies made available to experimental stations. In the wavelength range extending from 15 to 30,000 m, less than half a percent of the spectrum is available for use in experiments. Such a distribution is exceptionally disproportionate and does not correspond to needs. This practice allows related agencies, possessing great numerical strength, to displace legitimate scientific research. Such a policy is obviously quite short-sighted and is directed against public interests, but it is impossible for individual physicists to fight it in the proper way.

R. Scattering of Radio Waves

In Section C we spoke of the “zone of silence,” or “skip region,” which surrounds transmitting stations operating at a sufficiently high frequency. Points in this area lie outside the region of the ground wave, but at the same time are not far enough away to receive the ordinary spatial “sky” wave from the E- or F-region. This zone, however, is not always a zone of complete silence, since at points that are normally inaccessible, distinct signals of moderate intensity sometimes appear. It is often clear to an experienced radiotelegraph operator that these signals have a somewhat unusual character. Dots and dashes have a hollow, loud character, reminiscent of the echo of steps on a stone staircase. By transmitting surface signals simultaneously, and also on a longer wavelength, Taylor and Young[^172] were able to show that these capricious echoes were abnormally delayed. Upon arrival at a point located only 420 km from the transmitter, the echoes had different delay times corresponding to paths of length from 2000 to 10,000 km. At first they attributed these echo signals, scattered back into the “zone of silence,” to distant mountainous regions. Later, on the basis of direct observations, they came to the conclusion[^173] that the distant scattering object could have been the sea.

Eckersley\(^{287-290}\) suggests that the ionosphere has a cloud-like structure which can produce a complex scattering effect. He also suggests that scattering may occur as a result of multiple splitting. Hogg\(^{291}\) collected many observations on this question, including Megele’s opinion that directed beams produce scattering only at the apex of the ray path. Our own observations\(^{179}\) definitely indicate the existence of inhomogeneous cloud-like ionic formations and seem to prove that the scattering centers are located in the ionosphere and not on the ground. Ionic formations observed at great distances from our transmitter appear capable of producing echoes of the type observed by Taylor and Young at a time when the \(E\)- and \(F\)-layers are easily penetrable.

S. Interaction of Radio Waves

In the usual mathematical treatment of the phenomenon of radio-wave propagation, it is tacitly assumed that the ionosphere is a linear transmitting medium, and that therefore the behavior of a given wave is not affected by other waves which happen to pass at the same time through the same region of space. In 1933, therefore, great interest was aroused in Europe when it was discovered that a powerful broadcasting station in Luxembourg produced “cross modulation,” which could be faintly heard on waves emitted by other stations. When this was first reported by Tellegen\(^{292}\) and by various radio-broadcast listeners\(^{293-295}\), such reports were treated skeptically, since it was obvious that spurious “cross modulation” could easily occur in the broadcast receiving network.

The reality of this effect, however, was thoroughly confirmed by van der Pol\(^{296, 297}\); it was found that waves passing directly over a powerful transmitter, as shown in Fig. 4, undergo maximum distortion.

A possible explanation of the effect was proposed by Bailey and Martyn\(^{298-300}\), who found that a 200 kW station operating at a wavelength of 1190 m can produce a noticeable change in the average velocity of electron motion in the ionosphere at points situated directly above the transmitter. This, in turn, will produce a change in the frequency of collisions of electrons with molecules, and hence a change in the absorbing capacity of this region of the ionosphere. The absorbing capacity changes, therefore, in accordance with the modulation frequency of the station, and in this way modulation will be imposed on any wave which may cross the given region. A quantitative treatment of the problem was also given.

It is interesting to mention the experiment carried out by Ferrié and Donnet, who studied telephony over an ultraviolet and over an infrared beam of light, although the connection between the two effects,

located by them, probably does not exist. They assert that an absorber placed near the transmitter, where the rays are concentrated—

Fig. 15. Reflection conditions during the solar eclipse of 1936.

Fig. 16. Reflection conditions during the solar eclipse of 1932.

—gives a different effect than in the case when it is placed in a weaker radiation field near the receiver.

T. Observations During a Solar Eclipse

By means of observations made during a total solar eclipse, one can obtain additional information about the nature of the incident solar radiation and about the stratification of the ionosphere.

The spatial model shown in Fig. 15 illustrates the general character of the effect produced by an eclipse of the Sun. In this spatial model, which will soon be described in greater detail elsewhere, the coordinate \(X\) is the time of day (from midnight to noon), the coordinate \(Y\) is the transmitter frequency (from 2500 to 8500 kc), and the vertical coordinate \(Z\) is the height of the layer. The sharp ridge occupying the central part of the model is the boundary separating \(F_1\)-reflection from \(F_2\)-reflection. The shaded area represents wave penetration. We can pass from one type of reflection to another by changing the frequency or the time of observation. On a normal morning this boundary ridge would gradually rise. The large \(V\)-shaped sag arises as a result of the passage through the ionosphere of the Moon’s shadow. This depression, within the accuracy of the observations, coincides with the time of the total solar eclipse. The model of Fig. 15 was prepared by Pierce and is based on extensive data obtained by our group during the Russian eclipse of July 19, 1936, with simultaneous application of the constant- and variable-frequency methods, of which we spoke in Section N. The measurements were made at Ak-Bulak in Western Turkestan. Although the observations of each of the earlier eclipses \(^{177,\ 302–309}\) are less complete, when combined they prove to be in good agreement with Fig. 15. Fig. 16 presents a model of the 1932 eclipse, obtained by combining our own observations with data reported by other groups. Since in New England this eclipse occurred late in the afternoon, the time scale here runs from noon to midnight, the frequency scale from 500 to 6500 kc, and the general tendency of the boundary ridge \(F_1F_2\) is directed downward. The smaller ridge below the main boundary \(F_1F_2\) represents the transition from \(E\) to \(F_1\)-reflections. It was omitted in Fig. 15, since the field equipment taken to the USSR was intended primarily for investigation of the \(F\)-region. The fact that the \(F_1F_2\) boundary in the 1936 eclipse was displaced toward higher frequencies corresponds rather to the course of the sunspot cycle than to geographical differences.

The general similarity of Fig. 15 and Fig. 16 is of considerable interest, since it can be shown that the hypothetical corpuscular radiation accompanying the light of the Sun should have produced, in these two cases, a noticeably different course of the phenomenon. The general simplicity of the effect of a solar eclipse seems to indicate that ultraviolet light is responsible for all the observed phenomena.

The large magnitude of the change and the fact that it can be observed with considerable accuracy show that eclipses

yield valuable quantitative data suitable for the numerical testing of any theories of ionization and recombination that may be proposed to explain the stratification of the ionosphere. These quantitative observations should be continued; it is possible that partial solar eclipses will also be of interest[^275].

U. Conclusion

In this comparatively new branch of physics it is possible to carry out a large number of different experiments, some of which yield exact quantitative data. The physical system under investigation is exceptionally complex and must be studied by statistical methods. The classical magneto-ionic theory gives a satisfactory quantitative interpretation of many individual experimental facts, although there are some anomalies requiring further attention. Up to now, no careful study of the processes of molecular and atomic ionization and recombination, aimed at explaining the observed stratification of the ionosphere, has yielded a generally accepted and clear theory. However, this large theoretical problem, with the detailed experimental material already available, deserves serious attention at the present time.

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1. See Uspekhi fizicheskikh nauk 18, 57, 1937. ↩