Variations of the Earth’s Magnetic Field and Auroras1

E. O. Hulburt, Washington

Contents

Introduction

A. Meteorology, electricity, and magnetism of the upper atmosphere

Meteorology of the upper layers of the atmosphere. Ionization of the higher layers of the atmosphere. Regions of long and short free paths. Conductivity. Motion of ions in opposing fields, gravitational-magnetic drift. Dynamo effect. Diamagnetism.

B. Solar diurnal variations of the Earth’s magnetic field

Observational data on solar diurnal variations. Theory of the atmospheric dynamo. Diamagnetic theory. Theory of drift currents.

C. Lunar variations of the Earth’s magnetic field

Observational data. Theory of the atmospheric dynamo.

D. Magnetic storms and auroras

Observational data on magnetic storms. Magnetic disturbances, radio communication, the ionosphere, and the Sun. Observational data on auroras. Corpuscular theory of magnetic storms. Corpuscular theory of auroras. Theory of ultraviolet radiation, general considerations. Theory of ultraviolet radiation as applied to auroras. Theory of ultraviolet radiation as applied to magnetic storms. Theory of the “narrow beam” and of “broad nondirectional radiation” in solar eruptions.

Conclusion.

Introduction

As observations show, the Earth’s magnetic field is subject to slow and rapid changes, the former being measured in years, and the latter—in days, hours, or minutes. The magnitude of the magnetic changes, considered from the point of view of the entire terrestrial globe, is always small, for it rarely exceeds a few percent of the total magnetic field of the Earth. Gauss, using harmonic analysis, showed that the slow variations are caused by a special kind of changes in the Earth’s crust or in the inte—

…internal parts of the earth, whereas more rapid changes arise under the action of influences which, at least in part, are external with respect to the surface of the earth. The sources of these influences cannot be located in the lower layers of the atmosphere, and if they are not located in the terrestrial globe at all, then only the upper layers of the atmosphere can be their location.

Two kinds of rapid changes are distinguished: periodic and irregular. Periodic changes, associated with the solar and lunar days, are known under the name of solar and lunar variations of the earth’s magnetic field. Irregular changes, which have received the name of magnetic disturbances or storms, are thought to be connected chiefly with solar activity, namely with spots, faculae, and prominences; some of the irregular changes are possibly caused by causes not connected with the sun, such as meteors and other material bodies that “settle” upon the earth as it moves through space.

Despite the unceasing interest in these questions, at the beginning of this century it was not possible to note any very significant successes in their study. Only a few years ago there began a new, intensive study of these questions, which has not ceased up to the present time. This impetus is due, to a great extent, first, to discoveries in the field of electrical and magnetic phenomena, old from the standpoint of physics but new in application to the upper layers of the atmosphere; second, to the proposal—new at first sight, but already partly confirmed by experiments—according to which magnetic storms and auroras are caused by flashes of ultraviolet radiation on the sun; and, third, to the recently begun experimental investigations of the ionosphere by means of radio waves.

The following paragraphs constitute a summary of the most important facts in the field of magnetic variations and an exposition of some of the theories that have been advanced to explain them. Since auroras and magnetic disturbances are closely connected with one another, facts and theories from the field of auroras are also discussed below. For the same reasons, it would have seemed proper to touch upon questions concerning the light of the night sky, the zodiacal light, and the solar corona; this, however, is not done in the present article, thereby giving those who wish to do so the opportunity to continue the line of investigation.

All theories of variations of the magnetic field proceed from the assumption that magnetic changes are caused by a special action of electric charges and differ from one another in the choice of the mechanism of this action and in the location of the charges.

Three kinds of action are known: the dynamo effect, diamagnetism, and gravitational-magnetic drift currents. The most important theories operate with charged particles located in the upper layers of the atmosphere. Other theories, for the most part newly advanced…

...bent or already rejected, place charged particles at distances of several terrestrial radii from the terrestrial sphere; such particles, strictly speaking, are already beyond the limits of the upper layers of the atmosphere.

A. Meteorology, Electricity, and Magnetism of the Upper Layers of the Atmosphere

Meteorology of the Upper Layers of the Atmosphere

Merris’s calculations ¹ of the diffusion rate of the gases composing the atmosphere showed that, owing to air currents, the atmosphere is uniformly mixed up to an altitude of 150 km. Consequently, with the exception of water vapor and ozone, the gaseous composition of the earth’s atmosphere up to an altitude of about 150 km is the same as at sea level. Deviations and irregularities in the observed trajectories of meteors ² give direct indications of winds and air currents at altitudes up to 110 km. Above 150 km one may assume a state of equilibrium of gases in the earth’s gravitational field, in which the content of light gases increases with altitude. Observations made during recent stratosphere-balloon flights ²ᵃ confirm the correctness of the results obtained in calculating diffusion. Air samples taken at various altitudes made it possible to determine the amount of oxygen at altitudes up to 29 km, helium up to 21 km, and nitrogen up to 21.5 km. It was found that the volume content of the corresponding gases at different altitudes differs by no more than a few percent from the content on the earth. Only small and irregular deviations from the constant composition were observed. This circumstance still awaits its explanation and, apparently, may be ascribed to inhomogeneities in the lower layers of the atmosphere, arising, for example, under the influence of weather.

Observations of sounding balloons ³ that reached an altitude of 33 km showed that the temperature of the atmosphere increases from 219° K at an altitude of 20 km to 226° K at an altitude of 33 km. All assumptions concerning the temperature at altitudes exceeding 33 km are theoretical. The results of calculations by Merris, Gowen ⁴, and others ⁵ concerning the possibility of heating of the upper layers through absorption of solar and terrestrial radiation may be formulated as follows: calculations based on reasonable hypotheses show that the upper layers of the atmosphere are heated, but these calculations do not make it possible to determine exactly how much the atmosphere is heated, nor to resolve the question of whether the layers remain heated at night or whether they undergo cooling.

Proceeding from a daytime temperature at altitudes exceeding 80 km of 360° K, assuming complete mixing of the gases from sea level to an altitude of 130 km and thermal equilibrium at altitudes above 130 km, Merris compiled a table of molecular densities of gases,

included in the composition of the atmosphere at great heights, which in general opinion is the most substantiated. Part of these computations is given in Table 1, where \(n\) is the number of molecules in \(1\ \mathrm{cm}^3\), and \(z\) is the height above sea level. It is assumed here that oxygen and nitrogen are in the molecular state. If these gases are in the atomic state, then the values of \(n\) for values of \(z\) exceeding \(200\ \mathrm{km}\) must be increased by a factor of two or even more.\(^{6}\) Above \(z=400\ \mathrm{km}\) collisions occur extremely rarely, and the usual gas laws prove inapplicable; this region constitutes the outer envelope of the atmosphere.

Table 1

Computed values of the number of molecules in \(1\ \mathrm{cm}^3\) \((n)\) and of the mean free path \((\gamma)\) in the upper layers of the atmosphere

\(z\) in km	\(n\)	\(\gamma\) in cm
60	\(9.9\cdot 10^{15}\)	0.03
80	\(1.0\cdot 10^{15}\)	0.25
100	\(1.6\cdot 10^{14}\)	1.5
120	\(2.6\cdot 10^{13}\)	9.6
140	\(4.4\cdot 10^{12}\)	57
160	\(7.7\cdot 10^{11}\)	320
180	\(1.4\cdot 10^{11}\)	1800
200	\(2.5\cdot 10^{10}\)	\(10^4\)
250	\(2.5\cdot 10^8\)	\(10^6\)
300	\(7.7\cdot 10^6\)	\(10^7\)
350	\(7.3\cdot 10^5\)	\(10^8\)
400	\(4.1\cdot 10^5\)	\(10^9\)

Fig. 1. The dashed line shows the distribution of ionization in the upper layers of the atmosphere at equatorial noon in 1933–1934, according to measurement data;\(^{7}\) the hatched areas show the distribution of ionization adopted in theories of terrestrial magnetism.

The temperature of \(360^\circ\mathrm{K}\) with which Maris operated may seem exaggerated; however, there are further indications that at times the temperature may reach still higher values. Calculations show\(^{6}\) that the absorption of solar rays by molecular oxygen in the band from 1850 to 1250 Å at a height of approximately 180 to 300 km can increase the temperature by \(50^\circ\mathrm{K}\) per hour. The existence of the ionized layer \(F_2\) at a height greater than 300 km is fairly definite evidence that the values of \(n\) in Table 1 for heights \(z\) greater than 250 km are underestimated. Observations of radio waves may be interpreted in the sense that the heated atmosphere at heights above 150 km cools at night.

Ionization of the Upper Layers of the Atmosphere

Very complete measurements of the ionosphere[^7] by means of observations of radio-wave reflections, using the Breit and Tuve method,[^8] were carried out in New York, Washington, and Huancayo (Peru) during the years of the sunspot minimum (1933 and 1934). The results of the observations were summarized and analyzed;[^6] in the present section we shall give the most essential conclusions. Observations of the ionosphere show that, when the sun is at the zenith, the equivalent electron concentration1 \(y\) in the layers \(E\), \(F_1\), and \(F_2\) has values of the order \(1.5 \cdot 10^5\), \(3 \cdot 10^5\), and \(10 \cdot 10^5\), respectively, at altitudes of 100, 200, and 300 km; at the same time there is almost no information about the concentration in the intervals between these values, and it is known only that these values are not exceeded. These data are illustrated in Fig. 1.

According to the familiar and as yet undisputed view that the upper layers of the atmosphere are electrically neutral or nearly neutral, the quantity \(y\) also represents the number of positive ions in \(1\ \mathrm{cm}^3\).

Investigation of the ionized layer by means of observations of radio-wave reflection makes it possible to determine the lowest frequency \(f_c\) that just penetrates through the layer. The relation between \(f_c\) and the number of charged particles in \(1\ \mathrm{cm}^3\) is established by setting equal to zero the refractive index of the medium for the frequency \(f_c\), and has the form:

\[ f_c^2=\frac{e^2 c y}{\pi m}, \tag{1} \]

where \(m\) and \(e\) are the mass and charge, in CGSM units, of the charged particles, and \(c\) is the speed of light. The particles are assumed to be charged with unit charge, since \(e\) is the charge of the electrons. If the ions carry more than one charge, then the right-hand side of expression (1) is replaced by the corresponding sum. Expression (1) is valid in the absence of a magnetic field; in the presence of a magnetic field the formula takes on a more complicated form and is not given here. Thus, by determining \(f_c\) experimentally, from formula (1) one can calculate the ratio \(y/m\), and even the quantity \(y\), in cases where the mass \(m\) is known. For example, if the measured value of \(f_c\) is 5000 kHz, it follows from (1) that \(y\) takes the value \(3.1 \cdot 10^5\) for electrons and \(1.24 \cdot 10^{10}\) for ions with mass \(3.6 \cdot 10^{-23}\) g, i.e., 40,000 times greater than the mass of the electrons.

On the abscissa axis of Fig. 1 two scales are plotted: the lower one for electron concentration, the upper one for ion density, under the assumption that the mass of an atmospheric ion is, on average, \(3.6 \cdot 10^{-23}\) g.

The observed^7 magnetic splitting of radio waves reflected from the ionosphere indicates that at heights greater than 200 km, i.e., in the layers \(F_1\) and \(F_2\), the ionization is due chiefly to electrons. Consequently, the part of the dotted line in Fig. 1 corresponding to heights greater than 200 km is represented by the lower scale. Experiments have not yet made it possible to establish definitely whether the ionization of region \(E\) is due to electrons or to ions; the greater part of the experiments indicates the presence of ions, and the smaller part—of electrons. Accordingly, for the part of the curve below 200 km one may use one of the two scales, or a special scale constructed on the assumption of a known mixture of ions and electrons. As will be shown below, this question is of substantial importance for theories of variations of the magnetic field, and if future experiments show that the ionization below 200 km is due mainly to electrons, then all these theories will prove untenable or will require radical revision.

It was shown^6 that the observed values of \(y\) at the maximum point of the curve \(y=f(z)\) for the \(E\) layer during 1933 and 1934 satisfied a relation which followed from the hypothesis according to which the ionization is caused by ultraviolet radiation from the sun,

\[ v = y_0(\cos \beta)^{\frac{1}{2}}, \tag{2} \]

where \(\beta\) is the zenith distance of the sun, \(y_0\) is the value of \(y\) when the sun is at the zenith, i.e., when \(\beta=0\). Expression (2) is valid for values of \(\beta\) from zero to approximately \(85^\circ\). For the layers \(F_1\) and \(F_2\) the observed values of \(y\) differ substantially from the values following from formula (2); however, quite satisfactory theories have been proposed to explain these deviations. Thus, at present the suitability of formula (2) for the approximate determination of ionization over the illuminated half of the terrestrial globe meets with no objections. The average value of the ionization at night is approximately 0.1 of the midday value.

Comparing the experimentally determined electron concentration of \(10^6\) in the \(F_2\) layer with the number of molecules in \(1\ \mathrm{cm}^3\) at heights greater than 300 km (Table 1), it is easy to see that both quantities are of the same order. From this we conclude that the outer shell of the ionosphere is practically completely ionized. This conclusion is also easily reached on the basis of theoretical considerations, since the sun is a very powerful source of ionization; however, it is very difficult to hope that this can be demonstrated by direct experiments.

Regions of Long and Short Free Paths

In the upper layers of the atmosphere two regions should be distinguished^9: the region of short and of long free paths. In the first region

the radius of gyration \(r\) of electrons or ions in the magnetic field is large in comparison with the mean free path \(\gamma\); in the second region, on the contrary, \(\gamma\) is small in comparison with \(r\). The radius \(r\) is determined by the formula

\[ r=\frac{mv}{He}, \tag{3} \]

where \(v\), \(m\), and \(e\) are respectively the velocity of thermal motion, the mass and charge of the charged particle, and \(H\) is the component of the Earth’s magnetic field perpendicular to the velocity \(v\). The free path length \(\gamma\) of ions and electrons is expressed by the formula:

\[ \gamma=\frac{1}{\sqrt{2\pi n a^2}}\gamma=\frac{4}{\pi n a^2}, \tag{4} \]

where \(n\) is the number of molecules in \(1\ \mathrm{cm}^3\), and \(a=3\cdot 10^{-8}\ \mathrm{cm}\) is the mean diameter of atmospheric molecules or atoms as determined from kinetic theory.

The values of \(\gamma\) for ions are given in the last column of Table 1. From formula (3) it follows that the radius \(r\) for ions and electrons at the equator \((H=0.3\ \text{gauss})\) takes the values \(20\ \mathrm{cm}\) and, respectively, \(1.3\ \mathrm{cm}\). In the case of ions the ratio \(\dfrac{\gamma}{r}\) becomes large at altitudes exceeding \(150\ \mathrm{km}\), and in the case of electrons—at altitudes greater than \(100\ \mathrm{km}\). Accordingly, at the equator the region of short free paths passes into the region of long free paths at an altitude of about \(150\ \mathrm{km}\) for ions and at an altitude of \(100\ \mathrm{km}\) for electrons. In temperate latitudes, where \(H=0.5\) gauss, at a temperature of \(360^\circ\mathrm{K}\) the corresponding regions are located approximately \(10\ \mathrm{km}\) lower. If oxygen and nitrogen in the upper layers of the atmosphere are in the atomic state, then the quantity \(n\) assumes values greater than those given in Table 1, as a result of which the boundaries between the regions rise by \(10\)—\(30\ \mathrm{km}\).

Conductivity

The conductivity \(\sigma\) of a unit volume of ionized gas is expressed in the CGSM system by the following formula:

\[ \sigma=\sum ye^2\frac{\gamma}{2mv}, \tag{5} \]

where \(y\) is the number of charged particles in \(1\ \mathrm{cm}^3\); the summation extends over all types of charged particles. If the ionized gas is in a magnetic field, then the conductivity in the direction \(H\) is not disturbed by the magnetic field, and \(\sigma\) is still determined by formula (5). The conductivity \(\sigma'\) in the direction perpendicular to the magnetic field is expressed by the approximate formula\({}^{10}\)

\[ \sigma'=\frac{\sigma}{1+\dfrac{\gamma^2}{r^2}}. \tag{6} \]

More accurate calculations by Page 11 lead to the formula

\[ \sigma'=\frac{\sigma\left(1+\dfrac{2r'^2}{r^2}\right)} {\left(1+\dfrac{r'^2}{r^2}\right)^2}. \tag{7} \]

Equation (6) was derived by averaging the effect of collisions that shorten the helical path of ions in a magnetic field, while equation (7) was derived by the same averaging, but with the additional inclusion of the translational motion of the ions in the direction of the magnetic field. These equations differ from one another only insignificantly, and both lead to \(\sigma'=0\) in the region of long free paths and to \(\sigma'=\sigma\) in the region of short paths.

Motion of ions in opposing fields, gravitational-magnetic drift

Let an ion with charge \(e\) and mass \(m\), placed in a magnetic field \(H\), be acted upon by a constant force \(X\). The directions of the forces \(H\) and \(X\) coincide with the positive directions of the \(x\)- and, respectively, \(y\)-axes. The equations of motion of the ion in CGSM units are represented in the following form:

\[ m\ddot{x}=X+He\dot{y}, \]

\[ m\ddot{y}=-He\dot{x}, \tag{8} \]

\[ m\ddot{z}=0. \]

Denote \(-\dfrac{He}{m}=\omega\), and put, for \(t=0\), \(\dot{x}=\dot{x}_0\), \(\dot{y}=\dot{y}_0\), and \(\dot{z}=\dot{z}_0\). The solution of equations (8) is expressed by the formulas

\[ \dot{x}=\dot{x}_0\cos\omega t+\left(\dot{y}_0+\frac{X}{He}\right)\sin\omega t, \]

\[ \dot{y}=-\frac{X}{He}+\left(\dot{y}_0+\frac{X}{He}\right)\cos\omega t-\dot{x}_0\sin\omega t, \tag{9} \]

\[ \dot{z}=\dot{z}_0. \]

It follows from equation (9) that the ions move along a cycloidal trajectory, at the same time shifting in a direction perpendicular to \(X\) and \(H\). If the initial values \(\dot{x}_0,\dot{y}_0,\dot{z}_0\) are equal to zero, then the velocities \(\dot{x},\dot{y},\dot{z}\), averaged over time, since the periodic components vanish, take the values

\[ 0,\quad -\frac{X}{He},\quad 0. \tag{10} \]

Thus the ions move (drift—drift \(^{12-14}\)) along the \(y\)-axis with a constant velocity \(\dfrac{X}{He}\). On averaging, the loops of the cycloidal path are smoothed out.

At the equator, where the magnetic force is horizontal and directed northward, under the action of terrestrial gravity the ions are attracted downward and, consequently, according to formula (10), move (drift) in the horizontal direction with a velocity \(v\) determined from the expression

\[ v=\frac{mg}{He}. \tag{11} \]

In this case positive ions move eastward, and negative particles westward, creating an electric current directed from west to east, called the “magneto-gravitational drift current.”

At an altitude of \(200\) km, at the equator, \(g=920\) cm/sec, \(H=0.29\) gauss, and the velocity takes the values \(11.8;\ 5.3\) and \(1.3\) cm/sec, respectively, for nitrogen molecules, oxygen molecules, and helium atoms.

Under the action of an electric field \(E\), perpendicular to \(H\), as follows from the same equation (10), ions of both signs come into motion in a direction perpendicular to \(E\) and \(H\), with a common velocity

\[ v=-\frac{E}{H}. \tag{12} \]

If the field \(E\) is directed eastward, then ions at the equator move upward; with a westward direction of the field the ions move downward. This displacement (drift) does not constitute an electric current, since ions of both signs move in one and the same direction, and moreover with the same velocity.

The magneto-gravitational drift (11) and the magneto-electric drift (12) can manifest themselves with sufficient intensity only in the region of long mean free paths; in the region of short free paths the drift is absent. Following Pedersen \(^{10}\), one may assume that the magnitude of the drift in both cases is connected with the length of the mean free path approximately by the following relation:

\[ \frac{1}{1+\frac{r^{2}}{q^{2}}}. \tag{13} \]

Dynamo Effect

By the dynamo effect is meant the induction of an e.m.f. \(u\) in a conductor moving with velocity \(v\) across a magnetic field \(H\). Expressing all quantities in CGSM units, we have

\[ u=-vH, \tag{14} \]

where \(u\), \(v\), and \(H\) are directed respectively along the positive directions of the axes \(x\), \(y\), and \(z\). This follows directly from Faraday’s law of electromagnetic induction. The region of short free paths in the upper layers of the atmosphere is a conductor, and if, under the action of winds, thermal expansion, or tidal forces, this region begins to move in the earth’s magnetic field \(H\), then, in accordance with equation (14), an e.m.f. is induced in it. But in the presence of conductivity, the e.m.f. inevitably gives rise to currents, which in turn create a magnetic field.

The motion of the region of long free paths in the magnetic field is likewise accompanied by the appearance of an e.m.f. \(e\) according to equation (14), since the forces that set this region in motion produce, in accordance with formula (10), a drift of positive and negative charges equivalent to the motion of charges necessary for the creation of \(u\) according to equation (14).

Diamagnetism

The region of long free paths in the upper atmosphere is diamagnetic\(^{15}\). The intensity of magnetization \(i\) of the free charges, which are ions and electrons, is expressed by the formula:

\[ i=-\frac{ykt}{H}, \tag{15} \]

where \(t\) is the temperature in degrees Kelvin, \(y\) is the number of charges in \(1\ \mathrm{cm}^3\), and \(k=1.372\cdot 10^{-6}\ \mathrm{erg/deg}\ \mathrm{K}^{\circ}\). Just as in the case of drift current, the magnitude \(i\) varies depending on the free path length, in accordance with expression (13), becoming zero in the region of short free paths.

B. Solar diurnal variations of the earth’s magnetic field

Observational data on solar diurnal variations

The averaged diurnal variations of the earth’s magnetic field, denoted by us by \(S\) at various geographical latitudes, are given in Fig. 2, where the change is shown in the quantities \(N\), \(V\), and \(W\), which represent respectively the northern horizontal, vertical, and western horizontal components of the quantity \(S\), as functions of local time\(^{16}\). For latitudes below \(40^\circ\), \(N\) tends toward a maximum during the daytime hours, while for latitudes above \(40^\circ\) it tends toward a minimum. The daytime maximum or minimum of the quantity \(N\) occurs 1 or 2 hours before noon, i.e. between 10 and 11 o’clock. The amplitude of \(S\) increases with an increase in the number of sunspots, becoming in periods of sunspot maximum approximately twice as great as in a period of minimum. The changes in \(S\) consti-

...in the years of maximum and minimum, respectively, amount to \(30\gamma\) (\(1\gamma = 10^{-5}\) gauss) and \(15\gamma\). Harmonic analysis shows that approximately three quarters of the magnitude \(S\) are due to causes external with respect to the earth, while one quarter is caused by currents induced in the earth \(^{17}\).

Fig. 2. Diurnal variations of the elements of the earth’s magnetic field at the equinox \(^{16}\). Inclination characterizes magnetic latitude.

Theory of the atmospheric dynamo

The theory of the atmospheric dynamo as applied to the diurnal variations \(S\) was originally proposed by Balfour Stewart, and later worked out in detail by Schuster \(^{17}\). According to this theory, the variations \(S\) are caused by the horizontal displacement of the conducting upper layers of the atmosphere in the vertical components of the earth’s magnetic field. The e.m.f. induced during the motion, according to equation (14), creates electric currents and, consequently, changes in the magnetic field, shown in Fig. 2. The character of the electric...

electric currents in the atmosphere, necessary for producing the observed pattern of diurnal variations \(S\), was calculated by Bartels \(^{18}\) and is shown in Fig. 3; the numbers by the lines express the strength of the current in thousands of amperes. As follows from the figure, the total daytime current in the northern hemisphere reaches 62,000 A; the current lines form closed paths in the counterclockwise direction with a center at \(40^\circ\) latitude and 11 hours. At night the current changes direction to the opposite one, and the total current strength is 32,000 A. Thus the daytime current exceeds the nighttime current by 94,000 A. The figures given refer to a year occupying an average position in the sunspot cycle. The greatest current density occurs at 11 o’clock and is located at the equator, where the daytime value by \(3 \cdot 10^{-5}\) CGSM units exceeds the nighttime value.

Fig. 3. Calculated system of electric currents in the upper layers of the atmosphere, necessary for producing the observed diurnal variations \(^{18}\), compiled according to data of the Earth’s magnetic field in 1902 (year of sunspot minimum)

The horizontal displacement of the upper layers of the atmosphere was calculated on the basis of observations of diurnal oscillations of atmospheric pressure. In this case two components of the barometric oscillations were detected: a periodic component, with a period of 12 hours and an amplitude of oscillations of 1 mm of mercury at the equator, and a less regular, irregular component with an amplitude of about 0.3 mm. The question of the possible cause of the barometric oscillations, for which thermal or tidal forces could be assumed, was subjected to lengthy discussion \(^{19}\). If the semidiurnal solar component is due to tidal forces, then it is necessary to put forward a new hypothesis to explain resonance in the free atmosphere, since the solar semidiurnal oscillations exceed by a factor of 15 the lunar semidiurnal oscillations with an amplitude of 0.063 mm, whereas the tidal attraction of the Sun amounts to only \(2/5\) of the corresponding attraction of the Moon. The diurnal component can be satisfactorily explained by assuming that it is due to a thermal effect and arises from the redistribution of air masses occurring in expanding regions heated by the Sun.

In qualitative terms, air currents diverging from regions of high pressure, located at noon near the equator, create currents of the same character as in Fig. 3. In daytime, at latitudes above \(40^\circ\), air currents moving northward in the vertical field \(H\) create an e.m.f. directed westward, which, under the natural assumption that the conductivity

As the zenith distance increases, they diminish to small nocturnal values, leading to the formation of closed currents as in Fig. 3. Currents of the same character arise under the action of 12-hour tidal motions of the atmosphere with 12- and 24-hour components, whose amplitudes are determined by the dependence of the conductivity of the high layers of the atmosphere on the zenith distance.

As a result of painstaking mathematical analysis, Schuster established that, although the electric currents corresponding to the observed changes in atmospheric pressure are, in character, consistent with the calculated currents, in phase they differ noticeably from those shown in Fig. 3. In fact, the phases of these currents are almost opposite; according to the calculations, the quantity \(N\) should attain its maximum value from 14 to 16 hours, whereas in fact the maximum is observed from 10 to 11. There is also a discrepancy between the observed and theoretical ratio of the amplitudes of the 24- and 12-hour periodic components, as determined by harmonic analysis; the observed ratio is close to 9, and the calculated one to 3. The conclusion—one must say, an unexpected one—to which we are led is that, if the atmospheric-dynamo hypothesis is regarded as correct, then it must be assumed that the motion of air in the upper layers of the atmosphere is not connected in a simple way with the readings of the barometer at the surface of the earth. Analysis of later magnetic and meteorological observations, carried out by Walker \(^{21}\), Chapman \(^{22}\), and others, confirmed Schuster’s point of view. The theory remained “hanging in the air.”

The conductivity \(\sigma\) of the upper layers of the atmosphere was calculated under the rather improbable assumption that the 12-hour pressure oscillations are caused by tidal phenomena of the simplest character, in which the tidal motion uniformly embraces the vertical column of the atmosphere. In this case an oscillation amplitude of \(1\) mm means that

\[ \frac{1}{2 \cdot 760} \]

of the atmosphere remains, as it were, immobile with respect to the sun, as a result of which horizontal tidal and ebb motions arise in the atmosphere with an average velocity of

\[ \frac{1}{1520} \]

of the circumferential speed of the earth’s rotation. At the equator this speed is \(30\) m/sec, or \(1\) km/hour.

From equation (14) it follows that \(\sigma = \dfrac{i}{vH}\), and, putting \(i = 3 \cdot 10^{-5}\), \(H = 0.3\) gauss, and \(v = 30\), we find: \(\sigma = 3 \cdot 10^{-6}\) CGSM units for equatorial noon, which is the value obtained by Schuster. It should not be thought that these brief calculations reproduce Schuster’s much fuller arguments; they give only an idea of the physical picture of the phenomena and lead to a numerical value of the correct order.

If the existence of atmospheric resonance is assumed, then the motion of the air will differ from the motion calculated above (under the assumption of the simplest tidal action on a resonating atmosphere), and the obtained value of \(\sigma\) will lose its meaning.

If the barometric oscillations are attributed to the heating of the atmosphere by the sun, then the atmospheric flows and the electrical conductivity required by the theory of the atmospheric dynamo cannot be determined until the thermal regime at all heights of the atmosphere is known or specified.

The theory of the atmospheric dynamo may be reconsidered in light of the results obtained from ionospheric measurements. Of the three-day layers of the ionosphere, only the layer \(E\) can provide the necessary conductivity in the field \(H\), since the layers \(F_1\) and \(F_2\) are located in the region of long free paths. Referring to Fig. 1, let us assume that the ionization of the layer \(E\), having a constant value within the limits from 100 to 150 km, is due to an equal number of electrons and positive ions, the number of which in \(1\ \mathrm{cm}^3\) is determined by formula (2); ionospheric measurements show that the greatest number of electrons in \(1\ \mathrm{cm}^3\), \(y_0\), calculated by formula (1), does not exceed \(y_0 = 1.5 \cdot 10^5\).

With these data, one can calculate the conductivity of the region \(E\) above the illuminated half of the terrestrial globe. Electrons cannot move perpendicular to the magnetic field \(H\), and the conductivity of a vertical column of air of cross-section \(1\ \mathrm{cm}^2\) from 100 to 150 km in height is determined by formulas (2), (5), (6) on the basis of the data of Table 1

\[ \sigma = 7.2 \cdot 10^{-10}(\cos \zeta)^{\frac{1}{2}} . \tag{16} \]

The mean value of the daytime conductivity \(\sigma\) for latitudes from \(0\) to \(40^\circ\) is about \(5 \cdot 10^{-10}\), which is approximately four times smaller than the value found by Schuster.

The total current westward (Fig. 3), flowing in the daytime at latitudes from \(0\) to \(40^\circ\), exceeds the nighttime value by 94,000 A, which corresponds to an average current density of \(2 \cdot 10^{-5}\) CGSM units in a vertical column of cross-section \(1\ \mathrm{cm}^2\) in the region \(E\). To create such a current through the dynamo effect, it is necessary to assume the existence of winds on the illuminated half, at latitudes above \(40^\circ\), with a velocity determined from equation (14)

\[ \frac{2 \cdot 10^{-10}}{5 \cdot 10^{-10} \cdot 0.5} = 8 \cdot 10^4\ \mathrm{m/sec}, \]

or \(2900\ \mathrm{km/hour}\). In the calculation it was assumed that \(H = 0.5\) gauss.

The existence of such high velocities of air motion is highly improbable, and we arrive at the conclusion that the theory of the atmospheric dynamo does not satisfy the initial assumptions.

An acceptable theory must operate with air flows of moderate velocities, not exceeding \(100\ \mathrm{km/hour}\). Then the conductivity of \(E\) would have to exceed the value \(5 \cdot 10^{-10}\) by at least 30 times. But the conductivity of the layer \(E\) cannot be considered increased as a result of an increase in the number of electrons beyond the value indicated by ionospheric measurements.

The way out of the difficulty may be found in the fact that ionospheric measurements do not prevent one from assuming that the ionization of the \(E\) layer is caused by ions, the number of which in \(1\ \mathrm{cm}^3\) is determined from equation (2) for \(y_0 = 6 \cdot 10^9\). If such a concentration really exists at heights from 100 to 150 km, then \(\sigma\) is \(4 \cdot 10^{-5}\), and the creation of a current of 94,000 A can be effected by a “breeze” with a speed of only 35 m/hour, i.e. by a very moderate “breeze.” Thus there is a certain freedom within the limits allowed by measurements of the ionization of the \(E\) layer in the choice of the character of the ionization (electrons or ions) necessary for bringing the theory of the atmospheric dynamo into agreement with the observed facts. This had already been quite clearly revealed in earlier discussions of the question of the ionosphere,\(^9\) when, within admissible limits, an arbitrary choice was made between electrons and ions.

The remarks made apply equally to all the theories of magnetic variations set forth below, in those parts of them which treat currents in the upper conducting layers of the atmosphere; the reason for the existence of these currents cannot be regarded as convincing in the case when the region of short free paths is assumed to consist chiefly of electrons.

Further study of the dynamo theory reduces to the investigation of secondary phenomena, in order to ascertain whether they give a satisfactory explanation of the observed facts and whether they do not come into contradiction with observations. Thus, for example, a flow of air moving in the daytime northward at latitudes above \(40^\circ\) induces an e.m.f. directed westward, which together with \(H\), according to formula (12), causes in the daytime in the ionospheric regions \(F_1\) and \(F_2\) (regions of long free paths) a downward motion, and at night—upward. The speed of this drift is of the same order as that of the northern breeze. Consequently, the dynamo theory, which assumes a breeze speed of 40 km/hour, must be prepared to accept the existence of a drift in the layers \(F_1\) and \(F_2\) with a speed of 20–40 km/hour downward in the daytime and a drift with the same speed, directed upward, in the region of the night layer \(F\).

We leave the theory of the atmospheric dynamo with the remark that this theory has neither been proved nor refuted. The dynamo theory is one of the possible ones; however, for it to be convincing, the ionization of the \(E\) layer must be due chiefly to ions.

Diamagnetic Theory

Noting the circumstance that the ionization of the region of long free paths makes this region, in accordance with equation (15), diamagnetic, Gunn\(^15\) developed a diamagnetic theory of the daily variations of \(S\). The intensity of magnetization \(i\) of a vertical atmospheric column with cross-section \(1\ \mathrm{cm}^2\) in the region of long free paths, on the illuminated half of the terrestrial globe, containing \(y\)

charged particles, is expressed by the equation

\[ i=i_0\cos \zeta, \tag{17} \]

where at night \(i\) is less than \(1/10\) of the midday value. The diamagnetism of this medium creates[^15] a magnetic field fully corresponding to the observed diurnal variations (Fig. 2). Repeated calculations carried out by Chapman led to the same results.

Substituting expression (15) into equation (17), we have

\[ y't=y'_0t_0\cos \zeta, \tag{18} \]

where \(y'_0\) and \(t_0\) refer to \(\beta=0\).

Observations of the ionosphere[^7], carried out after the development of the theory, showed that

\[ y' \cong (\cos \beta)^{\frac{1}{2}}, \]

i.e., they confirm the view according to which \(t\) reaches a maximum at noon and, consequently, is in good qualitative agreement with equation (17).

For quantitative agreement of the theory with the observed changes in \(S\) (the horizontal component \(H\) of external origin at equatorial noon, at the equinox and with an average number of sunspots, is about \(15\gamma\)), it is necessary that \(y'_0=5\cdot 10^{10}\) at the midday \(t^\circ=360^\circ\) K. From equation (15) it follows that \(y'_0\) may also have a smaller value, but at a correspondingly higher temperature of the layer.

Assuming an equal number of electrons and positive ions, from the dotted curve in Fig. 1, using the lower scale on the abscissa axis, we determine the value of \(y\) in the region \(F_2\), constant at heights from 300 to 400 km and equal to \(10\cdot 10^5\). This corresponds to \(y'_0=3\cdot 10^{13}\) charged particles, i.e. \(1/1700\) of the \(5\cdot 10^{16}\) particles required by the diamagnetic theory. If, however, on the segment of the curve from 150 to 200 km the majority of charged particles are ions, then from the upper scale of Fig. 1 we find that in this case the number of charged particles reaches \(5\cdot 10^{16}\).

The diamagnetic theory is not able to give a satisfactory explanation of the observed minimum of the quantity \(N\) at the equator around 10 o’clock (Fig. 2); the simple expression (17) explains only the midday minimum. An increase in the mean height of ionization during the day by 30 km, with a maximum at 14, as was shown[^23], shifts the phase of the diamagnetic effect into the afternoon hours. Measurements of the height of the ionosphere show a maximum height at noon; however, it is not excluded that in reality there is nevertheless a displacement of the maximum by 2 hours after noon. This is due not so much to the inaccuracy of the measurements as to the fact that what was determined in measurement was not the actual, but only the equivalent height of the layer.

In discussing the question of diamagnetism, Cowling[^24] came to the conclusion that electric currents arise at the boundary of the diamagnetic region, destroying the diamagnetic effect outside this ...

region. This opinion repeated the earlier views of Bohr and Van Leeuwen\(^{25}\), relating to the diamagnetic theory of metals. Cowling came to this conclusion by assuming that collisions of ions are perfectly elastic. If, however, one admits (and it must be said that there are weighty grounds for doing so) that after a collision an ion and an electron have a greater probability of continuing their motion in an arbitrary direction, then the currents at the boundary of the region disappear and the diamagnetic effect remains in pure form. Thus Cowling’s analysis shows to what extent the phenomenon of diamagnetism depends on the mechanism of collisions.

The diamagnetic theory is in approximately the same position as the theory of the atmospheric dynamo, for it requires a larger number of charged particles in the upper layers of the atmosphere than that which, at first sight, is consistent with ionospheric measurements; but, on the other hand, it would be wrong to assert that ionospheric measurements necessarily exclude such a possibility. This theory is simpler than the dynamo theory, since it does not require the postulation of a system of atmospheric currents encompassing the entire globe.

Theory of drift currents

Chapman\(^{13}\) developed a quantitative theory of variations based on currents of gravitational-magnetic drift in the region of long free paths. In the most general case, when \(H\) and \(g\) form an angle \(\Phi\) with one another, expression (11) takes the form

\[ v = mg \sin \frac{\Phi}{He}. \tag{19} \]

For a uniformly magnetized sphere, which is approximated sufficiently closely by the terrestrial globe, the magnitude \(H\) at latitude \(\theta\) is determined from the expression

\[ H = H_0 (1 + 3 \sin^2 \theta)^{\frac{1}{2}}, \tag{20} \]

where \(\cos \theta = 2 \tan \Phi\), \(H_0 = 0.32\) gauss (at the equator, at sea level). From (19) and (20) it follows that

\[ v = \frac{mg \cos \theta}{He(1 + 3 \sin^2 \theta)}, \tag{21} \]

whence \(v = 0\) at the magnetic poles and \(v = 8.5\ \text{cm/sec}\) at the equator.

If the total number of ions \(y'\) in the region of long free paths in a vertical column with cross section \(1\ \text{cm}^2\) is composed of equal numbers of positive and negative ions of identical charges and masses, then the current of gravitational-magnetic drift, directed eastward, is represented by the formula

\[ i = vey'. \tag{22} \]

The eastward drift of positive ions causes an accumulation of positive charges on the evening side of the earth; in exactly the same way

the westward drift of negative ions leads to an accumulation of negative charges on the morning side. As a result, in the region of long free paths an electric field arises, directed toward the west. This region, however, is electrically connected with the lower region of short free paths, since charges will be able freely to penetrate into the lower region, moving along \(H\), especially at high latitudes, where \(H\) makes a considerable angle with the vertical. As a result, under the action of an e.m.f. directed toward the west, electric currents arise in the region of short free paths, which, for a corresponding distribution of conductivity (in the same region), create a system of currents analogous to Fig. 3.

Substituting into formula (22) the equatorial current obtained, \(i = 3 \cdot 10^{-5}\) (Fig. 3), we find \(y' = 2 \cdot 10^{14}\), which is less than the value required by the diamagnetic theory. The theory of drift currents gives no explanation of the afternoon maximum of \(S\). Having reached this point, Chapman abandoned the theory, suggesting that, in order to explain this phase advance, it may be necessary to turn to the dynamo effect.

The region of long free paths may participate in the diurnal variations of \(S\) owing to its diamagnetic properties and drift currents. For the first effect to be effective it is necessary that the distribution of ionization approximately obey equation (18); for the second effect to be effective, an analogous distribution must occur in the region of long free paths and, in addition, the conductivity or ionization in the region of short free paths must satisfy a known distribution (which is not specified). The results of a quantitative investigation intended to determine the distribution of ionization proved favorable for the diamagnetic theory and unfavorable for the theory of drift currents.

In the investigation the following assumptions were made: 1) that the ionization is caused by the ultraviolet radiation of the sun, 2) that in the region of long free paths, for vertical incidence of the solar rays, \(y' = 5 \cdot 10^{16}\), in accordance with the diamagnetic theory; this corresponds to ionization \(y = 5 \cdot 10^{9}\) in the region from 150 to 200 km, and 3) that in the region of short free paths, under vertical illumination by the solar rays, \(y = 5 \cdot 10^{9}\) at an altitude of 150 km and decreases exponentially to the value \(1.4 \cdot 10^{7}\) at an altitude of 100 km; this leads to \(\sigma = 1.44 \cdot 10^{-5}\). The shaded areas in Fig. 1 correspond to the assumptions made. It would seem that the shaded areas should not have extended beyond the dotted line, which would mean that the assumed ionization exceeds the measured values. However, there is still no disagreement with experiment, since the dotted line refers to the year of the sunspot minimum, whereas the shaded areas refer to the mean number of spots; it is known \(^{27}\) that the ionization during the period from the minimum (in 1923) to the maximum (in 1928) of the sunspot number increased on average by 50%.

Basing ourselves on the three assumptions made, and taking into account ionic recombination, diffusion, and electric and magnetic drift, the ionization of the upper layers was calculated; the rather complicated details of the calculations are omitted here, and should be consulted in the original papers^9. Analysis shows that the ionization of the long-free-path region is in agreement with equation (18), and consequently also with the diamagnetic theory. The daytime conductivity of the short-free-path region has high values at tropical latitudes and falls to a comparatively low value at latitudes above \(40^\circ\); in the night half of the terrestrial globe, in the tropical zone, the conductivity falls to \(1/5\) of the daytime value.

Fig. 4. Curve 1 shows observations^28, and curve 2 the calculated values^9 of the horizontal component \(\Delta H\) of the earth’s constant magnetic field caused by external causes.

Consequently, the chain of the eastern electric drift current in the region of long free paths is closed not by currents flowing by day at high latitudes westward (as shown in Fig. 3), but partly (by \(3/4\)) by the western current in the daytime tropical region of short free paths, and partly (by \(1/4\)) by eastern currents in the night region of free paths.

A detailed examination shows that the system of currents embracing the whole terrestrial globe is directed mainly along the parallels and is composed of: 1) currents in the illuminated half of the earth, flowing in the region of long free paths in an easterly direction, which at the points of sunrise and sunset split into two systems of currents; 2) one of the systems is directed westward and flows in the region of short free paths, directly under currents 1; 3) the second system is, as it were, a continuation of currents 1, is directed eastward, and embraces the night half of the earth. The main mass of the current (approximately \(4/5\)) flows in the equatorial region between \(40^\circ\) northern latitude and \(40^\circ\) southern latitude, and falls to small values at high latitudes. The total values of the current strength of the three systems are respectively: \(2.1 \cdot 10^7\), \(1.6 \cdot 10^7\), and \(5 \cdot 10^6\) A. The eastern and western daytime currents, being subtracted from one another, create a residual current of \(5 \cdot 10^6\) A, encircling the earth and flowing continuously. The distribution of the current strength along the latitudes is shown in Fig. 4 (curve 2).

Studying in 1922, by means of harmonic analysis, the permanent magnetic field of the earth, Bauer[^28] came to the conclusion that a part of the field, about \(2\%\), is due to external causes. The values he found for the horizontal component \(\Delta H\) of the external field at different latitudes are presented as curve 1 in Fig. 4, along whose abscissa axis the field strength is plotted in \(\gamma\) \((1\gamma = 10^{-5}\) gauss). The computed values of the horizontal component of the field, due to a ring current of \(5\cdot10^6\) A, are shown in the same figure by curve 2. The calculated curve agrees fairly well with the experimental one in the region of tropical latitudes. At high latitudes a noticeable discrepancy is observed; however, it must be borne in mind that, because of the small number of observations in the polar zone, these points of the curve are determined with insufficient accuracy.

The computed values of the vertical component of the magnetic field, which are not given here, agree with the experimental data to the same degree as the horizontal components shown in Fig. 4.

On the basis of what has been said, the conclusion was drawn that the currents caused by gravitational-magnetic drift, instead of the system of surface currents shown in Fig. 3, give rise to a circular current encircling the earth; this current accounts for the external part of the permanent field of the earth. As analysis[^9] shows, this conclusion remains valid for a distribution of ions even somewhat different from that shown by the hatched areas in Fig. 1.

We conclude the section by making the trivial remark that the correct explanation of \(S\) apparently consists in the simultaneous consideration of all three processes in the upper layers of the atmosphere: the dynamo effect, diamagnetism, and the currents of gravitational-magnetic drift.

B. Lunar variations of the earth’s magnetic field

Observational data

Small variations \(L\) of the earth’s magnetic field, whose amplitude is about \(3\gamma\), have been established as being due to the action of the moon. The character of the lunar changes \(L\) is shown in Figs. 5 and 6. The eight upper curves represent changes in the eastern horizontal component \(L\), as a function of the time of the lunar day, according to the data of the observatory in Batavia[^29]; the curves correspond to different phases of the moon. It follows from the curves that the amplitude of the changes during the solar day is greater than the amplitude of the changes during the night. The mean of the eight curves is shown by the lower curve of Fig. 5, in which the influence of the sun on the lunar variations is excluded and where \(L\) acquires the symmetrical form of semidiurnal oscillations analogous to tidal variations. Fig. 6 shows the changes of the northern horizontal \(N\), vertical \(V\), and western horizon-

...the tangential \(W\), the components \(L\) at different latitudes, compiled by averaging observations at a number of observatories \(^{30}\).

Harmonic analysis shows that, just as in the case of \(S\), \(3/4\) or \(2/3\) of the changes in \(L\) are due to external causes, and \(1/4\) or \(1/3\) to currents induced in the earth. If \(L\) is caused by the magnetic action of currents in the upper layers of the atmosphere, then the maximum current density at the equator must amount to \(4\cdot 10^{-6}\) CGSM units. The amplitude of \(L\) varies with distance to the moon approximately according to the same law as the lunar tidal force. In contrast to \(S\), \(L\) depends only slightly on the mean annual number of spots, although with increasing magnetic activity \(L\) changes from day to day to a greater extent than \(S\).

Fig. 5. Lunar variations \(W\) in Batavia \(^{29}\)

Theory of the atmospheric dynamo

The only theory suitable for explaining the variation is the Schuster-Stewart theory of the atmospheric dynamo, which was first developed in detail by Bemmelen \(^{31}\), and subsequently by Chapman \(^{22}\). As in the case of \(S\), the changes are attributed to the magnetic action of currents in the upper layers of the atmosphere. The theory assumes that currents arise under the action of an e.m.f., which in turn is produced by the tidal motion of the upper layers of the atmosphere in the vertical components of the earth’s magnetic field; the tidal motions are calcul—

Fig. 6. Averaged lunar variations of the elements of terrestrial magnetism \(^{30}\)

are found from observations of lunar barometric variations. In Batavia, at the equator, the amplitude of the 12-hour component (in lunar time) reaches \(0.063\) mm of mercury; the dependence of the amplitude of barometric oscillations on latitude has not been determined. As calculations show, the tidal motions of the atmosphere generate a system of electric currents which, in character, corresponds to the observed variations \(L\). The situation is complicated, however, by the fact that between the theoretical and the actual changes in \(L\) there is a phase shift reaching \(223^\circ\), i.e., these changes are almost opposite in phase. This phase discrepancy is all the more difficult to explain because, apparently, the sole cause of the lunar barometric variations is tidal forces[^20]. Consequently, the theory of \(L\) leaves much less room for maneuvering than the theory of \(S\), in which one can always assume a complex interaction of tidal and thermal forces. The phase discrepancy in the theory of \(L\) is a much sharper contradiction for the theory than the phase discrepancy in the theory of \(S\).

To determine from the observed \(L\) the conductivity \(\sigma\) in the upper layers of the atmosphere, we replace the complicated calculations[^22] by simpler ones. With a lunar barometric amplitude of \(0.063\) mm, the mean velocity of the atmospheric “flood” and “ebb” is

\[ \frac{1}{0.063 \cdot 760} \]

of the circumferential velocity of the earth’s rotation. This corresponds to a velocity \(v = 2\) cm/sec, or \(0.07\) km/hour. Substituting into the formula \(\sigma = \frac{i}{vH}\), \(i = 4 \cdot 10^{-6}\), \(H = 0.3\) gauss, and \(v = 2\), we obtain \(\sigma = 5 \cdot 10^{-6}\). This quantity is the mean value of the conductivity at different points around the earth, at the equator, since \(L\) was taken from the lower curve of Fig. 5. Consequently, the obtained (maximum) value of \(\sigma\) must exceed the computed quantity by 3 or 5 times, depending on the assumed law of the diurnal variation of \(\sigma\). Assuming that \(\sigma\) is a function of the cosine of the sun’s zenith angle, we must, in order to obtain the derived conductivity at the equator, choose the factor 4; in this case the conductivity proves to be equal to

\[ \sigma = 20 \cdot 10^{-6}. \]

Chapman arrived at approximately the same value; this is about 7 times greater than the conductivity found by Schuster on the basis of \(S\). Since these values are based on theories which have been only partially justified, they cannot be regarded as reliable.

In order to explain the discrepancy between the theories, on the one hand, and the observed facts, on the other, numerous assumptions have been advanced, such as: resonance in the atmosphere, its viscosity, and the possibility that \(S\) and \(L\) are due to currents at different levels of the atmosphere[^22]. So far, however, none of these assumptions has made it possible to explain

all contradictions. We believe that the further development of the theory in the direction outlined above cannot follow in the very near future, since this will require statistical processing of very small quantities obtained from observations at many observatories scattered over the entire globe, and over a long period of time.

G. Magnetic storms and aurorae

Observational data on magnetic storms

Irregular variations or disturbances of the earth’s magnetic field are so diverse that it seems difficult to establish a sufficiently complete classification for them. Disturbances may arise at any time of day; they may encompass the entire globe or be local in character. The most serious disturbances, classified as storms, almost always manifest themselves over the whole globe and are usually accompanied by aurorae.

Fig. 7. Horizontal component during three general magnetic storms, according to observations at Cheltenham[^32]

Among these disturbances, storms with a clearly expressed, sudden onset are singled out as a special class. The curves of recording instruments at magnetic observatories may, for several hours, have an entirely quiet character, and it would seem that nothing foretells any disruption of their smooth course. And suddenly, abruptly, a sharp oscillation arises in the course of the curve, which in low and middle latitudes is manifested most strongly in the course of the horizontal component \(N\). Within a few minutes \(N\) may

may change by 50 γ or even more. A rather large percentage of the strongest storms begins precisely with such a sharp fluctuation, which is not without reason regarded as a forerunner or beginning of the storm. Fig. 7 gives magnetograms of \(N\), obtained at the Cheltenham Observatory (Cheltenham, Maryland), (USA), for three general (worldwide) storms\(^{32}\), which illustrate: a) the sudden beginning mentioned above, when \(N\) rises sharply; b) a storm that began with a sharp rise and then fall of \(N\), and, finally, c) a storm that began gradually. Fig. 8 gives curves of \(N\) from observations at a number of observatories, relating to a brief but clearly expressed storm that began suddenly at 7 o’clock Greenwich time on March 14, 1922.

Fig. 8. Horizontal component at different stations during the magnetic storm of March 14, 1922.

In some of the general storms the “sudden commencement” is at once accompanied by a strongly disturbed period, whereas in other cases several hours pass between the first impulse and the storm proper; finally, cases have been noted in which, for 12 hours after the sharp impulse, nothing, even remotely resembling a storm, was observed. The “sudden commencement” of general storms occurs at all stations simultaneously, within 3 min.\(^{33,34}\) Fig. 9 shows the beginning of the magnetic storm of May 3, 1921, which began at 13 h 10 m Greenwich time\(^{13}\). This is one of the two strongest storms in the interval from 1908 to 1928. The storm continued for 5 days; during this time four impulses of the “sudden commencement” type were recorded, each of which was observed simultaneously over the entire globe.

With the exception of the “sudden commencement,” in the course of magnetic storms it is impossible to detect characteristic features that would manifest themselves over the entire globe. A high peak and a deep trough, observed

...given on magnetograms, usually already disappear without a trace at stations removed from the place of observation by a distance of the Earth’s semicircumference[^33]. Analyzing magnetograms over 12 years, from 1913 to 1924, W. Wills[^33] found only one short and sharp disturbance which was undoubtedly observed at all stations. This was a deep, sharp-pointed depression on the curve in Fig. 9, which occurred at \(15^{15}\) Greenwich time.

Fig. 9. Record of the horizontal component during the beginning of a magnetic storm, May 13, 1921.

In magnetograms in the region of low[^35] and middle latitudes, sharp changes, resembling in character a “sudden commencement,” appear in almost all cases over the entire globe. This, however, is no longer true of magnetograms obtained in high latitudes. Thus, for example, on the magnetogram of the Eskdalemuir Observatory (Scotland) one can see a large number of “sudden commencements,” in addition to those that have already been registered at all other observatories and that are no longer observed at remote magnetic stations[^36]. Records at stations in polar regions during magnetic storms are so irregular that the most varied changes can be found in them.

The initial increase of \(N\) at the moment of a “sudden commencement” is often characterized as the first phase or “impetus”[^37] of a magnetic storm. Following this increase, in most cases, sooner or...

later a noticeable decrease in \(N\) is observed, usually attributed to the second phase of the storm; this decrease is accompanied by irregular oscillations of the field, during which \(N\) diminishes by about \(100\gamma\) relative to its initial value. Toward the end, an “after-effect period” is observed, which may also be accompanied by

Fig. 10. Course of worldwide storms at different latitudes\(^{38}\); time is counted from the beginning of the storm.

oscillations. Some of these features may be noticed in Figs. 7 and 8. Chapman\(^{38}\) selected about 40 storm-time curves of this character from observations at a number of observatories, averaged them, and, after subtracting the diurnal variation of a quiet day, subjected them to a twofold treatment, constructing on their basis curves of the change of the magnetic field as a function of “storm time” (the origin of the time count corresponds to the beginning of the storm), characterizing storms from the standpoint of the entire globe, and curves of the change of the magnetic field according to local time, characterizing the diurnal variation of disturbances during storm periods. These averaged curves are shown in Figs. 10 and 11\(^{38}\). As follows from Fig. 10, magnetic storms considered in “storm time” proceed approximately alike at high and low latitudes; Fig. 11 shows that the diurnal variation of disturbances during storm periods increases with latitude.

The energy density in a medium with magnetic permeability \(\mu\), at magnetic-field intensity \(H\), is expressed by the formula

\[ E=\frac{\mu H^{2}}{8\pi}. \tag{23} \]

Let \(x_{0}, y_{0}, z_{0}\) and \(x, y, z\) denote the mean components of \(H\) along rectangular axes, respectively for the quiet and disturbed states of the field. Let further \(\Delta x=x_{0}-x,\ \Delta y=y_{0}-y,\)

\(\Delta z = z_0 - z\). Then the change in energy \(E\) during the disturbance, for \(\mu = 1\), will be represented in the form

\[ \Delta E = \frac{(x_0 \Delta x + y_0 \Delta y + z_0 \Delta z)}{4\pi} + \frac{[(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]}{8\pi} \tag{24} \]

or, in view of the small error, discarding the second term,

\[ \Delta E = \frac{H_0 \Delta H}{4\pi}. \tag{25} \]

Using the data of the observatories Bowdoin Harbor, Sodankylä, Sitka, Cheltenham,

Fig. 11. Daily changes of the elements of magnetism
during storms at different latitudes

Tucson, Vieques, Honolulu, Antipolo, Huancayo, Pilar, Vassouras, and Waterloo, Wels computed the mean \(\Delta E\) for the storms of March 14, 1922, and January 29, 1924, which lasted, respectively, 17 and 26 hours.

The results of the calculations, presented as a curve in Fig. 12, show that at the magnetic equator \(\Delta E\) undergoes a clear maximum; between \(20\) and \(40^\circ\) magnetic latitude there is a shallow minimum, then it reaches a high maximum between \(60\) and \(80^\circ\), and gradually decreases toward the magnetic pole, reaching at the latter

of the same value as at latitude 60°. The course of the curve \(\Delta E\) corresponds to the recurrence curve of polar auroras[^39]. Stagg[^40], who carried out an analogous investigation, arrived at the same conclusions.

It also follows from Fig. 12 that the mean density of the disturbed energy of the magnetic field during storms is about \(10^{-5}\) ergs/cm\(^3\). Multiplying this value by the volume of the Earth, we obtain \(10^{22}\) ergs—the total energy of the magnetic storm, which should be increased to \(3 \cdot 10^{22}\) to allow for the magnetic field in the space around the Earth. If this energy were obtained from the Sun over the course of 28 hours, which

Fig. 12. Mean values of the energy density \(\Delta E\) during the magnetic storms of March 14, 1922, and January 29, 1924.[^33]

corresponds to \(3 \cdot 10^{17}\) ergs/sec, then this would constitute a small fraction of the \(2 \cdot 10^{24}\) ergs of the total energy of solar radiation received by the Earth every second.

Magnetic disturbances, radio communication, the ionosphere and the Sun

With the introduction into operation of short-wave radio communication lines of great length, working on wavelengths from 15 to 40 m, it was discovered almost immediately that during strong magnetic storms radio communication was disrupted, and at times lines even became unusable for operation. As analysis shows[^41], the disturbances manifest themselves chiefly in the daytime: communication on radio lines passing over the illuminated half of the Earth is disrupted from the beginning of the storm, whereas on lines immersed in darkness normal conditions are preserved until dawn, when communication may also be disrupted; the disruption of daytime radio communication often continues even after the onset of darkness.

Up to the present we possess only incomplete information about the state of the ionosphere during magnetic storms. Schafer and Goodall,

based on their own observations and on the observations of other authors, came to the conclusion that during severe magnetic storms the absorption of the ray reflected from the ionosphere increases, accompanied by its scattering or splitting, which is manifested in a large number of rays reflected from layers of the ionosphere differing only slightly from one another in height, making their exact determination difficult. During moderate magnetic storms it is usually difficult, from observations of the character of the reflections, to determine a disturbance that is beginning. \(f_c\) of the \(E\) and \(F_2\) layers changes only slightly as a function of the magnetic state; \(f_c\) of the \(F_1\) layer decreases with increasing magnetic activity, but only in rare cases by more than 20%.

The program of worldwide investigation of the ionosphere stands to gain enormously from the transition to continuously recording installations and from the expansion of the radio-frequency spectrum. It may be hoped that in the next few years important results will be obtained that will make it possible to clarify much in the phenomena of terrestrial magnetism.

Already at the present time new discoveries have been made that make it possible to outline lines of further research. Dellinger^42 was the first to call attention to a new phenomenon in the propagation of short radio waves on the illuminated half of the terrestrial globe. The phenomenon consists in the sudden disappearance, usually for several minutes, of radio signals, the complete process of “fading,” from the beginning of weakening to full recovery, taking about 15 min. This phenomenon encompasses simultaneously all daytime communication lines and does not occur at all at night. Such “universal radio fadings” were observed during magnetic storms and, at least in 1935, recurred after 54 days. To verify the supposition that the cause of the “universal fadings” is a special kind of solar activity, spectroheliograms in the hydrogen \(H_{\alpha}\) lines obtained at the Mount Wilson Observatory were analyzed.^43 In two cases of fading, on July 6 and August 20, 1935, the spectroheliograms were obtained at the appropriate time, and on them abrupt and noticeable changes were found in the form and intensity of hydrogen flocculi, coinciding in time, with an accuracy of several minutes, with the moment of fading. On those days complete observations of the ionosphere were not being carried out.

Two circumstances seemed evident: first, that the phenomenon belongs to the class of short-lived ones, lasting only a few minutes; and second, that for its further study it is necessary to establish continuous observations of the Sun, of radio communication, and of the ionosphere; continuous observations of the Earth’s magnetic field had already been an “accomplished fact” for many years. The recurrence period of 54 days, although its reality had not yet been established, at least gave an indication of when such observations might reward the effort.

On October 24, 1935, a hydrogen eruption of moderate brightness was observed, accompanied by partial fading, which na-

disrupted communication at the highest frequencies; at the same time a general magnetic storm was noted. Observations of the ionosphere^44 showed that \(f_c\) of the \(F_2\) layer increased during the period from 10 to 23 October to a very high value and then on 24 October fell to half the value, while on 25 October and in the following days it again returned to its initial high values. At the same time the effective height of \(F_2\) on 24 October rose to 460 km, whereas on the preceding and following days it was only 250 km.

Subsequently bright eruptions in the \(H_\alpha\) lines were recorded on 16 and 17 December 1935, but no unusual phenomena in the propagation of radio waves were observed on those days. General fading was observed on 6, 14, and 17 February 1936; moreover, one of them, namely that of the 14th, was especially significant. On 6 February no special changes in solar activity were noticed, while cloudy weather at the Mount Wilson Observatory prevented observations from being made from 10 to 19 February.

On 8 April 1936 an exceptionally bright solar eruption was observed at Mount Wilson^43 and at Huancayo (Peru); it began at \(16^{45}\) Greenwich time, increased in brightness until \(16^{47}\), and returned to normal at \(17^{03}\).

Deep and widespread fading on the daytime radio-communication lines began at \(16^{46}\) on 8 April, continuing on different frequencies from 15 to 30 min. A general magnetic storm suddenly began at \(16^{46}\) in Huancayo, and during the interval from \(16^{40}\) to \(16^{51}\) the component \(N\) increased by \(108\gamma\). Reflection of radio waves from the ionosphere suddenly ceased at \(16^{45}\) and was restored only an hour later. The bright hydrogen eruptions, the general radio fading, and the abrupt changes in \(N\) and in the ionosphere constitute unusual but clearly expressed phenomena. Richardson^43 came to the conclusion that, at least in this case, solar activity was directly connected with phenomena on the earth and that the energy was transmitted with the speed of light.

Data from observations of auroras

Apparently, the most complete summary of facts relating to auroras was compiled by Kree^46 and Vegard^47. Curve 1 in Fig. 13, characterizing the dependence of the mean number of observed auroras on the magnetic latitude of the locality, shows that the maximum recurrence of auroras^39 is observed at a distance of approximately \(23^\circ\) from each of the magnetic poles. The part of the curve corresponding to latitudes above \(67^\circ\) is shown by a dotted line, since detailed data in this region are lacking; it is known only that the recurrence of auroras at these latitudes decreases. Diffuse clouds and pulsating glow are observed at heights from 85 to 150 km, while rays and oscillating draperies are observed at heights from 110 to 600 km^48,49.

In the region of the maximum of auroras, auroras are observed almost daily; auroras spread to low latitudes during

...of magnetic storms; moreover, the more intense the magnetic storm, the deeper the auroras extend.

In periods of relatively quiet magnetic conditions, at different stations it is not possible to detect a regularity in the diurnal course of auroras, which is to a large extent determined by local meteorological conditions in the upper layers of the atmosphere (above the station), such as air currents and the conditions of excitation of atmospheric atoms and molecules[^50],[^51]. During strong storms, moving and colored auroras are most often observed in the evening, while diffuse, weak, and quiet forms occur in the mornings.

A large number of spectral lines of auroras have been identified[^52] with the emission lines of nitrogen molecules and oxygen atoms; moreover, the conspicuous green line (5577 Å) is due to metastable atomic oxygen. Helium and hydrogen lines have not been found in the spectrum of auroras. Störmer[^53] drew attention to very high auroras, colored violet-gray, sometimes reaching 1000 km. They are located in the region illuminated by the Sun. The spectrum of such auroras differs noticeably from ordinary auroras, situated in the region of the Earth’s shadow, chiefly in that the intensity of the green line is weaker than the lines of the nitrogen series[^53],[^54].

Fig. 13. Mean frequency of auroras at different latitudes according to observations (curve 1)[^39] and according to calculations (curve 2).

Corpuscular Theory of Magnetic Storms

A corpuscular theory of magnetic storms does not exist in a completed form. At various times assumptions have been put forward that certain phenomena of terrestrial magnetism are caused by charged particles ejected by the Sun, but these assumptions either suffered from uncertainty or proved untenable. It has long been known[^55] that the increase in \(N\), common to the whole terrestrial globe, during the first phase of a magnetic storm can be explained by the sudden appearance of a ring current directed eastward and encircling the Earth, mainly in the region of the tropics, while the decrease in \(N\) during the second phase of the storm can be explained by a similar current directed westward. Assuming that these ring currents consist of electrons or positive ions, the question of their formation, of maintaining a constant value, and of their disappearance was not subjected to discussion. Evidently, the number of difficulties...

arising when this postulate is advanced exceeds the number of those difficulties which can be resolved with its aid.

Chapman’s corpuscular theory of magnetic storms, developed by him^57, did not withstand Lindemann’s criticism^58, as a result of which the author was forced to abandon his theory^57. In this theory it was assumed that particles of like charges, ejected by the sun in the form of corpuscular rays, enter the outer layers of the atmosphere, where they set the conducting layers in motion, directed downward. As a consequence of the dynamo effect [equation (12)] eastern currents are formed around the earth, causing an increase of \(N\) during the first phase of the storm. Under the action of electrostatic repulsion of the charged particles, following the downward-directed motion, there is an expansion of the atmosphere upward, in which a western current is induced—the second phase of the storm. Meanwhile Lindemann, developing the idea put forward by Schuster^59, came to the conclusion that a ray composed of particles of like charges, whose density corresponds to the energy of the storm, owing to electrostatic repulsion cannot exist in the form of a ray at a distance greater than one or two solar diameters; moreover, because of the charge that the earth acquires almost instantaneously, such particles can fall to the earth only during the first few seconds.

Chapman and Ferraro^60 attempted to create another theory, based on the supposition that the sun ejects a stream of particles, electrically neutral, which consists of equal numbers of positive and negative charges. They envelop the earth at a distance of \(50\,000\) km or even more and, owing to their diamagnetic properties, lead to an increase of \(N\) during the first phase of the magnetic storm. As the charged particles penetrate into the earth’s magnetic field, the positive particles are deflected to the west, and the negative ones to the east. The idea was advanced that the particles could encircle the earth, forming a western current necessary for explaining the second phase of the storm. The authors, however, came to the conclusion that they were not able to explain the physical process of formation of the circular current. Chapman^61 recently remarked on this matter that “the theory as a whole appears speculative and difficult; apparently the most doubtful part of it is the circular current, whose existence and formation are explained very uncertainly.” The theory was left in schematic and unfinished form. The theory gave no explanation for the diurnal variations in the course of storms and did not clarify how the particles penetrate into the ionosphere and produce there the changes observed during magnetic storms.

Corpuscular Theory of Polar Auroras^1)

The well-known corpuscular theory of polar auroras of Birkeland, Störmer, and Vegard^47 encounters Schuster’s difficulty^59,

^1) This chapter has been made brief and incomplete because I was warned by the editor about an article on polar auroras being prepared for the journal, in which the question of the corpuscular theory will be examined.

which, as Lindemann^58 and Swann^62 noted, this theory could never dispense with. Størmer’s calculations, devoted to the focusing of charged particles by the earth’s magnetic field in the auroral zone, refer to a single charged particle, for example, to an electron or an α-particle, whereas the theory of aurorae must operate with an aggregate (cloud) of such particles; it was shown^58,60,62 that a stream of electrons or ions, or a stream consisting of a combination of these and others, cannot be the cause of aurorae. Chapman and Ferraro^63 conclude that “a reconsideration of the conditions under which the motion of the stream from the sun to the earth takes place has compelled us finally to abandon the tempting supposition that at least a part of the stream, sufficient to explain the formation of aurorae, can reach the earth by being deflected in the same way as individual corpuscles in Størmer’s theory (or at least by following this law approximately); our work has confirmed Lindemann’s conclusion that the only acceptable form of the stream is a stream which, to a close approximation, may be regarded as electrically neutral.”

Theory of Ultraviolet Radiation, General Considerations

The theory of ultraviolet radiation as applied to magnetic storms and aurorae has been developed in detail, and even quantitatively, in a number of works^41,50,64.

Here we give a description of the most essential physical ideas on which this theory is based. As Table 1 shows, in a column of the atmosphere with a cross-section of 1 cm², above the level of 300 km, there are approximately \(10^{16}\) molecules. Above this level the particles practically do not undergo collisions, but move upward and downward (as if “jumping”): upward—under the action of upward-directed forces arising upon contact with other particles^1), and downward—under the influence of gravity. This is precisely what the outer boundary of the atmosphere appears to us to be. The \(10^{16}\) molecules at an altitude of 300 or 400 km undergo \(10^{14}\) collisions. At a temperature of \(360^\circ\mathrm{K}\), a normal collision imparts to a particle a speed of the order of 1 km/sec, which rarely ejects the particle to an altitude exceeding 2000 km.

It is assumed that during a quiet period of solar activity, i.e. in the absence of magnetic storms and aurorae, \(10^8\) out of \(10^{16}\) contacts are collisions of the second kind with excited molecules and atoms, in which the molecules acquire a speed of 10 km/sec. In the course of from 3 to 6 hours they reach altitudes of 40,000–80,000 km and, if they remain un-ionized, they fall back to the earth along various orbits,

^1) When approaching other particles. Translator’s note.

whose shape is determined, as follows from Fig. 14, by the initial angle of ejection.

It is assumed that during 3 or 6 hours of flight, under the action of ultraviolet solar radiation, the particles become ionized. Once ionized, they continue their motion already along the magnetic lines of force and enter the region of high latitudes of the atmosphere, releasing their energy in the form of auroras and magnetic disturbances. The energy flux at different latitudes was calculated, and the results of the calculation are shown as a dotted line in

Fig. 14. Curves \(a, b, c\), etc. represent the lines of force of the earth’s magnetic field. The numbers beside these curves indicate the magnetic latitude at which these lines enter the earth. Curves \(E, F, G\), and \(K\) represent the trajectories of particles ejected from the earth at a velocity of \(10\ \mathrm{km/sec}\), at angles with the vertical of, respectively, 1, 22, 45, and \(60^\circ\).

Fig. 13, in good agreement with curve 1. The energy transported, under the assumptions made above, into the region of auroras amounts to \(5 \cdot 10^{13}\ \mathrm{erg/sec}\), which may be considered sufficient for a quiet aurora, but is far from sufficient for the formation of powerful auroras, whose energy reaches \(10^{15}\ \mathrm{erg/sec}^{64}\).

It is further assumed that during active periods the sun emits intense ultraviolet radiation for half an hour. If, for example, \(1/10\,000\) of the solar surface were to radiate as a black body at a temperature of \(30\,000^\circ\mathrm{K}\), then the solar constant would increase by \(0.74\%\), and the solar energy at wavelengths 3500, 4000, 5000, and 6000 Å—respectively by 3.2; 1.7; 0.75 and \(0.032\%\). The corresponding values of fluctuations of solar energy observed\(^{65}\) over short intervals of time (about an hour) are approximately 1.8, 2.1 and \(0.2\%\), reaching at times,

even higher values. The energy of ultraviolet radiation in the regions 3000–2000, 2000–1000, and 1000–0 Å is expressed as a value, respectively, 1.5, \(10^2\), and \(10^5\) times greater. Calculations analogous to those made and based on the laws of black-body radiation should be regarded only as illustrative; they may be very far from reality, since there is no doubt that emission lines and absorption lines play a far from negligible role. This energy increases the ionization of the upper layers of the atmosphere and of particles thrown high upward, and is the cause of heating, expansion, and the appearance of currents in the upper layers of the atmosphere, which in turn gives rise to auroras and magnetic disturbances.

The theory of ultraviolet radiation as applied to auroras

In the spectrum of ultraviolet solar flares, wavelengths shorter than the boundary of the series of the given atom are apparently the most effective for ionizing the atom, whereas longer waves produce only excitation of atoms. In general, one may suppose the existence of certain varieties of ultraviolet flares, namely: 1) flares containing chiefly exciting wavelengths, and 2) flares containing both exciting and ionizing wavelengths of various intensities, etc. Flares of the first type cause the appearance of a large number of excited atoms. These atoms, in turn, stimulate the appearance of atoms or molecules thrown high upward, which, undergoing ionization, fall into the polar regions and create auroras. Since such flares do not cause ionization in temperate latitudes, they should not be accompanied by general magnetic storms. Consequently, in these cases strong auroras at high latitudes may not be accompanied by magnetic disturbances in temperate latitudes—at least not so strong that they could be classified as storms. Examples of this may be found in the strong auroras in the Antarctic region on April 20 and 27 and from June 18 to 21, 1908, at Cape Royds,^66 on May 29, June 19, and July 7, 1913, at Cape Denison. The magnetic field at these stations during the auroras was disturbed,^66 whereas in temperate latitudes magnetic storms were recorded neither on the day of the auroras nor on the nearest days. Many bright auroras not accompanied by magnetic storms in temperate latitudes were noted during the expedition on the Maud^67 from 1922 to 1925 in the Arctic Ocean off the shores of Siberia.

Flares of the second type, in addition to the large number of ions formed, also create many particles thrown upward, which, owing to the unusual intensity of the ionizing waves, become ionized long before they reach great heights. As a result, the particles do not enter the polar regions, but, following along the magnetic lines of force

the Earth’s field, penetrate into temperate latitudes, and in sufficient number to cause the appearance of auroras. In accordance with this one may suppose that strong magnetic storms must be accompanied by auroras in the high regions of temperate latitudes; moreover, the stronger the magnetic storm, the deeper into the southern latitudes the auroras should penetrate. The penetration of auroras into the region of southern latitudes had already long ago been noted^68. Auroras in temperate latitudes were observed by Barnard^60 at the Yerkes (Jerk) Observatory during the years 1902 to 1909 over the course of 140 nights; 120 of these auroras were accompanied by magnetic storms.

On those nights when the absence of magnetic storms was noted, the auroras were weak, and it is quite probable that the magnetic disturbances which could be observed at that time were not sufficiently strong to classify them as storms.

A particle flying upward from the atmosphere with a velocity of 10 km/sec reaches an altitude of 40,000 km in approximately 3 hours. If at this altitude the particle is ionized under the action of solar rays, then several hours are required for its return fall into the polar region; the exact time depends on the curvature of its spiral trajectory and on its velocity at the moment of ionization, if we assume that the only factors acting on the ion are the force of gravity and the Earth’s magnetic field. The action of other causes is possible, such as light pressure, the electric field, etc.; however, it does not seem possible to establish how great their significance is.

After falling to an altitude of 300 to 400 km, the further descent of the ionized particle proceeds by diffusion^64; moreover, as calculations show, from 3 to 6 hours are required to reach an altitude of 100 km. If the ultraviolet flash which causes the migration of ions into the polar regions at the same time creates strong ionization in the upper layers of the atmosphere and, consequently, is the cause of a magnetic storm, then the aurora should be observed several hours after the beginning of the storm. Owing to the fact that the migration of ions toward the poles during flashes of great intensity may be interrupted, there is reason to suppose that the delay in the appearance of auroras at high latitudes will be greater in the case of prolonged and intense magnetic storms than in the case of short storms.

Observations of auroras, as is evident from the reports of the British and Australian Antarctic expeditions^60,70, as well as of the Arctic expedition on the Mod^67, confirm the theoretical assumptions set forth above. In Fig. 15 are given observational data for an aurora at Cape Denison (Antarctica), and the beginning and end are marked of a very strong magnetic storm which began on September 17, 1912, at 2:00 hours. The aurora was observed 40 hours after the beginning of the storm.

There were altogether 11 magnetic storms for which observations in the Antarctic and Arctic were sufficiently complete that it proved possible to construct curves analogous to Fig. 15. The processing

these materials shows^64 that auroras begin approximately twenty-four hours after the occurrence of a magnetic storm at low latitudes, and that the time interval between the aurora and the storm increases for magnetic storms of greater intensity; however, in view of the insufficient number of observations, the latter conclusion cannot be regarded as entirely reliable. Carrying out an extensive statistical analysis of observations of auroras during Byrd’s first Antarctic expedition, Davis^71 obtained further confirmation of the existence of the “delay phenomenon” and came to the conclusion that “a comparison of the daily characteristic numbers of auroras and of international magnetic indices showed an obvious connection between the maximum of the auroras and the maximum of the curve of magnetic indices; the maximum of the auroras occurred either on the same day or twenty-four hours later.”

Fig. 15. Intensity of auroras at Cape Denison (Antarctica) and the magnetic storm of September 17, 1912.

There are no indications that the spectrum of auroras has been reproduced under laboratory conditions. Kaplan^72 succeeded in obtaining many features of the auroral spectrum by observing a quiet discharge in oxygen and nitrogen, and in gathering important information on the processes of excitation of atoms. As a result of these experiments, very valuable information may be obtained concerning the physical state of the atmosphere during auroras.

In conclusion it should be noted that all theories of auroras are rather geometrical theories, for they deal chiefly with the mechanism of energy transfer into the region of auroras, leaving entirely aside the question of how the transition of energy into polar light is effected. A complete theory must give an answer to these questions as well, and must, above all, be based on precise knowledge of the energy levels of atmospheric atoms and molecules, of metastable states and the probabilities of their transitions, just as on knowledge of the processes by which polar light arises. Then, an idea that has long suggested itself, according ...

in which the process of emission of polar light is determined not only by the energy of the ion flux, but also by the suitable, and perhaps even critical, conditions in which that region of the atmosphere penetrated by the flux is found; these conditions may depend on accidental causes, such as atmospheric currents and the state of excitation of atoms and molecules.

Theory of ultraviolet radiation as applied to magnetic storms

An active region (flare region), occupying \(^{1}/_{10\,000}\) of the surface of the Sun at a temperature of \(30\,000^\circ\), will send to the Earth an energy of \(10^{22}\) ergs/sec, which approximately corresponds to the mean energy of a magnetic storm lasting one day. Consequently, an active surface smaller in area, or a less powerful flare lasting more than 1 sec., is also capable of creating the energy of a storm. The radiation of this flare includes ionizing wavelengths shorter than \(1500\) Å, which cause an increase of ionization in the region of long and short free paths above the illuminated half of the terrestrial globe; flares with different spectral characteristics may increase ionization in the region of long and short free paths in different proportions. An increase of ionization in the region of long free paths increases the eastward current of \(5\cdot10^6\) A encircling the Earth, as a result of which \(N\) increases and \(V\) decreases, as is observed during the first phase of a storm. An increase of ionization in the region of short free paths entails an increase of conductivity and, consequently, an increase of the western daytime current. As a result of this the eastward current of \(5\cdot10^6\) A decreases, and a western current, as it were, arises encircling the Earth; \(N\) decreases and \(V\) increases, as occurs in the second phase of a storm.

In addition, there are subsidiary phenomena common to all types of flares, such as, for example, heating of the upper layers of the atmosphere at the level of \(100\) km. Heating entails an expansion of the atmosphere, which in turn is the cause of the dynamo effect and the “retarding effect” (engulfing effect). The dynamo effect is due to the upward motion of air masses in the field \(H\) and is manifested most strongly in low latitudes, where \(H\) is approximately horizontal. The dynamo effect creates a western electric field and a western current around the Earth, decreasing \(N\). With a velocity of motion of the short-free-path region (Fig. 1) upward of \(10\) km/hour, \(N\) decreases at the equator by approximately \(100\gamma\). The “retarding effect,” likewise manifesting itself with the greatest strength in the tropical latitude zone, is due to the fact that when \(H\) is approximately horizontal, ions with long free paths in the interval between collisions can pass only a short distance in the direction perpendicular to \(H\) and, consequently, are partially excluded from the free upward motion of neutral particles.

expanding atmosphere. Thus, after the beginning of a magnetic storm, a large number of ions in the region of long paths take part in the general upward motion of the air molecules; the length of their path is shortened, and they turn into ions with short paths. Since the ions experience a large number of collisions before recombination occurs, the daytime region of short paths increases at the expense of the region of long paths, as a result of which the westward current arises.

We may imagine the sequence of phenomena in the general storm, similar to that shown in Fig. 10, in the following way: a flash of ultraviolet radiation first of all causes an increase of ionization in the region of long paths, which entails the appearance of an eastward current and an increase of \(N\) above its normal value (the first phase of the storm). In the second phase the thermal effect of the flash manifests itself, the upper ions of the atmosphere expand, the ionized layer moves upward, and \(N\) decreases for several hours. When the upward motion in the layer ceases, \(N\), it would seem, should increase to its initial value (above normal); however, by this time, owing to the “retarding effect,” the region of long free paths has diminished, and, consequently, \(N\) again proves to be less than the normal value. After the flash ceases, \(N\) slowly rises to its normal value, the excess ionization decreases, and the atmosphere comes to an undisturbed state.

Magnetic storms are often encountered which begin not with an increase of \(N\) and which consist of a single second phase; an example of such a storm may be the third curve in Fig. 7. In these cases one may suppose that the flash chiefly emits energy that heats the upper layers of the atmosphere and produces mainly ionization of the region of short free paths. Storms consisting of a single first phase are extremely rare; for their formation the flash must increase ionization only in the region of long paths, without producing appreciable heating. Irregular and local disturbances may be caused by motions of ionized layers under the action of winds and induced earth currents.

Changes in the diurnal curve of the course of storms (Fig. 11) are explained by the action of ions thrown up high and entering the polar regions. Assuming that the earth as a whole carries no charge, it can be shown\(^{64}\) that particles flying out near the noon meridian at low latitudes enter, already in the form of ions, at a height of 300–400 km into high latitudes at 13 and 14 hours; here they are slowed in their motion and, diffusing, descend another 200 km during the following 3 or 6 hours. Possessing long free paths, these ions create an eastward current of gravitational-magnetic drift, and if the conductivity of the upper layers of the atmosphere changes depending on the zenith angle, following approximately equation (16), then they produce the current distribution shown in Fig. 16. Such a system of currents produces diurnal changes in the course of storms,

shown in Fig. 11. As was shown, the theory is acceptable also from the quantitative side. At the same time, the air currents in the ionized regions of the atmosphere, arising at the boundary of illumination and directed from the daytime to the nighttime half of the terrestrial globe, produce irregular magnetic disturbances of considerable strength. It is possible that the increase in the energy of magnetic disturbances observed at high latitudes, as is evident from Fig. 12, is due precisely to these currents.

New observations of the simultaneity of general radio fadings, changes in the ionosphere, magnetic disturbances, and solar eruptions^45 give detailed evidence for the correctness of the ultraviolet theory. However, instead of prematurely seeking final confirmation of the theory, it is better to await the results of future experiments. It is quite probable that many of these phenomena may proceed in a different way; for example, some of the general fadings or changes in the ionosphere may occur without magnetic disturbances or visible phenomena on the Sun, and conversely, only in the case of strongly pronounced phenomena is a causal connection observed between them. The wavelengths of ultraviolet radiation that produce terrestrial phenomena are screened by the atmosphere from direct observations, and consequently they are, as a rule, invisible. And only if the flare is accompanied by long-wave radiation—which, it must be said, is by no means obligatory—can the radiation become evident. Therefore, in a number of cases a flare may escape observation. Finally, the active region during a flare may be a very small point on the solar disk, or a group of such points inaccessible to observation.

Fig. 16. Theoretical distribution of electric currents in the upper layers of the atmosphere, producing diurnal variations of the field during magnetic storms

A very interesting program of observations of prominences, begun in 1928, was carried out by Perepelkin^73 at the Pulkovo Observatory. He found that the ratio \(i\) of the intensity of the \(H_{\varepsilon}\) line of the Balmer hydrogen series to the resonance line \(H\) of calcium varies together with the magnetic activity \(W_D\), as shown in Fig. 17, where \(W_D\) is the daily amplitude of the declination in Slutsk. The correlation between \(i\) and \(W_D\) was greater than between the relative number of sunspots and \(W_D\). This is an entirely new experimental fact, standing apart from the theory. Perepelkin notes that, unfortunately, the new index \(i\) applies only to the edges of the solar disk, where alone the spectrum of prominences can be observed. The mean value of \(i\) turned out ...

practically the same at different heliographic latitudes, but the individual values varied from prominence to prominence, which gave grounds to suppose that the cause of changes in \(i\) is not due to the Sun as a whole. A hypothesis was advanced concerning the existence on the solar surface of spots rich in ultraviolet radiation. If the relative number of hydrogen and calcium atoms is constant, this radiation increases the intensity of \(H_\varepsilon\) to a greater degree than \(H\), which is accompanied by an increase in \(i\).

The Theory of the “Narrow Beam” and of “Broad Undirected Radiation” in Solar Eruptions

Two theories were put forward interpreting the possible form of active solar radiations that give rise to magnetic disturbances. One theory assumes that the solar active radiation is a narrow beam[^74], like a searchlight, while the second assumes that the radiation is something like a volcanic eruption[^64], i.e., is undirected in character. Statistics of magnetic storms[^75],[^76] show that disturbed conditions have a tendency to recur approximately every 27 days, and to explain this Maunder[^74] proposed that the disturbing solar radiation comes from limited regions of the solar surface in the form of narrow beams of rays rotating together with the Sun.

Fig. 17. Relation \(i=\dfrac{H_\varepsilon}{H}\) in solar prominences and magnetic disturbances \(W_D\) according to observations at Slutsk

The synodic period of rotation of sunspots is expressed by the figures 26.9; 27.3; 28.3 days respectively at heliographic latitudes \(0\), \(15\), and \(30^\circ\); the period of rotation of the reversing layer is approximately \(2\%\) smaller. Thus, if the period of rotation of the beam coincides with the period of rotation of the solar surface, then the disturbing foci must be located near solar latitude \(15^\circ\). Assuming that the direct cause of magnetic storms is such rays, and admitting that the radiation propagates with the speed of light, one can calculate the width of the beam, which turns out to be \(13^\circ\) for a storm lasting one day, and \(1^\circ\) for a two-hour magnetic disturbance; at a lower vel—

of the propagation rate the width of the beam correspondingly decreases. An explanation of the “sudden onset” of magnetic storms requires a sharply defined leading edge (front) of the beam. This strict requirement on the form of the beam prompted the brilliant remark of Cree ^77: “The theory put forward hardly does justice to the physical side of the problem, but it is clear and definite and is not obscured by complicated formulations. It is, of course, not sufficiently complete and may be quite erroneous, but it is nevertheless exceedingly attractive...”

The theory of a rotating narrow beam encounters difficulties in various directions. The rotation of the surface of the sun accelerates by approximately 6% during the time from the minimum to the maximum of the number of spots ^78; however, no systematic lengthening or shortening of the 27-day recurrence period has been found either for series of years with a large or small number of spots, or for spots located at high and low latitudes.

It has long been found that magnetic activity is subject to annual variations, following, to a first approximation, a sinusoidal law, with a maximum at the equinox and a minimum at the solstice; moreover, in the period of maximum the number of storms increases almost twofold ^79.

The theory of the narrow beam explains the annual variations by the inclination of the solar axis relative to the terrestrial one, in other words, by annual oscillations of the “heliographic latitude of the earth” ^80.

A rigorous investigation of this theory, carried out by Bartels ^76, showed its untenability; more detailed information may be found in his article. Maris ^79, proceeding from the assumption that the ultraviolet flare produces nondirectional radiation with a wide angle, carried out detailed calculations which led him to a convincing explanation of the annual variations of magnetic disturbances based on the inclination of the solar axis relative to the earth.

At the same time he drew attention to the fact that not all magnetic disturbances are of solar origin, and that at least some of them are caused by the passage of the earth through regions filled with planetary fragments.

Maris and Hulburt ^81 pointed out that observations of comets can be used to judge the width of the active solar radiation. They based this on the fact that solar radiation which causes magnetic storms and auroras on the earth may at the same time be the cause of certain changes in comets.

Observations had been made of many irregular phenomena, apparently not obeying any laws, in the behavior of comets, well known from the history of comets; these include: a sudden increase in brightness, breaking up into separate pieces, the formation of new tails, etc. It was found that in most cases phenomena of this kind followed immediately after magnetic disturbances.

A comparison of the positions of the sun, the earth, and the comet for 28 similar phenomena showed that the mean angle of aperture of the solar

radiation is about \(90^\circ\). A direct connection of phenomena on comets with magnetic disturbances is completely inexplicable in the theory of the “narrow beam.”

On this basis one may conclude that the evidence is in favor of the theory of radiation “at a wide angle” and against the theory of the “narrow beam.” This conclusion, however, leaves unexplained the recurrence of magnetic storms. Especially to explain this, the supposition was advanced that the periodic occurrence of flares is due to a special kind of pulsations of the sun[^81]. Thus both points of view are equally unusual, since they are based on unforeseen properties of solar flares: the theory of the rotating beam requires a physically unfounded narrow ray, while the theory of broad radiation requires a pulsating “geyser-like” action of the sun, whose period by accidental coincidence is almost the same as the period of the sun’s rotation.

Conclusion

Above, the theories of variations of the earth’s magnetic field and the theories of polar aurorae have been considered and compared with one another.

Theories of solar diurnal variations may be based on the dynamo effect, on the phenomena of diamagnetism, and on drift currents. The theory of the atmospheric dynamo requires high values of the conductivity of the upper layers of the atmosphere, at first sight greater than those values which measurements of the ionosphere indicate; however, it cannot be said that observations of the ionosphere definitely exclude such a conductivity. In addition, this theory requires a general circulation of the air in the upper layers of the atmosphere, as if the air were spreading in all directions from the region situated beneath the sun. Such a system of currents is, generally speaking, possible; however, its existence has not been proved. The diamagnetic theory likewise requires an ionization greater than that which had been assumed; here too, however, observations of the ionosphere do not definitely reject the possibility of such ionization. This theory is simpler than the theory of the atmospheric dynamo, since it does not require a general circulation of the atmosphere. The theory of drift currents, as was shown, requires a distribution of ionization in the atmosphere that is in contradiction with the hypothesis according to which ionization is caused by the ultraviolet radiation of the sun. The data of the ionosphere are in agreement with this theory.

The only theory of lunar variations of terrestrial magnetism is the dynamo theory, which holds that the influence of the moon is caused by tidal motions in the upper layers of the atmosphere. Calculations based on observations of oscillations of atmospheric pressure at sea level lead to the correct character of the magnetic lunar variations, which, however, differ in phase from the observed variations. This discrepancy appears serious and has so far received no explanation.

Theories of magnetic storms and auroras are based on the assumption that these phenomena are caused by streams of charged particles emanating from the sun or by ultraviolet radiation. A complete corpuscular theory consistent with the observed phenomena has not been proposed.

Various incomplete theories have encountered fundamental difficulties which they have never been able to overcome; for example, because of the electrostatic repulsive forces acting along the path from the sun to the earth, a stream of charged particles cannot possess, at the earth, energy sufficient for a noticeable disturbance of the earth’s magnetic field. The theory of ultraviolet radiation successfully explains the complex changes in the earth’s magnetic field during storms: auroras, the penetration of auroras during strong storms into low latitudes, the delay in the appearance of auroras after the onset of storms, and other observed facts. Recent observations of the ionosphere, of radio-wave propagation, and of solar eruptions have shown that in a number of cases the solar radiation causing various phenomena on the earth propagates, within the accuracy of the observations, at the speed of light, which has served as a new and substantial confirmation of the ultraviolet theory.

The recurrence of magnetic disturbances may be explained by hypotheses according to one of which the solar radiation causing the disturbance is emitted by the sun in the form of a narrow beam, no wider than \(10^\circ\), rotating together with the sun; another hypothesis assumes that the eruption occurs over a wide angle and is periodically repeated. Both theories are equally unusual, since they are based on unexpected properties of solar flares: the theory of the rotating beam requires a physically unjustified thin ray, while the theory of wide emission requires repeated geyser-like action or pulsation. Observations of terrestrial phenomena and of comets provide evidence favorable to the theory of wide emission and unfavorable to the theory of the narrow ray.

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1. By electron concentration, here and below, is meant the number of electrons in \(1\ \mathrm{cm}^3\). Translator’s note. ↩↩