UPPER LAYERS OF THE ATMOSPHERE1

On May 4, 1939, a joint meeting of the Chemical, Physical, and Meteorological Societies of Great Britain was held in London, devoted to questions concerning the structure of the upper layers of the atmosphere.

In his introductory address, Prof. F. A. Paneth stated that the questions connected with the structure of the upper layers of the atmosphere are so broad that there is no possibility of covering them in any detail at the conference. With this in mind, it was decided to devote the papers to questions of meteorological, physical, and chemical research on the upper layers of the atmosphere and to make use of the simultaneous presence of representatives of three scientific fields (which, incidentally, occurs far from often) for an appropriate exchange of views. The subjects selected for the papers were questions of the composition, density, and temperature of the upper layers of the atmosphere.

The exclusion from consideration of other questions connected with the structure of the upper layers of the atmosphere by no means indicates that they are of lesser importance. This was done in order to make use of every opportunity for a fuller discussion of at least a narrow range of questions. And if, for example, questions concerning the study of the electrical state of the atmosphere did not appear in the conference program, this points to the vastness of this problem, as a result of which there was no possibility of discussing it exhaustively alongside the other questions.

Below is given a brief account of the principal papers, as well as the most interesting remarks made during their discussion.

A. COMPOSITION OF THE UPPER LAYERS OF THE ATMOSPHERE

DIRECT CHEMICAL ANALYSIS OF THE ATMOSPHERE

(Paper by Prof. F. A. Paneth)

From a purely chemical point of view, the analysis of air in the region of the stratosphere is not of particular interest.

Chemical analysis is important as a means of determining the altitude of the stratosphere at which the air may be regarded as being in a state of rest. Of course, this rest should not be understood as absolute, since observations of the flights of pilot balloons and stratospheric balloons, as well as of the trajectories of tracer projectiles, quite definitely indicate the existence of air currents even at great heights.

As is known, in a relatively calm atmosphere, under the action of gravity, a diffusive separation of the light and heavy gases that make up the atmosphere should be observed. Experimental discovery of a predominance of lighter gases in the high regions of the atmosphere would constitute confirmation of this proposition.

Beginning such a study, it is, of course, necessary to have exhaustive data on the composition of the atmosphere at the surface of the earth. Unfortunately, despite countless measurements, the composition of the air at the earth’s surface still cannot be regarded as known with complete precision, since individual measurements show somewhat different results depending on the method used and on the individuality of the experimenter.

The most reliable present-day volume composition of dry air is given in Table 1.

Table 1

Volume composition of air in the troposphere region (in %)

In compiling Table 1 the amount of water vapor, whose content can fluctuate within very considerable limits, was not taken into account. For the same reasons the content of nitrogen dioxide and formaldehyde was not taken into account, since both gases are observed only in the immediate vicinity of human habitation.

The most convenient means of detecting separation of the gases making up the atmosphere is to study the relative content of two gases, one of which is lighter and the other heavier than normal air. The densities of the gases composing the atmosphere are given in Table 2.

Table 2

Densities of the gases composing the atmosphere

Despite the fact that the density of oxygen is only slightly greater than the density of normal air, it is convenient to choose it precisely as the representative of the “heavy gas.” The reason for this lies in the exceptional simplicity of the chemical detection of oxygen. As the representative of the “light gas” we shall choose helium. Despite the great difficulty of measuring it, the fractional-distillation method developed in recent years makes it possible to determine the helium content with sufficient accuracy even in those cases when the total quantity of air does not exceed several cubic centimeters.

\(^{1}\) Content variable; increases with altitude.
\(^{2}\) Content variable; decreases with altitude.

To establish a reliable basis for the measurements, it was necessary first to make sure of the constancy of the helium content in the atmosphere at various points on the globe, bearing in mind that in some regions of the earth’s crust (for example, in oil-bearing regions) helium is released in larger quantities than in others (for example, over the ocean).

The results of a survey of the helium content at various points of the globe, scattered over almost the entire surface of the earth, are given in Table 3.

Table 3

Helium content (in \(10^{-6}\ \mathrm{cm}^3\) per \(1\ \mathrm{cm}^3\) of air) at various points of the globe

In not a single case did the helium content differ from the mean value by an amount exceeding the accuracy of the measurements. In the earlier measurements the error was \(0.5\%\). Subsequently, as the measuring technique was improved, the error of the measurements decreased to \(0.2\%\). It is possible that, by applying in all cases a more advanced technique, it would be possible to reduce still further the already small fluctuations in the helium content. In any event, the figures in Table 3 show that the helium content in the lower layers of the troposphere is so constant that, from measurement of its content with altitude, one can reliably judge the separation of gases.

Fig. 1. Heights reached by airplanes, stratostats, and balloon-sondes.

The curve characterizes the dependence of atmospheric pressure on altitude (the flights during which air samples were taken are underlined).

In the figure the following are indicated: Stuttgart (31/7–34), Stuttgart (6/5–36), Kirov (30/8–37), Stevens (11/11–35), Prokofiev (30/9–32), Lemann (22/10–38), Adam (30/6–37), Sveshnikov (28/9–36); balloon-sondes, stratostats, airplanes; stratosphere, troposphere; summit of Everest. The axes are marked in km and mm Hg.

Figure 1 schematically shows the heights reached during the taking of air samples with the aid of balloon-sondes and stratostats. Table 4 gives the results obtained in this way for measurements of the contents of helium and oxygen.

The figures in Table 4 show that at altitudes below 20 km the composition of the air, within the limits of measurement accuracy, may be considered constant. At altitudes exceeding 20 km, however, all measurements without exception indicate an increase in the helium content and a decrease in the oxygen content. This gives groun-

...it should be assumed that the diffusive separation of heavy and light gases begins at an altitude of 20 km. The separation is more noticeable with respect to helium, which is quite understandable from the greater difference in the densities of helium and normal air as compared with the difference for oxygen and normal air.

Table 4

Content of helium and oxygen in the atmosphere at various altitudes

It follows from Fig. 1 that, under existing conditions, the most suitable means for studying the separation of gases in the atmosphere are radiosondes that have reached an altitude of 31 km. From stratonauts, the separation of gases was observed only by Stevens on the stratoship Explorer II, which reached an altitude of 22 km. The same graph shows that the chemical analysis of air samples at altitudes above 32 km, owing to the extreme rarefaction of the atmosphere, cannot yield positive results.

The abrupt changes in the relative content of helium and oxygen with increasing altitude are explained by the unavoidable air currents in this region. A sharp transition to a state of rest would seem extremely improbable. For this reason, one should not expect exact agreement in the content of helium and oxygen in air samples taken at different times and at different points on the globe.

In order to become finally convinced that the observed small changes in the content of helium and oxygen do indeed characterize diffusive separation, it would be highly useful to determine the content of helium and oxygen in one and the same air sample. Work in this direction is being carried out. For the present, however, one must be satisfied with the fact that the data of Table 4 indicate the beginning of the separation of the light and heavy constitu-

ting air at altitudes in the interval from 20 to 30 km. The question of the extent to which the observed separation can develop in the region of great heights and lead to a composition of the air quite different from the usual one is considered in the report by Prof. Chapman.

SPECTROSCOPIC AND OTHER METHODS OF STUDYING THE CHEMICAL COMPOSITION AND THE PROCESS OF DISSOCIATION IN THE ATMOSPHERE

[Report by Prof. S. Chapman (S. Chapman)]

1. The fundamental propositions of Prof. Paneth’s report are the constancy of the composition of the air at altitudes up to 20 km and signs of an incipient separation of gases at greater altitudes. In this, no account was taken of accidental constituents of the atmosphere, such as water vapor, the content of which depends on meteorological conditions, as well as components depending on proximity to cities.

The lighter constituents of the atmosphere always possess a greater rate of diffusion than the heavier constituents; in a mixture of several gases of a given composition this rate is inversely proportional to density and therefore increases with altitude as the density decreases; near the earth’s surface the rate of diffusion is negligibly small, as a result of which mixing processes in this region of the air are dominant.

Exchange of air in the vertical direction can take place only in the presence of forces that produce this exchange and overcome the “vertical stability” of the atmosphere. As is known, a medium will be in a state of unstable equilibrium when the density increases from below upward, which for most liquids corresponds to the case of a fall of temperature with height; for compressible media, such as air, vertical stability is disturbed when the temperature falls with height faster than the “adiabatic gradient”; in the troposphere the latter quantity is half the former, as a result of which this region of the atmosphere should be regarded as stable. In the “isothermal region” of the stratosphere the vertical stability is higher than in the troposphere and reaches still higher values in the region where temperature increases with height, where the air is exceptionally stable. Above this region the temperature, as may be thought, first falls and then increases again. The oscillations of vertical stability caused by these changes of temperature create causes that favor the mixing of air. At present we are not in a position to assess these forces and the degree of mixing of air caused by them; consequently, we cannot predict to what extent (and in what region) diffusion proves to be the dominant factor and causes a change in the composition of air with height. Thus the possibility is not excluded that the traces of diffusive separation of air observed at altitudes above 20 km are connected with the exceptional vertical stability of the overlying layer of increasing temperatures.

1. If it is assumed that at altitudes above 20 km diffusion exceeds the forces of mixing, then radical changes must occur in the composition of the upper layers of the atmosphere, since the principal constituents of the atmosphere at great heights must become the lighter gases. In this connection oxygen and nitrogen will predominate only in the lower layers of the atmosphere. This is illustrated by Figs. 2 and 3, drawn up on the assumption that, beginning at a certain altitude (20 km in Fig. 2 and 10 km in Fig. 3), mixing completely ceases, and under the assumption of a definite temperature regime of the atmosphere. When compiling Fig. 3 it was assumed that helium and hydrogen are retained at all heights, which is why at altitudes above 100 km the atmosphere is shown as consisting mainly of hydrogen. In compiling Fig. 2, the existence in the upper layers only of helium was assumed, as a result of which at great heights the atmosphere is shown as consisting mainly of helium.

In connection with this, the following questions arise: is the atmosphere at altitudes greater than 100 or 150 km hydrogenous? Is it helium in this region? Or, perhaps, as a result of certain processes, in this region too the atmosphere has almost the same composition as at the surface of the earth, i.e., consists mainly of nitrogen and oxygen?

1. An indication in this regard can be obtained from the spectrum of aurorae, emitted by particles of air. It is believed that air particles are brought into an excited state by a stream of rapidly moving corpuscles emitted by the sun. The spectrum of aurorae indicates the presence in the upper atmosphere, chiefly (if not exclusively), of nitrogen and oxygen and contains not even traces of helium and hydrogen. The spectrum is emitted by layers of air situated in the region of altitudes from 90 to 600 km. It seems surprising that at such great altitudes the density of the air is sufficient for the emission of light; even more remarkable is the circumstance that this spectrum indicates the presence of nitrogen and oxygen, which, judging from Figs. 2 and 3, are almost absent at these altitudes. This fact, independently of whether helium or hydrogen can emit light under auroral conditions, makes it probable to suppose that the entire atmosphere up to an altitude of 600 km consists mainly of nitrogen and oxygen.

Fig. 2. Composition of the atmosphere at different altitudes (Chapman and Milne). $H_d$ is the altitude at which diffusion begins

Fig. 3. Composition of the atmosphere at different altitudes (A. and K. Wegener)

1. The predominance of nitrogen and oxygen as constituent parts of the atmosphere throughout its entire thickness can be explained by the assumption that at all altitudes the processes of mixing predominate over diffusion; it is assumed in this that the observed slight predominance of helium at altitudes greater than 20 km does not undergo further development at great altitudes. In this respect it is desirable and possible to carry out experimental observations.

As another possible explanation one may put forward the supposition that, under the action of the high temperature of the upper layers of the atmosphere (see section B), the speed of motion of the molecules increases so much that the light gases (hydrogen and helium), overcoming the attraction of the earth, leave the limits of the atmosphere.

1. Further information about the composition of the atmosphere in inaccessible regions can be obtained on the basis of studying the spectra of the atmosphere, among which three types of spectra should be distinguished. The simplest of all is to observe the spectrum of the sun’s rays absorbed by the thickness of the atmosphere; separating the absorption lines in the earth’s atmosphere from the absorption lines in the chromosphere presents no difficulty. Two other spectra: the spectrum of aurorae (observed during strong excitation of air molecules)

and the spectrum of the night-sky glow (emitted by the upper layers of the air during the night hours) are emission spectra.

Both emission spectra indicate the presence of lines of molecular nitrogen; during intense auroras, along with the lines of neutral nitrogen, lines of ionized nitrogen appear. Without doubt, ions of molecular nitrogen are constantly present in the atmosphere during the night hours; however, under ordinary conditions the energy is insufficient for their excitation to a state of light emission, for which reason the normal spectra of the night-sky glow do not indicate the presence of such ions.

None of the emission spectra shows lines of molecular oxygen; however, lines of atomic oxygen are observed in both spectra.

This circumstance once again indicates that at considerable altitudes oxygen undergoes dissociation and, apparently, is already completely dissociated at altitudes exceeding 100 km; in the lower layers atomic and molecular oxygen exist simultaneously, which, incidentally, explains the formation of ozone, which readily arises in a medium where molecules and atoms of oxygen are present simultaneously.

In addition, the spectrum of the night-sky glow indicates the presence of lines of atomic sodium, whose existence in the upper layers of the atmosphere is an unresolved problem.

1. The dissociation of molecular oxygen in the upper layers of the atmosphere is due to the absorption of the sun’s ultraviolet rays in a broad band of frequencies with a center near 1,500 Å. The ozone formed also absorbs ultraviolet rays, but in another broad band with a center near 2,500 Å, which abruptly cuts off the solar spectrum at 3,000 Å; the absorption of radiation by ozone leads to its dissociation. At the expense of the energy released during the dissociation of molecular oxygen, the night-sky glow apparently also arises.

2. Nitrogen is ionized more readily than it is dissociated, at least under the action of sunlight. The spectrum of the night-sky glow only in rare cases indicates the existence of atomic nitrogen in the upper layers; however, the spectra of auroras give some indications of the presence of atomic nitrogen, which may be formed under the unusual excitation conditions that occur during auroras.

3. All that has been said permits the conclusion that the chemistry of the upper layers of the atmosphere is apparently, in the main, the chemistry of nitrogen and oxygen; moreover, it is necessary to take into account the possibility of the existence of oxygen in various forms.

VERTICAL DISTRIBUTION OF OZONE

[Report by G. M. Dobson (G. M. B. Dobson)]

The vertical distribution of ozone in the Earth’s atmosphere is of interest from two points of view: first, the connection between the ozone content and meteorological conditions in the lower-lying region is well known; second, according to widespread notions, the region of elevated temperatures in the interval from 40 to 60 km is caused by the absorbing action of ozone located in this region, as a result of which the calculation of temperatures can be made only with knowledge of the ozone content.

The vertical distribution of ozone in the atmosphere can be found either with the aid of instruments on a balloon-sonde, or with the aid of apparatus installed on the ground. In both cases, at a given point in time, the quantity of ozone above the point of measurement is determined by comparing the intensities of two portions of the solar spectrum, one of which is strongly absorbed by ozone, while the other is transmitted with insignificant absorption.

In Figs. 4 and 5 the results of measurements made with the aid of ground-based apparatus are shown in the form of graphs. The curves in Fig. 4 were obtained at Arosa (Arosa, Switzerland), Fig. 5 at Tromsø (Norway). During the measurements, both the absolute content of ozone in centi-

COMPOSITION OF THE UPPER LAYERS OF THE ATMOSPHERE

Fig. 4. Vertical distribution of ozone in the atmosphere according to measurements at Arosa (Switzerland).

a—along the abscissa axis is plotted the ozone content in centimeters per kilometer (i.e., \(10^{-6}\,\text{cm}^3\) per \(1\,\text{cm}^3\) of air); b—relative ozone content in \(1\,\text{cm}^3\) of air.

Fig. 5. Vertical distribution of ozone in the atmosphere according to measurements at Tromsø (Norway).

Along the abscissa axis are plotted the same quantities as in Figs. 4, a and b.

meters per 1 km of altitude, as well as the relative ozone content in the air. The inscriptions on the curves correspond to the total amount of ozone. Despite comparatively large measurement errors, the difference in the course of the curves in Figs. 4 and 5 should apparently be regarded as real.

Fig. 6. Vertical distribution of ozone in the atmosphere according to balloon-sonde measurements (after Regener)

Along the abscissa axis is plotted the ozone content in centimeters per kilometer.
In the figure: total ozone content \(= 0.260\) cm; curves: Arosa, Regener, Tromsø.

Among observations with a spectrograph installed on a balloon-sonde, the most substantial should be considered the work of Regener, who succeeded in obtaining excellent spectra at altitudes up to 30 km. The noticeable expansion of the spectra with increasing altitude in the region of shorter waves indicates a rapid decrease of the overlying ozone layer as the sonde passes through the region from 25 to 30 km. In other words, it should be considered that in this altitude interval the sonde passes through a large part of the ozone layer. Regener’s observational results are presented in Fig. 6, where, for comparison, the curves obtained from ground-based observations at Arosa and Tromsø are plotted.

Photographs of spectra were also obtained during two flights of stratospheric balloons in the USA. These stratospheric balloons, however, did not reach the altitudes that Regener was able to investigate. The data obtained differ greatly from those set forth above, chiefly in the region of altitudes up to 15 km. Thus, according to the American data, up to 15 km the atmosphere contains a negligible amount of ozone, which then increases sharply. The reason for the discrepancy between the results of these experiments and those mentioned above has not been established.

B. DENSITY AND TEMPERATURE OF THE ATMOSPHERE

DIRECT MEASUREMENTS AND OBSERVATIONS OF THE PROPAGATION OF SOUND WAVES

[Report by F. J. W. Whipple]

As early as 1793, J. Dalton, basing himself on barometric measurements during ascents of high mountains, expressed the supposition that, with increasing altitude, the temperature of the air falls uniformly (approximately by \(6^\circ\) for each kilometer of altitude) up to 20 km. A century passed before it became possible to verify experimentally the correctness of his supposition. Measurements carried out with the aid of balloon-sondes showed that Dalton was not far from the truth in extending the results of measurements in mountainous regions to the free atmosphere.

The first sonde to reach an altitude of 15 km was launched in 1893. After repeated flights of balloon-sondes in France and Germany, a new temperature regime in the stratosphere was in all certainty discovered. Each flight of a sonde showed a uniform fall of temperature up to a certain altitude, after which there began a region of constant temperatures. Thus, the law formulated by Dalton proved valid for altitudes up to 10 km. This fact gave occasion to propose the terminology now generally accepted: troposphere—for the lower layers of air, which are in a regime of mixing, and strato-

sphere—for higher layers, where the temperature is almost independent of altitude.

In the northern hemisphere the temperature of the stratosphere is usually within the limits from 220 to 230° K. Sounding-balloon ascents in the tropics indicate a lower temperature of the stratosphere. The lowest temperature was recorded on November 5, 1913, in Batavia (181° K). In the Arctic the stratosphere extends into a lower region of the atmosphere.

Fig. 7. Dependence of atmospheric temperature on altitude according to measurements by sounding balloons (Hamburg, 2/11 1929—29/1 1931).

Thus, observations at Franz Josef Land show that the mean height of the lower boundary of the stratosphere is 8 km when its temperature is 210° K in winter and 220° K in summer.

Observations by means of sounding balloons at altitudes exceeding 30 km are of exceptional interest. The record flights of sounding balloons in Pavia in 1911 (35 km) and in 1913 in California (32 km), unfortunately, cannot be used for our purposes, since these balloons were not equipped with the appropriate apparatus.

The results of temperature measurements during balloon-sonde flights in the period from 1929 to 1931 in the Hamburg region (one of the sondes reached an altitude of 33.8 km) are reproduced in Fig. 7. None of the five plotted curves indicates any appreciable deviations of the temperatures from constancy in the region of the stratosphere.

The study of the regime of the upper layers of the atmosphere by means of sound waves is based on the fact that, during explosions of great force, zones of silence are observed. As observations have shown, the internal radius of the zone of silence is determined by the meteorological situation, whereas the external radius is practically independent of the weather.

The existence of zones of silence shows that sound waves can travel considerable distances in the atmosphere and, after undergoing complete internal reflection, return again to the earth. In order to obtain an idea of the composition of the atmosphere it is necessary to know the propagation time of the waves, as well as the angles of inclination of the rays arriving at the receiving point. The latter can be determined with the aid of the sound locators used in military practice.

Observations of the propagation of explosive waves were made in Birmingham, Cardiff, and North Walsham during artillery firing at Woolwich. At each of the receiving stations mentioned, three-microphone sound locators were installed, by means of which the angles of inclination were determined; the latter reached appreciable values, as high as 35°.

The propagation time of the reflected waves usually exceeded the time required for sound to travel along the ground by 80–100 sec. Taking as a basis a certain distribution of temperatures with height (it is usually assumed that in the lower region of the stratosphere, and up to a certain height, the temperature is constant, after which it begins to increase linearly with height), it was possible to calculate the trajectory of the rays. In most cases the summit of the trajectory lies only slightly above 40 km. The observational results agree well with the following temperature values: 280°K at an altitude of 40 km, 310°K at an altitude of 45 km, and 335°K at an altitude of 50 km. The values obtained are not dependent on the assumed form of the temperature transition at the boundary between the regions of constant and linearly increasing temperature. Balloon-sonde observations in the Hamburg region showed that the region of constant temperatures extends up to 35 km. This makes it possible to consider that the region of increasing temperatures begins at an altitude somewhat below 40 km.

OBSERVATIONS OF METEORS

[Report by Prof. F. A. Lindemann (F. A. Lindemann)]

Observations of meteors make it possible to advance four arguments in favor of the view that at great heights the density and temperature of the atmosphere are considerably higher than the values which would obtain under the assumption that the temperature of the stratosphere is constant and equal to 220°K.

The visible trajectory of a meteor begins at the point where evaporation of the meteor body becomes abundant, and ends where the entire mass of the meteor turns into gas. The heat flux causing evaporation cannot attain large values until a protective cushion of compressed air has formed in front of the moving meteor; this can occur when the evaporating molecules collide with air molecules before their last ones have time to escape in the direction opposite to the motion. On this basis one can determine the minimum air density at which the visible trajectory begins.

A meteor can become visible only after it has passed through a certain mass of atmosphere necessary to raise its temperature to the value at which the mass of the meteor begins to evaporate. Since the heat released depends on the velocity of the meteor and the density of the atmosphere, the mass of the overlying layer of air can be calculated from the height of the beginning of the visible trajectory.

A meteor disappears after all its mass has evaporated; in other words, after the heat it has received becomes equal to the latent heat of evaporation. Consequently, the height at which the trajectory ends also depends on the mass of the overlying layer of air. The size of a meteor can be determined from its brightness, duration, and speed, since a large part of the energy is radiated.

Finally, a meteor cannot attain a temperature exceeding the temperature of the cushion of adiabatically compressed air formed in front of the moving meteor. Thus, the temperature reached is determined only by the initial temperature of the air and by the speed of the meteor’s motion. By measuring the latter quantity, one can determine the minimum temperature of the air.

All the arguments listed lead to concordant values of the temperature and density of the upper layers of the atmosphere; according to these data, the temperature of the atmosphere at great heights reaches 300–400°K, and the density exceeds the density of the stratosphere by several hundred times; the temperature of the stratosphere at heights greater than 10 km is constant and equal to 220°K.

STRUCTURE OF THE ATMOSPHERE ON THE BASIS OF IONOSPHERIC MEASUREMENTS

[Report by Prof. E. V. Appleton (E. V. Appleton)]

1. Nature of the quantities determined in ionospheric measurements. With the aid of ionospheric stations that use radio waves to sound the upper layers of the atmosphere, the following quantities are determined: a) the effective reflection heights $h'$ as a function of the frequency $f$; b) the reflection coefficient $\rho$ of the ionosphere as a function of the frequency $f$, and c) the state of polarization of the reflected waves.

On the basis of item (a) one can determine the law of variation of electron concentration with height in each of the ionized layers. These data, under known assumptions, make it possible to determine how the gases subjected to ionization (i.e., oxygen or nitrogen) are distributed with height.

On the basis of item (b) one can determine the absorption experienced by radio waves on their upward and downward paths and, under known assumptions, the values of the collision frequency of electrons with neutral molecules can be calculated.

On the basis of item (c) we obtain data that serve as a guiding thread in the search for a formula that makes it possible, from the structure of the ionosphere, to derive the law of variation of electron concentration with height (measured according to item (a)).

It is also appropriate to note the following. Assuming that the dependence of pressure on height throughout the entire mass of the atmosphere follows the law valid for small heights, it can be shown by the simplest calculations that at a height of 300 km each 1 cm³ would contain only about 1,000 molecules. At the same time, ionospheric observations show that at these heights in daytime the electron concentration is of the order of $10^6$ electrons/cm³. Hence it is not difficult to conclude that in the high layers of the atmosphere certain factors are operating that cause the molecules to be displaced upward. These factors may be either an increase in the temperature of the upper layers of the atmosphere or the presence, at great heights, of light gases such as, for example, helium.

2. Dependence of the height of the homogeneous atmosphere on the structure of the ionized layers. When the complex structure of the ionosphere was first discovered, the supposition was immediately put forward that the presence of several ionization maxima may be due to the ionization of different gases entering into the composition of the atmosphere. This view still enjoys general recognition, and individual differences of opinion concern the question of precisely which gas is ionized in producing one layer or another.

In one respect, however, it may be considered that the experimentally observed law of variation of ionization with height in a given layer gives an idea of the character of the variation with height of the gases composing the atmosphere. The relation between the density of the atmosphere \(n\) and the height \(h\) is expressed by the formula

\[ n=n_0 e^{-\frac{h}{H}}, \tag{1} \]

where \(n_0\) is the density of the atmosphere at ground level, and \(H\) (the reduced height of the terrestrial atmosphere) is a coefficient determined by the formula

\[ H=\frac{kT}{mg}. \tag{2} \]

In the last formula \(k\) is Boltzmann’s constant, \(T\) is the absolute temperature, and \(g\) is the acceleration of gravity. The quantity \(m\) depends on the extent to which the atmosphere may be considered sufficiently well mixed. With complete mixing of the gases composing the atmosphere, the quantity \(m\) may be taken equal to the mean molecular mass. In the presence of diffusive separation of gases, \(m\) should be taken as the molecular mass of that one of the gases entering the atmosphere whose distribution is of interest to us.

The problem of determining the structure of the atmosphere may simply be reduced to finding the value of \(H\) at all points of the atmosphere. In this case, the change of \(H\) with height may be ascribed either to a change in temperature or to a change in molecular mass.

Some idea of the value of \(H\) for the so-called “simple ionized layer” can be obtained from the following reasoning. As has recently been shown, the change of electron concentration with height (measured from the level of maximum ionization) may be approximately expressed by a parabolic dependence:

\[ N=N_{\max}\left(1-\frac{y^2}{4}H^2\right). \tag{3} \]

Introducing certain simplifying assumptions, it can be shown that the relation between the effective height \(h'\) and the frequency \(f\) of an ordinary ray reflected from an ionized layer may be represented by the equation

\[ h'=h_0+H\frac{f}{f_{\mathrm{кр}}}\ln\frac{f_{\mathrm{кр}}+f}{f_{\mathrm{кр}}-f}, \tag{4} \]

where \(h_0\) is the height of the lower boundary of the ionized layer, corresponding to \(N=0\), and \(f_{\mathrm{кр}}\) is the critical frequency of the layer. Comparing the experimentally obtained dependence of \(h'\) on \(f\) with the curve constructed according to equation (4), it becomes possible to determine the values of \(H\) and \(h_0\) for which these dependences agree with one another in the best way.

The values of \(H\) obtained in this way as early as 1937 for wintertime were of the order of 10 km for the \(E\) layer and 40–50 km for the \(F\) layer. The appreciable difference between them may be due either to the high temperature of the \(F\) region, or to the presence in this region of light gases, such as helium, possibly together with some degree of diffusive separation of gases.

In recent years, by the same method, it has been possible to obtain more accurate values of \(H\). Thus, for the \(E\) layer during the summer solstice, values \(h_0=96\) km and \(H=11.1\) km were obtained. Consequently, the height of the maximum ionization, determined by the formula \(h_{\max}=h_0+2h\), is about 120 km. In winter, for the merged \(F\) layer, \(H\) is of the order of 40 km, but in summer, when the \(F\) region splits into two layers, the value of \(H\) for the upper (\(F_2\)) layer reaches 70 km. For comparison it is important to note that for the stratosphere, assuming its complete mixing and a temperature of 220°K, the value of \(H\) is only 6.4 km.

The conclusions that may be reached on the basis of all the foregoing are conveniently formulated by using equation (1), which for this purpose may be given the form:

\[ h = H \ln n_0 - H \ln n. \tag{5} \]

Consequently, in an atmosphere with constant \(H\), there must be a linear dependence between \(\ln n\) and \(h\). Since the quantity \(H\) cannot be considered constant, the dependence between \(h\) and \(\ln n\) has the form of the curve in Fig. 8. The slope of this curve is proportional to the value of \(H\) at the corresponding altitude.

At the height of layer \(E\), the quantity \(H\) increases to a value of \(11.4\) km, which corresponds to a temperature of \(385^\circ\mathrm{K}\) (under the assumption that the mean molecular mass does not change, i.e., that oxygen does not dissociate). As for still larger values of \(H\) in the region of layer \(F\), they may be due either to a further increase in temperature or to the predominance of lighter gases.

It is very noteworthy that there is a seasonal variation in the value of \(H\) in layer \(F_2\), which may be explained by seasonal temperature changes or by the supposition that, in the summer months, ionized constituents with small molecular or atomic mass enter the region of the layer (for example, O, N, or \(H_2O\)). In both cases it is assumed that the structure of the upper layers changes from local winter to local summer.

Fig. 8

3. Determination of air density on the basis of measurements of collision frequency. Introducing the known assumptions, it appears possible, on the basis of measurements of radio-wave absorption, to calculate the mean collision frequency \(\nu\) of electrons at the altitudes located in the region of maximum ionization. In round numbers, the collision frequencies determined in this way are: for layer \(E\) (120 km), \(10^4\) collisions; and for layer \(F\) (from 250 to 300 km), \(10^3\) collisions. Under normal atmospheric pressures and temperatures, \(\nu\) reaches values of \(2 \cdot 10^{11}\), with a total number of molecules in \(1\ \mathrm{cm}^3\) of \(2.56 \cdot 10^{19}\). Neglecting differences in temperatures and assuming that the number of collisions is proportional to the molecular density, we find values of \(10^{12}\) molecules/\(\mathrm{cm}^3\) in layer \(E\) and \(10^{11}\) molecules/\(\mathrm{cm}^3\) in layer \(F\).

As follows from the above, the given altitudes reach the following values:

a) \(H = 6.4\) km for altitudes up to 100 km,
b) \(H = 11.5\) km at an altitude of 120 km,
c) \(H = 40\text{–}50\) km at altitudes greater than 200 km,

increasing in the summer months at altitudes of the order of 250 km to values \(H = 70\) km.

Drawing, with allowance for these data, the curve of Fig. 8, we obtain molecular densities that agree excellently with the figures given above.

Observations of the propagation of sound waves show that, at an altitude of about 50 km, there must exist in the stratosphere a region of elevated temperatures reaching \(320^\circ\mathrm{K}\), which corresponds to \(H = 9.3\) km. To bring the curve of Fig. 8 into agreement with these data, we must alter it as shown by the dashed line. In order for the form of the curve to remain unchanged in the region of the ionized layers, it is necessary to assume that, beyond the region of elevated temperatures, there is a region of lowered temperatures. In this connection it is appropriate to recall,

that Humphreys, as well as Martyn and Pulley, have expressed the supposition that below region \(E\) there is a layer of low temperature (\(180^\circ\mathrm{K}\)). Quite recently Budden, Ratcliffe, and Wilkes, observing the daily fluctuations of reflections of long radio waves from a layer at an altitude of \(70\) km, came to the conclusion that the temperature in this region drops to \(180^\circ\mathrm{K}\) (the value \(H=6\) km found by these authors corresponds to a temperature of \(203^\circ\mathrm{K}\)).

DISCUSSION OF THE REPORTS

Below is a brief summary of the individual contributions.

Dr. D. F. Martyn finds that the contradiction between Chapman’s views, according to which the atmosphere in the region of altitudes up to several hundred kilometers consists chiefly of nitrogen and oxygen, and Paneth’s experimental works, which revealed diffusive separation at altitudes greater than \(30\) km, can be removed by supposing that at great altitudes forces again arise that cause mixing of the atmosphere. The speaker believes that the existence of such forces is confirmed by the connection established at Australian ionospheric stations between the electron concentration of layer \(F_2\) and meteorological conditions at the level of the earth.

Dr. Martyn introduces the concept of the “climate” of the upper layers of the atmosphere, in the establishment of which the functions of the binding link are possibly performed by ozone.

Fig. 9.

1 — number of electron collisions (Martyn and Pulley); thickness of layer \(F_2\) (Fuchs and Appleton); 2 — number of electron collisions (Beynon and Martyn); 3 — luminous night clouds (Humphreys); reflection of long radio waves (Ratcliffe); 4 — oscillations of the atmosphere (Pekeris); 5 — meteors (Lindemann and Dobson); 6 — propagation of explosive waves (Whipple)

As regards the question of the distribution of temperatures in the stratosphere, the speaker considers that the most satisfactory way of reconciling the measurements of individual authors is by constructing the curve reproduced in Fig. 9. In explanation of the curve, the authors who determine the corresponding temperatures are indicated.

Prof. Lindemann believes that the traces of diffusive separation of gases discovered by Prof. Paneth are of exceptional interest. Proceeding from the content in the earth’s crust of radioactive substances that ultimately produce helium, estimating the geological age of the earth at \(10^9\) years, and comparing the figures obtained in this way with the actual content of helium in the lower layers of the atmosphere, the speaker considers that over the indicated period each square centimeter of the earth’s surface lost \(5.5\cdot 10^{21}\) helium atoms. Analyzing the possible causes of such leakage of helium, Prof. Lindemann rejects the loss of helium as a consequence of the high temperature of the upper layers of the atmosphere, which, in his opinion, contradicts spectroscopic measurements of the intensity of nitrogen lines in the spectrum of auroras. The opinion of Prof. Chapman, who affirms the absence of helium in the upper layers of the atmosphere because its spectrum is not observed during auroras, the speaker considers untenable, since the electric field developing during auroras may prove insufficient to excite the helium lines. Moreover, about 99% of the helium energy falls in the region of ultraviolet rays, which, naturally, will not be detected by terrestrial observers.

If spectroscopic observations are not regarded as entirely erroneous, then in all regions of the atmosphere the helium content must increase with height. It is necessary to bear in mind that heating under the action of solar radiation can outweigh adiabatic cooling in those cases where the energy absorbed in 1 sec. by a mass of 1 g exceeds \(gv\), where \(g\) is the acceleration due to gravity and \(v\) the convective velocity. Consequently, if the velocity of displacement is relatively small, then even in the absence of an adiabatic temperature gradient, intense convective mixing may arise, which will lead to instability of that region of the atmosphere where the air temperature decreases with height. If some gas begins to rise upward, while remaining warmer than the surrounding air, it will continue its ascent until it mixes with other gases. As a result, it is difficult to imagine that oxygen and nitrogen situated above layer \(E\), while remaining there, would seep downward. Even if this should occur, forces would inevitably arise that lift the aforementioned gases upward until complete mixing. These processes cannot occur in the lower layers of the atmosphere, where the ionizing radiation has for the most part been absorbed, but in the upper layers such mixing is inevitable.

Thus, in the upper layers of the atmosphere, owing to convective mixing, the relative content of oxygen, nitrogen, helium, and water vapor does not change over a large interval of heights. The mixing processes cease in the region of very low pressures, where the convective velocity is insufficient to move air particles. Below it is considered to what extent the views set forth agree with observations over ionized layers.

The origin of layer \(D\) may be attributed to the ionization of \(O_3\) or, possibly, \(O_2\) by small quanta of radiation.

Layer \(E\), apparently, is wholly due to the ionization of \(O_2\). According to the speaker’s calculations, the electronic concentration at a height of 80 km should reach \(1.2\cdot 10^5\) electrons/\(\text{cm}^3\). Considerations concerning the duration of the existence of electrons in connection with the observed thickness of the layer force one to suppose that oxygen constitutes only a small part of the atmosphere in this region; the principal gases are apparently nitrogen and helium.

Layer \(F_1\), in all probability, is due to the ionization of atomic oxygen, which is present in large quantity above layer \(E\). As in the case of layer \(E\), satisfactory agreement with observational results (with respect to the number of collisions of electrons with neutral molecules) can be achieved only if it is assumed that a large part of the collisions occurs with molecules of helium or nitrogen. The assumption that layer \(F_1\) is due to the ionization of \(N_2\) encounters difficulties in explaining the long duration of the existence of electrons.

The speaker believes that the ionization of layer \(F_2\), in addition to the ultraviolet rays of the sun, may be due to the action of material particles entering the earth’s atmosphere (meteors, cosmic dust, and atoms falling into the sphere of terrestrial attraction, in particular \(N_2\), \(O_2\), and even Na, whose presence in the spectrum of the night-sky glow has hitherto been an unexplained enigma). True, such particles, on entering the earth’s atmosphere, can cause ionization only if they collide with particles whose mass is comparable with their own, otherwise producing only an acceleration of molecular motion. It was pointed out above that, owing to convective currents, oxygen and nitrogen reach great heights, as a result of which such collisions will very often be followed by ionization. On the other hand, an increase in the velocity of molecular motion will lead to a local increase in temperature (insignificant from the point of view of the general temperature of the upper layers), which will entail the atmospheric loss of light gases, in particular helium. This fully explains the leakage of helium over the geological period, which was discussed above.

Attributing such a character of ionization to the \(F_2\) layer, it seems possible to explain (or to find paths toward a reasonable explanation of) such phenomena as the winter anomaly, the daily maxima of ionization in the morning and evening hours, the annual course of ionization, etc. The dependence of the ionization of the \(F_2\) layer on the 11-year period of solar activity becomes comprehensible, as does the connection between the ionization of the \(F_2\) layer and the intensity of the green oxygen line in the spectrum of the nightglow, the existence of Na lines, the phenomenon of the aftereffect during magnetic disturbances, etc. Under such a mechanism of ionization of the \(F_2\) layer, its electron concentration should not follow the height of the sun and should vary greatly with latitude, which is fully confirmed by experimental observations.

M. P. Dolukhanov, Leningrad

1. Abstract of the article “The upper atmosphere” (Quarterly J. Roy. Met. Soc., Vol. LXV, No. 281, July, 1939). ↩