PHYSICS OF THE UPPER ATMOSPHERE*

J. Bartels, Eberswalde

1. Aerology. 2. High clouds. Twilight. 3. Geometrical picture of radiation. 4. The light of the night sky. 5. Falling stars and meteors. 6. Ozone. 7. Propagation of sound. 8. Composition and pressure. 9. Data of terrestrial magnetism. a) General remarks. b) Periodic diurnal variations. c) Magnetic storms. d) Dependence of magnetic disturbances on processes on the Sun. 10. Ionizing action of monochromatic radiation. 11. Summary. 12. Concluding remark. 13. Literature.

No instrument has so far risen higher than 36 km. What we know about the higher layers is based on various kinds of indirect observations, which in most cases amount to a patient, more or less passive following of large-scale experiments carried out, for example, by the Sun or the Moon. These experiments, performed by nature itself, differ fundamentally in their setting from laboratory experiments: namely, in nature the experimental conditions—the geographical position, the time of day and year, solar radiation, the influence of terrestrial magnetism—change from case to case. In such cases, typical for geophysics, the effects of individual variables can be separated from one another only by suitable statistical treatment of a sufficiently large number of observations.

At the end of the present survey I shall dwell in somewhat greater detail on the interpretation of phenomena in the upper layers of the atmosphere from the point of view of terrestrial magnetism, since the treatment of the extensive observational material on terrestrial magnetism may in many respects serve as a prototype for the formulation and significance of experiments with electromagnetic waves, and since such geophysical methods, lying between observation and theory, are often rather far removed from pure or technical physics.

Leaving aside the aurorae proper and electromagnetic waves, which are discussed in separate reports, we must first briefly consider certain other phenomena on the basis of which conclusions can be drawn about the physics of the upper layers of the atmosphere. The most interesting from the standpoint of radio—

* J. Bartels, Überblick über die Physik der hohen Atmosphäre; a lecture delivered on September 21, 1932, at a meeting of the Heinrich Hertz Society in Bad Nauheim, “ENT,” special issue, 1933. Translated by V. V. Furduev.

...for technology, part of the Earth’s atmosphere lies no lower than at an altitude of 50 km; since, however, this part rests upon the underlying layers, whose physical state affects it, we shall also have to speak of the lower layers.

1. Aerology

Airplanes or aerostats carrying people have reached altitudes of approximately about 10 km; Piccard, in his free balloon with an airtight gondola, twice reached an altitude of 16 km. Up to the present time, only unmanned aerostats have risen to greater heights. The directions of winds in the high layers can be found from observations of the motion of clouds while simultaneously determining their altitude; a fuller picture is given by small pilot balloons observed with a theodolite. Temperature, pressure, and humidity can be determined by means of larger balloons capable of lifting light recording meteorographs. These balloons are filled with several cubic meters of hydrogen; as they ascend they expand more and more until the thin rubber envelope bursts at its weakest point; from this highest point of ascent the meteorograph descends by parachute. Many such balloons have risen to more than 20 km; with improvement and careful testing of the rubber envelope before ascent, already in 1914 in Batavia, and recently also in Germany, an altitude of over 30 km was reached, in one case even over 35 km* ^6,7.

The principal result of these experiments was the well-known division of the atmosphere into two parts ^8,10. In the lower part, the troposphere, the temperature regularly decreases with altitude by approximately 4–8°/km; clouds almost always form only in this layer. In the overlying stratosphere the temperature changes only slightly with altitude. The boundary surface between the troposphere and the stratosphere lies at the equator at an altitude of about 16 km, in central Europe at an altitude of 10.5 km, and at the poles still lower. At an altitude of 21 km, where the air pressure on average amounts to no more than \(1/20\) of the pressure at ground level, the stratosphere over the equator (−80°C) is colder than over central Europe (−55°C).

This subdivision of the atmosphere into two parts was established on every ascent. However, the altitude at which the stratosphere begins fluctuates at the same location, varying by several kilometers. Under ordinary meteorological conditions the air pressure, as is known, is proportional to the mass of the atmosphere above the barometer; more precisely, the weight of the column of mercury in the barometer is equal to the weight of a column of air of the same cross-section. Radiation of known penetrating power, falling vertically...

* On September 30, 1933, the stratospheric balloon “USSR” rose to an altitude of 19,000 m, i.e. 3 km higher than Piccard, thereby setting a world altitude record. — Ed.

still in the atmosphere from outside, reaches a certain surface of equal pressure (Isobarenfläche); thus changes in the height of this surface find their reflection in analogous fluctuations of the depth of penetration of the radiation. A. Schedler (Schedler)\(^{9}\), using data from European ascents of recording instruments, calculated the absolute value of the mean change in pressure over a series of days (daily variability) and found the same value at all heights up to 13 km—about 3 mm. The greatest and smallest values of air pressure over the course of an entire year differ from one another by more than 10 times the daily variability; at the earth’s surface—by 30 mm, which corresponds to a change in the height of the surface of the 760-millimeter isobar by 330 m. It may be assumed that also at a height of 13 km over Europe the air pressure, equal on average to 123 mm, may in exceptional cases differ from this value by \(1/4\). Accordingly, the surface of equal pressure may shift upward and downward by approximately 1500 m. Within the range of heights reached by balloons carrying recording instruments, the vertical oscillations of surfaces of equal pressure increase considerably with height. This is only an expression of the fact that at heights up to 10 km, over regions of low pressure on the weather map, the atmosphere is, as a rule, colder, and over regions of high pressure—warmer than normal; therefore the difference of pressures increases with increasing height. Taking into account temperature changes and observations of ozone, one may think that at a height of 100 km the surfaces of equal pressure over a series of days descend and rise by many kilometers. This, perhaps, unexpectedly explains the two maxima at a separation of 5 km in altitude which Störmer (Störmer)\(^{101}\) found for the frequency of auroral heights; however, these data are based on a relatively small number of observations (22 evenings in Oslo, 1911–1922), in which the element of chance has probably not been eliminated.

The acceleration acquired by particles of air is directly proportional to the pressure gradient and inversely proportional to the density of the air. By the term “gradient wind” is meant that ideal case in which the wind blows perpendicular to the direction of the gradient, i.e. along an isobar, with such a speed that the accelerations due to the gradient and to the Coriolis force balance each other. Outside the influence of friction at the earth’s surface, i.e. at a height of about 1 km, the wind, in general, has a magnitude of the order of the gradient wind. Since at a certain definite height the mean change in pressure from one day to another is approximately proportional to the mean horizontal pressure gradient at that height, from observations of the daily variability of pressure one may conclude that up to a height of 13 km the pressure gradients have one and the same order of magnitude; the mean strength of the wind must therefore increase with height—

which is inversely proportional to the density of the air. Observations confirm this supposition: in Potsdam[^11] in summer the speed of cumulus clouds at a height of 2 km averages 8 m/sec, the speed of cirrus clouds at a height of 9 km is 21 m/sec. The greatest cloud speeds observed at the level of stratocumulus clouds (about 2 km in height) are around 35 m/sec; at the level of cirrus clouds (about 10 km in height), from 70 to 100 m/sec. Knowledge concerning winds in the stratosphere is not very systematic, since observations with pilot balloons at such a great height are possible only when the lower layers are clear and relatively calm.

2. High Clouds. Twilight

On thin high cumulus clouds near the sun, a coloring of the edges is sometimes observed, which is explained by the refraction of light in water droplets. Such clouds usually also appear at their normal height, about 4 km. Much rarer and more striking are iridescent clouds, glowing with pure colors. In 1871–1892 they were repeatedly observed in Norway. In recent years they have again been observed by Størmer[^12], who determined their height by a photogrammetric method he had developed for determining the height of aurorae. The following heights were thereby determined with certainty: 27 km (30 December 1926), 23–26 km (13 January 1929), and from 20 to 30 km in numerous observations in January and February 1932. From the apparent radius (18°) of the red ring of the lunar halo once observed on these clouds, Størmer concludes that the diameter of the cloud particles does not exceed 0.0025 mm. The horizontal speed of the clouds on 30 December 1926 was determined as 75 m/sec, whereas on 13 January 1929 no noticeable horizontal motion at all was present. Størmer considers it possible that iridescent clouds are rather frequent over large areas of low pressure, but that they are rarely visible—for example, only where a warm föhn wind gives an opportunity to see them through the lower cloud cover.

In 1885–1891, from mid-May to June in Berlin, bright silvery clouds were visible even at midnight. Størmer, who observed similar clouds in 1889 in Norway and saw them again in July 1909 and July 1932[^24], describes them as “bluish-white, without any hint of the spectral coloration so characteristic of iridescent clouds.” Jesse (O. Jesse)[^13] photographed these clouds simultaneously at various places (Berlin-Steglitz, Rathenow, Nauen); from the displacement of the clouds relative to the stars he found their height to be from 82 to 83 km. Their height was extraordinarily constant. From year to year the brilliance of the clouds weakened; finally, waviness could be distinguished on them, similar to that of cirrus clouds. The clouds usually moved from east to west at a speed of about 100 m/sec.

Similar anomalously high clouds were observed also in subseq-

stria 14–24. Kerven (A. de Quervain) 14 calls them “ultra-cirrus.” In July 1932 Størmer 24 succeeded in photogrammetrically determining their altitude, which reaches 70–80 km.

Luminous night clouds in 1890 were probably connected with the powerful eruption of the Krakatoa volcano in the Sunda Islands (1883). In connection with this eruption, twilight phenomena were observed over the entire globe. Ordinary evening twilight disappears when the sun descends below the horizon by approximately 16°; a simple geometrical consideration shows that the last twilight gleams of scattered sunlight in the west must occur at an altitude of about 60 km. The brightness and coloration of twilight are not distributed continuously 25; experienced observers distinguish separate “twilight arcs,” which may be regarded as a consequence of the layered structure of the atmosphere; the difficulties of the theory of atmospheric scattering do not permit precise conclusions. Two post-twilight arcs observed by Wegener (A. Wegener) 26 in Greenland are attributed by him to scattering of light at an altitude of more than 700 km. It may be supposed that zodiacal light 27–29 also belongs to twilight phenomena in the very high parts of the atmosphere.

The anomalous twilights mentioned above also occurred after subsequent volcanic eruptions, for example after the eruption of Katmai (Alaska, June 1912) 17; the crimson Bishop’s ring around the sun was especially striking. Newspaper reports of the gigantic eruption in the Andes (summer 1932) mention enormous masses of ash ejected by the volcano. It is believed that the ash was thrown high into the stratosphere, whence it descended only very slowly, over the course of weeks or months, being dispersed by winds over the whole earth. This supposition simply explains the phenomenon of anomalous twilights. By contrast, the nature of luminous night clouds still remains unknown. Wegener 18 considers it entirely possible that they are cirrus-like ice clouds formed from the normal water vapors of the atmosphere; Lindemann and Dobson (Lindemann, Dobson) 19, on the contrary, assert their direct connection with large volcanic eruptions, during which the ejected water vapor, mixed with hydrogen and methane, is carried by light particles and by a heat current into the upper layers, where it condenses into ice clouds.

As early as 1891, Hesse not without reason complained of the “small participation of the learned world in the study of this remarkable phenomenon”; unfortunately, during the subsequent 40 years the night clouds were not subjected to photogrammetric measurements, until Størmer 24 did so in July 1932.

One of the most remarkable twilight phenomena was connected with the fall of the great Siberian meteorite 30 (30 June 1908, 0h15m after Greenwich midnight, 61° N lat., 101°.3 E long.). In 1927 the Russian expedition of L. Kulik found

the place of fall in a crater-like depression, where meteorites were found in numerous pits. In the central zone all vegetation was scorched; at distances up to 60 km trees were felled outward. Kulik assumes that the cloud of incandescent gas in front of the meteorite reached the earth together with it, where it also spread out to the sides. The seismic waves of air pressure1 were clearly recorded in Siberia and Europe. On the evening of June 30, as well as on July 1 and 2, unusually bright nights were observed in Europe, the brightness of which gradually decreased over the course of three weeks. This phenomenon is probably explained by the scattering of sunlight by highly suspended particles; however, the connection with the fall of the meteorite was first established only 20 years later. In Aberdeen (Scotland) the glow

Fig. 1. Solar sunrise in a free atmosphere along a meridian. The lines connect points at which the sun rises at a definite hour.

arose suddenly after 22ʰ Greenwich time; in Heidelberg, on the night of June 30 to July 1, it was impossible to photograph Venus, since already at 1ʰ 15ᵐ it was bright day. At the same time, luminous nocturnal clouds of wavy form were observed many times; they must have been moving from the east at a speed of about 80 m/sec at an altitude of at least 50 km.

3. Geometrical Picture of the Radiation

The boundary of the shadow in the atmosphere is a cylindrical surface. The height \(h\) at which the boundary of the shadow passes after sunset at the zenith of a place depends only on the angular depression \(\eta\) of the Sun below the horizon. If the Earth is taken to be a sphere of radius \(a\), then

\[ h = a\left(\frac{1}{\cos \eta} - 1\right). \]

Owing to refraction, the Sun on the horizon appears to an observer on the surface of the Earth shifted upward by approximately \(0^\circ.6\).

PHYSICS OF THE HIGH LAYERS OF THE ATMOSPHERE

Since the last ray of the setting Sun, before and after touching the earth’s surface, passes symmetrically, it may be assumed that at great heights—above 50 km—the setting Sun appears displaced upward by \(1^\circ.2\). The astronomical altitude of the Sun is referred to the center of the solar disk; from the point of view of illumination it is more interesting to know when its upper edge disappears. Therefore in Figs. 1 and 2, where sunrise in a free atmosphere along the meridian is shown (the lines connect the points at which the Sun rises at a definite hour), the boundaries of the shadow are represented in such a way that they connect those points along a certain meridian at which the upper edge of the Sun appears at a definite moment of true time; Fig. 1 refers to the time of the solstice, Fig. 2 to the time of the equinox. From these are constructed Figs. 3 and 4, which are schematic maps of the morning side of the Earth (between \(0^h\) and \(12^h\)); the meridians are designated here by their true local time. The curves connect points (on the surface of the Earth and at altitudes of 50, 100, 250, 500, and 1000 km),

Fig. 2. The same as Fig. 1.

Figs. 3 and 4. Maps of the hemisphere between the midnight and noon meridians. The meridians are designated by their true local time. The lines connect points of sunrise on the surface of the Earth, at altitudes of 50, 100, 250, 500, and 1000 km.

at which sunrise is observed. The relations on the evening side are symmetric with respect to these data. Fig. 5 gives the altitude of the boundary of the shadow at midnight, for various circles

latitudes. North of the northern boundary of Germany (about \(55^\circ\)) the atmosphere in the middle of summer is illuminated at midnight already beginning at an altitude of 100 km. Of course, for kilometers directly above the boundary of the shadow, solar radiation is very much weakened owing to the great length of the path traversed in the Earth’s atmosphere; likewise, clouds and mountains can shift the boundary of the shadow upward by several kilometers. Particularly noteworthy is the great difference between sunrise and sunset at the Earth’s surface and at altitude in the polar regions; for many hours there, every night, luminous nocturnal clouds are possible, as are rays of the polar aurora illuminated by the Sun.

Fig. 5. Height of the boundary of the solar shadow at midnight at latitudes \(40\)—\(90^\circ\) during the year.

Meteorologists are well aware that on a summer day the pole receives more than 30% more solar radiation than a place lying on the equator. Here the comparison is of the integral radiation passing through a unit horizontal surface “outside” the atmosphere (Fig. 6). Of course, the radiation observed at the Earth’s surface, owing to the considerable weakening, during passage through the atmosphere, of the rays of the low-standing Sun at the pole, is less than at the equator. Thus this well-known fact, relating to the so-called “solar climate,” has no significance for the climatology of the lower layers of the air, just as do the numerous calculations \(^{32—34}\) relating to the distribution of solar radiation on Earth and abstracting from the influence of the air envelope. On the contrary, the calculations underlying Fig. 6 are applicable, without substantial changes, to the question of the geographical distribution of the intensity of those components of solar radiation which are wholly or partly absorbed by the upper layers of the atmosphere \(^{10}\).

In the period of nearness to the Sun (beginning of January) the intensity of solar radiation is \(1/15\) greater than the mean value, than in the period of remoteness from the Sun (beginning of July). At the mean distance of the Earth from the Sun, the radiation through a surface outside the atmosphere, perpendicular to the direction of the rays, reaches \(1.93\ \mathrm{cal}/\mathrm{cm}^2\,\mathrm{min} = 1.35 \cdot 10^6\ \mathrm{erg}/\mathrm{cm}^2\,\mathrm{sec}\) (the solar constant).

4. Light of the Night Sky

In addition to the light of the stars and the Moon, the night sky emits a faint glow[^43], in which the green line of the aurora (5577.3 Å), belonging to the oxygen atom, is expressed so distinctly that it can be observed on every not entirely cloudy night[^35]; in an interferometer it gives a distinct system of rings[^36]. In addition, the night sky also emits a continuous spectrum, the energy distribution in which was measured by Lord Rayleigh (Rayleigh)[^37]–[^39], McLennan (Mc. Lennan)[^45] and Dufay[^42],[^47]. According to Rayleigh’s measurements, made with filters, the light of the night sky is relatively richer in red rays than the blue light of the daytime sky. The green light emitted by the night sky Rayleigh calls “non-polar aurora,” since this phenomenon is not confined to the polar regions, but is also observed in the tropics. The spectrum of a true polar aurora must, according to Rayleigh, be characterized, along with the green line, also by the bands \(N_2^+\), absent in the light of the night sky. Sommer’s (L. A. Sommer) single observation in Göttingen is not yet a decisive contradiction to Rayleigh’s opinion[^46]; however, according to Dufay’s most recent spectral measurements[^47], the nitrogen spectrum, as a rule, is present in the glow of the night sky, although it is expressed very weakly.

Fig. 6. Total radiation received from the Sun by a horizontal surface of \(1 \text{ cm}^2\) outside the atmosphere during the day. “Equatorial hour” is the energy received by an area of \(1 \text{ cm}^2\) at the equator with the Sun at the zenith over the course of an hour. On the right are the daily amounts in ergs, calculated from the solar constant \(1.93\ \text{cal}/\text{cm}^2\ \text{min} = 1.35 \cdot 10^6\ \text{erg}/\text{cm}^2\). The variable distance to the Sun has been taken into account (according to Hessler).

Variations in the intensity of the light of the night sky during the night and the year, both systematic and irregular in character, have been observed repeatedly[^37]–[^40]. Thus, Lord Rayleigh[^44], on the night of November 8 to 9 in Essex, under a clear moonless sky, recorded a fourfold increase in intensity compared with the normal value, with an unchanged distribution of light in the red, green, and blue regions. On the basis of observations in England, South Africa, and Australia, Jones (H. S. Jones)[^40] believes that further

observations should also reveal a connection between the fluctuations in the intensity of the light of the night sky and the aurora proper.

The absolute intensity of the green line in the light of the night sky was measured by Rayleigh ^41; his measurements, reduced to quanta of the corresponding magnitude (2.22 V), indicate that, on average, each square centimeter of the earth’s surface receives per second \(1.8 \cdot 10^8\) oxygen atoms undergoing transitions associated with the emission of the green line. Chapman ^1 believes that this energy is of solar origin, being stored in the atmosphere during the day and slowly expended during the night (cf. § 11).

5. FALLING STARS AND METEORS

By means of simultaneous observation of falling stars from two points, abundant material has been collected concerning the heights at which they flare up and disappear, as well as concerning their velocity. Lindemann and Dobson ^48,49 made an attempt, on the basis of these data, to draw conclusions about the state of the atmosphere at great heights. As a typical case they consider a falling star that flares up at a height of 100 km, traverses a path of 60 km at a velocity of 40 km/sec, and disappears at a height of 80 km, while to an observer at a distance of 150 km the falling star appears as bright as a star of the 1st magnitude. Under certain assumptions they obtained, for a falling star consisting of iron, a diameter of about 1 mm. Owing to the compression of the air displaced by the falling star, it becomes incandescent and evaporates at a temperature of from 2000 to 2500°. The theory of this process leads Lindemann and Dobson to an estimate of the density of the air. Since the density of the air at a given height depends essentially on the rarefaction (Auflockerung), i.e., on the temperature of the underlying air masses, it is also possible to estimate this factor. The assumption that the aerologically observed temperature of the stratosphere (220° abs.) also prevails at greater heights leads, however, to excessively small air densities at the height of falling stars. Therefore Lindemann and Dobson consider it probable that at a height of about 50 km the temperature rises to 300° abs.

Against this opinion Sparrow ^50 raised objections, leading to excessively high values of density and temperature. He considers the cause of the heating of the falling star to be collisions between it and the molecules of the air. Radakovic ^51 set forth both theories thoroughly and critically; in his opinion—also supported by Vegener ^53—the nature of the phenomena relating to falling stars has not yet been sufficiently clarified to draw from them conclusions about the rarefaction of the atmosphere. Maris (H. B. Maris) ^52 likewise does not draw conclusions about the density of the atmosphere from his theory of falling stars.

Sometimes an appearing meteor leaves behind a trail that can be observed for several seconds, and in isolated cases—even for hours. Kahlke[^51] collected and discussed observational material. The altitude of smoky trails (Rauchschweif), visible by day, lies between 30 and 80 km, whereas the more frequent nocturnal luminous trails preferentially choose an altitude between 80 and 120 km. The trails change their appearance during the time of their visibility. From the general picture of the winds one can also infer the direction of the wind at altitude. Below 80 km easterly winds predominate (as also in observations of luminous night clouds); the higher nocturnal trails indicate variable directions. In any case it seems that at altitudes of about 100 km the wind direction changes greatly depending on the place, and perhaps also on the time.

For the Siberian meteorite see § 2; a not very convincing attempt to establish a connection between swarms of shooting stars and magnetic disturbances is mentioned in § 9d.

6. Ozone

The spectrum of the sun and stars breaks off rather sharply in the ultraviolet part. Under favorable circumstances it has once been possible to reach 2863 Å. The short-wave spectrum breaks off the farther away, the lower the luminary stands in the sky, i.e. the longer the path of the light in the atmosphere. Making use of various considerations advanced by Fabry and Buisson[^50] in 1913–1921, it was convincingly proved that the limitation of the spectrum is due to absorption bands of atmospheric ozone[^55–^60]. If all atmospheric ozone were gathered into a horizontal layer at 0° C and atmospheric pressure, the thickness of this layer would be a full 3 mm, which corresponds to \(10^{19}\) molecules of \(O_3\) per \(1 \text{ cm}^2\) of the earth’s surface. Thus the partial pressure of ozone is only \(1/2000\) mm Hg; ozone occupies \(1/3000000\) of the volume of the entire atmosphere. In 1918 Lord Rayleigh[^64] was still able to photograph the mercury line 2536 Å (from a mercury lamp) at a horizontal distance of 6.4 km. Thus the location of ozone should be sought at great heights. Since then, on Dobson’s initiative, a large number of systematic measurements were undertaken in various places on the earth, with both the quantity and the height of ozone being determined. Detailed reports on the methods of measurement and on the results are set forth elsewhere[^55,^56]. The main results amount to the following.

The amount of ozone varies from day to day. In 1925, on February 28, Dobson’s measurements in Oxford gave 3.7 mm, and on March 7—2.4 mm; the absolute greatest and smallest values measured in Oxford are 4.2 and 1.7 mm. At the same time a connection with the weather was clearly revealed: namely, the values change in oppo-

is opposite to changes in pressure at the Earth's surface: large values are observed in regions of low pressure, small ones in regions of high pressure. Similar changes over the whole Earth have not been proved. Nor has the regularity of the diurnal variation and the difference between day and night been reliably proved; on the contrary, an annual variation is clearly expressed outside the tropics: in both hemispheres large values are observed in spring, small ones in autumn. For example, at Arosa the mean value for 1926–1929 was 3.1 mm in April and 2.2 mm in October. Spring values at polar stations exceed 3.5 mm, while at equatorial stations they fluctuate only slightly around 2.1 mm. The center of gravity of the ozone layer lies (in temperate latitudes) at an altitude of 40–50 km; Götz found in Spitsbergen an altitude of only 25 km. Chalogne (D. Chalogne) ^69a warns against a literal understanding of the expression “ozone layer”: in reality ozone is distributed at an altitude between 20 and 80 km.

Recently ^61 Götz and Ladenburg, as well as Fabry and Buisson, have more accurately determined by an optical method the insignificant ozone content in the lower part of the atmosphere; the values, calculated per kilometer of a horizontal section of air, increase from 0.015 mm on the plain to 0.029 mm at Arosa.

Already Lindemann and Dobson ^4, ^48, ^49 substantiate the assumption of a higher temperature of the ozone layer by its strong absorption of ultraviolet rays. The course of the reasoning ^65 is roughly as follows: each layer of the Earth’s atmosphere is under the action of two fluxes of radiation with entirely different ranges of wavelengths: the direct radiation of the Sun, with a maximum in the visible part, and the long-wave radiation of the Earth’s surface and of other atmospheric layers. A layer of gas that absorbs only waves of certain lengths emits waves of the same lengths and, moreover, if the layer is sufficiently thick, emits them as a black body with the temperature of the gas. Even if the radiant energy is uniformly distributed over a broad range of wavelengths, a gas absorbing the ultraviolet band of the radiation flux must have a higher temperature than a gas absorbing infrared rays—on the assumption that the absorbed energy is returned in the form of temperature radiation. These considerations explain, generally speaking, the low temperature of the stratosphere (220° abs.) by the infrared absorption band of water vapor and carbon dioxide, taken by these gases from the Earth’s radiation; on the contrary, the ultraviolet bands absorbed by ozone from solar radiation must, in equilibrium with radiation, give a higher temperature, estimated at 300° abs. When several absorption bands are present—in particular, ozone has a band at 9.5 μ—the relations become less simple. Gowan (E. H. Gowan) ^62 calculated the equilibrium distribution for various vertical distributions of ozone and water vapor; beginning with 30 or 40 km, depending on

of the assumptions made, the temperature rises to approximately 80 km to about 400° abs., and at greater heights may perhaps be still higher. Rosseland (S. Rosseland)57 and others objected to these calculations, since the transformation of the energy of absorbed ultraviolet rays into thermal motion is conceivable only with frequent collisions, but by no means when the average duration of stay in the excited state is less than the time between two successive collisions. Ladenburg and Meyer (E. Meyer)57 further point out that under atmospheric conditions the structure of the bands may differ greatly from that which corresponds to laboratory observations on concentrated O₃.

We have no indications that ozone in the layer of greatest concentration directly affects the ionization of the atmosphere and the propagation of electromagnetic waves. Therefore, for the electrophysics of the high layers of the atmosphere, the only circumstance of importance is that the temperature of the ozone-containing layer may be higher than the temperature of the lower-lying stratosphere, owing to which the surfaces of equal pressure rise. In addition, the presence of ozone sheds light on the question of whether atomic oxygen exists in higher layers, which, according to Chapman’s supposition1, supplies ions to the upper ionized layer (220 km). This question, in connection with the question of ozone formation, will be considered in § 11.

In any case, the connection between ozone content and weather—if this connection really exists and is not distorted by phenomena of turbidity in the troposphere (Tepler69)—allows one to conclude indirectly that changes in ozone content are connected rather with the lower than with the upper layers of the atmosphere. Otherwise a connection would have been established between the weather not only and the ozone content, but also with processes in the higher layers, which should have manifested itself in magnetic disturbances; meanwhile, the colossal body of observations of terrestrial magnetism does not provide a single convincing example of a connection with the weather.

7. Propagation of Sound

The propagation in the atmosphere of the sound of an explosion is characterized by the following long-known feature: the sound is audible in the vicinity up to a distance depending on meteorological conditions; at distances exceeding 50 km, audibility disappears. It is striking that this “zone of silence” has an outer boundary: at distances greater than 110–190 km the sound is again heard well. Systematic observations of the travel time of sound from artificial explosions have shown that the occurrence of zones of silence is typical. The dependence of travel time on distance, represented in the form of a curve, makes it possible to draw conclusions (using methods developed

for the study of earthquake waves) with respect to the path of sound rays and the speed of sound at the highest points[^70-74][^78]. Thus, for “anomalous sound,” reaching the outer zone of audibility, limiting heights of 40–50 km and sound velocities at these heights of 350–370 m/sec were found.

The speed of sound is equal to

\[ v=\sqrt{\frac{\chi RT}{M}} \]

(\(\chi\)—the ratio of specific heats, \(R\)—the universal gas constant, \(T\)—absolute temperature, \(M\)—molecular weight); to this speed is also added the wind speed. For air (\(M=28.95\)), at temperatures of \(-55^\circ\text{C}\), \(0^\circ\), and \(+40^\circ\text{C}\), \(v\) is respectively equal to 299, 331, and 354 m/sec. The greater velocities of normal sound at altitude could thus be explained by higher temperatures in the upper part of the stratosphere. The mean values obtained in this way from several German[^70] and English[^82] measurements are presented in Fig. 7. Together with this, the generally known fact is also explained that on clear windless nights sound near the earth’s surface propagates especially far; on such nights, a layer of cold air forms at the radiating surface of the earth, above which the air is many degrees warmer.

Fig. 7. Temperature of the upper stratosphere according to observations of sound propagation. \(E\)—English data (after Whipple), \(D\)—German (after Duckert).

This view is supported by considerations on the basis of which the temperature-increase effect is attributed to ozone, whose maximum concentration corresponds to the same height. However, objections to this temperature hypothesis have still not been overcome. First of all, attention is drawn to the influence of wind, whose direction and strength, generally speaking, change with height, which undoubtedly has substantial significance for the propagation of sound. The wind hypothesis cannot be considered decisively refuted by observations; in any case, the temperature hypothesis explains the phenomena with less strain; in particular, it explains the observed cases of a closed ring-shaped form of the outer zone of audibility. Much more substantial is Kölzer’s indication[^76] that the bending back (Rückleitung) of sound toward the earth, even at short distances, cannot be explained by the known laws of refraction and reflection.

The older view, which connected the increase in the speed of sound not with an increase in temperature, but with a decrease in mole-

...of molecular weight is now abandoned; it cannot be admitted that already at an altitude of 40 km there is so much hydrogen or helium that this could have a substantial influence on the speed of sound.

It may be that further indications concerning the state of the upper stratosphere, at altitudes up to 50 km, may be expected from aerial photography. Of great interest are Whipple’s observations2, processed by him, of the zone of silence during the detonation of meteors. Altitudes exceeding 80 km cannot be reached by artificially produced sound waves, since the attenuation there is too great3.

8. Composition and Pressure

All the older works proceeded from the assumption that in the lower atmosphere the gases are mixed sufficiently well for the proportion in which the principal constituents are mixed to remain constant, but that in the stratosphere convection, as indicated by the absence of a vertical temperature gradient, is insignificant. It was therefore assumed that, beginning at a known altitude, the turbulence of the atmosphere is insufficient to prevent the vertical stratification of the individual constituents according to their molecular weight. Starting from this level, the composition of the atmosphere should change continuously with height, since in a gas mixture at rest in a gravitational field each constituent is distributed with height as if it alone were present.

The basic equation of statics gives, for the change in pressure of a homogeneous gas with height \(h\) above the Earth’s surface:

\[ dp = -g\rho\, dh \]

(\(p\) is pressure, \(g\) is the acceleration due to gravity, \(\rho\) is density). Since

\[ p = \frac{R\rho T}{M} \]

(\(R\) is the absolute gas constant, \(T\) is absolute temperature, \(M\) is molecular weight), the first equation may be rewritten as:

\[ \frac{dp}{p} = -g\frac{M}{RT}\, dh. \]

The distribution can most easily be described by means of the concept of the “height of a homogeneous atmosphere”

\[ H = \frac{RT}{gM}. \]

An atmosphere with uniform temperature \(T\) and pressure at the earth’s surface \(p_b\) would have, near the surface, the density

\[ \rho_b = p_b \frac{M}{RT}. \]

Let us imagine an incompressible hypothetical “homogeneous atmosphere,” having at all heights the density \(\rho_b\) and exerting on the earth the pressure \(p_b\). For such a homogeneous atmosphere the fundamental equation of statics in its first form would read

\[ \frac{dp}{dh} = -g\rho_b. \]

Corresponding to the constant decrease of pressure, the pressure would reach zero at the height

\[ H = \frac{P_b}{g\rho_b}, \]

which, according to the gas equation, also gives the right to write \(H = RT/gM\). Thus \(H\) depends only on the molecular weight and on the temperature of the gas.

Let us denote the value of \(H\) at \(T = 273^\circ\) by \(H_0\); then

for air \(H_0 = 7.99\) km	for carbon dioxide \(H_0 = 5.23\) km
for nitrogen \(H_0 = 8.26\) km	for water vapor \(H_0 = 12.8\) km
for oxygen \(H_0 = 7.23\) km	for helium \(H_0 = 58\) km
for argon \(H_0 = 5.80\) km	for hydrogen \(H_0 = 115\) km.

After introducing \(H_0\), the fundamental equation of statics is written as

\[ d(\ln p) = -\frac{273}{T}\frac{dh}{H_0}. \]

If \(T\) changes little in the height interval under consideration, then the common logarithms of the pressure decrease by one unit at each height step equal to \(2.30\,H_0 \cdot T/273\). In a rectangular coordinate system (\(\lg p\) along the abscissa and \(h\) along the ordinate), the pressure in any isothermal height interval would be represented by a straight line, the slope of which has just been indicated. If, however, \(T\) changes with height, then the curve of pressure decrease may be constructed, by graphical integration, from separate segments of such straight lines, with the mean temperatures being taken for the correspondingly selected height intervals.

In light gases the pressure decreases more slowly than in heavy ones. For example, at \(T = 273^\circ\), when rising to 264 km, the pressure of hydrogen falls to \(1/10\) of the pressure at the earth’s surface, the pressure of helium—to \(1/100\), while for atmospheric air it is less than \(10^{-14}\) of the initial value. In a state of diffusive equilibrium, beginning from some definite height, light gases must finally predominate, even if near the surface they were present only in a very small percentage amount.

In one of their earlier works Chapman and Milne (Milne) ^84 considered this view and the consequences following from it; in this connection, for the lower atmosphere their calculation gives, in volume units, for He \(1/250000\), and for \(\mathrm{H}_2\) \(1/1000000\); or, in units of mass, \(1/1800000\) for He and \(1/1400000\) for \(\mathrm{H}_2\). The content of water vapor in the atmosphere varies greatly, but in calculating pressure in the high layers it may be neglected, since at the low temperatures at the base of the stratosphere it cannot exceed, by volume, \(1/8000\). Likewise the mass of ozone is too small to affect the pressure distribution. The amount of carbon dioxide in the lower atmosphere varies, amounting roughly to \(1/3000\) in volume units; in the high layers it is absent by virtue of its high molecular weight. In the lower atmosphere ammonia occurs in an amount up to

Fig. 8. Number of molecules in \(\mathrm{cm}^3\), calculated on the assumption that above an altitude of 20 km convective mixing is absent and a temperature of \(-54^\circ\)C prevails.

Fig. 9. Percentage composition of the atmosphere under the same assumptions as in Fig. 8, but without hydrogen.

\(1/60000000\) by weight; owing to its small molecular weight it might acquire importance at great altitudes; however, since the spectrum of the aurora gives no indication of this, ammonia may also be neglected. Figs. 8 and 9* show the results of the assumption according to which, above 20 km, diffusive equilibrium prevails and the temperature of the stratosphere is everywhere \(-54^\circ\)C. Since partial pressures add, in Fig. 8 the line of total pressure coincides with the line of greatest partial pressure. Further calculations lead to the following conclusions: at an altitude below 100 km the pressure and composition depend little on whether light gases are present in the atmosphere and at what altitude the mixing ceases—

* Figs. 8–11 are intended only to illustrate the significance of different assumptions; concerning the actual ratios, cf. § 11.

mixing; on the contrary, this dependence obtains at altitudes above 150 km. At an altitude above 150 km the air, under the assumptions made, consists practically only of helium. The higher turbulent mixing spreads in the atmosphere (Chapman and Milne computed for the upper boundary of convection figures from 20 to 50 km), the smaller is the number of molecules of light gases at altitude; this is easy to see from Fig. 8, since in the mixing zone the curves run parallel as a result of the constant proportion of the mixture.

Einstein (P. S. Epstein)86 developed the theory of the separation (Entmischung) of gases. He calls the time of separation the interval of time after which the concentration of an individual gas, under unimpeded diffusion, differs by more than 50% from the initial state of complete mixing. For hydrogen, helium, and carbon dioxide the time of separation has the following orders of magnitude: at the earth’s surface 1000 years, at an altitude of 110 km—1 year, at an altitude of 150 km—1 week, at an altitude of 200 km—several minutes. Owing to the counteraction of turbulence, separation becomes effective only at altitudes above 100 km; at altitudes above 170 km the gases are probably completely separated.

Maris85,145–147 estimates the pressure at the base of the upper layer, where diffusive equilibrium should prevail, at \(1/20000\) mm Hg. Taking account of the absorption and emission of radiation by water vapor, carbon dioxide, and ozone, he arrives at the assumption of large diurnal temperature variations at altitude; in mid-summer at latitude 50° and an altitude of 200 km, at noon a temperature of \(+100^\circ\text{C}\) should prevail, and at night \(-40^\circ\text{C}\). Hence, for the altitude of the base of the diffusion layer he finds a figure of about 150 km for a summer day and about 110 km for a summer night. The most important results of these calculations are reproduced in Fig. 10 and in Table 1; this is done not because they are more reliable than others, which can readily be obtained by making certain assumptions, but in order to demonstrate the significance of the premises. The computations themselves leave a certain latitude in estimating the temperature—100 degrees and more. For orientation, Fig. 11 shows the influence of temperature on the decrease of pressure in the case when the air preserves up to 300 km the composition it has near the earth’s surface.

Periodic diurnal temperature variations in the part of the atmosphere accessible to us are at all large only in the immediate vicinity of the earth’s surface; the surface is heated during the day and convectively heats the lower layer of air. Already at an altitude of 1 km the diurnal temperature variations do not exceed a few degrees. Maris derives significant amplitudes at great altitudes from the assumption that there, in contrast to the lower layers, the atmosphere directly

TABLE 1

Ratios in the high layers of the atmosphere during a summer day at latitude 50° (according to Maris’s hypothesis)

Height (km)	Abs. temp.	$N_2$	$O_2$	A	$CO_2$	Kr	He	$H_2$	Total (without $H_2$)	Mean free path length (cm)	Pressure (mm)
0	288°	19,30	18,73	17,39	15,89	15,40	14,01	15,41	19,41	$6\cdot10^{-6}$	$7,6\cdot10^2$
20	223°	18,17	17,60	16,26	14,76	12,85	14,28	14,28	18,28	$9\cdot10^{-5}$	$4,5\cdot10^1$
40	280°	16,93	16,36	15,01	13,51	13,02	11,64	13,03	17,03	$2\cdot10^{-3}$	3,1
60	286°	15,89	15,32	13,97	12,47	11,98	10,60	12,00	16,00	$2\cdot10^{-2}$	0,37
80	350°	14,91	14,33	12,98	11,48	11,00	9,61	11,01	15,01	$2\cdot10^{-1}$	0,037
100	363°	14,08	13,51	12,17	10,67	10,18	8,80	10,19	14,19	1	0,0059
120	365°	13,30	12,73	11,39	9,89	9,40	8,12	9,41	13,41	6	0,0010
140	365°	12,54	11,97	10,62	9,12	8,63	7,25	8,65	12,65	$4\cdot10^1$	$1,7\cdot10^{-4}$
160	365°	11,79	11,17	9,72	8,16	6,41	6,75	7,89	11,88	$2\cdot10^2$	$3,0\cdot10^{-5}$
180	365°	11,05	10,34	8,68	7,01	4,21	6,65	7,84	11,13	$1\cdot10^3$	$5,2\cdot10^{-6}$
200	370°	10,33	9,51	7,65	5,88	2,01	6,54	7,78	10,39	$6\cdot10^3$	$9,5\cdot10^{-7}$
300	370°	6,80	5,44	2,52	0,26	— 8,8	6,04	7,53	6,89	$2\cdot10^7$	$3,0\cdot10^{-10}$
400	370°	3,3	1,4	—	—	—	5,5	7,3	—	—	—

is heated through the absorption of ultraviolet radiation from the Sun. Such considerable diurnal temperature fluctuations

Fig. 10. Decrease with height of the partial pressure of nitrogen and helium by day and by night (in summer), according to Maris’s hypotheses.

Fig. 11. Calculation of the decrease of pressure with height in completely mixed air at various absolute temperatures.

must entail strong diurnal-periodic motions of the air; however, according to observational data on terrestrial magnetism, these air motions appear to be unlikely.

In connection with observations of very high rays of the aurora borealis (from 500 to 1000 km), which reliably establish the presence of nitrogen and oxygen at these altitudes, we must review our figures and tables in order to establish their relation to this possibility. The result proves disappointing: even according to Maris’s most extreme assumptions, at an altitude of 500 km in the daytime there is less than one molecule of oxygen or nitrogen in 1 cm³. Attempts have been made to get around this difficulty by means of various devices: hypotheses of still higher temperatures, deviations from the exponential decrease of density, perhaps as a result of collisions of the second kind, the action of air pressure, etc. It is striking, however, that in the spectrum of the aurora borealis there is not a single line of helium or hydrogen; yet it is difficult to decide whether this circumstance argues against the presence of these gases, especially since the indication of oxygen was obtained for the first time only in recent years, and moreover in a completely unexpected way. Against hydrogen there is also the fact that it readily combines with oxygen. The idea that oxygen or nitrogen may be lifted to a height by mixing with light gases is false, since, on the contrary, such mixing would result in the light gases being lowered together with the heavy ones. On the other hand, it is quite possible (according to Chapman, see § 11) that oxygen, and perhaps even nitrogen, at heights above 120 km is dissociated to a considerable extent. Owing to this, the height of the homogeneous atmosphere is doubled, and hence the decrease of $\lg p$ is reduced by half; if Maris’s data in the above table are altered accordingly for a summer day, then for an altitude of 400 km we obtain more than $10^7$ oxygen atoms in 1 cm³, i.e. 400,000 times more than for molecular oxygen.

The mean free path already at an altitude of 100 km is equal to 1 cm, and at altitudes from 18 to 200 km—to 10 m; thus for most molecules the time between two collisions is of the same order of magnitude as that assumed for the duration of the residence of atoms in a metastable state. This leads to a theory of the green line of the aurora borealis corresponding to the transition of an oxygen atom from a metastable state.

The molecular viscosity of a gas does not depend on pressure. Thus the kinematic viscosity, i.e. the ratio of viscosity to density, must increase with altitude inversely proportional to the density[^84]. The usual coefficient of viscosity of air at normal temperature is equal to $1.77 \cdot 10^{-4}$, so that the kinematic viscosity is equal to $0.14\ \text{cm}^2/\text{sec}$. It should be noted, however, that near the surface of the earth the apparent viscosity of the air—as it is expressed in the apparent friction against the Earth, in the increase of wind with height, and is caused by vortices of large scale—is approximately 100,000 times greater than the molecular viscosity.

When a molecule acquires a velocity exceeding \(11\ \mathrm{km/sec}\), it can leave the earth along a hyperbolic path and no longer return. Individual molecules must acquire such velocities already in ordinary thermal motion \(^{22}\). Jeans \(^{87,88}\) calculated the losses of the earth’s atmosphere as a result of such processes and showed that even for the lightest gases this loss may be neglected; on the contrary, it is precisely by this that the loss of the Moon’s atmosphere should be explained. Recently Hulburt and Maris \(^{114-116}\), in connection with their theory of the aurora (see § 9c), pointed to another source of rapidly moving molecules and atoms—namely, the transfer of energy in collisions with excited atoms. However, this process too is sufficiently rare that it cannot cause any significant loss of atmosphere.

Helge-Petersen \(^{89,90}\) drew attention to the following obvious contradiction: depending on the assumptions concerning the distribution of He in the atmosphere, for its total amount at normal pressure and temperature one obtains a value of the order of \(10^{14}\ \mathrm{m^3}\). The helium fields in North America annually release into the air more than \(10^{7}\ \mathrm{m^3}\), and the entire earth’s surface in earlier geological epochs probably released still far more. Despite this, helium cannot be detected in the upper atmosphere. According to Jeans, thermal scattering into outer space requires a temperature of approximately \(1000^\circ\mathrm{C}\); Helge-Petersen connects such “heating,” which can arise only accidentally during magnetic storms and auroras, with the penetration into the atmosphere of corpuscular radiation from the Sun.

9. DATA OF TERRESTRIAL MAGNETISM

a) General remarks.

One of the most powerful sources of our knowledge of the physics of the highest layers of the atmosphere is the study of variations of terrestrial magnetism. At present more than 40 magnetic observatories record the total field intensity with remarkable accuracy, down to \(1\gamma = 10^{-5}\) gauss, i.e. roughly to \(1/50000\). True, their geographical distribution is unsatisfactory; however, in view of the universal character of magnetic variations, the network of stations is sufficient for constant observation of magnetic disturbances and, moreover, in contrast to observations of the aurora, day and night, quite independently of the weather.

With the exception, perhaps, of slow secular variations, every change in the vector of the Earth’s magnetic field is caused primarily by electrical processes at altitude; in any case, secondary induction phenomena inside the Earth are added to them. In order, from the recorded curves, to draw any conclusions about physical processes,

requires, generally speaking, knowledge of the change of the field over the whole Earth. In order to be able to survey the manifold variations, it is necessary to introduce, between the use of the registered data and the physical theory, also a statistical treatment of the material; the latter often constitutes the main part of the work. The basic idea here is the interpretation of the results of experiments carried out daily in the atmosphere by the Sun and the Moon. The simplest experiment is performed by the Moon: this experiment consists in a slight rhythmic motion of the atmosphere in the form of ebb and flow. The corresponding lunar variations of terrestrial magnetism are small, of the order of \(1/10000\) of the strength of the Earth’s magnetic field; however, owing to the purity of the experiment, they are especially meaningful. As for the Sun, it, if one may put it so, performs too many experiments at once: it causes motion of the atmosphere not only

Fig. 12. Solar (left) and lunar (right) periodic variations of the easterly magnetic declination in summer at Greenwich.

because of the daily oscillations of temperature connected with radiation, but also because of the electric fields arising when the corpuscular radiation of the Sun penetrates. Moreover, it has a substantial influence on the ionization of the highest layers, and in two entirely different ways: on the one hand—by radiation received only by the day side of the Earth; on the other—by electrically charged corpuscular rays which, being deflected by the Earth’s magnetic field, can also reach the night side of the Earth. The latter phenomenon manifests itself especially strongly in certain periods characterized by magnetic disturbances and auroras.

As to the nature of the radiation of the first kind, we can draw only indirect conclusions, since it does not reach heights accessible to us; it is usually considered ultraviolet radiation. Chapman\(^1\) adduces various grounds for the conclusion that, in addition to this, on the day side of the Earth ionization is also caused by neutral particles of solar origin, and moreover even in lower layers (100 km altitude as compared with 220 km altitude of the upper layer; cf. § 9b and § 11).

b) Periodic daily variations. The regular solar and lunar daily-periodic variations, which we (together with Chapman) shall for brevity denote by \(S\) and \(L\), are stronger by day than by night, and stronger in summer than in winter (Figs. 12 and 13). As early as 1878 Balfour Stewart (B. Stewart)\(^{104}\), discussing the observational data on \(S\) and \(L\), за-

concluded that they must arise in the upper layers of the atmosphere and that in these layers the air must be far more electrically conductive than at the surface of the Earth. This famous hypothesis, subsequently substantiated by A. Schuster (Schuster) ^103, was fully confirmed 20 years later, after the discovery of radio waves; or rather, it was not confirmed but developed anew, since even today few people know that our conception of the upper layers of the atmosphere derives from the study of terrestrial magnetism.

The basic ideas are as follows. According to observational data from all magnetic observatories, the diurnally periodic varying field \(S\) can, by Gauss’s method ^91, be decomposed into an external and an internal component. The external component is more than twice as large as the internal one. Purely formally, the external component can always be represented as the magnetic field of a surface (flächenhaftes) current system in the atmosphere, its height, on other grounds, being estimated at approximately \(100\) km. According to the so-called theory of the “atmospheric dynamo,” put forward to explain the diurnally periodic variations, this current system arises in the following way: under the influence of temperature oscillations or tidal forces, the conducting layers of the atmosphere undergo a diurnally periodic motion, and, owing to the constant magnetic field of the Earth, Foucault currents are induced in them (the atmosphere is the armature of the dynamo, the ionized layers the winding). A detailed calculation carried out by Chapman ^94,96 gave, for the conductivity of the upper layers of the atmosphere on the dayside of the Earth, a value of about \(10^{-3}\ \mathrm{cm}^{-1}\cdot\Omega^{-1}\); the mean conductivity of sea water is \(6\cdot10^{-2}\ \mathrm{cm}^{-1}\cdot\Omega^{-1}\). Thus the conductivity of the upper layers of the air is \(10^{13}\) times greater than near the surface of the Earth. At altitude, the conductivity at night falls to less than \(1/20\) of the daytime value.

Fig. 13. Lunar periodic variations of the eastern magnetic declination component in Greenwich and Batavia. The lunar day is reckoned from one lower culmination to the next. The first four pairs of curves correspond to the phases: new moon, first quarter, full moon, last quarter. For the daylight hours (between sunrise and sunset) the curves on the surface are printed in bold; at this time the variations are most intense, precisely in Batavia. The lower curves represent regular double waves averaged over the entire month; thus the influence of the Sun is excluded here.

In Figs. 14 and 15 are shown patterns of the current lines of solar

Figs. 14 and 15. Maps of the atmospheric current system, computed from the solar variations of the Earth’s magnetism in the year of sunspot minimum (1902). Fig. 14 — annual average; Fig. 15 — the northern summer. The meridians are denoted in local time, 12 — noon. Lines of equal values of the current function are shown. Unit — 1000 A; between every two lines a current of 1000 A flows in the direction of the arrow.

Figs. 16 and 17. Maps of the atmospheric current system, computed from variations of the Earth’s magnetism averaged over whole months, i.e., pure semidiurnal waves. Fig. 16—annual mean; Fig. 17—northern summer. The meridians are denoted by local lunar time: lower culmination at 0 and 24, upper culmination at 12. The values of the current function are in units of 1000 A; between each pair of lines there flows 500 A in the direction of the arrows.

variations, computed by me from Chapman’s potential expansion[^95]. The current strength of the main vortex on the daytime hemisphere in summer reaches, for solar variations, up to 89,000 A; the annual mean is 62,000 A. The oppositions of day and night, summer and winter, are clearly expressed. In Figs. 16 and 17 the current system for lunar variations is shown (means over whole months); here, owing to the gradual displacement of the Moon (as compared with the Sun), the diurnal variability of ionization is smoothed out, and pure semidiurnal waves are obtained, as should also be expected under constant ionization owing to tidal motions of the atmosphere. However, if one considers the separate phases of the Moon in isolation, then, as is quite clearly seen in Figs. 18 and 19 for the new moon, the dynamo effect on the daytime side gives a more powerful current vortex as a result of the enhanced ionization. In summer at new moon the main vortex of the lunar current system increases to 11,000 A. Variations of the Earth’s magnetism can readily be derived from the current system by the right-hand rule. In any case, even if one doubts the physical existence of the current systems, they may be used as a formal synopsis of the complex variations of the Earth’s magnetism. But from terrestrial-magnetism data alone it is not yet possible to determine the height of the layer.

The total conductivity of the atmosphere can be represented, roughly but vividly, by replacing the atmosphere with an iron shell enveloping the whole Earth, the individual points of which are movable relative to one another and can describe elliptical trajectories (mainly horizontal) about 5 kilometers in extent; along such trajectories air particles move under the action of tides. Such a shell would have to have, on the daytime side, a thickness of about 3 mm, and on the nighttime side about 0.05 mm.

The conductivity of air perpendicular to the Earth’s magnetic field decreases sharply with height, i.e. where the mean free path of ions and electrons is large compared with the radius of the spiral described by them around the lines of force of the Earth’s magnetic field[^94]. Therefore electrons at heights above 90 km and ions at heights above 170 km scarcely increase the transverse conductivity at all. From below, the layer with high conductivity is limited by the usual decrease of ionization and of the mean free path. Thus the position of the layer in which, owing to the dynamo effect, diurnally periodic currents arise is determined by the interval between 100 and 170 km.

Of the two ionized layers which, according to Appleton’s observations[^149] of radio waves, lie at heights of 100 km (E-Region) and 220 km (F-Region), only the lower one can be the location of the lunar current system. Observations show that L is strongly connected with the activity of terrestrial magnetism; on days of magnetic disturbances L is considerably more intense,

Figs. 18 and 19. Maps of the atmospheric current system, computed from lunar variations of terrestrial magnetism for the moment of new moon. Fig. 18—annual mean; Fig. 19—northern summer. The meridians are marked in local lunar time, which at the moment of new moon coincides exactly enough with solar time \((12 =\) noon), so that the daytime side of the Earth occupies the middle part of the map. The values of the current function are in units of 1000 A; between each pair of lines flows 500 A in the direction of the arrows.

than on days of magnetic calm (Fig. 20). A parallel change should also be assumed for the ionizing force, which is fully confirmed by radio-wave measurements for the lower layer.

Chapman¹ concludes from this that the 100-kilometer layer is ionized chiefly by neutral corpuscular radiation from the Sun. The course of his reasoning is as follows: magnetic disturbances are strongest near the poles, precisely in the zones of aurorae. In these regions the ionization is probably caused by charged particles of solar origin (§ 9d). According to Milne’s theory¹¹²,¹¹³ concerning the corpuscular emission of the Sun, one should expect that the surface of the Sun emits atoms having strong absorption lines in the solar spectrum; under the accelerating action of radiation pressure they acquire terminal velocities of one and the same order of magnitude.

Fig. 20. Lunar variations of magnetic declination at Greenwich and Batavia on days of magnetic calm (top) and on disturbed days (bottom). The opposite phases of the waves of the two stations are explained by their location in the northern and southern hemispheres.

Some of these atoms are ionized, others neutral; radiated together, they do not separate until they enter the region of the Earth’s magnetic field. Here the ions are deflected toward the zones of aurorae, while the neutral atoms can penetrate only to the day side of the Earth. Their depth of penetration must be of one and the same order of magnitude, and consequently their influx and the resulting ionization must, to a certain extent, vary proportionally for both types. This means that the intensity \(L\) must vary in parallel with magnetic changes (the activity of terrestrial magnetism). It should be expected that neutral atoms ionize molecular nitrogen in just the same way as charged particles do in the polar zones (the \(N_2^+\) bands in the spectrum of the northern lights). This agrees with Slipher’s observation, confirmed by MacLennan⁴⁴, according to which, in the last gleam of daylight in the west, bands of singly ionized nitrogen appear, so characteristic of the auroral spectrum. Positive ions on their way from the Sun must be accompanied by approximately the same number of electrons (or negative ions), for on the whole the flux must be neutral; however, it may be supposed that in the ionization of the atmosphere electrons play only a secondary role. As for neutrons, in this respect very little is yet known about them.

Chapman \(^{98,99}\) also indicated how observations of radio waves during a solar eclipse may help resolve the question of whether ionization is caused by ultraviolet light or by corpuscles. The basis is the considerably stronger aberration of the corpuscular shadow compared with the optical shadow of the Moon. When the Moon is between the Earth and the Sun, its velocity relative to the Sun in the direction of the Earth’s orbit is approximately \(29\ \mathrm{m/sec}\). The corpuscles move in the direction of the solar radius with a speed of about \(1600\ \mathrm{m/sec}\) (according to Milne). The shadow cylinder cut out by the Moon from the corpuscular stream will therefore be inclined to the solar radius at an angle of about \(1^\circ\); at the mean distance to the Moon of \(384\,000\ \mathrm{km}\), the Moon’s corpuscular shadow will follow its optical shadow at a distance of \(7000\ \mathrm{km}\). Since during a solar eclipse the Moon moves in the same direction as the Earth, but lags behind it by \(0.9\ \mathrm{km/sec}\), the axis of the cylinder of the corpuscular shadow will reach the Earth 2 hours before the phase of total eclipse begins. Owing to the daily rotation of the Earth, the corpuscular eclipse will not only occur earlier than the optical one, but will also cover entirely different regions*. During the eclipse of 31 August 1932 it was proposed to make observations in the zone of the corpuscular eclipse; in any case, decisive results cannot yet be expected from a single observation.

The daily solar variations of terrestrial magnetism (\(S\)) depend on magnetic activity distinctly less than do the lunar ones (\(L\)). In recent years \(^{3}\), in addition to the dynamo-effect theory, other possibilities for the origin of \(S\) have also been indicated—namely, the diamagnetic hypothesis and the drift hypothesis (Driftstromhypotese), based on taking into account the influence of the Earth’s magnetic field on the thermal motion of ions and electrons. Initially these hypotheses were applied by Ross Gunn and Chapman to the Sun’s magnetic field; however, in their simplest form they did not withstand the criticism of Cowling \(^{100}\). In any case, it cannot be considered improbable that the origin of \(S\), in view of its differences from \(L\), should be sought at least in part in the upper layer at an altitude of \(220\ \mathrm{km}\), whereas \(L\) should be referred to the lower layer at an altitude of \(100\ \mathrm{km}\).

The lunar variations of terrestrial magnetism are caused by tides in the atmosphere \(^{37}\). The resulting air velocities are of the order of \(0.1\)—\(1\ \mathrm{m/sec}\). The obviousness with which these small periodic motions produce magnetic effects makes it possible to regard as impossible the occurrence, on days of magnetic calm, at the same level, of variable

* In the preceding abstract (“Z. techn. Phys.”, 13, 613, 1932) the corresponding paragraph must be corrected.

winds of the order of 10 m/sec. On the contrary, the steady winds are probably caused by a constant external magnetic field.

The amplitudes of the solar and lunar magnetic variations are related to one another in approximately the same way as the periodic solar and lunar pressure oscillations observed at the Earth’s surface (about 15:1). This excludes the possibility that the components of the periodic winds caused by the activity of the Sun are at a height considerably greater than those caused by the activity of the Moon, as well as the possibility of temperature oscillations as strong as those admitted, for example, by Maris^85.

Fig. 21. Hour scale for a 24-hour sinusoidal wave of the diurnal-periodic variations of the horizontal intensity over 171 days of calm (Watheroo Observatory, Western Australia). The initial point of the coordinate system is marked by an asterisk.

Of great significance for our understanding of the diurnal magnetic variations and the processes connected with them in the high layers may apparently be the following line of investigation. Chapman and Stagg (J. M. Stagg)^139 established that even on days of complete magnetic calm the diurnal variations may be very different; I continued their study by entirely different methods^140–142. A typical example is shown in Fig. 21, where observations of the diurnal variation of horizontal intensity are presented, made over 171 days of calm during the southern summer (from November to February) at the Watheroo Observatory (Western Australia, 30°.3 S lat.) of the Carnegie Institution in Washington. Only waves of 24-hour period are presented, computed by means of harmonic analysis. Each point on these “clocks” represents a separate day; the unshaded vector from the initial point (*) of the coordinate system determines by its length the amplitude (in units of the Earth’s magnetic-field intensity \(\gamma = 10^{-5}\) gauss, according to the scale indicated), and by its direction (according to the reading on the hour scale at the edge) the time of occurrence of the maximum of the 24-hour wave.

On average over all days the amplitude is small, corresponding to the fact that the center of the vortex goes around Huetero (Fig. 14). The “ellipse of probability,” characterizing the distribution of points, is noticeably elongated and shows that the insignificant mean amplitude is observed only because on some days the maximum occurs predominantly at midnight (\(0^h\)), and on other days—at noon (\(12^h\)). This may be interpreted as follows: on some days the center of the vortex passes between Huetero and the equator, and on others—between Huetero and the south pole.

This method can be generalized by using the orthogonality of the expansion into a Fourier series and the components of terrestrial magnetism.

c) Magnetic storms. Strong magnetic disturbances, called magnetic storms, occur several times each year. Often a calm suddenly changes into a storm over the entire earth simultaneously (to within an accuracy of determining the time from 1 to 2 minutes). The average course of a magnetic storm is known to a certain extent; however, in individual cases there are significant deviations. Typical is a brief initial increase in the horizontal intensity, which, however, very soon, after several minutes, is replaced by a strong decrease. From the minimum value corresponding to the principal phase of the storm, the horizontal intensity then rises over the course of several days to the normal value. Fig. 22 (giving daily means) illustrates the striking uniformity of this process over the whole earth; the data of three observatories differ only in amplitudes, but not in the shape of the curves4. Periods of disturbances, determined by the characteristic numbers (§ 9d), are characterized over the whole earth by small horizontal intensities; the adjacent periods of calm are clearly noticeable (for example, from November 5 to 9).

All attempts to explain magnetic storms proceed from the assumption of the action of some radiation received by the earth from the Sun, for the magnetic field of the Sun is too weak to exert a direct effect; the legitimacy of assumptions about a solar origin will be considered below (§ 9d). Both corpuscular streams and ultraviolet radiation from the Sun have been brought under consideration.

The corpuscular theory became known thanks to the works of Norwegian investigators—thanks to Birkeland’s experiments with the “terrella,” recently so elegantly repeated by Brüche[^102], and, further, thanks to Størmer’s theoretical calculations[^101] and the photogrammetric investigations of the aurora by Vegard and Størmer. In this, the motion of individual particles, for example electrons, and their deflection by the earth’s magnetic field were considered, as well as by the magnetic field of the ring current created by electrons in the plane of the magnetic equa-

of the Earth. These theories related chiefly to the aurora borealis, and to a lesser degree to magnetic storms; magnetic disturbances during aurorae were regarded as the result of the direct action of the magnetic field of moving charges. As early as 1911 Schuster advanced various objections to these theories; in particular, he pointed out that a stream of like-charged particles cannot, by virtue of mutual electrostatic repulsion, remain compact, but must disperse within a few seconds; only when the stream is so tenuous that its magnetic field is too weak does Schuster consider Birkeland’s theory acceptable, but by no means for explaining magnetic storms.

Fig. 22. Course of the daily mean horizontal intensity at Seddin (near Berlin), Huancayo (Peru), and Watheroo (Western Australia) from October 14 to November 19, 1928. Abscissae of the mean values for an interval of 24 hours (centered on Greenwich midnight) are indicated by vertical lines. Below: international characteristic numbers. Scale of the horizontal intensity in units \(\gamma\); \(1H = 100\,000\,\gamma\).

Schuster held the opinion that, like daily-periodic magnetic variations, magnetic storms are caused by horizontal electric currents in the upper layers of the atmosphere. Schmidt (Ad. Schmidt)\(^{107}\) already regarded a current vortex moving in the atmosphere as an element of magnetic storms. Schuster believes that electromotive forces are always present in the atmosphere, but their action is intensified only when, owing to the penetration of corpuscular radiation from the Sun, the conductivity is greatly increased. Chapman\(^{108}\), above all,

put in order and discussed the material of observations on the course of magnetic storms, and then, on the basis of this material, justified a theory of atmospheric currents proceeding from the assumption of corpuscular radiation predominantly of one sign; however, this attempt had to be abandoned, since various subsequent works confirmed the correctness of the view earlier expressed by Lindemann109, according to which the only possible type of corpuscular radiation is a stream that is, to a considerable extent, electrostatically neutral. Positive and negative charges are present in such a stream in equal quantities and move with identical mean velocities110, 111. Thus the stream is not surrounded by any appreciable magnetic field.

Milne112, 113 (qualitative description3) indicated a process in which rising atoms and ions can leave the Sun, “breaking out of their absorption lines”; for Ca+ ions a terminal velocity of 1600 km/sec is obtained, reached already at a distance of 10 solar radii. With such velocities Chapman106 succeeded in explaining the main features of magnetic storms by means of very rarefied solar clouds, whose density is approximately \(10^{-22}\) g/cm\(^3\) (i.e. 1–2 Ca ions, or 60 hydrogen atoms, in 1 cm\(^3\)). Of course, the theory of the motion and electric polarization of such clouds in the Earth’s magnetic field is very complex. At the same time, the former assumption must be abandoned that magnetic storms are connected with the stationary state of a cloud enveloping the whole Earth; rather, magnetic phenomena are connected with the approach of clouds, and substantial changes arise at a distance of several Earth radii from the Earth. The cloud is a good conductor of electricity. When it enters the Earth’s magnetic field, electric currents are induced on its surface, shielding the inner part of the cloud from the Earth’s field; the current-carrying layer pulls together the lines of force of the terrestrial magnetic field and thereby causes an initial increase in the horizontal intensity of the Earth’s field. In this process, those parts of the cloud which are directly turned toward the Earth are retarded, while the outer parts move onward without hindrance. Beyond the Earth the cloud again partly closes, and around the Earth there is formed a westward-directed current, decreasing the horizontal intensity during the main phase of the storm. This ring current dies away over the course of several days. One of the essential features of the theory is the distance at which the primary electric currents flow—namely, several Earth radii; these currents are closer to the Earth than Birkeland’s and Størmer’s equatorial currents, yet nevertheless they lie outside the Earth’s atmosphere, in which, in any case, secondary electric currents are induced. Neutral atoms and molecules—such as should be expected in the cloud—without deviation pro-

penetrate to the day side and bring about there the increase in ionization known to us from the study of lunar variations. Neutrons should behave in the same way.

An entirely different theory of magnetic storms and polar aurora was developed by Hilbert and Maris 114–116. They assume that these phenomena are caused by corpuscles of terrestrial origin, which arise owing to collisions of the second kind under the action of ultraviolet radiation during eruptions on the Sun; rising to a height of up to 5 Earth radii, they descend from there along the lines of force of the Earth’s magnetic field to the polar zones. This ingenious theory at first sight appears quite acceptable; in its separate parts, concerning comets and the zodiacal light, it may well correspond to reality. However, in its main point—the explanation of magnetic storms and polar aurora—it, as Chapman 117 has shown, does not withstand quantitative verification.

In small magnetic disturbances, lasting only about an hour, there is sometimes observed a peculiar tendency to arise for many days in succession at one and the same time of day; a typical case of such “germination” (“Aufkeimen”) of a more considerable disturbance was observed, for example, in January 1924 in Potsdam 135. On the basis of similar observations A. Schmidt 136 as early as 1904 concluded that “the medium to which the immediate cause of the disturbances belongs possesses a certain spatial structure, remaining unchanged over a long period of time; this medium determines the character of the course of the phenomenon caused by solar influences.” One may think that what is involved is as it were an “infection” of some limited part of the high atmosphere, which may be caused, like the polar aurora, by charged corpuscular radiation from the Sun; in sufficiently high layers the increased ionization may be maintained for several days with an insignificant tendency toward recombination.

In connection with observations of a similar periodicity in the radio-wave region, the so-called “elementary waves,” or “micropulsations,” of terrestrial magnetism 137, 138 are of interest. Typical micropulsations with especially large amplitudes are shown in Fig. 23; the fine sinuosities of the registered curves are much more frequent. The pulsations of September 12, 1930, comprise 50 complete oscillations with an average period duration of 2 min. Sometimes such pulsations are recorded simultaneously at two stations situated close to one another (Abisko and Tromsø), but in other cases this certainly does not occur; thus we are not dealing here with a phenomenon observed simultaneously over the whole Earth. I would therefore agree with the opinion of Harang (L. Harang) 138 that the matter consists in the action of local electric-

of currents in the upper atmosphere, but not in periodic motions of electrons around the entire Earth, as Schtermer imagines it[^101]. Perhaps the occurrence of these currents (as also the occurrence of daily variations, according to the theory of the atmospheric dynamo) is explained by waves at the boundary of horizontal layers of air—similar to wave clouds.

d) Dependence of magnetic disturbances on processes on the Sun. Although we still know very little about the mechanism of the transfer of solar energy, nevertheless the solar origin of magnetic disturbances has been established beyond doubt. Here it is necessary also to say briefly something about the statistical methods by which

Fig. 23. Micropulsations of the declination \(D\), horizontal intensity \(H\), and vertical intensity \(Z\) according to records at Abisko (Sweden) and Tromsø. Time is Greenwich Mean Time.

this assertion is substantiated, since they may perhaps also find application in the investigation of electromagnetic waves.

First of all, the matter concerns establishing a measure for the degree of magnetic disturbances (activity). Beginning in 1906, magnetic disturbances have been characterized daily (the day is reckoned from Greenwich midnight) by the “international characteristic numbers of terrestrial magnetism” \(C\)[^118]. They are average values from the data of approximately 40 observatories, each of which, depending on the type of curves recorded, defines the day as quiet (0), slightly disturbed (1), or strongly disturbed (2). The numbers \(C\) represent quite satisfactorily the fluctuations of activity from day to day. The fact that all observatories consistently estimate the degree of activity (0—in calm conditions, 2—in strong magnetic disturbances) indicates not only the well-known universality of magnetic activity, but also the value of the methods

definition of \(C\). Of course, the decimal subdivision of the numbers \(C\), obtained in determining the mean values, corresponds to a certain natural gradation of magnetic activity. Typical specimens of the recorded curves are presented in Figs. 24 and 25 (after Flemming\(^ {118a}\)).

Fig. 24a. Simultaneous records from two observatories in Peru and western Australia, separated from one another by more than 15,000 km, on a day of calm with international characteristic number 0.0. The magnetograms represent 9 August 1929 from noon Greenwich time to midnight. Designations \(D\), \(H\), and \(Z\), see Fig. 23.

That long-known fact that both periods of magnetic disturbances and periods of magnetic calm tend to recur after approximately 27 days (the period of rotation of the Sun) has been convincingly demonstrated by Cri (C. Chree) and Stagg\(^ {119}\) with the aid of characteristic numbers. In doing so they proceeded from the so-called international days of “calm” and “disturbance,” the dates of which (5 for each month) were chosen by the Netherlands Meteorological Institute on the basis of the characteristic numbers. From the data for 1906 to 1914 all disturbed days were selected; next, the characteristic numbers were written out for dates separated from them by intervals of 27, 54, 81, and 108 days in both directions (each date was associated with the adjacent 5–7 days); from the total of 1,140 series the mean values were computed. The result is presented in Fig. 26 together with similar data for days of calm; the middle line corresponds to the characteristic number 0.62, the mean for all 19 years. The recurrence of periods of calm and disturbance can undoubtedly be traced in both directions over the course of four periods of rotation of the Sun. Systematic deviations from 27-day periodicity, which should have been expected in view of the increase in the speed of rota-

Fig. 24b. Records of the same observatories on a disturbed day with international characteristic number 1.6 (4 December 1929).

PHYSICS OF THE UPPER LAYERS OF THE ATMOSPHERE

...of the displacement of the solar surface in the direction from the equator to the pole is not observed. Likewise, no fractional values of the period (Unterperiode) are observed (Fig. 27); thus this does not indicate a symmetrical distribution of the centers of disturbances throughout the volume of the Sun.

Since in this calculation, on average, \(1/6\) of all days were considered “disturbed,” the mean degree of disturbance on these days is, understandably, not large. Therefore, in addition to the method of Chree, Greaves and Newton\(^{124,8}\) compiled a complete catalog of storms for the period from 1874 to 1927 in which the force component at Greenwich exceeded 0.0015 gauss. These storms, 403 in all, were divided into five groups in order of decreasing intensity of disturbances,

Fig. 25. Records from a station in the south polar region at south latitude \(78.6^\circ\) (the same days as in Figs. 24a and b).

Fig. 26. Mean values of the characteristic numbers in deviations from the mean for groups of 5–7 days adjoining a quiet and a disturbed day equally, and also for days separated from them in one direction or the other by 1, 2, 3, and 4 solar rotations.

and it was calculated—in what percentage of all cases the \(n\)-th day after a storm also proved to be stormy. In this connection an astonishing result was found; the strongest

storms did not show a tendency toward a 27-day period of recurrence; this period is clearly expressed only for weak storms, whose amplitude (the mean over the three components) is \(<\) 0.0018 gauss.

In view of the close connection between magnetic variations, on the one hand, and earth currents and auroras, on the other, it is clear that the latter phenomena too must exhibit a 27-day periodicity of recurrence, at least insofar as this can be established from observations that are inadequate (in the statistical sense). Indeed, by the method of Chree this was established by Peters and Ennis (Peters and Ennis)\(^{122}\) for earth currents, and by Sverdrup (Sverdrup)\(^{121}\) for northern lights. Schindelhauer (Schindelhauer)\(^{123}\) showed that a tendency toward a 27-day period of recurrence is also probable for atmospheric disturbances in wireless telegraphy.

Fig. 27. Mean values of the characteristic numbers in deviations from the mean for the time from 4 days before to 31 days after a quiet and a disturbed day.

On the occasion of the exhibition organized by the Carnegie Institution in Washington (December 1931), a graphical summary of data on magnetic activity was compiled, based on daily characteristic numbers from 1906 to 1931. The diagram, which at first was intended to illustrate visually only the 27-day periodicity, proved, moreover, to be suitable also for discussing the connection between magnetic and astrophysical data; it was published in the form of two-color tables\(^{93}\). Fig. 28 is a selection from these tables. Each day corresponds to a square of constant size, which is left white for days of calm and is shaded black for strongly disturbed days; the intermediate gradations are represented by a known sequence of black and white circles. The squares are arranged into a mosaic of rows, read in the same order as lines in a book; the date of the first day of each row is written on the left. A new row begins after 27 days; for greater clarity, the first 9 days of the following row are also repeated on the right. Thus the squares that stand one above another are separated by a 27-day interval. In Fig. 28 the years 1922 to 1924 have been taken as the most typical; at first there is the distinctly expressed periodicity, extending to solar spots, of the ending eleventh cycle (to the middle of 1923), shown in long columns of black and white signs; then there is the spot-like distribution of the first storms of the new cycle. Typical, too, are separate isolated disturbances among sequences (Sequenzen)

Of particular interest is the distinct sequence in the first half of 1923; it covers a period during which not a single spot was observed on the Sun for weeks at a time. One may expect that, by means of a similar representation of daily observations of the Sun, periods

Fig. 28. Influence of the period of solar rotation on the values of magnetic activity in the years 1922 to 1924.

of disturbances on the Sun can be compared with periods of magnetic disturbances. An attempt of this kind is presented in Fig. 29. Astrophysical observations, carried out by only a few observatories and not regularly, do not make it possible to provide such a

Fig. 29. Demonstration of the period of the Sun’s rotation in the values of the Earth’s magnetic activity (left), in the relative numbers of sunspots (middle), and in the intensity of bright hydrogen clouds in the central part of the solar disk (right). Scale: 0 — quiet, 5 — strongly disturbed, or many spots or clouds. In the right-hand part, certain days without observations are marked with a cross.

of detailed gradation, as characteristic numbers of terrestrial magnetism, continuously recorded by more than 40 observatories. Therefore only 6 steps were adopted, and in such a way that in the years from 1928 to 1930 (for which the diagram was first compiled) each of the three diagrams contained the same number of symbols of each group. The numbers of sunspots and the numbers characterizing bright hydrogen clouds[^125] refer to the central zone of the Sun, to a circle with a diameter equal to half the visible solar diameter, since for this part the probability of geophysical effects is greatest.

The numbers defining solar activity make it possible to recognize clearly the end of the sunspot cycle, whereas the magnetic activity of the Earth declines from 1931 onward. Further, from both solar diagrams one can clearly see the repeated appearance of centers of disturbances, readily coordinated with one another. Detailed statistical calculations4 show that the indices determined by the spectroheliograph are an exact reflection of the relative sunspot numbers determined visually or photographically. Comparison of the diagrams of terrestrial magnetism with the solar diagrams gives a peculiar and striking result: not one of the clearly expressed sequences of magnetic disturbances can be traced in the data of astrophysical observations, even if one takes into account the possible delay of solar influences. The study of individual 27-day sequences leads to a remarkable conclusion.

There must exist on the Sun certain limited regions (M-Regionen), the duration of whose existence, though limited (up to one year), nevertheless exceeds the average lifetime of sunspots. These regions are the cause of magnetic disturbances, probably owing to the emission of corpuscular streams. These regions, as individual objects, have so far eluded astrophysical methods of observation and can be detected—and moreover very manifestly—only in the magnetic activity of the Earth.

Because of this, observations of terrestrial magnetism have, besides their well-known geophysical significance, also an astrophysical significance, for they establish the periods during which the Earth is actually subjected to the action of corpuscular clouds of solar origin. It should not be thought that the penetration of these clouds into the terrestrial atmosphere is a relatively rare phenomenon associated with periods of truly strong magnetic storms. From Figs. 28 and 29 it is evident that this process is quite ordinary. Strangely, reliable statistical data on aurorae are extremely scanty. On the Scottish islands regular observations of aurorae were made; moreover, from 1924 to 1929, on 59 nights out of 100 during which observations could be made without hindrance, some sort of auroral phenomena were actually recorded.

forms of the aurora borealis ^126, ^127. In 5 cases even a ray-like (and not only diffuse) aurora borealis was observed, although, according to the magnetogram, there was complete calm at that time.

A peculiar discrepancy between magnetic and solar observations, expressed in individual 27-day sequences, occurs, however, also for weaker (and more frequent) magnetic disturbances. Quite often it is possible to establish an undoubted connection between strong magnetic storms and large groups of spots passing, shortly before the beginning of the storm, through the central meridian of the Sun ^128, ^130. The powerful magnetic storm of May 13–16, 1921, during which the southern aurora was observed as far as Samoa, was accompanied, for example, by a gigantic group of spots visible even to the naked eye; this group covered \(1/700\) of the solar surface and was the largest group of spots of all those observed at Greenwich on the solar equator. It passed through the central meridian of the Sun on May 14. Of the 17 strongest magnetic storms observed at Greenwich in the years from 1874 to 1927, 15 began in the interval from 4 days before to 4 days after the passage through the central meridian of groups of spots covering more than \(1/2000\) of the Sun’s surface and, consequently, visible to the naked eye ^130. Of the two exceptions to this rule, especially remarkable is the storm of November 13–14, 1894, which undoubtedly occurred in a period when there was no unusual solar activity whatever. The opposite case occurred on June 16, 1905, when a spot with an area exceeding \(1/600\) of the Sun’s surface passed through the meridian without causing, however, magnetic disturbances.

Fig. 30. Areas of sunspots, expressed in millionths of the area of the solar disk, for 6 days before and 1 day after the day of the magnetic disturbance. Mean for 250 and 116 disturbed days (according to Stetson).

In individual cases, with the aid of the spectrohelioscope, eruptions on the Sun have been observed which could be connected with subsequent magnetic storms. These cases were examined by Hale ^129. He considers the present methods of astrophysical observations insufficient and insists on the necessity of photographing in the light of the H\(\alpha\) line every half hour and even more often. It may be hoped that such a more or less continuous spectroheliographic investigation of the Sun will make it possible to establish a greater number of eruptions on the Sun and will provide an opportunity to supplement the data on the coincidence of solar and magnetic phenomena over a series of years.

As for the solar indices, not much can be expected in this direction, since, even according to the present insufficient observations, they are closely connected with the more easily determined numbers of sunspots.

Attempts to determine the time during which the cloud reaches the Earth have been discussed earlier³. For large storms this path requires from 24 to 36 hours, which approximately corresponds to Milne’s indicated velocity of about 1000 km/sec; for weaker disturbances¹³¹,¹³² figures of from 2.5 to 3 days were found (Fig. 30). These figures and the considerations on which their estimate is based cannot be regarded as final. Although, as has already been said, regions active with respect to terrestrial magnetism cannot be identified either with sunspots or with other astrophysically observed phenomena, nevertheless their

Fig. 31. Annual mean magnetic activity of the Earth (above) and relative sunspot numbers for the years 1835–1930. Ordinary annual means are marked by small circles.

Fig. 32. Monthly mean magnetic activity of the Earth (above) and relative sunspot numbers (below) for the years 1900–1930.

recurrence follows the same 11-year cycle. In compiling data on magnetic activity over a period of decades it is better to use objective figures, since the scale of estimates by characteristic numbers is not guaranteed against gradual changes over a number of years.

It is recommended to choose a measure based on the typical course of change in horizontal intensity; such a measure should be derived from the averaged absolute differences of the mean daily values of horizontal intensity over a consecutive series of days. Figs. 31 and 32 show the course over time of magnetic activity and sunspots; Figs. 33 and 34 show the correlations of their simultaneous values. The correlation coefficients are: for the annual mean, \(+0.88\); for the monthly mean, \(+0.65\); it would be very instructive to investigate the statistical basis for the difference between these two values.

Fig. 33. Simultaneous annual means of the relative sunspot numbers (abscissa) and of the Earth’s magnetic activity (ordinate) for 117 annual means (12-month intervals: January–December and July–July) for the years 1872–1930. The straight line is a straight line obtained as a result of adjustment by the method of least squares, and the curve is the fitted curve. Correlation coefficient \(+0.88\). In Figs. 33–35 a different scale has been chosen for magnetic activity than in Figs. 31–32.

Fig. 34. Simultaneous monthly means of the relative sunspot numbers (abscissa) and of the Earth’s magnetic activity (ordinate) for the years 1872–1930. Upper left: 20 years of low activity; lower left: 19 years of medium activity; upper right: 20 years of high activity; lower right: all 708 monthly means. Correlation coefficients in the same order: \(+0.30\); \(+0.36\); \(+0.38\); \(+0.65\).

We mention here only one result of these works, which is of great significance in investigating the correlation between any phenomena related to electromagnetic waves and processes on the Sun. Although, for the years from 1872 to 1930, the correlation coefficient (monthly mean) of the relative sunspot numbers and the Earth’s magnetic activity is very high (\(+0.65\)), during individual groups of years it is close to zero. For the 36 months from 1928 to 1930 this coefficient is practically equal to zero. Thus, even if we had a three-year series of observations of electromagnetic waves, as complete statistically as the observations of magnetic

activity of the Earth, one should be extremely cautious in drawing conclusions concerning a connection with phenomena on the Sun, since such a series of observations is too short4.

Magnetic disturbances occur predominantly in the months near the equinoxes; this semiannual wave constitutes the only systematic feature of the annual course (Fig. 35) of the Earth’s magnetic activity. An unambiguous explanation of this has not yet been found4. Fig. 36 gives a visual representation of the distribution of disturbances over the years from 1906 to 19304. During these years the international characteristic numbers exceeded or were equal to 1.62 on 392 days, i.e., on average, on 16 days per year. Of these, 175 fall in the 4 equinoctial months (March, April, September, October) and only 93 in the solstitial months (June, July, December, January).

Fig. 35. Annual course of the Earth’s magnetic activity in a strongly disturbed year (top), in a weakly disturbed year (middle), and in a year of quiet (bottom).

Fig. 36. Distribution of individual days with strong magnetic disturbances over the years 1906–1930

On millimeter paper, for each year a strip 365 mm long and 10 mm high was allotted; thus for each day there was an area of \(1 \times 10\ \mathrm{mm}^2\), which was shaded completely for a characteristic number of 2.0, and for numbers from 1.9 to 1.6 correspondingly less. The total area of the marks for whole years is shown in Fig. 36 at the right; the area of the marks for each month, below. The diagram shown in Fig. 36 is reduced and without the millimeter divisions. The column on the right represents the 11-year cycle, the areas below—double waves; the circumstance that the autumn equinox is more clearly expressed than the spring one is, apparently, accidental, and its repetition in the future is not necessary. In general, although

not the only one; with the exception of the equinoxes, the vertical chains of signs reveal no regularity indicating an annual periodicity of any definite dates. The opposite assertions of Maris \(^{133}\), establishing a connection between magnetic storms, on the one hand, and comets and falling stars, on the other, are hardly legitimate.

There are also diurnal variations of magnetic disturbances. In Potsdam, on the average over many years, the percentage of magnetic disturbances is minimal for 8 a.m. (13%), maximal for 9 p.m. (27%). Relatively little is known about similar periodic variations in other places on the earth. Owing to the inclination of the Earth’s magnetic axis to its axis of rotation, the possibility is not excluded that certain hours (according to universal time) may have a predominant significance; something of the sort appears from some observations \(^{134}\), but for a confident conclusion a considerably larger body of material is needed, which, although it already exists, has not yet been processed. The predominant significance of certain hours of universal time could be expressed only in the intensity of magnetic disturbances, since the moment at which the solar cloud enters the terrestrial atmosphere probably should not depend on the time of day. In fact, statistical data show that strong magnetic storms may occur at any time of day.

10. Ionizing Action of Monochromatic Radiation

Chapman \(^{143}\) examined in detail the following idealized problem:

1. The rotating Earth receives monochromatic radiation from the Sun. Before reaching the Earth’s surface, the radiation is absorbed by an atmosphere of homogeneous composition, with density decreasing exponentially upward.

2. The absorption of radiation at each point is proportional to the density of the air and to the intensity of the radiation reaching that point.

3. The energy of the absorbed radiation, or a constant fraction of it, is expended on the dissociation of some constituent part \(B\) of the air into two components \(B_1\) and \(B_2\), which may be either charged or electrically neutral.

4. Both components recombine, again yielding the constituent part \(B\). The number of particles \(B\) newly formed in \(1\ \mathrm{cm}^3\) during \(1\ \mathrm{sec.}\) is equal to \(\alpha n^2\), where \(\alpha\) is a constant independent of height and time, and \(n\) is the number of particles \(B_1\) or \(B_2\) per cubic centimeter.

5. The particles \(B_1\) and \(B_2\), as a rule, do not leave the volume in which they were formed.

The problem consists: 1) in calculating the absorption, dissociation, or ionization at each point, as a function of altitude, time of day and year, and geographical latitude, and 2) in determining the number \(n\) of dissociation products as a function of the same variables.

In what follows, without detriment to generality, we shall speak of the particles \(B_1\) and \(B_2\) as ions and electrons.

The differential equations to which this problem leads admit either an explicit or a numerical solution. This work, whose results quantitatively coincide with the earlier investigations of Försterling and Lassen (Försterling und Lassen) \(^{144}\), is especially valuable in its choice of units, by means of which the calculation can be carried out and discussed in an entirely general way; definite numerical values are substituted only at the very end, so that the results may be applied to any kind of radiation absorbed at various altitudes and producing various ionizing or dissociative effects.

Chapman takes the density \(\rho\) of the atmosphere at altitude \(h\) to be

\[ \rho=\rho_0 \exp\left(-\frac{h}{H}\right), \]

where

\[ H=\frac{RT}{gM} \]

is the already mentioned height of the homogeneous atmosphere, and \(\exp x\) is written instead of \(e^x\). Let the monochromatic radiation of the Sun have, outside the atmosphere, intensity \(S_\infty\). Let, further, a beam of rays with cross-section \(1\ \mathrm{cm}^2\) pass through the layer between \(h\) and \((h-dh)\) at an angle \(\chi\) to the vertical; thus the volume of this element of the layer will be \(dh/\cos\chi\), and its mass \(\rho_0 \exp(-h/H)\,dh/\cos\chi\); the change \(dS\) of the intensity \(S\) on passing through the layer will be, according to assumption (2), equal to:

\[ dS=AS\rho_0 \exp\left(-\frac{h}{H}\right)\frac{dh}{\cos\chi}. \tag{1} \]

(\(A\) is the absorption coefficient). The solution of this differential equation is:

\[ S=S_\infty \exp\left\{\frac{A\rho_0 \exp\left(-\frac{h}{H}\right)}{\cos\chi}\right\}, \tag{2} \]

The absorption of radiation referred to \(1\ \mathrm{cm}^3\) of atmosphere is \(dS\cos\chi/dh\). Let the number of ions formed owing to absorption of radiation in \(1\ \mathrm{cm}^3\) be equal to \(\beta\). Then \(\beta\cos\chi\cdot \dfrac{dS}{dh}\) will give the number of ions formed in \(1\ \mathrm{cm}^3\) during \(1\) sec.; with

for given \(S_\infty\), \(\rho_0\), and \(H\) it depends only on \(h\) and \(\chi\). We denote this number by \(J(\chi,h)\). According to (2), we have:

\[ J(\chi,h)=\beta A S_\infty \exp\left\{-\frac{h}{H}-A\rho_0\frac{H}{\cos\chi}\exp\left(-\frac{h}{H}\right)\right\}. \tag{3} \]

The total number of ions formed in a vertical column with cross section \(1\ \mathrm{cm}^2\), with complete absorption of the radiation \(S_\infty\), will be \(\beta S_\infty \cos\chi\).

The number of ions arising in \(1\ \mathrm{cm}^3\) has, at height \(h(\chi)\), a maximum determined by the condition \(dJ/dh=0\), or

\[ \exp\left[\frac{h(\chi)}{H}\right]=\frac{A\rho_0 H}{\cos\chi}. \tag{4} \]

The maximum value \(J(\chi)\) of the number \(J(\chi,h)\) will be equal to

\[ J(\chi)=\beta S_\infty \frac{\cos\chi}{H}\cdot \exp 1, \tag{5} \]

where \(\exp 1=2.718\ldots\). Denote by \(h_0\) and \(J_0\) the values of \(h(\chi)\) and \(J(\chi)\) for \(\chi=0\) (vertical incidence of the radiation). Then

\[ \exp\left(\frac{h_0}{H}\right)=A\rho_0 H;\quad J_0=\beta S_\infty/H\exp 1; \tag{6} \]

further, instead of (4) and (5) one may write:

\[ h(\chi)=h_0+H\ln\left(\frac{1}{\cos\chi}\right), \tag{7} \]

\[ J(\chi)=J_0\cos\chi, \tag{8} \]

and instead of (3):

\[ J(\chi,h)=J_0\exp\left\{1+\frac{h_0-h}{H}-\left(\frac{1}{\cos\chi}\right)\exp\left(\frac{h_0-h}{H}\right)\right\}. \tag{9} \]

Since, relative to \(h_0\), the distribution with height depends only on \(H\), the thought naturally suggests itself to express the height in units \(H\), counted from the height \(h_0\) of maximum ionization under vertical incidence. Therefore Chapman proposes

\[ z=\frac{h-h_0}{H}. \tag{10} \]

Now, according to (7),

\[ z(\chi)=\ln\left(\frac{1}{\cos\chi}\right) \tag{11} \]

and, according to (9),

\[ J(\chi,h)=J_0\exp\left\{1-z-\frac{e^{-z}}{\cos\chi}\right\}=J(\delta,\theta,t,z), \tag{12} \]

where in the last expression the independent variables mean: the declination of the Sun \((\delta)\), the angular distance of the place of observation from the northern pole \((\theta)\), the time of day \((t)\), and the height \((z)\).

At the moment of true noon the zenith distance of the Sun is

\[ \chi=\frac{\pi}{2}-(\theta+\delta). \]

Further, according to (8) and (11), the maximum value of the ionization

\[ J=J_0\sin(\theta+\delta) \]

takes place at the height

\[ z=\ln\left[\frac{1}{\sin(\theta+\delta)}\right]. \tag{11a} \]

The distribution of ionization with height can be calculated by formula (9); the result is presented for various values of \((\theta+\delta)\) in Fig. 37. At \(\delta=0\) (equinox) the largest curve corresponds to the equator, the smallest—to the point at latitude \(83.5^\circ\). Chapman gives further curves and tables of the diurnal course of ionization at various heights and geographic latitudes at different times of day and year.

Fig. 37. Number of ions formed at noon in \(1\ \mathrm{cm}^3\), as a function of height (expressed in units \(H\), the height of a homogeneous atmosphere) at various latitudes at the moment of equinox. The numbers of ions \(J\) are expressed through the ratio to the maximum number of ions \(J_0\) at height \(z=0\) with the Sun overhead and are referred to units of time and volume.

It is typical that the number of ions formed decreases downward (toward negative \(z\)) from the level of maximum ionization \((z=0)\) considerably more rapidly than upward (toward positive \(z\)). At the equator \(J/J_0\) falls from 1 at the height \(h_0\) \((z=0)\) approximately to \(1/8\) at \(z=-1.5\) and at \(z=+3.0\). Thus the principal part of the ions formed falls within a height interval equal to \(4.5H\) (for example, 39 km, if \(H=8.4\) km, which corresponds to an atmospheric-air temperature of \(300^\circ\) absolute). Above \(z=+3\) the formation of ions at noon is almost the same for all latitudes and seasons. The position of the layer of maximum ionization at noon (relative to its position at the equator) is determined according to (11a); for example, at the moment of equinox \((\delta=0)\) at latitude \(\theta=30^\circ\) we have the number \(+0.69H\).

One should sharply distinguish the number \(n\) of ions contained in \(1\ \mathrm{cm}^3\) from the number of ions being formed, since \(n\) depends on recombination. For the number of ions in \(1\ \mathrm{cm}^3\) we shall put:

\[ \frac{dn}{dt}=J-\alpha n^2; \tag{13} \]

the assumption (4) pertaining here has been made for the sake of simplification, although we cannot say anything definite about the actual conditions of recombination at low pressures in the upper layers of the atmosphere. Chapman expresses the time of day \(t\) in the angular measure \(\varphi\), increasing by \(2\pi\) from midnight to midnight; thus

\[ t=\frac{86400\varphi}{2\pi}=1.37\cdot 10^4\varphi. \]

Then from (13) and (12) one obtains:

\[ \frac{1}{1.37\cdot 10^4}\cdot\frac{dn}{d\varphi} = J_0\exp\left\{1-z-\frac{e^{-z}}{\cos\chi}\right\}-\alpha n^2. \tag{14} \]

If the Earth rotated very slowly, then, instead of the coefficient \(2\pi/86400\), the coefficient on the left-hand side would be much smaller, so that the left-hand side would be close to zero; then at noon at the height \(h_0\) (i.e. \(z=0\)) above the equator the equilibrium (largest possible) value would be obtained

\[ n_0=\sqrt{\frac{J_0}{\alpha}}. \tag{15} \]

Chapman further introduces the quantity \(\sigma_0\), defined by the equality

\[ \frac{1}{\sigma_0}=1.37\cdot 10^4\sqrt{J_0\alpha}; \tag{16} \]

\(n_0\) and \(\sigma_0\) may be regarded as parameters determining \(\alpha\) and \(J_0\):

\[ \frac{1}{\alpha}=1.37\cdot 10^4 n_0\sigma_0,\qquad J_0=\frac{n_0}{1.37\cdot 10^4\sigma_0}. \tag{17} \]

Putting \(\nu=n/n_0\), and dividing by \(J_0\), one may rewrite (14) as follows:

\[ \sigma_0\frac{d\nu}{d\varphi}+\nu^2 = \exp\left\{1-z-\frac{e^{-z}}{\cos\chi}\right\}. \tag{18} \]

This equation is valid for the daytime hours; for the night the right-hand side must be set equal to zero, i.e.

\[ \sigma_0\frac{d\nu}{d\varphi}+\nu=0, \tag{19} \]

the solution of this equation gives:

\[ \nu=\frac{\sigma_0}{\varphi+C} \quad\text{or}\quad \frac{1}{\nu}=\frac{\varphi+C}{\sigma_0}. \]

The arbitrary constant \(C\) drops out as soon as the difference of the values \(\left(\frac{1}{\nu}\right)\) for sunrise and sunset is found; it is equal to the quotient obtained by dividing by \(\sigma_0\) the difference of the corresponding values ...

... of \(\varphi\), i.e. the duration of the day in angular units. The correct solution of equation (18) is that which gives these correct differences of the values of \(\left(\frac{1}{q}\right)\) for the beginning and end of the day.

The solution referring to the times of the equinoxes and solstices was found by trial for three values of \(s_0\), namely \(1\), \(1/5\), and \(1/25\), at various heights above the equator; for \(s_0 = 1/25\), also at various heights at latitude \(60^\circ\) \((\theta = 30)\). Seeking the dependence of \(s_0\) on only one variable, \(\alpha\), we find, according to (16), that \(\alpha\) is proportional to \(\frac{1}{s_0^2}\), i.e. small values of \(s_0\) correspond to high recombination rates. Typical examples are shown in Figs. 38–40, from which it is seen that for small values of \(s_0\) (i.e. with rapid recombination) the maximum ion density in the layer of maximum ionization \((z = 0)\) and below is reached only for a short time near noon, while in layers lying above the zone of maximum ionization (positive \(z\)) the ion density remains approximately constant from sunrise to sunset. For \(s_0 = 1\) the ion density in the evening is considerably greater than in the morning; however, for \(s_0 = 1/5\) the ion density is the same at hours symmetrically situated with respect to noon.

Fig. 38. Daily variation of the number of ions in \(1\ \mathrm{cm}^3\), in fractions of that maximum number of ions \(n_0\) which would be established under sufficiently prolonged illumination by normally incident radiation at the height of maximum ionization; the numbers are given for different heights above the equator under two different assumptions concerning the constant \(s_0\) (after Chapman).

Fig. 39.

For the first (necessarily unreliable) application of his calculations, Chapman assumes that, according to data on lunar variations of the Earth’s magnetism, \(s_0\) is approximately equal to \(1/25\) in the layer at a height of about \(100\ \mathrm{km}\).

According to radio-measurement data, he estimates the maximum (at noon) number of positive ions at \(10^6\) or \(10^7\) per cubic

Fig. 40. Distribution of the number of ions as a function of altitude at different times of day (according to Chapman).

centimeter. The values \(\sigma_0 = 1/25\) and \(n_0 = 10^6\) give: \(\alpha = 2 \cdot 10^{-9}\), \(I_0 = 2 \cdot 10^3\); the values \(\sigma_0 = 1/25\), \(n_0 = 10^7\) give \(\alpha = 2 \cdot 10^{-10}\), \(I_0 = 2 \cdot 10^4\).

Fig. 41. Increase of the morning number of ions at various altitudes. The altitude of maximum ionization is taken to be approximately \(100\) km. The solid curves give the actual relations with allowance for the spherical shape of the Earth; the dashed curves correspond to a plane Earth (according to Chapman).

The total number of ions formed above the equator at noon, referred to \(1\ \mathrm{cm}^2\), is equal to \(\beta S_\infty\), or, according to (6), \(\overline{H} I_0 \exp 1\); for \(H = 8.4\) km one obtains the number \(5 \cdot 10^9\) or \(5 \cdot 10^{10}\).

When the Sun is low (solar altitude less than \(15^\circ\)), the solar rays, owing to the spherical form of the Earth, traverse a longer path than that which corresponds to the law \(\frac{1}{\cos z}\). Chapman investigated the relations also in twilight; in doing so it was necessary to introduce one further parameter, namely the distance of the absorbing layer from the center of the Earth, expressed in units of \(H\). When the Sun is low, the layer of maximum absorption lies higher; for example, at the place where

the Sun is rising or setting, it lies \(H - 1.5H\) higher than at the place where the Sun is at the zenith. The earlier sunrise of the Sun at great heights, illustrated in Figs. 1–4, cannot manifest itself to a sufficient degree, since for tangential incidence the absorption is very large; however, from Fig. 41 it is clearly seen that in the high layers \((z = 3—6)\) the ion content at sunrise increases considerably faster than in the low layers \((z = 0)\).

Chapman’s calculations were continued by Millington (G. Millington) \(^{99a}\), who presented them in the form of four illustrative maps showing the maximum ion concentration as a function of geographic latitude and longitude (or local time).

11. Summary

On the basis of the considerations set forth above and of others, Chapman \(^{1}\), in his Bakerian lecture, gave a general picture of the processes in the high layers of the atmosphere, which we reproduce here briefly, without a detailed examination of doubtful points and possible variants. Chapman assumes that the Sun radiates as a black body with a temperature of \(6000^\circ\); the ultraviolet part in the radiation observed at the Earth’s surface is cut off, being absorbed in the region from 2900 to 2200 Å by ozone, and in the region below 2200 Å—probably by oxygen. The absorption of solar radiation, for the most part, since it has not yet reached the troposphere, takes place in three rather sharply separated layers (Fig. 42). Restricting ourselves to the part of the atmosphere lying below \(100\) km, we must take the height \(H\) of a homogeneous atmosphere to be approximately \(10\) km. The absorbing layers lying below \(100\) km must have a thickness of \(50\) km. The ozone layer, with maximum concentration at a height of about \(50\) km, is probably caused by the absorption by oxygen of solar radiation with wavelengths of \(1850\) Å and less; the absorption coefficient of these wavelengths reaches a maximum at the height \(h_0 = 50\) km. Thus the principal part is absorbed at heights between \(35\) and \(85\) km; this remains true also in the case where corpuscular radiation is involved, with the height of maximum absorp—

Fig. 42. Diagram of three atmospheric layers in which vertically incident solar radiation is absorbed. \(N_0\) is the maximum number of dissociated molecules and ionized atoms in \(1\ \mathrm{cm}^3\) in 1 sec. (according to Chapman).

... approximately 50 km. From observations of electromagnetic waves[^149] we know of the existence of two ionized layers at altitudes of about 100 and 220 km (for vertical incidence of the radiation). Even if large values are assumed for \(H\) (owing to high temperatures or dissociation), even then the three layers turn out to be quite sharply separated from one another.

Ozone absorbs ultraviolet radiation in the region from 2200 to 3400 Å; for absorption of this kind the formulas of § 10 are not exactly valid, since the ozone concentration, as a consequence of continuous decomposition and re-formation, does not correspond to the assumption of a normal atmosphere with exponentially decreasing density.

The theory of chemical equilibrium in the ozone layer led Chapman[^67] to two conclusions. The existence of ozone presupposes the formation of atomic oxygen through the dissociation of \(\mathrm{O}_2\) molecules. This is probably caused by ultraviolet radiation. At sufficiently great heights recombination takes place so slowly that few \(\mathrm{O}_3\) molecules are formed; on uniting, the oxygen atoms, owing to diffusion, rise to altitude and (in the probable absence of \(\mathrm{H}_2\) and He) form, perhaps together with atomic nitrogen, the principal constituent of the highest layers. In the lower layers the oxygen atoms combine with \(\mathrm{O}_2\) molecules, forming \(\mathrm{O}_3\). Hence it may be concluded that above the level of maximum density the concentration of \(\mathrm{O}_3\) decreases rapidly with height; the concentration of \(\mathrm{O}\) increases with height and, finally, the concentration of \(\mathrm{O}_2\) predominates. At an altitude of 80 km, \(1\ \mathrm{cm}^3\) contains \(3\cdot10^{11}\) oxygen atoms and \(10^{14}\) molecules of \(\mathrm{O}_2\); at an altitude of 120 km—\(3\cdot10^{11}\) oxygen atoms and \(10^{12}\) molecules of \(\mathrm{O}_2\). Thus the ratio between \(\mathrm{O}\) and \(\mathrm{O}_2\) increases from \(1:300\) to \(1:3\). The chief argument in favor of this assumption is the “non-polar aurora,” which proves the presence at altitude of a considerable quantity of oxygen atoms (though not their altitude).

The ionizing action of solar radiation is illustrated by the following table, which gives the dissociation or ionization energies in volts, the corresponding limiting wavelengths, frequencies, and numbers of quanta of the required (or greater) energy received by a column of the atmosphere with a cross section of \(1\ \mathrm{cm}^2\) during 1 sec. when the Sun is at the zenith.

Accordingly, the ionization of helium is not due to ultraviolet radiation; on the contrary, it is precisely this radiation that causes the ionization of atomic oxygen, since it alone absorbs radiation between 910 and 770 Å.

The theory of photoelectric ionization leads Chapman to the following maximum numbers of electrons in \(1\ \mathrm{cm}^3\) (at the equator): \(4\cdot10^6\), if the absorbing gas is atomic oxygen (\(\mathrm{O}\)); \(6\cdot10^5\) for \(\mathrm{O}_2\), \(2.5\cdot10^5\) for \(\mathrm{N}_2\), and \(10^6\) for \(\mathrm{H}_2\). The number

atoms or molecules at the same altitude will be \(2.5\cdot 10^9\) for O, \(7\cdot 10^9\) for O\(_2\), \(9\cdot 10^9\) for N\(_2\), and \(3\cdot 10^{10}\) for H\(_2\). To estimate the altitude of this layer, one may indicate, with sufficient confidence (with the exception of H\(_2\)), the altitude of the upper layer, i.e. 220 km.

TABLE 2

Gas	Energy in V	Wavelength less than	Frequency greater than	Number of quanta
		Dissociation
O\(_3\)	\(4\frac{1}{4}\)	2900 Å	\(1.0\cdot 10^{15}\)	\(5\cdot 10^{15}\)
O\(_2\)	\(6\frac{1}{2}\)	1850 Å	\(1.6\cdot 10^{15}\)	\(1\cdot 10^{14}\)
		Ionization
O	13.6	910 Å	\(3.3\cdot 10^{15}\)	\(7\cdot 10^8\)
O\(_2\)	16.1	770 Å	\(3.9\cdot 10^{15}\)	\(8\cdot 10^6\)
H\(_2\)	16.1	770 Å	\(3.9\cdot 10^{15}\)	\(8\cdot 10^6\)
N\(_2\)	16.9	730 Å	\(4.1\cdot 10^{15}\)	\(2\cdot 10^6\)
He	25.3	490 Å	\(6.2\cdot 10^{15}\)	0.3

Since the action of ultraviolet radiation as the ionizer of the upper layer is absent for the lower layer, for this layer at 100 km it is necessary to find another radiation—though necessarily of solar origin, in view of the clearly predominant importance of the daytime side of the Earth. Already in the section devoted to terrestrial magnetism (§ 9a) it was said why one may admit only neutral corpuscular radiation, ionizing, first of all, molecular nitrogen.

The difference between the ionized layers at altitudes of 100 and 220 km extends not only to the kind of ionization. It should also be accepted that in the upper layer the number of free electrons is almost as great as the number of positive ions, since by the addition of electrons to neutral atoms and molecules only a small number of negative ions can be formed. On the contrary, in the lower layers there are probably considerably more ions than electrons. The presence of electrons is, it is true, proved by measurements of the polarization and double refraction of electromagnetic waves; however, these measurements do not speak against the presence of a large number of ions, since with respect to wave propagation one electron can be replaced by \(4\cdot 10^4\) ions (the mass ratio of ion and electron). Ion densities of \(10^8\)—\(10^9\) in 1 cm\(^3\), required by the theory of atmospheric dynamo (§ 9b), by no means appear improbable; one may

suppose that these are positive N\(_2\)-ions and negative O-ions. Since the mean lifetime of a free electron is inversely proportional to the density of the air, it becomes understandable why the height of the lower ionized layer at night appears, according to radio-measurement data, to be increased.

In connection with this Chapman touches upon the green line in the light of the night sky. The absolute photometric intensity of this light was measured by Lord Rayleigh\(^{41}\); expressed in quanta of the corresponding magnitude (2.22 V), this intensity permits the conclusion that in every second, in a column of atmosphere with a cross-section of 1 cm\(^2\), \(1.8\cdot10^8\) oxygen atoms undergo transitions associated with the emission of the green line; \(1.8\cdot10^8\) quanta of 2.2 V constitute a fairly considerable part (\(^{1}/_{23}\)) of the energy of \(7\cdot10^8\) quanta of 13.6 V which is delivered in 1 sec. during the day for the ionization of atomic oxygen. The energy of the green line must be dissociation energy; this energy is absorbed during the day, and later (and even at night), owing to collisions during recombination, or reactions of another kind among the dissociated particles, goes into the formation of metastably excited oxygen atoms. Since the intensity of the green line changes little during the night (although over the course of the whole night \(10^{13}\) transitions occur in a column of 1 cm\(^2\)), the number of particles accumulating solar energy from day to night must be very large. That is why oxygen atoms are under discussion.

The assumption that the lower layer at 100 km is ionized by corpuscular radiation from the Sun encounters, when the ranges (Reichweiten) are considered, a substantial difficulty. At a velocity of 1600 km/sec, Ca\(^+\)-ions in air at a pressure of 760 mm have a range of 0.15 cm. The equivalent path in air of particles referred to penetrating into the atmosphere down to a height of 100 or 80 km must be equal to at least 1.5 or 10 cm. However, the fastest \(\alpha\)-particles have a range of only 7 cm. Chapman’s attempts to get around this difficulty are rather dubious; the only possibility is that, at the insignificant density in the upper layers of the atmosphere, particles penetrate farther than one may assume by extrapolating the data of laboratory experiments according to the law of equivalent masses. In any case, the aurora borealis argues that charged particles of solar origin penetrate down to a height of 80 km; thus there is no reason to think that neutral particles (neutrons?) penetrate to a lesser depth.

Among other kinds of radiation, \(\gamma\)-rays should be mentioned; the \(\gamma\)-rays Ra C are most strongly absorbed at an altitude of 26 km; \(\beta\)-rays—at an altitude of about 50 km. Penetrating radiation apparently has no great influence on the ionization of the high layers of the atmosphere; Benndorf (H. Benndorf)\(^{150}\) analytically dis-

produced a significant effect of penetrating radiation only because he took exceptionally high values for the recombination coefficients \(\sigma\). On the contrary, Gelbert \(^{147}\)—whose views on ionization \(^{146—148}\) differ greatly from those of Chapman, whom he generally takes little into account—believes that penetrating radiation creates, at an altitude of 50 to 70 km, a permanent weakly conducting layer, to which the constancy of propagation of long radio waves should be attributed. However, there is no need at all to explain ionization on the night side by omnidirectionally penetrating cosmic radiation. At such altitudes, where recombination proceeds very slowly, nighttime ionization may be regarded as a remnant (Rückstand) of daytime ionization; where the night is long (polar winters), charged corpuscles of solar origin, penetrating to the night side owing to the proximity of the magnetic pole, act as the ionizer. Only very soft, but intense, components of penetrating radiation, not observed near the surface of the Earth, can be active.

12. CONCLUDING REMARK

Electromagnetic waves now give us a powerful tool for the electrical investigation of the atmosphere. One can only wish that, in doing so, sufficiently careful account were taken of the manifold connection with terrestrial magnetism, for which such abundant observational material exists.

LITERATURE

General surveys

1. S. Chapman, Some phenomena of the upper atmosphere (Bakerian Lecture), “Proc. Roy. Soc. London”, (A), 132, 353—574, 1931.
2. J. Bartels, Die höchsten Atmosphärenschichten, Ergebnisse d. exakten Naturwiss., 7, 114—157, 1928, “Die Naturwiss.”, 16, 301—307, 1928.
3. J. Bartels, Geophysikalischer Nachweis von Veränderungen der Sonnenstrahlung, Ergebnisse d. exakten Naturwiss., 9, 38—78, 1930.
4. G. M. B. Dobson, The uppermost regions of the earth’s atmosphere (Halley Lecture), Oxford 1926, p. 22.
5. Int. Research Council Reports of the Commission appointed to further the study of solar and terrestrial relationships, 3 reports 1926, 1929, 1931.
   Distributed through Prof. Chapman (Imperial College of Science and Technology, South Kensington, London S. W. 7).

Aerology

1. E. Frankenberger, Zur Steigerung der Höhenleistung von Registrierballonen, “Gerlands Beitr. z. Geophys.”, 33, 112—117, 1931.
2. A. Wigand, Hochfahrten von Registrierballonen, “Beitr. z. Phys. d. freien Atm.”, 17, 286—289, 1931.

1. A. Wagner, Klimatologie der freien Atmosphäre (in W. Köppen and R. Geiger, Handbuch der Klimatologie, Vol. 1, Part F), Berlin, Gebr. Borntraeger, 1931, p. 70.

2. A. Schedler, “Beitr. z. Phys. d. freien Atm.,” 7, 88, 101, 1915.

3. F. M. Exner, Dynamische Meteorologie, 2nd ed., p. 284, 1915.

4. Hann-Süring, Lehrbuch der Meteorologie, 4th ed., p. 302, Leipzig 1926.

High clouds. Twilight

1. C. Störmer, Merkwürdige Wolken im Höhenintervall 23 bis 26 km über der Erde, “Gerlands Beitr. z. Geophys.,” 32, 63—68, 1931; “Geofysiske Publik.,” 5, No. 2, Oslo, 1927; 9, No. 4, Oslo, 1932; “Quart. Journ. Roy. Meteorol. Soc. London,” 58, 307—309, 1932.

2. O. Jesse, “Meteorol. Zeitschr.,” 1, 127, 1884 and subsequent years up to 8, 306, 1932.

3. A. de Quervain, “Meteorol. Zeitschr.,” 34, 132—133, 1917.

4. K. Boll, “Meteorol. Zeitschr.” 35, 316, 1918.

5. V. Malzev, Luminous night clouds, “Nature,” 118, 14, 1926.

6. C. Dorn, Beobachtungen der Dämmerung und von Ringerscheinungen um die Sonne 1911 bis 1917, Abhandl. Preuss. Meteorol. Inst., 5, No. 5, Berlin 1917.

7. A. Wegener, “Meteorol. Zeitschr.,” 42, 402—405, 1925.

8. F. A. Lindemann and C. M. B. Dobson, “Meteorol. Zeitschr.,” 43, 102—103, 1926, with an addendum by A. Wegener.

9. L. Schwarz, Beobachtungen von leuchtenden Nachtwolken auf der Schneekoppe, “Meteorol. Zeitschr.,” 36, 102—103, 1919.

10. W. Malsch, Leuchtende Bänder am Nachthimmel, “Das Wetter,” 39, 61—63, 134—136, 1922.

11. M. Wolff, C. Hoffmeister, J. Hartmann, “Astron. Nachr.,” 213, 353—356, 1922; 216, 43—35, 89—91, 1922.

12. A. Peppler, Trübungserscheinungen in der Stratosphäre, “Zeitschr. angew. Meteorol.” (“Das Wetter”), 46, 225—233, 1929.

23a. C. Hoffmeister, Ueber Leuchtstreifen und hellen Nachthimmel, “Zeitschr. angew. Meteorol.,” 49, 267—272, 1932.

1. C. Störmer, Leuchtende Nachtwolken, “Meteorol. Zeitschr.,” 49, 359, 1932.

2. P. Grunert and H. Kleinert, Die Dämmerungserscheinungen (Probleme der kosmischen Physik, Vol. 10), Hamburg, H. Grand, 1927.

3. A. Wegener, Beobachtungen der Dämmerungsbögen und des Zodiakallichtes in Grönland, Sitz.-Ber. Akad. Wien. Math.-naturw. Kl., Abt. 11a, 135, 323, 1926.

4. Fr. Schmid, Das Zodiakallicht (Probleme der kosmischen Physik, Vol. 11), Hamburg, H. Grand. 1927.

5. Rolf Müller, Photographisch-photometrische Untersuchungen des Zodiakallichtes, “Zeitschr. Astrophys.,” 1, 35—42, 1930.

6. E. O. Hulburt, The zodiacal light and the “Gegenschein” as phenomena of the Earth’s atmosphere, “Phys. Rev.,” (2) 35, 1098—1118, 1930.

7. F. J. W. Whipple, The Great Siberian Meteor, “Quart. Journ. Roy. Meteorol. Soc. London,” 56, 287—304, 1930; discussions and further literature.

8. R. Süring, Luftdruckwellen und leuchtende Nachtwolken infolge eines Meteorfalls, “Meteorol. Zeitschr.,” 47, 490—492, 1930.

Geometrical picture of radiation

1. M. Milankovitch, Mathematische Klimalehre (in W. Köppen and R. Geiger, Handbuch der Klimatologie, Vol. I, Part A), Berlin 1930.

2. J. von Hann, Handbuch der Klimatologie, 4th ed., edited by K. Knoche, pp. 104—110, Stuttgart 1932.

3. R. Gessler, Die Stärke der Sonnenbestrahlung usw., Abhandl. Preuss. Meteorol. Ins., 8, No. 1, 27 pp. Berlin 1925.

PHYSICS OF THE HIGH LAYERS OF THE ATMOSPHERE

Light of the night sky

1. E. Wiechert, “Physikal. Zeitschr.,” 3, 365, 1901/02.

2. H. D. Babcock, “Astrophys. Journ.,” 57, 209—221, 1923.

3. Lord Rayleigh, The aurora line in the spectrum of the night-sky, “Proc. Roy. Soc. London,” (A), 100, 367—368, 1928.

4. Lord Rayleigh, “Gerlands Beitr. z. Geophys.,” 19, 292—297, 1928.

5. Lord Rayleigh, The light of the night-sky, “Proc. Roy. Soc. London,” (A), 106, 117, 1924; 109, 428, 1925; 119, 11, 1928.

6. H. S. Jones, “Proc. Roy. Soc. London,” (A), 126, 246—259, 1930.

7. Lord Rayleigh, Absolute intensity of the aurora line in the night-sky, “Proc. Roy. Soc. London,” (A), 129, 458—467, 1930.

8. J. Dufay, Spectre, couleur et polarisation de la lumière du ciel nocturne, “Journ. de phys. et le Radium,” (6), 10, 219—240, 1929.

9. R. Ruedy, Das Licht des Nachthimmels und die grüne Linie 5577, 3 Å, “Naturwiss.,” 18, 401—411, 1939.

10. Lord Rayleigh, On a night-sky of exceptional brightness, and on the distinction between the polar aurora and the night-sky, “Proc. Roy. Soc. London,” (A), 131, 376—381, 1931.

44a. L. A. Sommer, “Z. Physik,” 57, 592, 1929; 77, 374—390, 1932.

1. J. C. Mc Lennan, The aurora and its spectrum (Bakerian Lecture), “Proc. Roy. Soc. London,” (A), 120, 327—357, 1928.

2. J. Bartels, “Naturwiss.,” 19, 190—191, 1931.

3. J. Dufay, Les bandes d’émission de l’aurore polaire dans le spectre du ciel nocturne, “Comp. Rend.,” 193, 1106—1108, 1931.

Falling stars

1. F. A. Lindemann u. G. M. B. Dobson, A theory of meteors etc., “Proc. Roy. Soc. London,” (A), 102, 411, 1923; 103, 721, 1923.

2. F. A. Lindemann, “Nature,” 118, 195—198, 1926.

3. C. M. Sparrow, Physical theory of meteors, “Astrophys. Journ.,” 63, 90—110, 1926.

4. M. Radakovic, “Meteorol. Zeitsch.,” 43, 441—455, 1926; 44, 326—331, 1927.

5. H. B. Maris, A theory of meteors, “Terrestrial Magnetism,” 34, 309—316, 1929.

6. A. Wegener, Anfangs- und Endhöhen grosser Meteore, “Meteorol. Zeitschr.,” 44, 281—284, 1927.

7. S. Kahlke, Meteorschweife und hochatmosphärische Windströmungen, “Ann. d. Hydrographie,” 49, 293—299, 1921.

Ozone

1. F. W. P. Götz, Das atmosphärische Ozon, Ergebn. d. kosmischer Physik, 1, 180—235, Leipzig 1931.

2. Ch. Fabry et H. Buisson, L’absorption des radiations dans la haute atmosphère, Mémorial des Sciences Phys., Fasc. 11, Paris 1930.

3. Rapport de la Réunion de l’ozone et de l’absorption atmosphérique, mis en ordre par Ch. Fabry, “Gerlands Beitr. z. Geophys.,” 24, 1—77, 1929.

4. G. M. B. Dobson, The ozone in the earth’s upper atmosphere, “Beitr. z. Phys. d. freien Atm.,” 16, 76—85, 1929.

5. G. M. B. Dobson and coworkers, Measurements of the amount of ozone etc., “Proc. Roy. Soc. London,” (A), 110, 660—693, 1926; 114, 521—541, 1927; 122, 456—486, 1929; 129, 411—433, 1930.

6. F. W. P. Götz a. G. M. B. Dobson, Observations of the height of the ozone, “Proc. Roy. Soc. London,” (A), 120, 251—259, 1928; 125, 292—294, 1929.

7. F. W. P. Götz u. R. Ladenburg, Ozongehalt der unteren Atmosphärenschichte, “Naturwiss.,” 19, 373—374, 1931.

8. E. H. Gowan, The effect of ozone on the temperature of the upper

atmosphere, “Proc. Roy. Soc. London,” (A), 120, 655—669, 1928; 128, 531—550, 1930. (Cf. 55, p. 225).

1. G. M. B. Dobson, A photoelectric spectrophotometer for measuring the amount of atmospheric ozone, “Proc. Phys. Soc. London,” 43, 324—337, 1931.

2. R. J. Strutt, “Proc. Roy. Soc. London,” (A), 94, 260, 1918.

3. H. Pelzer, “Ann. d. Physik,” 83, 362—384, 1927.

4. H. Hellmann, Über das Auftreten von Ionen beim Zerfall von Ozon und die Ionisation der Stratosphäre, “Ann. d. Phys.,” (5), 2, 707—732, 1929.

5. S. Chapman, A theory of upper atmospheric ozone, Memoirs Roy. Meteorol. Soc. London, 3, 103—125, 1930; On ozone and atomic oxygen in the upper atmosphere, “Phil. Mag.,” 10, 345—352, 369—383, 1930.

6. G. Herzberg, “Naturwiss.,” 20, 577, 1932.

7. O. Hoeppler, Untersuchungen über Sonnen- und Himmelsstrahlung, Veröff. meteorol. Obs. Aachen 1932.

69a. D. Chalonge, Sur la répartition de l’ozone dans l’atmosphère, “Journ. de phys. et le Radium,” (7) 3, 21—42, 1932.

Sound

1. P. Duckert, Über die Ausbreitung von Explosionswellen in der Atmosphäre, Ergebn. d. Kosm. Phys., 1, 236—290, Leipzig 1931.

2. O. Meisser, Luftseismik, Handb. d. Experimentalphys., 25, Pt. III. Leipzig 1930.

3. A. Wegener, Akustik der Atmosphäre, Müller-Pouillet, Lehrb. d. Phys. 5, Pt. I. Braunschweig 1928.

4. G. Angenheister, Das Problem der Schallausbreitung, “Meteorol. Zeitschr.,” 43, 467—471, 1926.

5. H. Bann(d)orf, Über die experimentelle Erforschbarkeit der höheren Schichten der Atmosphäre, “Physikal. Zeitschr.,” 30, 97—115, 1929.

6. H. Hergesell and P. Duckert, Die Ergebnisse der Sprengungen zu Forschungszwecken in Deutschland usw. Arbeiten d. Preuss. Aeron. Obs. Lindenberg, 16, H. B. 1927; H. D. 1929.

7. J. Kölzer, Beobachtungsergebnisse über Schallausbreitung auf nahe Entfernungen und Schlussfolgerungen zum Problem der anomalen Schallausbreitung, Abhandl. Preuss. Meteorol. Inst., 10, No. 1, p. 27, Berlin 1932.

8. B. Sandmann, Beiträge zur Schallfortpflanzung, “Gerlands Beitr. z. Geophys.,” 28, 241—278, 1930.

9. E. Wiechert, Über die Schallausbreitung in der Atmosphäre, “Meteorol. Zeitschr.,” 43, 81—91, 1926.

10. B. Gutenberg: Schallgeschwindigkeit und Temperatur in der Stratosphäre, “Gerlands Beitr. z. Geophys.,” 27, 217—225, 1930.

11. O. Meisser, Schallausbreitung in der Atmosphäre bei künstlichen Sprengungen, “Physikal. Zeitschr.,” 30, 170—175, 1929.

12. F. J. W. Whipple, The detonating meteor of 1926, sept. 6. An instance of an outer zone of audibility, Monthly Notices Roy. Astron. Soc. London, Geophys. Suppl., 2, 89—96, 1928.

13. F. J. W. Whipple, The investigation of air waves from explosions. Progress in England, “Quart. Journ. Roy. Meteorol. Soc. London,” 57, 331—335, 1931; 58, 471—478, 1932.

14. E. Schrödinger, Zur Akustik der Atmosphäre, “Physikal. Zeitschr.,” 18, 445—453, 567, 1917.

Pressure and Composition

1. S. Chapman and E. A. Milne, The composition, ionisation and viscosity of the atmosphere at great heights, Quart. Journ. Roy. Meteorol. Soc. London, 46, 357—398, 1920.

2. H. B. Maris, The upper atmosphere, “Terrestrial Magnetism,” 33, 233—255, 1928; 34, 45—53, 1929.

3. P. S. Epstein, Settling of gases and constitution of the atmosphere, “Phys. Rev.,” (2), 33, 269—270, 1929; Über Gasentmischung in der Atmosphäre, “Gerlands Beitr. z. Geophys.,” 35, 153—165, 1932.

1. J. H. Jeans, “Bull. Mount Weather Observ.,” 2, 347, Washington 1910.

2. J. H. Jeans, Dynamische Theorie der Gase, Braunschweig 1926.

3. Helge-Petersen, On the influence on the composition of the air of a possible high temperature in the highest strata of the atmosphere, Publ. Dan. Meteorol. Inst., No. 6, Kopenhagen 1928.
4. Helge-Petersen, Diskussion mit W. Anderson, “Phys. Zeitschr.,” 28, 510—513, 1927; 29, 232—233, 492—493, 1928.

Data of Terrestrial Magnetism

1. C. Angenheister u. J. Bartels, Das Magnetfeld der Erde, Wien-Harms, Handb. d. Experimentalphysik, B. 25. T. I, Leipzig 1928.
2. J. Bartels, Bericht über die Fortschritte unserer Kenntnisse vom Magnetismus der Erde, Geographisches Jahrbuch, 40, 316—373; 44, 1—36. Gotha, J. Perthes, 1926 und 1930.
3. J. Bartels, Terrestrial magnetic activity and its relations to solar phenomena, “Terrestrial Magnetism,” 37, 1—52, 1932.
4. S. Chapman, On the theory of the solar diurnal variation of terrestrial magnetism, Phil. Trans. London, (A), 122, 369—386, 1929.
5. S. Chapman, The solar and lunar diurnal variations of terrestrial magnetism, Phil. Trans. London, (A), 218, 1—1189, 1919.
6. S. Chapman, The lunar diurnal magnetic variation at Greenwich and other observatories, Phil. Trans. London, (A), 225, 49—91, 1925.
7. J. Bartels, Gezeitenschwingungen der Atmosphäre, Wien-Harms. Handb. d. Experimentalphysik, 25, T. I, 163—210, Leipzig 1928.
8. S. Chapman, The influence of a solar eclipse upon upper atmospheric ionization, Monthly Notices Roy. Astron. Soc. London, 92, 413—420, 1932.
9. J. C. P. Miller, Map of the corpuscular eclipse track of 1932 August, Monthly Notices Roy. Astron. Soc. London, 92, 421—422, 1932.
   99a. G. Millington, Ionization charts of the upper atmosphere, “Proc. Phys. Soc. London,” 44, 580—593, 1932.
10. T. G. Cowling, On the radial limitation of the sun’s magnetic field, Monthly Notices Roy. Astron. Soc. London, 90, 140—154, 1929.
11. C. Störmer, Über die Probleme des Polarlichtes, Ergebn. d. kosm. Phys., 1, 1—86, Leipzig 1931.
12. E. Brüche, Jahrbuch d. Forschungs-Inst. der AEG 2, 1930; “Naturwiss.” 18, 1085—1093, 1930; “Zeitschr. f. Astrophys.” 2, 1931; “Terrestrial Magnetism,” 36, 41—52, 1931.
13. A. Schuster, “Phil. Trans. Roy. Soc. London,” (A), 180, 467—518, 1889; 208, 163—204, 1907.
14. Balfour Stewart, Encyclopaedia Britannica, 9th ed., 16, 181—184, 1878.
15. A. Schuster, “Proc. Roy. Soc. London,” (A), 85, 45—50, 1911.
16. S. Chapman a. V. C. A. Ferraro, A new theory of magnetic storms, “Nature,” 126, 129—130, 1930; “Terrestrial Magnetism,” 36, 77—97, 171—186, 1931; 37, 147—156, 1932.
17. Ad. Schmidt, Über die Ursache der magnetischen Stürme, “Meteorol. Zeitschr.,” 16, 385—397, 1899.
18. S. Chapman, “Proc. Roy. Soc. London,” (A), 95, 61—83, 1918; 115, 242—267, 1927.
19. F. A. Lindemann, Note on the theory of magnetic storms, “Phil Mag.,” 38, 669—684, 1919.
20. S. Chapman a. V. C. A. Ferraro, Solar Streams of corpuscles, Monthly Notices Roy. Astron. Soc. London, 89, 456—479, 1929.
21. V. C. A. Ferraro, Monthly Notices Roy. Astron. Soc. London, 91, 174—187, 1930.
22. E. A. Milne, On the possibility of the emission of highspeed atoms from the sun and stars, Monthly Notices Roy. Astron. Soc., 86, 459, 578, 1926.

1. E. A. Milne, in Handbuch d. Astrophys., 3, 1. Hälfte, 173—183, Berlin, J. Springer, 1930.

2. E. A. Hulburt. The origin of the aurora borealis, “Terrestrial Magnetism,” 33, 11—13, 1928; “Phys. Rev.,” (2), 32, 993—996, 1928 (discussion by Chapman).

3. H. B. Maris a. E. O. Hulburt, A theory of aurorae and magnetic storms, “Phys. Rev.,” (2), 33, 412—431, 1929.

4. E. O. Hulburt, The ultraviolet light theory of aurorae and magnetic storms, “Phys. Rev.,” (2), 34, 344—351, 1929; 36, 1560—1569, 1930.

5. S. Chapman, On solar ultraviolet radiation as the cause of auroral and magnetic storms, Monthly Notices Roy. Astron. Soc. London, Geophys. Suppl. 2, 296—300, 1930.

6. International characteristic numbers are processed and published by the Netherlands Meteorological Institute in the journals “Terrestrial Magnetism,” “Atmospheric Electricity,” and “Meteorologische Zeitschrift” (on the meaning of characteristic numbers cf. A. d. Schmidt, “Meteorol. Zeitschr.,” 33, 481—492, 1916, and J. Bartels, “Terrestrial Magnetism,” 37, 1—52, 1932).

118a. J. A. Fleming, The Scientific Monthly, 39, 499—530, 1932.

1. C. Chree a. J. M. Stagg, Recurrence phenomena in terrestrial magnetism, Phil. Trans. London, (A), 227, 21—62, 1927.

2. J. M. Stagg, Meteorological Office London, Geophysical Memoirs, 4, No. 10, p. 8, 1927.

3. H. U. Sverdrup, Magnetic etc. results, Maud-Expedition, 1918—1925, Carnegie Inst. Washington, Publ. No. 175, v. 6, 1927.

4. W. J. Peters a. C. C. Ennis, The 27-day recurrence in earth currents, “Terrestrial Magnetism,” 31, 57—70, 1926.

5. F. Schindelhauer, “Naturwiss.,” 20, 672, 1932.

6. W. M. H. Greaves a. H. W. Newton, On the recurrence of magnetic storms, Monthly Notices Roy. Astron. Soc. London, 89, 641—646, 1929.

7. Internat. Astron. Union, Bull. for character. figures of solar phenomena, Eidgen. Sternwarte, Zurich. Since 1928, 4 issues per year; observations for 1923—1928, calculated by Brunner, were issued in 1932 in Zurich. The numbers for 1928—1930 were corrected by Brown.

   H. C. Brown, “Terrestrial Magnetism,” 35, 237—244, 1930; 36, 345—348, 1931.

8. A. W. Lee, Meteorol. Office, Profes. Notes, No. 56, London, 1930.

9. J. Bartels, “Naturwiss.,” 19, 190—191, 1931.

10. W. M. H. Greaves a. H. W. Newton, Monthly Notices Roy. Astron. Soc. London, 88, 556—567, 1928; 89, 84—92, 1929.

11. G. E. Hale, “Astrophys. Journ.,” 73, 379—412, 1931; W. Grotrian, “Naturwiss.,” 20, 55—56, 1932.

12. W. M. H. Greaves a. H. W. Newton, Monthly Notices Roy. Astron. Soc. London, 88, 556—567, 1928.

13. Ch. Maurain, “Ann. Inst. Phys. du Globe,” Paris, 5, 86—96, 1927.

14. J. M. Stagg, Meteorol. Office, Geophysical Memoirs, No. 42, London, 1928.

15. H. B. Maris, “Phys. Rev.,” (2), 37, 1680—1681, 1931; 39, 509—514, 1932.

16. J. Bartels, Eine universelle Tagesperiode der erdmagnetischen Aktivität, “Meteorol. Zeitschr.,” 42, 147—152, 1925.

17. J. Baltels, “Naturwiss.,” 12, 194—195, 1924.

18. Ad. Schmidt, “Meteorol. Zeitschr.,” 42, 238—241, 1925.

19. B. Rolf, Giant Micropulsations at Abisko, “Terrestrial Magnetism,” 36, 9—14, 1931.

20. Leiv. Harang, Observations of micropulsations in the magnetic records at Tromsö, “Terrestrial Magnetism,” 37, 57—61, 1932.

21. S. Chapman a. J. M. Stagg, On the variability of the quiet-day diurnal magnetic variation, “Proc. Roy. Soc. London,” (A), 123, 27—53, 1929; 130, 668—697, 1931.

1. J. Bartels, Use of magnetic data for investigating radiation from the sun, Trans. Amer. Geophys. Union, Twelfth Annual Meetg., 126—131, Washington 1931.

2. J. Bartels and W. J. Rooney, A typical case of variability of quiet-day diurnal variation in terrestrial magnetism and earth currents, “Terrestrial Magnetism,” 37, 53—55, 1932.

3. J. Bartels, Statistical methods for research on diurnal variations, “Terrestrial Magnetism,” 37, 291—302, 1932.

Ionization

1. S. Chapman, The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth, “Proc. Phys. Soc. London,” 43, 26—45, 483—501, 1931.

2. K. Försterling and H. Lassen, Die Ionisation der Atmosphäre und die Ausbreitung der kurzen elektrischen Wellen über die Erde, “Z. techn. Phys.,” 12, 453—469, 502—527, 1931.

3. E. O. Hulburt, Ions and electrical currents in the upper atmosphere of the earth, “Phys. Rev.,” (2), 34, 1167—1183, 1929.

4. E. O. Hulburt, Ionization in the upper atmosphere. Variation with longitude, “Phys. Rev.,” (2), 35, 240—247, 1930.

5. E. O. Hulburt, Atmospheric ionization by cosmic radiation, “Phys. Rev.,” (2), 37, 1—8, 1931.

6. E. O. Hulburt, Tables of the ionization in the upper atmosphere, “Phys. Rev.,” 39, 977—992, 1932.

7. E. V. Appleton and R. Naismith, Some measurements of upper-atmospheric ionisation, “Proc. Roy. Soc. London,” (A), 137, 36—54, 1932.

8. H. Benndorf, Über den durch die Hesssche Höhenstrahlung bedingten Ionisations- und Leitfähigkeitszustand der höheren Luftschichten, “Physikal. Zeitschr.,” 27, 686—692, 1926.

1. ... ↩

4. Reference 93. ↩↩↩↩↩