Upper Layers of the Atmosphere1

I. Bartels, Berlin-Eberswalde.

I. Introduction. Data of aerology. II. Scattering and the world illumination. III. Some optical phenomena. IV. Polar lights. a) Position. Occurrence. b) Spectrum. V. Ozone. a) Qualitative investigation. b) Methods of quantitative measurement. c) Data from investigations of the quantitative content of ozone. d) Height of the ozone layer. e) Temperature. Biological significance. VI. Propagation of sound. VII. Pressure and composition. VIII. Data of terrestrial magnetism. a) System of currents producing the daily variations. b) Basic idea of the explanation. c) Lunar variations. d) Data on electrical conductivity. e) Difficulties. f) Magnetic disturbances. g) Other variations. IX. Electromagnetic waves. X. Ionization. a) General. b) Ultraviolet radiation of the sun. c) Application of the theory of Ingham. d) Solar γ-rays. e) Penetrating radiation. f) Solar corpuscular radiation. g) Survey of data on electrical conductivity. XI. Bibliography.

I. Introduction. Data of Aerology.

At the present time meteorological measurements in the free atmosphere are made visually during ascents in a free balloon only incidentally or for special purposes. In order to establish the distribution of wind with height, theodolite observation from the ground of the motion of small free pilot balloons is sufficient; pressure, temperature, sometimes also humidity and wind speed are recorded by light meteorographs raised on kites and on free or tethered balloons without an observer. Heights above 10 km are reached only by free sounding balloons. The rubber envelope of the latter is filled with several cubic meters

of hydrogen, and is sealed. The balloon rises freely, expanding as atmospheric pressure decreases, until its envelope bursts. The meteorograph lifted by the balloon, attached to a parachute or to another smaller balloon, slowly descends from the altitude reached, which depends only on the strength and homogeneity of the rubber. Many such ascents exceed 20 km. The maximum altitude of ascents with recording was reached in 1913–1914 in Batavia and was 31 km (6); the pilot balloons of the kite station in Friedrichshafen reached 32 km.

Aerological ascents showed that the atmosphere is divided into two substantially different layers, lying one above the other; the boundary between them passes at the equator at approximately an altitude of 16 km, in central Europe at 10.5 km, and at the poles only slightly lower. In the lower layer, the troposphere, the temperature, as a rule, decreases with height, by approximately 5°C/km; clouds form almost exclusively only in this layer (cf., however, p. 198). In the upper layer, the stratosphere, on the contrary, the vertical distribution of temperature is very uniform; upward it increases very slowly. In connection with the fact that above the equator the boundary of the troposphere is situated higher, it should be noted that at the same altitude (for example 17 km) the stratosphere above the equator is colder (−80°) than above central Europe (−54°). During the aforementioned ascents in Batavia the lowest mean temperature was found at an altitude of 17 km and was −85°; in one case −92° was measured at an altitude of 15.5 km. At greater heights the temperature again rose (−55° at 26 km).

A theory of this division of the atmosphere was given by R. Emden and others. The water vapors of the atmosphere have an infrared absorption spectrum, and thanks to this the atmosphere absorbs the hot solar radiation falling from above less than the dark radiation of the earth’s surface and of the atmosphere itself. Under the influence of ascending and descending fluxes of radiant energy, the lower unstable layer (troposphere) is formed—the temperature conditions of which are determined, in the usual way, by convection (mixing-

mixing) and advection (horizontal displacement of air),—and an upper, stable, almost isothermal layer of about \(-54^\circ\) (the stratosphere), whose temperature in the upward direction apparently slowly tends toward a limiting value of about \(-20^\circ\) C.

At present the state of the higher layers can be inferred only indirectly. The question remains open whether it will be possible to send recording instruments to still greater heights, at least by means of rockets. I. Kölder designed a rocket meteorograph in which atmospheric pressure and temperature are recorded on a drum set in rotation by a clock mechanism. The instrument is fastened in the head of the rocket; at the highest point of flight a parachute opens automatically, on which the instrument descends, making its record during the descent. In tests, still few in number, the instrument withstood accelerations of about \(50\ \text{m/sec}^2\), and a height of \(700\ \text{m}\) was reached. A. Vigan’s meteorographic shell (9) is arranged without a clock mechanism; the readings of the aneroid during the fall of the parachute are recorded photographically on a special drum set in rotation by a bimetallic thermometer (the temperature is marked as a function of pressure). By following the descending parachute with a theodolite, one can also obtain information on the direction and speed of the wind. In addition, it has been proposed to determine the wind at great heights from the motion of artificial smoke clouds (8), produced by a shot, or from the deviation of a bullet directed vertically upward (7). During the war the French used pilot balloons to which firecrackers were attached, exploding after previously established intervals of time and whose sound was recorded on the ground at several stations (9a).

In any case, heights above \(30\ \text{km}\), just as depths of more than \(10\ \text{km}\), are still no more directly accessible to us than the Moon or another celestial body. However, there are various possibilities for indirectly judging the composition and state of the upper layers of the atmosphere. The most important of these theoretical and empirical methods and the data obtained,

considered by them will be discussed below; at the same time, some sections are set forth somewhat more briefly, with references given to the corresponding other surveys. The nature of geophysical problems is such that one has to enter into the discussion of many risky hypotheses, the resolution of which is still impossible.

II. Scattering into world space.

If the atmosphere rotated with the same angular velocity as the solid Earth, then on a circle of radius 42,000 km (6.6 Earth radii) in the equatorial plane the centrifugal force and the force of gravity would balance each other. M. Smoluchowski (11) investigated under what conditions this circle turns into a surface closed at the poles. If one assumes that along the boundary surface the pressure is everywhere the same and that inside it the atmosphere rotates, while outside it is at rest, then the surface takes the form of a spheroid with a polar radius of 28,000 km. This calculation, which has entered some textbooks, has, however, for a number of reasons only a purely academic significance, since at such a distance the density of the atmosphere is practically zero; a count gives there one molecule in the volume of a cube with edge \(10^{75}\) km, whereas the distance to certain spiral nebulae is only \(10^6\) light-years \(= 10^{19}\) km.

The question of under what conditions a planet is able, by its attraction, to compensate the tendency of its atmosphere to expand is most clearly solved by the concepts of the kinetic theory of gases (10,12). A body, initially at rest and attracted to the Earth from a very great distance, reaches its surface with the velocity \(c_0 = \sqrt{2ga} = 11\) km/sec (\(g\) — acceleration of gravity, \(a\) — Earth’s radius). Conversely, a body moving away from the Earth with a velocity greater than 11 km/sec will depart from it along a hyperbola and will not return to it again. According to the Maxwell–Boltzmann law of the distribution of velocities, in air there are always molecules with velocities greater than \(c_0\), and at sufficiently great heights (above 800 km) almost all molecules flying away from the Earth will not meet

on their way other molecules and will therefore be lost to the Earth.

If the planet’s gravitational field is characterized by the limiting velocity \(c_0\), and the gas by the mean velocity \(c\) of its molecules \(\left(c^2=\dfrac{3RT}{M},\ R\text{—the universal gas constant, }T\text{—absolute temperature, }M\text{—molecular weight}\right)\), then, according to Jeans (10), the time \(t\) in which the planet loses as much gas as is contained in an atmospheric layer 1 cm thick, situated at the beginning of the outer, assumed isothermal part of the atmosphere, is determined as follows:

\[ t=\frac{4.34}{c}\cdot \frac{e^{\frac{3}{2}c_0^2/c^2}} {1+\frac{3}{2}\frac{c_0^2}{c^2}} \ \text{sec}. \]

\(t\) is smaller, i.e. the atmosphere is dispersed the faster, the greater \(c\) is, i.e. the higher the temperature or the smaller the molecular weight of the gas. For the Earth’s atmosphere consisting of hydrogen at \(30^\circ\text{C}\), \(t\) would be \(10^7\) years; at \(300^\circ\text{C}\), \(t=1\) day; at \(500^\circ\text{C}\), \(t<1\) sec. Jeans solved this equation for \(c\) for various celestial bodies (for a given \(c_0\)); the table gives the critical mean molecular velocities \(c\) corresponding to different values of the dispersal time \(t\).

	Mass (Earth = 1)	Radius in km	Acceleration of gravity at the surface (Earth = 1)	Limiting velocity \(c_0\), km/sec	Critical mean velocity of molecules \(c\) (km/sec) for \(t=1\) day	Critical mean velocity of molecules \(c\) (km/sec) for \(t=10\) years	Critical mean velocity of molecules \(c\) (km/sec) for \(t=10^6\) years
Sun	300 000	696 000	27,9	620	140	130	110
Earth	1	6 370	1,0	11	2,7	2,4	2,1
Mercury	0,06	2 232	0,41	4,5	1,1	1,0	0,8
Moon	0,0123	1 740	0,165	2,4	0,60	0,54	0,46

Even negligible differences in the mean molecular velocity \(c\) cause a strong variation in the dispersal time.

The last three columns of this table should be compared with the above-cited data concerning \(c\) for several gases at different temperatures.

Molecular weight	Gas	Mean speed of molecules in km/sec at temperature:	Mean speed of molecules in km/sec at temperature:	Mean speed of molecules in km/sec at temperature:	Mean speed of molecules in km/sec at temperature:
Molecular weight	Gas	\(-100^\circ\) C	\(30^\circ\) C	\(300^\circ\) C	\(7{,}000^\circ\) C
2	Hydrogen	1.16	1.94	2.66	9.45
4	Helium	1.09	1.38	1.90
18	Water vapor	0.49	0.63	0.88
32	Oxygen	0.37	0.46	0.67
44	Carbon dioxide	0.31	0.39	0.57

Thus the Sun, despite its great attractive force, will lose through thermal motion only a vanishingly small amount of gas, notwithstanding the high temperature of the latter. The Earth will preserve its atmosphere for geological periods. Mercury, being close to the Sun, has so high a temperature that an atmosphere can hardly be supposed on it; and for the Moon, theory and observation agree that it has neither an atmosphere nor, consequently, liquid water.

III. Some optical phenomena.

Twilight (13), in its varied manifestations, is the clearest evidence for the presence of an atmosphere at great heights. The gradations of light and color are not entirely continuous; rather, different twilight arcs can be established, explained by the layered structure of the atmosphere. Quantitative data, however, are rather unreliable. From the disappearance of ordinary twilight at a solar depression of about \(16^\circ\) below the horizon, one may conclude that the height of the illuminated layer of air is about 60 km. Two post-twilight arcs observed by A. Wegener (23) in Greenland are attributed by him to the scattering of light at a height of more than 700 km; it is possible that the zodiacal light (20) also belongs to atmospheric twilight phenomena.

In connection with the eruption of the Krakatoa volcano (Sunda Islands, 1883), unusual twilights were observed over the entire globe; they were explained by the clouding of the upper atmosphere by erupted, very slowly settling particles of ash. Similar phenomena were also noted after subsequent volcanic eruptions, for example after the eruption of Katmai in Alaska in 1912 (12a). Characteristic was the crimson-brown Bishop’s ring around the sun, which had, for example, according to Dorno, an inner diameter of \(23^\circ\), an outer one of \(43^\circ\), at a solar altitude of \(20^\circ\).

It was first possible to determine accurately the height of luminous night clouds, the appearance of which coincided with the anomalous twilights. Beginning in 1885, from mid-May to June, silvery bright clouds were observed in Berlin, lasting until midnight. Jesse (14) photographed these clouds, illuminated by scattered sunlight, simultaneously from different places (Steglitz, Rathenow, Nauen); from the displacement of the clouds relative to the stars he found a height of from 82 to 83 km. The height remained extraordinarily constant. The brilliance of the clouds decreased from year to year until 1890, when the observations ceased; in the last years before their disappearance waves were noticed in the clouds, as in cirrus. The clouds moved predominantly from east to west at a speed of about 100 m/sec. Similar clouds have also been observed recently (18). V. Maltsev (17) rejects the volcanic theory, since silvery clouds have been observed every year independently of eruptions. A. Wegener (22) does not consider it possible that volcanic ash could reach a height of 80 km; his opinion that what is present here are ice clouds similar to ordinary cirrus is not shared by Lindemann and Dobson. Clarity could be brought only by further photogrammetric investigations. Störmer (21) in 1926 observed iridescent clouds at his photogrammetric polar stations in Norway and in one case determined a height of 27 km; the cloud was moving toward O-S-O at a speed of 75 m/sec.

Meteorites, or falling stars, appear on average at a height of 120 km, sometimes up to 200 km, and disappear approximately

tively 40 km lower. They consist of iron or stone and are often no larger than a pea. Owing to their great velocity (10 to 100 km/sec) they compress the air in front of them; in this compression so much heat is developed that the meteor evaporates completely, if its mass is not sufficiently great for it to reach the earth. Dobson and Lindemann (16) attempted, from observational data, to draw conclusions about the density of the air along the path of a meteorite; according to their calculations this density proves to be so great that the atmosphere must be more rarefied than is usually assumed, and moreover, in regions above 50 km the air temperature must reach 300° abs. Although this consequence is confirmed by other observations (cf. p. 218), Sparrow1 cast doubt on the very line of reasoning, and indeed its theoretical foundations seem unreliable. Vetener (24), too, who investigated the initial and final heights of large meteors, considers it premature to draw conclusions from this about the stratification of the atmosphere.

Sometimes meteors leave a luminous tail, visible for several seconds. From the deflection of these tails one can determine the direction of the wind at altitude (15). Apparently, in these high layers as well, the wind direction depends both on place and on time (cf., however, p. 230). Between 30 and 80 km altitude in Europe and North America easterly winds prevail; above them—westerly winds.

IV. Aurora.

a) Position, origin. The position of the aurora in space is well known from Norwegian stereo-photogrammetric measurements (42, 45). Not a single measurement pertains to an altitude less than 77 km; most often the lower boundary lies approximately between 100 and 110 km. Of the various forms of aurora, arcs and curtains apparently do not reach above 200 km; rays, however, rise much farther. The maxi-

small heights of 300 km, coinciding with a time of weak solar activity, were exceeded, during the especially strong disturbances of 1920, by rays reaching 800 km; on September 8, 1926 (41), diffuse gray-violet forms of draperies were noted at a height of more than 1,000 km. Rays that reach great heights have, as a rule, a lower boundary that also lies high.

According to the theories of Birkeland (Birkeland) and Størmer (81), the aurora is, indisputably, the luminescence of atmospheric gases excited by the corpuscular radiation of the sun. Such a conception explains many particulars, for example: the intensification of aurorae during the maximum of the eleven-year period of sunspots; the connection with disturbances of the earth’s magnetic field; the coincidence of the direction of the rays with the lines of force of the latter; the greatest frequency of auroral zones near both magnetic poles. On the other hand, the question of the nature of the particles remains unresolved, as does the circumstance that, during their 36-hour journey from the sun to the earth, their swarm is not dispersed as a result of electrostatic mutual repulsion between them.

It is hardly possible to assume that above 500 km the atmosphere in its normal state is still so dense that it can glow as at a height of 100 km. The aurora reaches the greatest heights precisely during strong magnetic disturbances, and this suggests that, under the electrostatic action of the arriving charges, the atmospheric envelope of the earth undergoes a temporary expansion, like a charged soap bubble. This effect would explain certain characteristic features of magnetic storms; but a quantitative calculation indicates that the charge of the atmosphere is apparently insufficient. Størmer (43, 44) recently discovered that the highest rays always arise only in those parts of the atmosphere that are still illuminated by direct solar rays; there is no unambiguous explanation.

b) Spectrum. From the spectrum of the aurora one may infer the composition of the atmosphere at those heights where it appears, i.e. above 80 km. As long as the conception of a diffusional distribution of the atmosphere was maintained (cf. p. 221), they proceeded

searches for the spectral lines of the lightest gases, hydrogen and helium, were, however, quite unsuccessful. On the other hand, negative bands of nitrogen were discovered, belonging, according to V. Vegard (49), to its singly positively ionized molecules.

It had long been known that the characteristic yellow-green coloration predominating in the aurora is caused by the strong line 5577 Å, but only in recent years has it been possible to assign this line to an already known element. The history of this discovery is remarkable: E. Vikhert (48) established that this line is visible in the spectrum of the night sky every clear evening, and also by moonlight. Rayleigh (38) reported on a spectroscope adapted for visual observation. He was able to photograph this line with the aid of a high-aperture spectrograph of small dispersion (300 Å/mm), and, out of every three nights, two yielded successful photographs (in England) (37). The brightness of the line varies by a factor of 3–4, but without any visible connection with magnetic disturbances. In a true aurora, moreover, nitrogen bands are visible, which are absent in the spectrum of the night sky. The intensity of the “non-polar aurora” outside the polar zones changes little with geographical latitude. Rayleigh supplements these observations with visual photometry of the light of the night sky, the spectrum being subdivided by him, by means of filters, into red, yellow-green, and blue (39). Dufay (J. Dufay) (27) measured the ratio of the brightness of the auroral line to the total brightness of the continuous spectrum of the night sky between 4960 and 6000 Å; the spectrograph was directed approximately toward the pole of the sky. The ratio of the radiant energy of the auroral line to the energy of the indicated part of the spectrum fluctuated between 0.22 and 0.33.

H. D. Babcock (25), at Pasadena and on Mount Wilson, succeeded in measuring the wavelength of the green line very accurately; he simply directed an ordinary photographic camera, connected with a Fabry–Perot interferometer, at the night sky for several hours. It is remarkable that the light of the Moon and stars distorted the system of interference rings so little that photography was possible

almost every night between the first and last quarters of the Moon, even with some cloudiness. Interference was successfully observed for a path difference of the rays of up to 85,000 wavelengths. From the sharpness of the interference rings it follows that this line is simple and no broader than 0.035 Å. The wavelength is equal to \(5577.350 \pm 0.005\) Å.

Among the hypotheses on the origin of the green line, which are now chiefly of historical interest, mention should be made of Vegard’s nitrogen-dust hypothesis (46, 47). On the basis of experiments in the Leiden cryogenic laboratory, where the band spectra of solidified gases under the action of cathode rays were investigated, Vegard attributed the auroral line to the band spectrum of nitrogen; he supposed that in the upper layers of the atmosphere there are solid particles of nitrogen dust, maintained by mutual electrostatic repulsion. In the discussion that followed, one should note H. Peltier’s indication (36) that, in radiative equilibrium between the radiations of the Earth and the Sun, so low a temperature in the upper layers of the atmosphere is impossible—even on the shadow side of the Earth—as is required for nitrogen to freeze (\(-210^\circ\) C).

MacLennan (31, 32) [cf. the communication of V. Trottrian (28)] was the first to succeed in obtaining the green line under laboratory conditions. It belongs to atomic oxygen; its brightness is greatest when the oxygen pressure in the discharge tube is 2 mm Hg, and it increases with the strength of the discharge current (currents up to 0.165 A). The green line was only rarely obtained as early as the first discharge; apparently a considerable time is required for a sufficient quantity of oxygen to pass into the state necessary for the emission of the characteristic auroral rays. Strangely enough, the green line is intensified by admixtures of inert gases in oxygen: when observing in the longitudinal direction of a discharge tube 1 m long, in which there was a mixture of oxygen (partial pressure 1 mm Hg) and argon (10 mm Hg), with a current of 0.033 A and an exposure of 45 min., the green line on the photographic plate proved to be 85 times brighter than in pure

in oxygen at a pressure of 2 mm Hg, also 0.060 Å and an exposure of 9 hours; in the spectrum of O₂ there is only one oxygen line, 6158 Å, brighter than 5577 Å. Such an influence of the conditions of excitation makes it easier to answer the question why no other oxygen lines are seen in the spectrum of the aurora, if 5577 Å belongs to oxygen. It must be assumed that the conditions in the upper layers of the atmosphere enhance the 5577 Å line, in comparison with the others, much more than does an admixture of argon under laboratory conditions, and that the remaining lines prove to be completely suppressed.

After McLennan had measured the wavelength of the green line with the aid of a prismatic spectrograph, and his data agreed well with Babcock’s data,—G. Cario (26), using a large concave diffraction grating, established the wavelength as \(5577.348 \pm 0.005\) Å, and, finally, McLennan and McLeod (33), applying an interferometer (as Babcock had earlier), gave the wavelength \(5577.347 \pm 0.004\) Å and the line width 0.030 Å.

Until recently there was no clarity as to the series affiliation of the green line. J. J. Hopfield (30) found that the difference of the frequencies of two simple oxygen lines in the ultraviolet region (1217.62 and 999.47 Å) is equal to the frequency of oscillation of the green line (17,925 waves per 1 cm). V. Grotrian (29) sees a correspondence between the green line and the nebular lines which predominate in almost all nebulae having an emission spectrum, but which so far have not been detected in any spectrum of terrestrial light sources. The point is that, according to the investigation of J. S. Bowen, the brightest of these lines belong to oxygen and nitrogen; they arise in “forbidden transitions” from metastable initial states. The reason that these lines are so strong in nebulae lies in the negligible density of the mass of the latter; therefore the interval of time between two collisions of molecules there, in contrast to laboratory conditions, is at least \(10^4\) times greater than the lifetime (\(10^{-3}\) to

\(10^{-2}\) sec) of the metastable atom. However, the mean interval of time between two collisions at an altitude of 100 km in the Earth’s atmosphere is less than \(10^{-4}\) sec (cf. p. 222). The existence of non-polar aurorae at low latitudes proves that the auroral line arises not only under excitation by solar electrons, and therefore Chapman’s opinion (101), that the green line is emitted during the nocturnal decomposition of ozone molecules formed during the day, is convincing.

In a preliminary communication L. A. Sommer (40) indicates that the longitudinal Zeeman effect for the green line gives a splitting three times greater than the normal one. On this basis he succeeds in placing the green line in the term system of the spectrum of the neutral oxygen atom. It corresponds to a transition between metastable terms, which is entirely in the spirit of Bowen’s hypothesis and in agreement with the predictions of McLennan, based on Hopfield’s assertion (34). Such transitions do not occur under ordinary discharge conditions, but are quite possible with considerable rarefaction of the gas, which in the laboratory is achieved by admixture of inert gases. The excitation potential is equal to 2.23 volts.

V. Ozone.

a) Qualitative investigation.

The spectra of the sun and stars, investigated at the surface of the Earth, are found to be limited at about \(2900\ \text{Å}\), even when quartz optics are used. Hartley (69) already attributed this phenomenon to the absorption of rays by atmospheric ozone, and more accurate measurements of the spectra of the Sun and Sirius by Fowler and Strutt (63) confirmed this view. Ozone (\(\mathrm{O}_3\)) is formed from oxygen (\(\mathrm{O}_2\)) under the action of waves shorter than \(1800\ \text{Å}\). It has very strong absorption bands in the ultraviolet. The maximum of these bands lies near \(2550\ \text{Å}\); they extend with variable intensity approximately to \(3000\ \text{Å}\), and, including weaker bands (Huggins bands), to \(3400\ \text{Å}\). In the visible

parts of the spectrum the bands lie between 5000 and 6000 Å; finally, there are still narrow, little-studied bands in the infrared region, approximately at 4.5 and 9.5 μ. That this absorption spectrum arises only in the terrestrial atmosphere, and that consequently outside the Earth the solar spectrum in the ultraviolet region approximately corresponds to the spectrum of a black body at about 6000°, may be concluded from the fact that there is no difference between the short-wave region of the spectrum from the edge and from the middle of the solar disk, but that the intensity of the bands increases when the sun approaches the horizon, i.e., the path of light in the Earth’s atmosphere increases.

It has long been known that traces of ozone are present in the lower part of the atmosphere, but quantitative chemical analysis is so difficult [Dorno (57)] that the reported figures are very unreliable. If the maximum ozone content after a thunderstorm is taken as 2 mg/m³, then this corresponds to \(10^{-8}\) of the volume. But only Rayleigh (74) convincingly showed that in the lower layers of the atmosphere there is too little ozone to explain the absorption of sunlight. Making use of the idea expressed as early as 1913 by Fabry and Buisson (61), Rayleigh observed at night the spectrum of a quartz mercury-vapor lamp at a horizontal distance of 6.4 km. With an exposure of 1 hour he could still photograph the mercury line 2536 Å. At the altitude, however, for example, of the peak of Tenerife, the solar spectrum already ends at 2922 Å with an equivalent air path of only 5.9 km, and shorter waves cannot be detected with any exposure. Consequently, the lower layers of the atmosphere are transparent to ultraviolet light; ozone must be located higher up. Recently Goetz (F. W. P. Goetz) showed by comparative measurements of the solar spectrum at two stations in Switzerland, situated one above the other (Schwyz at an altitude of 600 m; Arosa—1860 m), that in the intermediate layer between them the presence of ozone is not optically detectable.

b) Methods for measuring the amount of ozone. In order, from the degree of absorption of light rays, to infer the amount of ozone contained in the air, it is necessary

preliminarily, by laboratory methods, determine the absorption coefficient of ozone as a function of the wavelength \(\lambda\). If light of wavelength \(\lambda\) (in Å) and brightness \(I(\lambda)\) passes through a thin layer of air, and if the ozone contained in this layer, at \(0^\circ\) C and \(760\) mm Hg, would form a layer of thickness \(d\xi\), then, owing to the absorption of light by ozone, its brightness will decrease by \(dI=-Iq\,d\xi\); after traversing a distance equivalent to a layer thickness \(\xi\), the brightness will be expressed as follows:

\[ \lg I-\lg I_0=-q\xi,\quad I=I_0 e^{-q\xi}=I_0\cdot 10^{-\alpha \xi}. \]

The attenuation coefficient \(\alpha\) therefore indicates the decrease in the decimal logarithm of the brightness after the light has passed through a layer of pure ozone \(1\ \mathrm{cm}\) thick; \(\frac{1}{\alpha}\) is the thickness of the layer that attenuates the light to \(0.1\) of its initial brightness.

\(\lambda\) in Å	2300	2400	2500	2600	2700	2800
\(\alpha\ (\mathrm{cm}^{-1})\)	50	95	120	120	91	46
\(10^{-0.3\alpha}\)	\(10^{-15}\)	\(10^{-28}\)	\(10^{-36}\)	\(10^{-36}\)	\(10^{-27}\)	\(10^{-14}\)
\(\lambda\) in Å	2900	3000	3100	3200	3300	3400
\(\alpha\ (\mathrm{cm}^{-1})\)	16.6	4.6	1.23	0.35	0.093	0.025
\(10^{-0.3\alpha}\)	\(10^{-5}\)	0.042	0.23	0.79	0.94	0.983

The table given (51) gives the value of \(\alpha\) for the ultraviolet; the second row contains the ratio of brightnesses \(I/I_0\) when the rays pass through \(0.3\ \mathrm{cm}\) of ozone. In the region of maximum absorption, a layer of gaseous ozone only \(0.0025\ \mathrm{cm}\) thick already weakens the brightness by half; the corresponding calculation shows that ozone absorbs these rays more strongly than metals absorb visible light.

For the course of the changes of \(a\) between \(2\,900\) and \(3\,300\) Å—the most essential—Fabry and Buisson found an empirical formula (common logarithms; \(\lambda\) in Å \(=10^{-8}\) cm):

\[ \operatorname{Lg} a = 17.58 - 0.00564\,\lambda . \]

From this one may conclude how the end of the spectrum \(\lambda_0\) shifts when the thickness of the layer \(x\) changes; by the end of the spectrum is conventionally meant that place where \(I=I_0/N\); \(N\) is a constant depending on the instrument. Then \(10^{ax}=N\); \(\operatorname{Lg} a_0+\operatorname{Lg} x=\mathrm{const.}\), or, using the empirical value of \(\operatorname{Lg} a\), we obtain:

\[ \lambda_0 = 177\,\operatorname{Lg} x + \mathrm{const.} \]

If \(x\) changes from \(0.2\) to \(0.4\) cm, then the last still noticeable wavelength shifts by \(53\) Å toward the red; an exact determination of the shift is hampered by Fraunhofer lines, within whose width observations are impossible, which is why jumps appear in the results.

Absorption in the Huggins bands (from \(3\,050\) to \(3\,400\) Å) was measured by I. and M. Duteil (59). In the visible region, between \(5\,000\) and \(6\,000\) Å, G. Colange (54) determined \(a=0.01\) at \(\lambda=5\,000\) Å, \(a=0.05\) at \(\lambda=6\,050\) Å.

Fabry and Buisson (60, 62) were the first to calculate the amount of ozone in the atmosphere from observations of the distribution of energy in the spectrum. Dobson (55, 56) and his collaborators continued systematic optical measurements of ozone in various localities and in connection with other geophysical phenomena. The essence of their method is as follows: let \(I_0(\lambda)\) denote the brightness of sunlight of wavelength \(\lambda\) at the boundary of the Earth’s atmosphere, \(Z\) (angle)—the zenith distance of the sun, \(h\)—the height of a particle of air above the Earth’s surface, whose curvature we shall neglect (cf. p. 213). Passing through a layer of air whose thickness in the vertical direction is equal to \(dh\), the light traverses a path

\[ \frac{dh}{\cos Z}, \]

and

its brightness \(I\) is weakened by \(I a \dfrac{dh}{\cos Z}\); \(a\) depends on the wavelength and, in addition, on the composition and density of the air, i.e. essentially on \(h\). Integrating

\[ -\frac{dI}{I}=a \sec Z \cdot dh, \]

we obtain:

\[ \lg I_0-\lg I=\sec Z \int_0^\infty a\,dh, \]

or, in common logarithms,

\[ \operatorname{Lg} I_0-\operatorname{Lg} I=\sec Z\,\operatorname{Lg} e \int_0^\infty a\,dh=k\sec Z, \]

whence we obtain the attenuation formula \(I=I_0\cdot 10^{-k\sec Z}\). Under constant atmospheric conditions the attenuation coefficient \(k\) depends only on \(\lambda\). In accordance with the various causes influencing the magnitude of \(k\), we put

\[ k=\delta+\beta+\alpha x. \]

\(\delta\) and \(\beta\) indicate the scattering of light by particles that are large (\(\delta\) independent of \(\lambda\)) or small (\(\beta \sim \lambda^{-4}\)) in comparison with the wavelength \(\lambda\); \(\alpha\) is the attenuation coefficient for ozone, and \(x\) is the thickness of the equivalent ozone layer, i.e. such a layer of pure ozone which near the earth’s surface (i.e. at normal pressure and temperature) would have the same absorption as all the ozone distributed through the atmosphere.

The measurement consists in photographing the solar spectrum between 2900 and 3350 Å with a quartz spectrograph at different positions of the sun; in the photographed spectrum 1 mm corresponds approximately to 15 Å. Fogging of the plates by longer-wave scattered light is avoided by placing before the apparatus a quartz vessel with a mixture of chlorine and bromine vapors of suitable concentration; bromine removes \(\lambda>3600\) Å, chlorine—\(\lambda<3600\), with a maximum at 3400 Å. Before the photographic plate a gray wedge is installed (carbon in a gelatin film

between quartz plates) so that its lines of equal thickness are arranged parallel to the extension of the spectrum. As a result of this, the brightness of each line on the photographic plate decreases in the direction of increasing ordinate \(y\); if \(i\) is the intensity of a wave of length \(\lambda\) before the wedge and \(K\) is the wedge constant (known), then the intensity of the line on the plate, after the ray has passed through the wedge, is equal to \(i \cdot 10^{-Ky}\).

In order to be able to compare different plates with one another, i.e. to eliminate differences in the conditions of development and in the sensitivity of the plates,—after the plate has already been removed from the spectrograph, one strip of it is exposed to the light of an incandescent lamp of constant brightness. Then the plate is photometered along the most clearly expressed Fraunhofer lines, beginning from the thin edge of the wedge (or from a definite level near it) to the point where the blackening in the solar spectrum is equal to the blackening of the normal strip; the ordinate of this point, beginning from the thin edge of the wedge, we shall call \(y\). Then \(i \cdot 10^{-Ky} = \mathrm{const.}\), i.e. \(\mathrm{Lg}\ I = Ky + c\), where \(c\) has been determined once for all with the aid of the comparison light source and, of course, does not depend on \(\lambda\). From two measurements made at different times \((Z = Z', Z'')\), we find for any wavelength \(\lambda\)

\[ \mathrm{Lg}\ I' - \mathrm{Lg}\ I'' = k(\sec Z'' - \sec Z') = K(y' - y''). \]

Here \(I_0\) is eliminated, so that \(k\) can be calculated.

Then the function \(k(\lambda)\) is graphically resolved into its three component parts, the ordinate being \(k\), and the abscissa \(\lambda^{-4}\) (Fig. 1). The quantity \((\delta + \beta)\), due to scattering, is represented on this diagram by a straight line. To determine it, use is made of the circumstance that for \(\lambda > 3300\ \text{\AA}\), \(\alpha\) is very small. The values of \(k\) for \(3300\ \text{\AA}\) are determined with a quartz spectrograph; by visual photometry \(k\) was found for \(5000\) and \(6000\ \text{\AA}\), and the straight line was established. Then \(\alpha x\) turns out to be the excess of \(k\) above this straight line.

function. Dividing \(ax\) by \(a\), the values of which were found under laboratory conditions, finally gives \(x\), determining the amount of ozone; the values of \(x\) found for different wavelengths must agree, whereby \(a\) is at the same time checked.

The method described, requiring several exposures at different positions of the sun, is too complicated for daily measurements. Therefore \(x\) is computed from only one spectral exposure, comparing the intensities for two wavelengths \(\lambda\) and \(\lambda'\). Then

\[ \begin{array}{ll} \text{for } \lambda & \mathrm{Lg}\, I_0-\mathrm{Lg}\, I=(\beta+\delta+ax)\sec Z,\\ \text{for } \lambda' & \mathrm{Lg}\, I'_0-\mathrm{Lg}\, I'=(\beta'+\delta+a'x)\sec Z. \end{array} \]

Consequently

\[ x=\frac{(\mathrm{Lg}\, I_0-\mathrm{Lg}\, I)-(\mathrm{Lg}\, I'_0-\mathrm{Lg}\, I')-(\beta-\beta')\sec Z}{(a-a')\sec Z}. \]

Here \(\delta\) has been eliminated, and \(x\) may be calculated—if it is assumed that the ratio of intensities outside the earth’s atmosphere, i.e. \(\mathrm{Lg}\, I_0-\mathrm{Lg}\, I'_0=\mathrm{Lg}\,\frac{I_0}{I'_0}\), is constant, and if \((\beta-\beta')\) is replaced by its approximate value \(\infty(\lambda^{-4}-\lambda'^{-4})\); the latter is permissible for the usually small differences between \(\lambda\) and \(\lambda'\). In order that the denominator in the expression for \(x\) should not prove too small, \(\lambda\) and \(\lambda'\) are taken as different as possible, but nevertheless so that the shortest wavelength would not be entirely cut off at a low position of the sun. At Arosa both pairs of wavelengths—3264, 3022 and 3232, 3062 Å—gave well-agreeing values of \(x\).

In July 1926 Dobson arranged a network of stations with 7 identical installations: Oxford, Valencia (south-west Ireland), Lerwick (Shetland Islands), Abisko (northern Sweden), Lindenberg (near Berlin), Arosa, Montezuma (near Calama in Chile).

The spectrophotometric method described is the most reliable of all. Götz (64, 65, 66), who has now also adopted it, determined the intensity of ultraviolet rays

photoelectrically, using cadmium photoelements; the entire range of action of the element, around \(3220\) Å, was divided by means of a glass filter into two regions, differing in the intensity of ozone absorption. Dorno (58) expressed doubt as to the applicability of filters in measurements over ozone; his objections apply still more to the observations of Edison Pettit (73), who measured solar radiation thermoelectrically, after filtering it through thin films of silver (transparent for \(0.32\,\mu\)) or gold (transparent for \(0.50\,\mu\)) and collecting it in the focus of a system of quartz lenses.

Fig. 1. Attenuation coefficient \(k\) as a function of \(\lambda^{-4}\) (after Dobson).

Continuous photography of the ultraviolet spectrum of the sun for determining the variable content of ozone was carried out only after 1925 by Dobson in England. Cabannes and Dufay (52) extended the series of data for ozone in another direction, calculating them for ozone bands in the visible spectrum and using observations at Mount Wilson (1908–1920) and at Calama (Chile) (1918–1920). In determining the solar constants, Abbot investigated the solar spectrum bolometrically at different solar altitudes; from this the transparency of the atmosphere was determined for ten wavelengths selected in different parts of the spectrum. Owing to the purity of the air in the locality where the investigations were made, the attenuation coefficient proved to be strictly proportional to \(\lambda^{-4}\), with the exception of the absorption bands of ozone and water vapor. Thus one can interpolate the result for \(6000\) Å and obtain its value, undistorted by absorp—

...and then, comparing it with the observed value for the same wavelength, to calculate the absorption of ozone.

c) Observational data on the amount of ozone. All measurements agree in determining the order of magnitude and give the thickness of the equivalent layer of ozone \(x = 0.3\) cm, which corresponds to \(10^{19}\) ozone molecules above \(1\text{ cm}^2\) of the earth’s surface. This quantity can fluctuate strongly over the course of a few days; for example, in Oxford on 28/II 1925, \(x = 0.370\) cm, the end of the photographed solar spectrum at \(3050\) Å; on 7/III 1925, \(x = 0.245\), the end at \(3000\) Å. English and American observations show a considerable annual variation, with a maximum in April of about \(x = 0.32\) cm and a minimum in October, \(x = 0.24\) cm; likewise the filter observations of Féty at Arosa (64) give a spring-to-autumn ratio of \(4:3\). At Kalama the seasonal fluctuation is smaller than at Mount Wilson and proceeds inversely (minimum in May) (52).

According to Dobson’s measurements, no influence of solar activity is observed in the mean monthly data; calculations by Cabannes and Dufay (50, 52) from the measurements at Mount Wilson confirm this circumstance, but point to fluctuations from year to year; the maxima occur in 1908 and 1918, i.e. near the maxima of the 11-year sunspot period. The amplitude of the annual mean data is \(30\%\). The same peculiarity is observed for terrestrial magnetism: its connection with solar activity is more strongly revealed in annual means than in monthly means; but for ozone this connection is apparently weaker. C. Chree (53) investigated the relation between individual daily values of ozone content and the characteristic numbers of terrestrial magnetism; apparently, the largest numbers for ozone coincide on average with enhanced magnetic disturbances, but the connection is only weakly indicated.

The clearest relation is that between ozone content and the distribution of atmospheric pressure (56). Almost without exception the ozone content is high in clearly expressed cyclones and low in anticyclones. If the annual variation is eliminated, then from the individual values the following correlation coefficients for \(x\) follow:

UPPER LAYERS OF THE ATMOSPHERE

with atmospheric pressure at the earth . . . . . . −0.46
“ pressure at an altitude of 9 km . . . . . . . −0.72
with the temperature at an altitude of 14 km . . . . . +051

The high correlation attracts all the more attention because there has long existed a tendency to associate the ozone content in the atmosphere with the conductivity of the Heaviside layer (p. 243), but no direct relationship has yet been found between the phenomena of terrestrial magnetism and meteorology. O. Hölper (70, 71) objected to the arguments for the existence of a connection between ozone content and pressure; he attributes the fluctuations of the observed data on ozone content to atmospheric turbidity. Dobson, however, does not consider these objections convincing.

d) Height of the position of the ozone layer. If the surface of the earth were flat, then the path of a solar ray through the ozone layer would increase, with increasing zenith distance \(Z\), as \(\dfrac{1}{\cos Z}\). Owing to the curvature of the earth’s surface, the true path of the rays is the shorter the higher the ozone layer is situated above the earth (Fig. 2). Let \(a\) be the radius of the earth, \(h\) the height of the lower boundary of the ozone layer,

\[ \eta=\frac{h}{a}, \]

\(d\) the thickness of the layer in the vertical direction (we assume that \(d \le h\)), and \(w\) the length of the path in the layer for a ray falling on the earth’s surface at an angle \(Z\) (the zenith distance) to the vertical. Already from Fig. 2 it is evident that \(w\) is less than the path

\[ w_0=\frac{d}{\cos Z} \]

for a flat surface of the earth. More precisely (neglecting refraction),

\[ \frac{\sin Z}{\sin Z'}=\frac{a+h}{a}=1+\eta; \]

therefore,

\[ \frac{w}{d}=\frac{1}{\cos Z'}= \frac{1}{\sqrt{1-\left(\frac{\sin Z}{1+\eta}\right)^2}}. \]

Thus, the influence of the curvature of the earth’s surface is the more noticeable the higher the layer is situated and the lower the sun stands.

Numerical example:

Zenith distance	\(Z=\)	\(0^\circ\)	\(70^\circ\)	\(80^\circ\)	\(85^\circ\)
\(\eta=0\)      \(h=0\) km	\(w/d=\)	1.00	2.92	5.5	11.1
\(\eta=0.01\)      \(h=64\) km	\(w/d=\)	1.00	2.73	4.5	6.1

Consequently, from observations with a low-standing sun it is possible to compute the height of the position of the ozone layer. However, in the evening and in the morning, when the path of sunlight in the atmosphere is longer, the ultraviolet part of the spectrum undergoes especially strong molecular scattering and is weakened by absorption by dust and vapors, which is particularly appreciable on plains.

Fig. 2. On determining the height of the ozone-containing layer above the earth’s surface.

In order to obtain a pure effect, P. Lambert (72) and his collaborators in 1924 made measurements on Mont Blanc; they found, for the quantity of ozone \(x=0.32\) cm, a height \(h=45\) km. Cabannes and Dufay (51) employ another method: they dispense with direct observation of sunlight and investigate the brightness of the sky at the zenith, i.e. light that has undergone absorption in the ozone layer and has then been scattered in the lower part of the atmosphere. It is assumed here that the scattering takes place chiefly below the ozone layer. Since, for the reasons mentioned, the edge of the spectrum on the short-wave side, at a low position of the sun, lies above \(3000\) Å, these measurements had to be made over the Götzis bands (\(3050\) to \(3400\) Å). The data on the height of the layer lie between 45 and 50 km, with an accuracy of up to several kilometers.

An essential assumption made in these calculations is that the quantity of ozone \(x\) does not change during the period of sunset.

If in reality \(x\) nevertheless decreased during this time—and this is not excluded, although it would contradict the observed constancy of the amount of ozone during the solar eclipse (68)—then the calculated height would be systematically greater than the true one. Further, one must take into account that at noon ozone reaches lower layers of the atmosphere than is indicated by evening observations; otherwise it would have been impossible to explain the dependence of the ozone content on the weather.

e) Temperature. Biological significance. From the circumstance that ozone selectively absorbs ultraviolet rays, Lindemann (16) and Dobson (2) concluded that the temperature of the atmospheric layer containing ozone must be higher than that of the stratosphere, namely about \(300^\circ\) absolute. Following G. Pelsier (36), we shall present their argument, which is very close to the explanation of the low temperature of the stratosphere by the infrared absorption of water vapor. Let in Fig. 3 \(EE\) be the distribution with respect to frequency \(\nu\) of all the radiant energy incident upon a layer of gas.

Fig. 3. Toward radiative equilibrium of gases possessing selective absorption (after G. Pelsier).

If the latter possesses only one region of selective absorption with frequency \(\nu\) and is transparent for all other frequencies, then, according to Kirchhoff’s law, it can emit only at the same frequency \(\nu\). Suppose that the gas has a temperature \(T_0\), such as if it emitted as a black or gray body; \(A_0A_0\) is the corresponding Planck distribution of energy in the radiation of a black body of temperature \(T_0\). If, in this case, the absorption band \(\nu_1\) lies in the ultraviolet (as with ozone), then radiative equilibrium cannot be established in the gas, because the incident energy \(U_1W_1\) is greater than the emitted \(U_1V_1\). Consequently, the temperature of the gas will rise to a higher value \(T_1\), at which the energy emitted at \(\nu_1\) becomes equal to the absorbed energy of the same frequency \(U_1W_1\).

If, conversely, the absorption band \(\lambda_{3}\) lies in the infrared region (as with water vapor or carbon dioxide), then the temperature must drop to \(T_{2}\). Pelzer, however, warns against neglecting the infrared absorption of ozone, which occurs alongside its ultraviolet absorption but is much weaker, because it can lower the equilibrium temperature.

Until this infrared absorption has been studied precisely, one cannot judge the diurnal variation of temperature at altitude. It is known that in the troposphere its amplitude decreases sharply with distance from the earth’s surface; for example, above Lindenberg on clear summer days the difference between the maximum and the minimum reaches \(11^\circ\) at a height of \(2\) m and only \(1^\circ\) at a height of \(2500\) m. A theoretical calculation by G. B. Merica (72a) gives diurnal variations of \(140^\circ\) at an altitude of \(60\) km, but in his preliminary communication the course of the reasoning is not set out.

In conclusion, the great biological significance of the ozone layer should be noted. For although there is only an amount of ozone equivalent to a layer of about \(3\) mm (\(\sim\) partial pressure \(0.0005\) mm Hg), and consequently its volume content in the atmosphere corresponds to only \(1:3\,000\,000\), nevertheless it protects our skin precisely from the physiologically active rays that would cause rapid and severe burns. It is worth noting in passing that, from the medical side, much attention is now being paid to the fact that ordinary window glass absorbs a considerable part of the ultraviolet rays that remain after passing through ozone.

VI. Propagation of Sound.

Casual observations of cannon fire, volcanic eruptions, explosions, etc., have long shown that near the earth’s surface the diminution of the strength of sound with distance from its source is not in general continuous; an inner and an outer zone of audibility are distinguished, in most cases separated by a zone of silence in which the sound is not noticeable. Usually only a certain

UPPER LAYERS OF THE ATMOSPHERE

a segment of the outer zone; but in several cases it apparently constituted a closed ring. The inner radius of the outer zone in Europe varies with the season; on the average it is 110 km in winter and 190 km in summer.

In recent years a systematic study of the acoustics of the atmosphere (75–78) has been carried out under the direction of the Commission for the Support of German Science (Notgemeinschaft der Deutschen Wissenschaft). At a specified time explosions were set off, the sound of which was investigated over a dense network of stations, both by ear and by recording instruments.

The travel time of sound \(L\), expressed as a function of the distance \(\Delta\), indicates the existence of normal and anomalous propagation of sound. If \(V_h = \dfrac{\Delta}{L}\) denotes the speed of propagation of sound in the horizontal direction, then the normal wave, observed near the source of the sound (\(\Delta =\) from 0 to 340 km), corresponds to propagation near the earth’s surface with the Laplace velocity

\[ V = \sqrt{\varkappa \frac{RT}{M}} \]

(\(\varkappa\) is the ratio of the specific heats, \(R\) the universal gas constant, \(T\) the absolute temperature, \(M\) the molecular weight). For air (\(M = 28.95\)) at various temperatures:

\(T=\)	\(-80^\circ\)	\(-55^\circ\)	\(-30^\circ\)	\(0^\circ\)	\(20^\circ\)	\(30^\circ\)	C
\(V=\)	278	299	312	331	343	348	m/sec.

The path of a normal sound ray is determined by the temperature and the distribution of wind in the lower atmosphere; sound is heard on the ground at great distances if the sound waves issuing obliquely upward from the source are again deflected toward the earth; this can occur only if the speed of sound increases with height. This explains two well-known phenomena: first, good all-around audibility on windless clear nights, when the air cools more strongly near the earth, owing to radiation, than higher up, so that \(V\) increases with height; and, second, the circumstance that sound is apparently carried by the wind:

wind, which near the ground is retarded by friction, is stronger at altitude than below, so that sound rays are bent against the wind upward, and with the wind downward. In general, \(T\), and with it \(V\), decrease with height, as a result of which sound rays bend upward, and at a sufficient distance the sound is no longer heard on the ground.

The velocity of the anomalous propagation of sound, measured in the horizontal direction, is only \(275\)—\(305\) m/sec; the anomalous sound ray, observed at distances \(\Delta =\) from 150 to 300 km, therefore arrives 1–2 min. later than the normal one. From the velocity curve (\(L\) as a function of \(\Delta\)) one may infer the path of the sound, just as for seismic waves. It has been established that the anomalous sound ray reaches greater heights than the normal one; between 40–50 km altitude it is again deflected toward the earth, and at the greatest height its velocity must be the same as at the surface of the earth, or even greater.

Aerological ascents provide nothing for explaining the anomalous propagation of sound, because the temperatures measured at altitude turn out to be excessively low. The direction of the wind also cannot be their cause, since it explains only one-sided propagation of sound, but not annular zones. Earlier attempts were made to justify the increase of \(V\) with height by a decrease in the mean molecular weight of air (\(M\) near the earth \(= 28.95\)), but then even for hydrogen one has to admit an admixture of more than 25%, which does not agree with other observations (aurora, ozone). Therefore for the time being it remains only to conclude that at an altitude of 40 km temperatures of about \(+30^\circ\)C predominate. Above, the possibility was indicated of explaining such a high temperature by the selective ultraviolet absorption of ozone (see p. 215).

VII. Pressure and Composition.

According to Dalton’s law, the individual gases in a resting mixture subjected to the action of gravity are distributed entirely independently of one another. For a change of pres—

of its decrease with height above the earth \(h\) is valid; consequently, for each gas the fundamental equation of statics is

(\(p_s\)—partial pressure, \(\rho_s\)—partial density, \(T\)—temperature; \(g\), taken independent of \(h\),—the acceleration of gravity; \(R\)—the gas constant, \(M_s\)—molecular weight)

\[ dp_s=-\rho_s g\,dh, \]

or, by virtue of the gas equation, also

\[ p_s=\frac{R\rho_s T}{M_s},\qquad \frac{dp_s}{p_s}=-\frac{gM_s}{RT}\,dh. \]

If, as usual, \(H_s\) denotes the “height of a homogeneous atmosphere,” i.e., the height which an atmosphere consisting of gas \(s\) would have if at every height it possessed the same density \(\rho_{s0}\) as at the earth, then from the first form of the fundamental equation of statics it follows that in such a homogeneous atmosphere \(p_s\), and from the gas equation also \(T\), decrease linearly with height \(h\). If \(P_s\) is the pressure at the earth’s surface, then, integrating, we obtain

\[ H_s=\frac{p_{s0}}{g\rho_{s0}}=\frac{RT_0}{gM_s}. \]

For example, for dry air one must take the mean molecular weight \(\overline{M}=28.95\), where \(\overline{M}\) is calculated from the molecular weights \(M_s\) of the individual gases composing the mixture, with fractions \(a_s\) per gram of mixture:

\[ \frac{1}{\overline{M}}=\sum \frac{a_s}{M_s}. \]

Consequently, \(H_s\) depends not on the pressure at the earth’s surface, but only on the molecular weight of the gas and on the temperature \(T_0\) at the earth. For \(T_0=273^\circ\) we find the following values of \(H_s\) for certain gases:

	Air	Nitrogen	Oxygen	Argon	Carbon dioxide	Helium	Hydrogen
\(H_s\) (km)	7.99	8.26	7.23	5.80	5.23	58.4	114.8

The fundamental equation of statics can be written

\[ \frac{dp_s}{p_s}=-\frac{T_0}{T}\cdot\frac{dh}{H_s}. \]

If \(T\) does not depend on \(h\), then from this it follows for the difference of the partial pressures at two heights \(h_1 > h_2\):

\[ \lg p_{s2} - \lg p_{s1} = \frac{T_0}{T_1}\frac{(h_1-h_2)}{H_s}. \]

In a rectangular coordinate system with abscissa \(\lg p\) and ordinate \(h\), the pressure as a function of height is represented in each isothermal height interval by a straight line; if \(T\) varies with height, then the pressure curve may be composed of separate straight-line segments, according to the known rules of graphical integration, with the mean temperatures of the corresponding atmospheric layers being taken. The pressure decreases the more slowly, the larger \(H_s\) is.

If the atmosphere were perfectly calm, then the higher one goes, the greater the content of light gases in it should become under diffusive equilibrium under the action of gravity; at sufficiently great heights there would be present practically only the lightest gas, however little of it there might be near the earth. In the troposphere, the mixing of gases in the vertical direction is so strong—it is caused, for example, already by the instability of radiative equilibrium—that it fully compensates for the very slow process of molecular diffusion. Smoluchowski (11) confirmed by calculation that the “rate of separation,” for example of nitrogen and oxygen, under the action of gravity is negligibly small. Right down to the content of water vapor and carbon dioxide, which depends on condensation and on processes near the earth’s surface, investigations of the air during aerological ascents (79) have not shown any appreciable change in the composition of the air with height.

On the other hand, in the stratosphere the temperature slowly increases with height; stable equilibrium prevails there, making vertical mixing more difficult. Until recent years the opinion was held that the states of rest in the stratosphere were sufficient for the air in it to be able to separate by diffusion. Chapman and Milne (1) investigated those states of the atmosphere which follow from various assumptions

about the height of the boundary between convection and diffusion. In Fig. 4 it is seen (solid lines) how, under free diffusion, the partial pressures decrease with height; moreover, in the initial conditions the already known composition of the atmosphere at 12 km is taken, and the temperature is everywhere assumed to be \(-54^\circ\) C. The total pressure (not shown in Fig. 4) more or less corresponds to the partial pressure of the gas predominating in the composition, i.e. at first it would follow the nitrogen curve, and later, above 120 km, the helium line. Thus one would obtain a lower oxygen–nitrogen sphere, with an increasing nitrogen content with height; at about 110 km it would pass rather rapidly into a helium sphere, the helium content near the earth being taken as equal to \(4\cdot 10^{-6}\) of all the air. If there were hydrogen in the air, then in the end, of course, one would obtain its predominance.

Fig. 4. Dependence of pressure on height; abscissa: common logarithms of the pressure, expressed in mm Hg.

Chapman and Milne left hydrogen out of consideration because the presence of the latter in the lower layers of the atmosphere is not reliable (in any case, by volume less than five parts in \(10^6\)); further, because hydrogen has the possibility of combining with oxygen, and finally, owing to the absence of hydrogen lines in the spectrum of the aurora. For processes below 100 km it is more or less immaterial whether light gases are present and where the lower boundary of diffusive equilibrium lies, but above 100 km both these circumstances are decisive for the pressure and composition of the air. At an altitude of 400 km, in \(1\ \mathrm{cm}^3\) of air (without hydrogen) there would still be \(4\cdot 10^9\) helium atoms (mean free path 400 m), but there would be less than one molecule of other gases in \(1\ \mathrm{l}\); at an altitude of 1,000 km there would be only \(10^5\) helium atoms per \(1\ \mathrm{cm}^3\), and the mean free path would equal

30,000 km; moreover, of course, upward it would be greater, and downward, smaller.

In contrast to these earlier views, the spectrum of the aurora indicates that even above 100 km the atmosphere consists of oxygen and nitrogen, while nothing reveals the presence of helium. According to acoustic investigations, above 30–40 km the temperature reaches 300° absolute. The presence of ozone would prove essential only in the respect that it would make it possible to explain so high a temperature; moreover, it would not affect the distribution of pressure, despite its large molecular weight, owing to its negligible partial pressure \((5 \cdot 10^{-4}\ \text{mm Hg}\) at an altitude of about 50 km). The thick dotted curve of Fig. 4 shows the decrease of the total pressure with height under the assumption (somewhat arbitrary) that the air is completely mixed down to the negligible admixtures of water vapor, carbon dioxide, and ozone, and that above 35 km the air temperature is 300° absolute. These assumptions form the basis of the table given below; as a consequence of them, the pressure and density at 90 km prove to be approximately 10 times greater than according to the earlier conceptions; at an altitude greater than 150 km, however, the pressure is reduced owing to the absence of helium.

	0	50	90	130	250	(500)
Height (km) . . . .	0	50	90	130	250	(500)
Pressure (mm Hg) .	760	1	\(10^{-2}\)	\(10^{-4}\)	\(10^{-10}\)	\((10^{-22})\)
Mean free path (cm) . . .	\(9 \cdot 10^{-6}\)	\(7 \cdot 10^{-3}\)	0.7	70	\(7 \cdot 10^{7}\)	\((7 \cdot 10^{19})\)
Number of molecules in \(1\ \text{cm}^3\)	\(2.7 \cdot 10^{19}\)	\(3.5 \cdot 10^{16}\)	\(3.5 \cdot 10^{14}\)	\(3.5 \cdot 10^{12}\)	\(3.5 \cdot 10^{6}\)	\((3.5 \cdot 10^{-6})\)

Consequences from other assumptions are easy to obtain by constructing similar curves, beginning from the level of the earth’s surface, which would indicate at each height the decrease of pressure corresponding to the newly adopted temperature and composition, according to the formula on p. 220.

In conclusion, one should point out one further possibility: the circumstance that in the spectrum of the aurora, up to now

... up to now only oxygen and nitrogen have been detected is not unconditional proof of the absence of other gases there. A warning against such hasty conclusions is (in addition to analogous false conclusions in astrophysics) the history of the discovery of the green line, the only line of oxygen so far detected in the aurora. If, bearing this in mind, one admits the presence in the atmosphere of light gases (helium), then the great height of the atmosphere would be explained more simply than under the assumption of a purely nitrogen–oxygen atmosphere; for the admixture of helium would so reduce the mean molecular weight of the air that the pressure would decrease with height much more slowly than without helium, even at very high temperatures.

VIII. Data of Terrestrial Magnetism.

a) System of currents of the diurnal (solar) variations (81, 82).

The hypothesis of the existence of a high electrically conducting layer of the atmosphere is usually attributed to Heaviside (1902) and Kennelly, who wished to explain why the electromagnetic waves of wireless telegraphy do not propagate in space in a straight line, but bend around the curved surface of the earth. In this connection it is often overlooked that much earlier Balfour Stewart (1882) and A. Schuster (1886) had concluded that such a layer must exist, proceeding from the diurnal variations of the earth’s magnetic field.

Already in the registration of the elements of terrestrial magnetism, for individual days, a diurnal variation is found which can be freed from the influence of non-periodic changes by taking an average over several days (months, etc.). The amplitudes of these diurnal courses reach about \(10^{-3}\) of the mean permanent field, i.e. \(0.0005\) CGS. According to observatory observations, they vary in a rather irregular manner depending on the time of year and the place. The diurnal change of the field-force vector is more significant by day than by night, greater in summer than in winter; furthermore, in the character of the diurnal oscillations an 11-year periodicity is observed, parallel ...

to the periodic change of sunspots. Variations at stations of one and the same geographic latitude are very similar, so that, as a first approximation, one may take the course of the daily variation with respect to place and time at one place as typical for the whole circle of latitude. With the same approximation, therefore, the magnetic state at any time along the whole circle of latitudes is known.

Thus, with the aid of stations at various latitudes, maps are obtained which, for a definite time (Greenwich time), give the geographic distribution of the daily course of the deviations from the mean daily value. The magnetic field, known over the entire surface of the sphere, is decomposed into three parts, according to the well-known theorems of Gauss, by the expansion of spherical functions: namely, into two parts that depend on a potential and express the magnetic action of currents or magnets placed outside or inside the surface of the sphere, and into a part having no potential, which may be regarded as the action of currents piercing the surface of the earth vertically.

Calculation shows that the part having no potential is absent, and that the principal part of the daily periodic field is produced by causes localized above the earth’s surface—in contrast to the constant field, the source of which is almost entirely concentrated within the terrestrial globe. Since one cannot admit the existence of moving permanent magnets outside the surface of the earth, then, obviously, in the case of daily periodic variations the matter lies in the magnetic influences of systems of electric currents; the latter can be computed purely formally from magnetic data (Figs. 5 and 6). Characteristic is a strong vortex of current on the daytime side of the summer hemisphere; at night the currents are weak. If one imagines that the system of currents moves from east to west above the earth’s surface, then it is easy to calculate, according to the known rules, that, for example, in Potsdam (52.5° N lat.) in summer a magnetic oscillation of the following kind should occur: a minimum of the northern component at noon; for the eastern component a maximum at 8 o’clock, a minimum at 13 o’clock; the vertical component (positive direction downward) has a minimum at noon.

b) Fundamentals of the explanation. I base the explanation of this system of currents on the well-known fact that in an electrical conductor moving relative to a magnetic force field, a current is induced. The upper layers of the atmosphere must be such conductors. They are set in motion by those, predominantly horizontal, oscillations which are connected with the diurnal periodic oscillations of atmospheric pressure and which are caused partly by the diurnal periodic heating and cooling, and partly by the force of ebb and flow. Since this phenomenon

Fig. 5. Equinox.

Fig. 6. Northern summer.

Figs. 5–6. Diurnal periodic system of currents at the time of the minimum of sunspots. Maps of the earth. The meridians are marked in local times, 12 = noon. Current lines are at intervals of 10,000 A. The unit of the numbers is 1,000 A. Arrows indicate the direction of the current. The total force of the current of the main vortex at noon is equal to 62,000 A at the equinox, and to 89,000 A in summer.

is like the excitation of current in a dynamo-machine, it is spoken of, for purposes of comparison, as an “atmospheric dynamo.” The constant magnetic field of the earth corresponds to the stationary magnet; the atmosphere corresponds to the armature, moved both by the thermal radiation of the sun and by the tidal forces of the sun and moon; and the high conducting layers correspond to the “windings” in which currents are excited.

Schematic Fig. 7 illustrates this basic idea by the simplified example of a semidiurnal atmospheric ebb and flow. These are two schematic representations of the terrestrial hemisphere, where \(N, S\) are the north and south poles, \(A'A'\)—

equator. The left-hand illustration shows a pressure wave (dotted), a maximum at \(M\), a minimum at \(M'\); the body causing the tide (for example, the moon) is therefore situated above the point \(M\). Since the wave, together with the moon, moves over the earth from east to west, the lines of the air current (solid lines) converge at the point \(A\), midway between \(M\) and \(M'\). The electric forces are determined from the lines of the air current, and from them the lines of force of the electric currents (shown in the right-hand drawing by dotted lines). In the present case the angle of \(11.5^\circ\) between the magnetic axis and the axis of rotation of the earth has not been taken into account. Since the air moves horizontally and

Fig. 7. Two schematic views of the earth (hemispheres) explaining diurnal periodic variations of the earth’s magnetism. On the left: tidal and ebb waves; lines of equal atmospheric pressure (dotted) and lines of air currents (solid). On the right: lines of electric current at altitude (dotted) and horizontal magnetic lines of force (solid), arising at the earth’s surface under the action of this system of currents (according to S. Chapman).

the electrically conducting layer is likewise situated horizontally, then for induction only the vertical component of the earth’s magnetic field is significant. At the equator it vanishes; at the north pole it is directed vertically downward, and at the south pole upward. The current lines at higher latitudes are obtained directly from the rule that the velocity of the air, the magnetic field, and the induced electric field form a right-handed system. Since the surface is closed, the current lines must close in the equatorial zone. Consequently, there they are directed oppositely to those weak electromotive forces

forces that are induced by an insignificant vertical component of the constant field and that, in the stationary state, are compensated by the electric field of static charges.

The theory of magnetic variations is complicated by the fact that the variable magnetic field of external currents excites currents inside the earth, whose magnetic field is likewise detected in registration. The actions of the internal and external systems of currents are strengthened in the horizontal magnetic components, whereas the vertical oscillations of the field mutually weaken one another; the primary external field is approximately 2.5 times stronger than the secondary internal one.

S. Chapman (84) brought Schuster’s theory to a known degree of completeness. The current strength depends (in rough average) on the product \(\sigma D u Z\) (\(\sigma\)—the mean specific electrical conductivity, \(D\)—the thickness of the layer, \(u\)—the horizontal velocity of the air, \(Z\)—the vertical component of the constant magnetic field). However, it is impossible to decide which of the two factors \(\sigma\) and \(u\) determines the variation, because both of them change at one and the same place over the course of the solar day. Therefore it should be considered a very successful idea to bring into the investigation, alongside the solar ones, also the lunar diurnal oscillations of the earth’s magnetism.

c) Lunar variations. In the reports of magnetic observatories the magnitudes of the elements of terrestrial magnetism, or the force components, are published for each hour. From these, first of all, the solar diurnal variation is eliminated, and the remainder is arranged according to lunar time, with the lunar day, equal on average to 24.84 solar hours, being uniformly divided into 24 lunar hours, beginning with the upper lunar culmination. Then, averaged over all lunar phases, there is obtained a lunar variation of an exceedingly simple form, namely pure sinusoids with a period of 12 lunar hours and with amplitudes whose order of magnitude is another ten times smaller than that of the solar wave. The lunar oscillation of declination at Potsdam amounts, on the average over a year, to about 10 seconds of arc; to detect such negligible variations, it is of course necessary to process data over many years.

According to Schuster’s theory, one would expect a simple form of the lunar wave. This is because, on the one hand, only gravitational influences can come from the Moon, and the motion of the air should have the form of a simple tide and ebb; this is known directly also from the lunar oscillations of pressure, whereas in the solar waves of pressure thermal influences predominate. On the other hand, it may be assumed that the total electrical conductivity \(\sigma D\), which depends essentially on the position of the Sun, is, on the average over all lunar phases at each place, constant, because at each hour of solar time during the course of a month all positions of the Moon occur equally often.

The picture becomes, however, quite different if the data for the separate phases of the Moon are treated separately, such as: new moon, first quarter, etc.; then in each group each lunar hour coincides with a definite solar hour. It then turns out (Fig. 8) that other terms are added to the semidiurnal wave, owing to which the variations by day are substantially stronger than by night. This convincingly proves that the total electrical conductivity in fact depends on the position of the Sun.

d) Numerical data for electrical conductivity. If self-induction is taken into account, then the joint treatment of solar and lunar variations at the time of maximum sunspots gives \(\sigma D = 3 \cdot 10^4\ \Omega^{-1}\) for those points where the Sun is at the zenith; the figures for night are substantially smaller than for noon, amounting to no more than one-twentieth of them. Iron at \(0^\circ\text{C}\) has a specific electrical conductivity of \(10^5\ \text{cm}^{-1}\ \Omega^{-1}\). The whole conducting layer in the atmosphere, with respect to electrical conductivity, is therefore equivalent to a metallic shell whose thickness varies with the position of the Sun, the time of year, and the sunspot-forming activity of the Sun within the limits from \(3\ \text{mm}\) to \(0.05\ \text{mm}\).

e) Difficulties. The theory created by Chapman, in its general outlines, explains the observations well. The discrepancy between observation and calculation is probably due chiefly to the internal system of currents. With the relatively high electrical conductivity of sea water in com—

to its fall over land and in the differences in the diurnal variations over land and over the sea, the general system of currents, moving from east to west, must be complicated by local irregularities; the latter have still not been determined more closely, owing to the insufficiency and poor distribution of magnetic observatories—

Fig. 8. Lunar diurnal course of the western magnetic component in Batavia for 8 lunar phases. At the right edge is inscribed the mean solar time of the upper culmination of the Moon in the corresponding phase. The time when the Sun is above the horizon corresponds to the thick curve. For each of the 8 curves the distance between the abscissa axes corresponds to \(4 \cdot 10^{-5}\) gauss; the total amplitude of the course, averaged over all phases, is \(5.4 \cdot 10^{-5}\) gauss.

magnetic observatories (there are only 50 in all, of which 20 are in Europe, i.e. on \(\frac{1}{50}\) of the whole Earth’s surface, and only 9 in the southern hemisphere). It is reassuring that the ratio of solar variations to lunar variations, equal to 10:1, more or less corresponds to the ratio of atmospheric-pressure waves at the Earth’s surf-

ity (16:1); consequently, the order of the computed electrical conductivity is correct.

On the other hand, the strange circumstance emerges that atmospheric oscillations at altitude are opposite in phase to the oscillations at the surface of the earth. For the time being this can be explained only hypothetically, in view of the complexity of the theory of forced oscillations of atmospheric pressure on a rotating earth. It may be pointed out that the lower atmosphere oscillates in resonance with the forcing forces; since the period of the natural oscillation of a wave moving from east to west and having the form approximately \(\cos^2\varphi \cdot \sin 2\lambda\) (\(\varphi\)—geographical latitude, \(\lambda\)—longitude) agrees, to within a few minutes, with 12 solar hours, the solar semidiurnal wave proves to be amplified 60-fold, and the lunar one 3-fold, in comparison with the values they would have under equilibrium between the pressure gradient at the earth and the forcing force. As a consequence of resonance, the periodic pressure gradients aloft are the reverse of those below; and the thought is admissible that internal waves are formed on the surfaces of the temperature discontinuity, thanks to which, above these surfaces, the motion is the opposite of that at the earth. In contrast to this, Chapman seeks the cause in independent diurnal temperature oscillations and the air circulation associated with them in the conducting layer; their source is the strong absorption of sunlight by ozone (cf. p. 214).

f) Magnetic disturbances. Up to now we have been speaking only of diurnal periodic variations obtained as averages over many days. During the eleven-year period of sunspots the diurnal course changes its amplitude; its character changes more weakly; however, there is a remarkable difference in the behavior of the solar and lunar oscillations. In Greenwich, for example, the amplitude of the declination between the minimum and maximum of sunspots changes, for the solar oscillations, by 60–70%, whereas for the lunar oscillations by less than 20%. On the other hand, the lunar oscillations are much more sensitive to small magnetic disturbances that vary from day to day.

In clearly expressed magnetic disturbances, not only is the normal diurnal variation increased, but an additional diurnal variation of an entirely different kind is joined to it; over the whole terrestrial globe it can be represented by essentially one-day waves (84). Since disturbances, apparently, are always caused by the penetration of corpuscular rays into the zone of the aurora, then in the region of their intrusion one should assume a stronger ionization, and the additional variations are to be explained thereby. True, there is as yet no clarity on this point; nor is there any satisfactory theory explaining the course of magnetic disturbances, despite the fact that the majority of magnetic storms proceed more or less uniformly.

g) Other variations. Schuster’s theory was confronted with the legitimate question why only negligible periodic displacements of the air—the velocity of which at the surface of the earth reaches several cm/sec and which near the earth are completely covered by nonperiodic winds—act inductively on terrestrial magnetism, whereas nonperiodic motions are not detected. This question must be answered only in the sense that, in days complicated in the magnetic respect, nonperiodic motions similar to our cyclones and anticyclones near the earth are indeed impossible within the electrically conducting layer, because the dependence of disturbances on the state of sunspots is so strong that hardly any appreciable share of the disturbances is excited otherwise than by solar corpuscular rays. Only by them are extensive air displacements also caused, simultaneously with an increase in electrical conductivity. Stationary winds at altitude, similar to trade winds, would have to reveal themselves in the form of a systematic external part of the magnetic field, but the existence of the latter is unreliable.

According to A. D. Schmidt (86), empirical-statistical searches for an influence on terrestrial magnetism on the part of oscillations of penetrating radiation, periodic in sidereal time, as well as on the part of the ionization caused by it, are doomed to failure (p. 241).

Rapid changes in the earth’s magnetic field are not detected by ordinary variometers because of the great inertia of the latter. Therefore closed cables are used, measuring the electric current induced in them; the principle is the same as in the loop reception of electromagnetic oscillations in radiotelegraphy. In this way it was discovered that the seemingly smooth course of the magnetic elements in time is in fact resolved into small, strikingly regular oscillations, which have received the name of elementary waves or pulsations; their period ranges from 5 to 100 sec (80, 85). Apparently they are excited, like the diurnal variations, by regular atmospheric oscillations in the high electrically conducting layers. The thought arises of fading, whose periods have the very same magnitude (p. 236).

IX. Electromagnetic Waves.

It has already been mentioned (p. 223) that the propagation of electromagnetic waves also led to the assumption of a high electrically conducting layer of the atmosphere. True, owing to the electrical conductivity of the earth the wave also propagates along its surface, bending around it (a surface wave) (99), although the attenuation of this wave owing to absorption turned out in reality to be smaller than the theoretically expected value. But only in recent years has the experience with short waves led to the recognition of a conducting layer in the atmosphere. The great range of propagation of shorter waves is found for 15-meter waves, which circle the terrestrial globe twice in 0.138 sec (100). In practice this recognition is taken into account by directing the wave energy upward at a certain angle with the aid of special antennas (reflectors) (95); for 11- and 15-meter waves between Nauen and Buenos Aires the minimum of reception intensity occurred when the reflector was inclined at 38°.

Here only the principal points will be touched upon, and other, more complete reports will be indicated (96, 97). After the first English and American observations of waves reflected from the Heaviside layer and reaching the earth, Apple—

... and his collaborators (87, 88, 89) set up systematic observations of the height of the layer. At a distance of about 100 km from the transmitting station, waves of 400 m are received by means of a combined system of various antennas; in this way it becomes possible to separate the wave coming from above from the wave traveling along the earth’s surface. The height of the layer deflecting the waves toward the earth proved to be from 90 to 130 km at night, in summer. In winter, during the last three hours of the night, 250–350 km were often observed; but as soon as the sun’s rays touched the atmosphere, the lower boundary of the layer again descended to 100 km. During the day, below the principal layer of Heaviside, apparently, the following ionized layer is formed (descending to 40–50 km below the first); however, it manifests itself more in the absorption of waves than in a noticeable change in the height attained by them.

The speed of a train (group) of electromagnetic waves in an ionized medium differs from the speed of light in a vacuum (93). The group velocity of the whole train of waves is smaller, while the phase velocity \(v\) of a single wavelength is greater than the speed of light \(c\) in a vacuum; \(v\) determines the curvature of the ray; the refractive index \(n\) is given by the relation:

\[ n^2=\frac{v^2}{c^2}=\varepsilon=1-4\pi N\frac{e^2}{m\omega^2}; \]

(\(\varepsilon\)—dielectric constant; \(N\)—number of ions in \(1\ \text{cm}^3\), \(e\) (electrostatic), \(m\)—their charge and mass, \(\omega=\frac{2\pi c}{\lambda}\)—the cyclic frequency of a wave of length \(\lambda\) in non-ionized space).

The constant magnetic field \(F\) of the earth affects the motion of ions. The latter may describe circles or spirals (of radius \(r\)) about the magnetic lines of force,—here collisions of ions with one another and with molecules are not taken into account,—with angular velocity \(\omega_0\). It is determined from the equality between the mechanical centrifugal force \(m\omega_0^2 r\) and the electric deflecting force

\[ \frac{eF\omega_0 r}{c} \]

as a result of the action of the magnetic field on it, i.e. on the rotating ion

\[ \omega_0=\frac{eF}{mc}. \]

For \(F=0.5\) gauss and \(e=4.8\cdot 10^{-10}\), we find for the electron \((m=9\cdot 10^{-28})\) \(\omega_0=8.9\cdot 10^6\), and for the hydrogen ion \((m=1.66\cdot 10^{-24})\), \(\omega_0=4.8\cdot 10^3\). The wavelengths corresponding to these frequencies

\[ \left(\omega=\frac{2\pi c}{\lambda}\right) \]

are equal to \(210\ \text{m}\) and \(390\ \text{km}\).

Just as in optics, the propagation of a wave in a magnetic field depends on the angle between the plane of polarization of the wave and the direction of the field; double refraction and rotation of the plane of polarization occur (the effects of Kerr and Faraday) (94). Instead of the expression given above for \(n^2\), other expressions are valid, in which \(\omega^2\) is replaced by \((\omega^2-\omega_0^2)\). Particular deviations from the case when the external magnetic field is absent should be expected when \(\omega\) is close to \(\omega_0\); consequently, in the region of radio waves the earth’s magnetic field can be of significance only in the presence of free electrons in the Heaviside layer. In the latter case, special phenomena should occur near the resonance wavelength, equal to \(210\ \text{m}\). Although there is still far from being a theoretical explanation of the distinct polarization observed in the reception of short waves (92) [by means of which the fading effect is also explained as interference between different wave fronts (91)], nevertheless the existence of this polarization is recognized as evidence of free electrons. Laboratory observations also confirm the probability of the fact (3) that at low pressures, as in the upper layers of the atmosphere, free electrons can exist for a long time, whereas in dense air near the earth they quickly settle.

Regarding the number \(N\) of electrons in \(1\ \text{cm}^3\), the following calculation gives indications (101): short waves, incident on the Heaviside layer at an angle \(a=60^\circ\), in the final analysis, undoubtedly acquire a velocity parallel to the earth’s surface; this was observed even for a steeper incidence at \(a=20^\circ\).

From the ratio of the indices of refraction

\[ \frac{n}{n_0}=\frac{\sin\alpha}{\sin 90^\circ}. \]

It follows that \(n=\sin\alpha\), since \(n_0=1\) in the lower atmosphere. Hence, since \(\omega^2\gg \omega_0^2\) (\(\omega=10^8\) for \(\lambda=19\) m), by the above formula for \(n^2\):

\[ \cos^2\alpha=1-n^2=\frac{4\pi Ne^2}{m\omega^2}. \]

Putting \(\alpha=60^\circ\), \(\cos^2\alpha=\frac{1}{2}\), we obtain

\[ N\frac{e^2}{m}=4\cdot 10^{15}, \]

whence

\[ N=1.5\cdot 10^6 \]

for electrons, or \(N'=2.8\cdot 10^9\cdot k\) for ions with a mass \(k\) times the mass of the hydrogen atom. In comparison with this, the content of electrons and charged atoms or molecules in the layers of the atmosphere near the earth proves to be only vanishingly small; the number of molecular complexes (ions with a mass many times greater than that of hydrogen), which determine the electrical conductivity of the air near the earth, is of the order of 700 per \(1\ \mathrm{cm}^3\). Since the number of electrons and ions must be more or less the same, it follows from this that the conductivity is caused chiefly by free electrons; for \(10^6\) ions per \(1\ \mathrm{cm}^3\) would give much smaller values for \(\cos^2\alpha\).

The greater \(N\) is, the stronger the refraction of the wave and the closer to the transmitting station the reflected or refracted waves return; on the other hand, the wave is then more strongly weakened by absorption. The reason is that the energy of oscillation absorbed by the ions is converted chiefly into heat upon collisions of the ions with gas molecules; consequently, the wave energy is absorbed the more rapidly, the denser the gas and the more strongly it is ionized. The coefficient of absorption is proportional to

\[ \frac{Ne^2}{m}\cdot \frac{\omega}{\tau}, \qquad \text{where } \tau=\frac{l}{V} \]

(\(l\) is the mean free path of the ion, \(V\) is its mean velocity due to disordered thermal motion,

whence \(\tau\) is the mean interval of time between two successive collisions). According to the kinetic theory of gases, the electrical conductivity is equal to (though, to be sure, not for electrons, in whose case values of \(\sigma\) that are too small are obtained):

\[ \sigma=\frac{Ne^{2}\tau}{m}\quad(\text{electrostatic}). \]

The quantity \(\frac{Ne^{2}}{m}\) was found above to be equal to \(4\cdot 10^{15}\). The mean free path (near the surface of the earth \(10^{-5}\ \text{cm}\)) increases from \(l=2.2\ \text{cm}\) at an altitude of \(100\ \text{km}\) to \(70\ \text{cm}\) at an altitude of \(130\ \text{km}\) (cf. p. 222). According to the kinetic theory the velocity of the electrons is \(V=1.2\cdot 10^{7}\ \text{cm/sec}\); consequently at an altitude of \(100\ \text{km}\)

\[ \sigma=8\cdot 10^{-4}\ \text{cm}^{-1}\Omega^{-1}. \]

From observations of the daily variations of terrestrial magnetism it follows: the maximum \(\sigma=10^{-8}\ \text{cm}^{-1}\Omega^{-1}\); at \(130\ \text{km}\), for this there would already suffice \(N=5\cdot 10^{4}\) electrons per \(1\ \text{cm}^{3}\). Thus the assumption that in the upper atmosphere there are from \(10^{5}\) to \(10^{6}\) free electrons per \(1\ \text{cm}^{3}\) satisfies the observations both in the field of terrestrial magnetism and in cable telegraphy.

The connection between the reception of radiotelegraphic waves and disturbances of terrestrial magnetism has been observed repeatedly; during strong magnetic storms, for example, transatlantic short-wave communication was interrupted. The possibility of explanation lies in the increased ionization due to intensified solar corpuscular radiation during magnetic storms; but observations are still too few. A magnetic disturbance affects above all the general conditions of reception (intensity of reception, path of the wave); under disturbed conditions, conditions usually occurring at night take place by day. The main part of the atmospheric disturbances proper—for example those heard by radio—apparently arises as a result of processes in the troposphere (for example, thunderstorms).

The slow periodic increase and decrease of the strength of reception (fading) recall magnetic elementary waves (p. 232). Here the matter is not so much the interference between the surface and reflected waves as the oscillations of intensity and polarization of the spatial wave. In the case of

of the existing dependence of wave propagation on the magnetic field, it is quite understandable that even insignificant oscillations of the latter, of \(10^{-4}\) gauss and less, have an effect (91).

X. Ionization.

a) General. The number \(n\) of ions in \(1\ \mathrm{cm}^3\) is connected with the number \(q\) (the ionization coefficient) of ion pairs arising in \(1\ \mathrm{cm}^3\) during one second, and with the number \(a n^2\) of ion pairs recombining in the same time (\(a\)—the recombination coefficient).

\[ \frac{dn}{dt}=q-a n^2. \]

In the stationary state, consequently, \(q=a n^2\).

Near the earth’s surface the air is ionized chiefly by the radioactive radiation of substances contained in the earth’s crust, sea water, and air. This terrestrial radiation does not reach the stratosphere; there other ionizing agents exist, each of which will be considered separately.

b) Solar ultraviolet radiation. A. Schuster was the first to interpret the strong dependence of the electrical conductivity of the upper layers of the atmosphere on the position of the sun in the sense that the chief ionizing agent is the sun’s rays, predominantly ultraviolet. In opposition to this, Svanne (105) asserted that the energy of the latter is far from sufficient, and that even the full solar energy emitted toward the earth could not maintain the degree of ionization required by so high an electrical conductivity. C. Chree (101), however, showed that Svanne’s conclusions are based on too large a recombination coefficient \(a\) \((=10^{-6}\), as at the earth’s surface)) and too small a value for the mobility of the ions. If the sun radiates as a black body of temperature \(6000^\circ\), then in the region most essential for ionization, namely below \(1350\ \text{\AA}\), which corresponds to an electron velocity of more than 9 volts, there proves to be only \(1.61\cdot 10^{-5}\) of the total energy \((1.93\ \mathrm{cal}/\mathrm{cm}^2\,\mathrm{min})\).

i.e. 22 erg/cm² sec at the Earth's surface. 9 volt-electrons correspond to the energy of ionization of one pair of ions, namely

\[ 4.77\cdot 10^{-10}\cdot \frac{9}{300}=1.4\cdot 10^{-11}\ \text{erg}. \]

Consequently, in a vertical column of air with a cross-section of 1 cm², the short-wave part of the radiation can create about \(1.6\cdot 10^{12}\) pairs of ions per second.

In order to judge whether this ionizing power is sufficient, one must have data on the recombination coefficient \(\alpha'\), which, above, where there are free electrons, is undoubtedly smaller than near the Earth. For this purpose Chapman considers the nocturnal decrease in the number of ions \(n\). At night, as compared with the daytime, \(q=0\); the solution of the equation \(\frac{dn}{dt}=-\alpha n^{2}\) gives

\[ n=\frac{n_0}{1+n_0\alpha t}. \]

Let at sunset \(t=0\); approximately three hours later \((t=10^{4}\ \text{sec.})\), \(n\) is still equal to \(10^{5}\) (p. 235), according to radiotelegraphic observations. Since \(n_0>n\), one may approximately put, for \(t=10^{4}\), \(1\ll n_0\alpha t\), and therefore

\[ n=\frac{1}{\alpha t}, \]

whence \(\alpha=\frac{1}{nt}=10^{-9}\). In the stationary state, at noon, \(q=\alpha n^{2}\), and if \(n=10^{6}\), then \(q=10^{3}\). In a vertical column with a cross-section of 1 cm² and a height of 300 km, \(3\cdot 10^{10}\) pairs of ions would be created per second; for this number the ionizing power of the ultraviolet radiation computed above \((1.6\cdot 10^{12})\) is quite sufficient.

c) Application of Saha’s theory (Saha). The successes of recent years in the field of astrophysics are based chiefly on the application of the laws of thermodynamics to the theory of ionization of gases (on this theory of Saha, see [102, 103]). A. Pannekoek (104) applied this theory, developed by Milne, Fowler, and Wolter, to the ionization of the Earth's atmosphere by solar rays. Let \(h\nu_0\) (\(h\) is Planck’s quantum of action, \(\nu_0\) the frequency of the exciting radiation) be the ionization energy required to detach one electron; if the energy \(h\nu\) \((\nu>\nu_0)\) is absorbed, then the part \(h\nu_0\) of it is expended on ionization, and the remainder passes into energy of motion. Thus there is formed a continuous absorption band, extending from \(\nu_0\) toward the sho—

short waves down to \(\nu=\infty\). The compensating process is the recombination of an ion with an electron.

The boundary of the absorption spectrum in the region of long waves is calculated from the already known excitation potentials (oxygen 16.1, hydrogen 16.1, nitrogen 16.9 volts); it proves to be 730 Å for nitrogen, 766 Å for oxygen and hydrogen. Pannekuk considers pure nitrogen, oxygen, and hydrogen atmospheres and computes for them the decrease of pressure with height at a temperature of \(-55^\circ\) C. The incident solar radiation has an already known intensity and effective temperature. Its active short-wave part is very strongly absorbed in passing through the atmosphere; for this atomic absorption values up to \(a=10^4\) are obtained (relative to \(a\), cf. p. 206). Under the action of these rays there arise \(n\) electrons per \(1\ \mathrm{cm}^3\); with the assumptions made, \(n\) is a function of pressure, and hence of height. At a certain height \(n\) reaches a maximum, as is seen from the following table (\(p\) in atmospheres, \(h\) in kilometers; decimal logarithms of \(p\) and \(n\)). The values of the heights given in the original work have been recalculated for the partial pressure of hydrogen near the earth, equal to \(10^{-8}\) atm. (respectively [11]).

		\(\lg p\)	\(-8\)	\(-9\)	\(-10\)	\(-11\)	\(-12\)	\(-13\)	\(-14\)
Nitrogen . . .	\(\lg n\)		\(-5.5\)	\(+4.8\)	\(+5.4\)	\(+5.0\)	\(+4.5\)	\(+4.0\)	\(+3.5\)
Nitrogen . . .	\(h\) (km)		121	136	151	167	182	197	212
Oxygen . .	\(\lg n\)		\(-10\)	\(+4.7\)	\(+5.7\)	\(+5.3\)	\(+4.8\)	\(+4.3\)	\(+3.8\)
Oxygen . .	\(h\) (km)		104	117	131	144	157	170	184
Hydrogen . .	\(\lg n\)		\(+3.1\)	\(+6.0\)	\(+5.8\)	\(+5.3\)	\(+4.8\)	\(+4.3\)
Hydrogen . .	\(h\) (km)		0	204	415	626	837	1049

The table and Fig. 9 show that the number \(n\) of electrons at first slowly increases as the earth is approached, correspondingly to the increase in the number of atoms in \(1\ \mathrm{cm}^3\); \(n\) reaches a maximum equal to from \(10^5\) to \(10^6\), and with further approach to the earth very rapidly falls to 0 owing to the strongly increasing absorption. In nitrogen the maximum lies at ...

146 km, the lower boundary of the ionized layer is about 130 km; for oxygen the corresponding numbers are 130 and 114 km. In hydrogen the maximum ionization lies much higher, although not as high as Pannekoek supposed, who based his calculations on a far greater hydrogen content. Nevertheless, his conclusion is correct that the existence of a hydrogen atmosphere excludes the possibility of placing the Heaviside layer at 100–200 km, because hydrogen in higher layers would absorb all radiation below 766 Å, whereas it is necessary for the ionization of oxygen and nitrogen.

Fig. 9. Ionization of the atmosphere by solar radiation. The number \(n\) of electrons in \(1\ \mathrm{cm}^3\) for oxygen and nitrogen.

Radiotelegraphic observations have sometimes led to the conclusion that the Heaviside layer at times descends below 100 km. According to Pannekoek’s calculations, below 100 km there can be no electrons produced by the photoelectric effect in oxygen and nitrogen. True, the atomic absorption coefficients are not reliable; but even reducing the assumed value to \(1/100\) would mean lowering the lower boundary of the ionized layer by only 30 km. Acoustic data rule out the other possibility, namely that the temperature is below \(-55^\circ\) and that the atmosphere is therefore more compressed.

However, if Chapman’s opinion on the connection between ozone and ionization proved to be correct, then ionization below 100 km would be possible: ozone absorbs much longer waves (2500 Å) than the three gases considered above. At present, however, there are no quantitative data.

d) Solar γ-radiation. If γ-rays fall normally on a material layer of thickness \(dl\) and density \(\rho\), then after passing through it the intensity of the radiation \(I\) is weakened by \(dI=-kI\rho dl\); \(k\) is the absorption coefficient characteristic of the type of rays. Chapman and Milne (1) assume that the degree of ionization is proportional to the absorbed energy; they find that the height \(h_m\) of the layer of maximum ionization is determined by the air density \(\rho(h_m)\), with \(\rho(h_m)\) proportional to \(\frac{1}{k}\). Consequently, \(h_m\) depends only on \(k\). For very hard γ-rays of RaC with \(k=0.0424\), one obtains \(\rho(h_m)=3.4\cdot 10^{-5}\), or \(h_m=26\) km. Near the earth the ionization is not noticeable; it is weaker than \(10^{-12}\) of the maximum value. Above \(h_m\) the degree of ionization decreases more slowly than below (the curve resembles Fig. 9); between 18 and 60 km the ionization is more than 1% of the maximum value. For ordinary X-rays (\(k=4\)), \(h_m\) would be about 60 km. These figures refer to a vertical incidence of the rays; for oblique incidence \(h_m\) is greater; for γ-rays with \(k=0.0424\), at the limiting inclination of the rays (angle of incidence \(90^\circ\)), \(h_m\) is about 45 km.

e) Penetrating radiation. Penetrating radiation is ten times harder than the hardest known γ-rays of radioactive elements. For ionization at sea level, approximately, \(q=2\); at an altitude of 9 km, \(q=80\). The absorption coefficient is about \(k=0.003\); the height of maximum ionization, i.e. \(h_m=15\) km. G. Benndorf (90) investigated ionization due to penetrating radiation in detail; he believes that night-time electrical conductivity could be explained by it. He considers the recombination coefficient \(a\) proportional to \(\frac{1}{\rho}\) (\(\rho\) is the density of the air), and therefore finds for...

heights of 100 km, \(a = 10^{-12}\). To this it must be added that, according to S. Chapman’s considerations (p. 238), there should then be no nocturnal disappearance of electrical conductivity there at all. With so small an \(a\), nocturnal ionizers in general, including penetrating radiation, become superfluous; the nocturnal electrical conductivity would appear chiefly as a consequence of daytime ionization; this seems probable.

f) Corpuscular radiation of the Sun. Although the absorption of \(\beta\)-rays does not follow the usual exponential law, nevertheless, for comparative computations one may put \(k = 3.3\) (1); then \(h_m = 62\) km (calculation as in section d), and between 48 and 100 km there is more than \(1\%\) of the maximum intensity. The \(\alpha\)-rays of radioactive substances, whose range in air at \(15^\circ\) C is from 6.9 to 2.5 cm, would penetrate the atmosphere from outside down to 95–104 km, if the air temperature above 35 km is taken to be 300° abs. In the previous calculations (219° abs.), naturally, smaller heights were obtained (80–85 km); the newly obtained numbers agree better with observations of the lower boundary of the aurora.

G. Petersen (96a) put forward the hypothesis that the kinetic energy of solar corpuscular rays remains with the Earth’s atmosphere in the form of thermal energy. On energetic grounds this possibility must be regarded as open until the nature of the radiation and the conditions of the transformation of energy have been clarified. The energy brought in, on average, in 1 sec is, during a magnetic storm, not less than \(10^9\) PS; and since all the heat received by the Earth from the Sun is \(2.4 \cdot 10^{14}\) PS, during disturbances the energy of corpuscular rays proves to be equal to the energy of the Sun’s ultraviolet radiation (p. 237). But the heating is probably confined to the heights of the aurora (above 100 km), because the ions cannot penetrate to 40 km, where, from acoustical considerations, one may already expect a higher temperature.

The heat of the diurnal periodic vortical current (p. 225) proves to be less than \(10^4\) PS and consequently raises the temperature only by negligible fractions of a degree (84).

g) Summary concerning electrical conductivity. Despite the unreliability of our information concerning many processes, one can sketch the following picture of the origin of the electrical conductivity of the higher atmospheric layers. The strong electrical conductivity is due not so much to the large average number of ions present as to their great mobility (electrons). On days quiet in the magnetic sense, the chief ionizer is short-wave solar radiation. With ionization there is apparently connected the formation and decomposition of ozone. If the number of ions in \(1\ \mathrm{cm}^3\) is assumed equal to \(10^6\), then in a layer of air \(300\ \mathrm{km}\) thick, above each \(\mathrm{cm}^2\) of surface there would be \(3 \cdot 10^{13}\) ions. Since the corresponding number of ozone molecules is \(10^{19}\), only 3 out of every \(10^6\) of its molecules need be ionized. By day the conducting layer must descend lower than by night, because after sunset the ionizing action of the Sun ceases and the ions in the lower, denser layers are neutralized more rapidly than above. At night the decomposition of ozone molecules might create conditions of excitation for the green line of the aurora, visible every night at all latitudes. Given a long lifetime of ions above \(80\ \mathrm{km}\), there is no need to seek a special source of nocturnal ionization, although an influence of penetrating radiation or also of a generally softer cosmic \(\gamma\)-radiation is possible. The above-mentioned (p. 228) strong dependence of electrical conductivity on the number of sunspots, even on quiet days, is noteworthy in that the increase in conductivity cannot be explained by a corresponding increase in the intensity of ultraviolet radiation, since the changes in the other parts of the spectrum are too insignificant; the way out may lie in the hypothesis that, during intense spot-forming activity of the Sun, its surface emits additional \(\gamma\)-rays, which, of course, do not reach the surface of the Earth.

During magnetic disturbances there is observed, simultaneously with them, the action of solar corpuscular rays, drawn into the Earth’s magnetic field, predominantly near the poles. There can be no doubt as to the existence of these rays,

just as in the strong increase in electrical conductivity which they temporarily produce. But it is unclear in what manner these rays traverse the path between the sun and the earth, and what the nature of these particles is—whether they are $\alpha$- or $\beta$-rays, or clouds of partially (not completely!) neutralized particles. In the above calculations of the penetrating power of various rays, the first foundations have been laid for suppositions on this score.

A survey of the main factual material is replaced by a reference to the compiler’s already published brief communication (5).

Literature.

Reviews.

1. Chapman, S. and Milne, E. A. The composition, ionisation and viscosity of the atmosphere at great heights. Quart. J. roy. meteorol. Soc. Lond. 46, 357, 1920.

2. Dobson, G. M. B. The uppermost regions of the earth’s atmosphere. (Halley-Lecture) Oxford 1926. 22 S.

3. Discussion on the electrical state of the upper atmosphere. Proc. roy. Soc. London. (A) III, 1, 1926.

4. A discussion on ionisation in the atmosphere and its influence on the propagation of wireless signals. Proc. phys. Soc. Lond. 37, D. I, 1925.

5. Bartels, J. Die höchsten Atmosphärenschichten. Naturwiss. 16, 301, 1928.

1. Aerology.

1. Bemmelen, W.; van. Verhandel Kon. Magn. en Meteorol. Observat. Batavia. Nr. 4, 1916; Naturwiss. 12, 441, 1924.

2. Richardson, L. F. How to observe the wind by shooting spheres upward. Meteorol. Office, Professional Notes Nr. 34, London 1924.

3. Stewart, C. D. Measurement of upper wind velocities by observations of artificial clouds. Meteorol. Office, Professional Notes. Nr. 38 London 1924.

4. Wigand, A. Geschossmeteorograph D. R. P. 410705 (1926).

9a. Kölzer, J. Wetter 38, 153, 1921; Z. Feinmech. u Präzis. Nr. 6, 1928.

LITERATURE

2. SCATTERING.

10a. Jeans, J. H. Bull. Mount Weather Observatory 2, Part 6, 347. Washington 1910.

10b.—Dynamische Theorie der Gase. Übers. von R. Fürth, Braunschweig 1926.

1. Smoluchowski, M. von. Über die Atmosphäre der Erde und der Planeten. Physik. Z. 2, 307 (1900/01)—Die ausführliche (polnische) Originalabhandlung ist abgedruckt in Oeuvres (Pism 1) 1, 217. Krakowie 1924.

2. Stoney, J. Of atmospheres of planets and satellites. Trans. roy. Dublin Soc. 6, 305, 1897.

3. OPTICAL PHENOMENA.

12a. Dorno, C. Beobachtungen der Dämmerung und von Ringerscheinungen um die Sonne 1911 bis 1917. Abh. preuss. meteorol. Inst. 5. Nr. 5. Berlin 1917.

1. Grunert, P. und Kleinert, H. Die Dämmerungserscheinungen (Probleme der kosmischen Physik 10). Hamburg H. Grand 1927.

2. Jesse, O. Die Höhe der Dunstschicht, durch welche die merkwürdigen Dämmerungserscheinungen der letzten Monate hervorgerufen worden sind. Meteorol. Z. 1, 127, 1884 u. folg. Jahre, zuletzt 8, 306 (1891).

3. Kahlke, S. Ann. Hydrogr. 49. 294. 1921.

4. Lindeman, F. A. Nature (Lond.) 118, 195, 1926.

5. Malzey, V. Luminous nightclouds. Nature (Lond.) 118, 14, 1926.

6. Quervain, A. de: Ultracirren. Meteorol. Z. 34 132 (1917); Boll. K.: Ebenda 35, 316, 1918.

7. Radacovic, M. Meteorol. Z. 43, 441, 1926; 44, 326, 1927.

8. Schmid, Fr. Das Zodiakallicht. (Probleme der kosmischen Physik II). Hamburg: H. Grand. 1927.

9. Stormer, C. Photogrammetuische Bestimmung der Höhe von irisierenden Wolken (Perlmutterwolken) am 30 Dez. 1926. Geofysiske Publ. Oslo 5, Nr. 2 (1927).

10. Wegener, A. Die Temperatur der obersten Atmosphärenschichten. Meteorol. Z. 42, 402, 1925. Diskussion mit F. A. Lindemann und G. M. Dobson. Ebenda, 43, 102, 1926.

23.—Beobachtungen der Dämmerungshöhen und des Zodiakallichtes in Grönland. Sitzungsber. Acad. Wiss. Wien, Math. naturwiss. Kl. Abt. IIa, 135, 328, 1926.

24.—Anfangs- und Endhöper grosser Meteore. Meteorol. Z. 44, 281, 1927.

4. AURORA.

1. Babcock, Harold D. A study of the green aurora line by the interferometer method. Astrophys. J. 57, 209, 1923.

2. Gario, G. Die Wellenlänge der grünen Nordlichtlinie. Z. f. Physik 42, 15, 1927.

Literature

1. Dufay, J. Intensité de la raie verte des aurores polaires dans le spectre du ciel nocturne. C. r. Acad. Sci. 185, 142, 1927.

2. Grotrian, W. Zur Frage nach dem Ursprung der grünen Nordlichtlinie. Naturwiss. 15, 869, 1927.

3. Über den Ursprung der Nebellinien. Ibid. 16, 177, 193, 1928.

4. Hopfield J. J. Phys. Rev., (2) 29, 923, 1927.

5. Mac Lennan, J. C. and Shrum: Proc. roy. Soc. Lond. (A) 106, 138, 1924; (A) 108, 501, 1925.

6. Mac Lennan J. C., Mac Leod, J. H. and Mac Quarrie, W. C. An investigation into the nature and occurrence of the auroral green line 5577 Å. Proc. roy. Soc. Lond. (A) 114, 1, 1927; Nature (Lond.) 118, 441, 1926.

7. Mac Lennan, J. C. and Mac Leod, J. H. Proc. roy. Soc Lond. (A) 115, 515, 1927.

8. Mac Lennan, J. C., Ruedy, Richard and Mac Leod J. H. On the origin of the auroral green line in the oxygen spectrum. Trans. roy. Soc. Canada (Sect. III), (3), 21, 27, 1927.

9. Paschen, F. Sitzungsber. preuss. Acad. Wiss., Physik.-math. Kl. 1927, 207.

10. Pelzer, H. Zur Frage des Vorhandenseins von festem Stickstoff in der Erdatmosphäre. Ann. Physik (4) 83, 362, 1927.

11. Rayleigh, Lord. The aurora line in the spectrum of the night-sky. Proc. roy. Soc. Lond. (A) 100, 367, 1922.

12. —On visual observations of the aurora line in the spectrum of the sky at night. Gerlands Beitr. z. Geophysik 19, 292, 1928.

13. —The light of the night-sky: its intensity variations when analyzed by colour felter. Proc. roy. Soc. Lond. (A) 106, 117, 1924; 109, 428, 1925; 119, 11, 1928.

14. Sommer, L. A. Über den Ursprung der grünen Nordlichtlinie. Naturwiss. 16, 219, 1928.

15. Stormer, C. On an aurora curtain of violet-gray colour situated at a high altitude photographed on September 8th, 1926. Gerlands Beitr. z. Geophysik 17, 254, 1927.

16. Résultats des mesures photogrammétriques des aurores boréales observés dans la Norvège méridionale de 1911 à 1922. Geofysike. Publ. Oslo. 4. Nr. 7. 1926.

17. —Action remarquable de la lumière du soleil sur la hauteur des aurores boréales. C. r. Acad. Sci. 185, 262, 1927.

18. —Nature, 120, 329, 1927.

19. Vegard, L. and Krogness, O. The position in space of the aurora polaris. Geofysis Publ. Oslo. 1, Nr. 1 (1920).

20. Vegard, L. Das Nordlicht und die höheren Atmosphärenschichten. Naturwiss. 13, 541, 1925.

21. Neuere Ergebnisse über das Leuchten verfestigter Gase und ihre Beziehungen zum Nordlicht. Ibid. 15, 438, 1927.

LITERATURE

1. Wiechert, E. Polarlichtbeobachtungen in Göttingen. Phys. Zs. 3, 365, 1901/02.

2. Wien, W. Phys. Zs., 24, 415, 1923.

5. OZONE

1. Cabannes, J. et Dufay, I. Transparence de l’atmosphère dans le spectre visible. Diffusion moléculaire. Absorption par l’ozone. J. Physique (6), 7, 257, 1926.

2. — Mesure de l’altitude et de l’épaisseur de la couche d’ozone dans l’atmosphère. Ebenda (6) 8, 125, 1927; C. r. Acad. Sci. 181, 302, 1925.

3. — Les variations de la quantité d’ozone contenue dans l’atmosphère. Ebenda (6) 353, 1927.

4. Chree, C. Atmospheric Ozone and terrestrial magnetism. Proc. roy. Soc. Lond. (A), 110, 693, 1926.

5. Colange, G. Étude de l’absorption par l’ozone dans le spectre visible. J. Physique (6) 8, 254, 1927.

6. Dobson, G. M. B. and Harrison, D. N. Proc. roy. Soc. Lond. (A) 110, 660, 1926.

7. Dobson, G. M. B. and Lawrence, J. Ebenda 114, 521, 1927.

8. Dorno, C. Abh. preuss. meteorol. Inst. Berlin (6) 283, 1919; Hann-Süring Lehrb. d. Meteorol. 4. Aufl., 6. Leipzig 1926.

9. Dorno, C. und Götz, F. W. P. Ozonmessungen auf spektrographischem Wege. Meteorol. Z. 44, 385, 389, 462, 1927.

10. Dutheil, J. und M. L’absorption de la lumière par l’ozone entre 3050 et 3400 Å (région des bandes de Huggins). J. Physique, (6) 7, 414, 1926.

11. Fabry, Ch. The absorption of radiation in the upper atmosphere. Proc. phys. Soc. Lond. 39, 1, 1927.

12. Fabry, Ch. et Buisson, M. L’absorption de l’ultra-violet par l’osone et la limite du spectre solaire. J. Physique (5) 3,196, 1913.

13. — — Ebenda (6) 2, 197, 297, 1921.

14. Fowler and Strutt Proc. roy. Soc. Lond. (A) 93, 577, 1917.

15. Götz, F. W. Paul. Der Jahresgang des Osongеhaltes der hohen Atmosphäre. Beitz. Z. Phys. d. freien Atm. 13, 15, 1926.

16. — Das Strahlungsklima von Arosa. Abschnitt IV. Berlin: J. Springer 1926.

17. — Ozon und Klima. Wetter 44, 241, 1927.

18. — Zum Ozonmangel der tieferen Atmosphärenschichten. (Wird erscheinen im Second Report) Committee on Solar and Terrestrial Relationships; Internat. Research Council).

19. — Verh. Schweizer. Naturforsch. Ges. Basel. 1927. Teil II, 116.

20. Hartley J. chem. Soc. Lond. 39. III, 1881.

21. Hoelpers, O. Über die Intensitätsverteilung im ultravioletten Sonnenspektrum. Z. Geophys., 3, 184.

LITERATURE

1. Hoeler, O. und Dobson, G. M. B. (Diskussion) Ebenda, 3, 307, 309, 1927.

2. Lambert, P., Déjardin, G. et Chalonge, D. Sur l’extrémité ultraviolette du spectre solaire et la couche d’ozone de la haute atmosphère. C. r. Acad. Sci. 183, 800, 1926; Bull. Observ. Lyon. 9, 45, 1927.

72a. Maris, H. B. Nature (Lond.) 120, 839, 1927.

1. Pettit, Edison Ultra-violet Solar Radiation. Proc. nat. Acad. Sci. U. S. A. 13, 380, 1927.

2. Strutt, R. J. Ultra-violet transparency of the lower atmosphere and its relative poverty in ozone. Proc. roy. Soc. Lond. (A) 94, 260, 1918.

6. SOUND.

1. Angenheister, G. Das Problem der Schallausbreitung. Meteorol. Z. 43, 467, 1926.

2. Gutenberg, B. Über die Ausbreitung des Schalls in der Atmosphäre. Naturwiss. 14, 338, 1926.

3. Wegener, A. Die äussere Hörbarkeitszone. (Mit ausführlichen Literaturangaben). Z. Geophys. 1, 297, 1924/25).

4. Wiechert, E. Über die Schallausbreitung in der Atmosphäre. Meteorol. Z. 43, 81, 1926; Nachr. Ges. Wiss. Göttingen, Math.-physik. Kl. 1926, 93, 201.

7. COMPOSITION.

1. Wigand, A. Die Änderung der Zusammensetzung der Luft mit der Höhl. Meteorol. Z. 33, 433, 1916.

8. TERRESTRIAL MAGNETISM

1. Absalom, H. W. L. Proc. roy. Soc. Edinburgh, 45, 297; Terrestr. Magnetism 32, 1, 1927.

2. Angenheister, G. In Geiger-Scheel, Hand. d. Physik. 15, 314. Berlin. J. Springer 1927.

3. Bartels, J. In. „Handb. d. Experimentalphysik“ herausg. von Wien-Harms, 25, 624. Leipzig, 1928.

83.— Gezeitenschwingungen der Atmosphäre. Naturwiss. 15, 860, 1927; Z. Geophys. 4, 1, 1928. Handb. d. Experimentalphysik, herausg. von Wien-Harms, 25, 163. Leipzig, 1928.

1. Chapman, S. The solar and lunar diurnal variations of terrestrial magnetism. Phil. Trans roy. Soc. Lond. (A) 218, 1, 1919; 225, 49, 1925.— J. Lond. Math. Soc. 2, 131, 1927.

2. Pödder, A. Micromagnetische Oszillationen in Irkutsk. Gerlands Beitr. z. Geophysik 17, 232 (1927).

LITERATURE

1. Schmidt, Ad. Enthalten die Variationen des Erdmagnetismus einen Bestandteil, der in Beziehung zur Sternzeit steht? Ber. üb. d. Tätigkeit d. preuss. meteorol. Inst. i. J. 1927, Anhang S. 89. Berlin 1928.

9. ELECTRIC WAVES.

1. Appleton, E. V. and Barnett M. A. F. Proc. roy. Soc. Lond. (A) 109, 621, 1925.

2. Appleton, E. V. Nature (Lond.) 118, 514, 1926; 120, 330, 1927.

3. Appleton, E. V. and Ratcliffe, J. A. Proc. roy. Soc. Lond. (A) 115, 291, 305, 1927.

4. Benndorf, H. Über den durch die Hesssche Höhenstrahlung bedingten Ionisations— und Leitfähigkeitszustand der höheren Luftschichten. Phys. Zs. 27, 626, 1926.

5. Breit, G. A. Suggestion of a connection between radio fading and small fluctuations in the earth’s magnetic field. Proc. Inst. Radio Engin., 15, 709, 1927.

6. Hollingworth, J. Nature (Lond.). 121, 171, 1928.

7. Howe G. W. O. Phasen— und Gruppengeschwindigkeiten in einem ionisierten Medium. Jb. drahtl. Telegr. 30, 42, 1927.

8. Lassen, H. Electr. Nachrichtentechnik 4, 324, 1927.

9. Meissner, A. Directional radiation with horizontal antennas. Proc. Inst. Radio Engin. 15, 928, 1927.

10. Pedersen, P. O. The propagation of radio waves along the surface of the earth and in the atmosphere. Danmarks Naturvidenskabelige Samfund. A. Nr. 15. Copenhagen 1927.

96a. Petersen, H. Phys. Z. 28, 510 (1927); Diskussion mit W Anderson: Phys. Zs. 29, 232, 492, 1928.

1. Sacklowski, A. Die Ausbreitung der electromagnetischen Wellen. Elektr. Nachrichtentechnik 4, 31, 1927. (Mit vollständigem Literaturverzeichnis).

97a.— Die Ausbreitung der electromagnetischen Wellen. Berlin, Weidmannsche Buchhandlung, 1928.

1. Smith-Rose, R. L. and Barfield R. H. Measurements on wireless waves received from the upper atmosphere. Proc. roy. Soc. Lond. (A) 110, 580, 1926; 116, 682, 1927.

2. Sommerfeld, A. Drahtlose Telegraphie. In: Frank-Mises, die Differential und Integralgleichungen der Mechanik und Physik 2. Braunschweig 1927.

3. Wagner, K. W. Naturwiss. 16, 104, 1928.

10. IONIZATION.

1. Chapman S. Ionisation in the upper atmosphere. Quart. J. roy. meteorol. Soc. Lond. 52, 225, 1926.

Bibliography

1. Emden, R. Thermodynamik der Himmelskörper. Enzyklop. math. Wiss. VI 2, 21. S. 515 ff. Leipzig, 1926.

2. Freundlich, E. In: Geiger-Scheel, Handb. d. Phys. 11, 203. Berlin: Jul. Springer, 1926.

3. Pannekock, A. Ionisation equilibrium in stellar atmospheres and in the earth’s atmosphere. Proc. Kon. Acad. Wetenschappen, Amsterdam 29, 1165, 1926.

4. Swann, W. F. G. Terrestr. Magnetism 21, 1; 1916.

1. Cf. the communication of Radaković (19). ↩↩