On the validity of Boltzmann's distribution law for the charges of aerosol particles in electrical equilibrium

Summary The validity ofBoltzmann's energy distribution law as applied to the charge distribution of monodisperse aerosols, i.e. aerosols which contain particles of one size only, was studied with improved equipment now available.Since monodisperse aerosols with particle size of about 10^–6 cm cannot yet be produced and because aerosols in general contain particles of different sizes, polydisperse aerosols stored in a large gasometer were used for the investigation. The composition and the average radius of these aerosols heterogeneous in particle size were determined by the Exhaustion Method employing a diffusion battery without end-pieces or connecting tubing.The experimental curve found for the ratio of the uncharged (N ₀) to the charged (N) nuclei versus radius (r) of the particles deviates for all investigated radii between 0.5 and 4.0·10^–6 cm from the theoretical curve of a monodisperse aerosol computed according to the Boltzmann law. For radii smaller than about 1.4·10^–6 cmN ₀/N is smaller than that given by Boltzmann's law, for radii greater than 1.4·10^–6 cm larger, or, in other words, forr<1.4·10^–6 cm the number of charged nuclei found in the aerosols investigated is greater than that predicted byBoltzmann's law, and forr>1.4·10^–6 cm smaller.The deviations from the theoretical curve forr>1.4·10^–6 cm can be fully explained by the polydispersity of the aerosols used; forr<1.4·10^–6 cm the deviations are too big to be attributed to polydispersity. From this it must be concluded thatBoltzmann's distribution law is not valid for the charge distribution of homogenous aerosols containing nuclei with radii smaller than about 1.4·10^–6 cm.The equivalent radius as deduced from a substitute monodisperse aerosol in charge equilibrium for which theBoltzmann law is assumed valid, deviates in the range of 1.0·10^–6<r<3.0·10^–6 cm (or 90%>100N ₀/Z>55%) on the average by up to 35% from the actual mean radius of the investigated polydisperse aerosols computed from the radii of their singly sized components.

---

Zusammenfassung Die Gültigkeit desBoltzmannschen Gesetzes der Energieverteilung für die Ladungsverteilung von monodispersen Aerosolen, das heisst Aerosolen, welche Teilchen von nur einer Grösse enthalten, wurde mit den jetzt zur Verfügung stehenden verbesserten Mitteln studiert.Da monodisperse Aerosole mit Teilchengrössen von ungefähr 10^–6 cm noch nicht erzeugt werden können und Aerosole im allgemeinen Teilchen von verschiedenen Grössen enthalten, wurden für die jetzige Untersuchung polydisperse Aerosole, welche in einem grossen Gasometer gespeichert waren, benützt. Die Zusammensetzung und der mittlere Radius dieser Aerosole mit heterogener Teilchengrösse wurden nach der Exhaustions-Methode unter Benützung einer Diffusionsbatterie ohne Endstücke oder Verbindungsröhren bestimmt.Die experimentell gefundene Kurve, welche das Verhältnis der ungeladenen (N ₀) und geladenen (N) Kerne als Funktion des Radius (r) darstellt, weicht für alle untersuchten Radien zwischen 0.5 und 4.0·10^–6 cm von der theoretischen Kurve eines monodispersen Aerosols, wie sie nachBoltzmann's Gesetz berechnet wird, ab. Für Radien kleiner als ungefähr 1.4·10^–6 cm ist das VerhältnisN ₀/N kleiner als es durchBoltzmann's Gesetz gegeben wird, für Radien grössen als 1.4·10^–6 cm grösser oder, mit anderen Worten, fürr<1.4·10^–6 cm ist die Zahl der geladenen Teilchen, die in den untersuchten Aerosolen gefunden wurde, grösser als die vonBoltzmann's Gesetz vorausgesagte, und fürr>1.4·10^–6 cm kleiner.Die Abweichungen von der theoretischen Kurve fürr>1.4·10^–6cm können vollkommen durch die Polydispersität der benützten Aerosole erklärt werden; fürr<1.4·10^–6 cm sind die Abweichungen zu gross, als dass sie der Polydispersität zugeschrieben werden könnten. Daraus muss geschlossen werden, dassBoltzmann's Verteilungsgesetz für die Ladungsverteilung eines homogenen Aerosols, welches Kerne mit Radien kleiner als ungefähr 1.4·10^–6 cm enthält, nicht gültig ist.Der äquivalente Radius, wie er von einem im Ladungsgleichgewicht befindlichen, monodispersen Ersatz-Aerosol, für welchesBoltzmann's Gesetz als gültig angenommen wird, abgeleitet werden kann, weicht im Bereich von 1.0·10^–6<r<3.0·10^–6 cm (oder 90%>N ₀/Z>55%) durchschnittlich bis zu 35% vom tatsächlichen mittleren Radius des untersuchten polydispersen Aerosols ab.

---

---

The research reported in this article has been supported in part by the Geophysics Research Directorate of the Air Force Cambridge Research Laboratories, through the European Office of the Air Force Research Division, United States Air Force under Contract AF 61(052)-26, by the United States Department of Army, through its European Research Office, Contract DA-91-591-EUC-1282 & 1657 and by the Instrumentation Engineering Physics & Analysis Laboratory of the General Electric Co., Schenectady, New York under Retainer Agreement.     

Infrared transmission by water vapour

Summary Values of infrared transmission by water vapour are required in order to prepare radiation charts, to establish electronic computer programs for flux calculations, to permit deduction of stratospheric vapour concentrations from infrared observations and to facilitate the interpretation of infrared satellite data. In this paper, approaches involving the extensive use of spectroscopic (and theoretically derived) parameters are explored fully and their limitations indicated. The central problem in the use of the random model for the water vapour spectrum is the choice of a suitable unit of spectral interval. This choice involves the testing of line positions for a random distribution, the combination or separation of closely-adjacent lines and the assessment of the effects of a variable band envelope. Techniques suitable for these purposes are developed. In the spectral region between bands, one must consider the background or continuous absorption due to distant but strong lines. Appropriate methods of doing this are presented. In this case, in particular, the calculation of flux transmission for non-homogeneous atmospheric slabs presents special problems, which are considered here.

---

Zusammenfassung Für die Konstruktion von Strahlungsdiagrammen, die Erstellung von Programmen für die Berechnung von Strahlungsstr?men mittels elektronischer Rechenmaschinen, für die Ermittlung von Wasserdampfkonzentrationen in der Stratosph?re durch Infrarotbeobachtungen und für die Auswertung von Strahlungsdaten, die von Satelliten gewonnen werden, sind genaue Angaben über die langwellige Transmission des Wasserdampfes erforderlich. In der vorliegenden Arbeit wird der Versuch unternommen, durch umfassenden Gebrauch von spektroskopischen (und auch theoretischen) Parametern diese Aufgabe zu l?sen, wobei, auch die Grenzen der Methode aufgezeigt werden. Das Kernproblem bei der Verwendung eines Zufallsmodells des Wasserdampfspektrums ist die Wahl einer geeigneten Einheit für die Spektralintervalle. Dies bedeutet eine überprüfung der Lage der Absorptionslinien im Hinblick auf eine Zufallsverteilung, die Vereinigung oder Trennung benachbarter Spektrallinien und die Beurteilung der Frage, inwieweit die Wahl verschiedener Einhüllender der Spektralbanden das Ergebnis beeinflu?t. Es wurden dafür geeignete Methoden entwickelt. In den Spektralbereichen zwischen den Banden mu? auch der Betrag der kontinuierlichen Absorption, hervorgerufen durch die auseinanderliegenden, aber starken Linien in Rechnung gestellt werden. In diesem Fall ergibt sich das besondere Problem, die Strahlungsstr?me für nicht homogene Atmosph?renschichten zu berechnen.

---

Résumé Il est indispensable de posséder des données exactes de la transmission pour les longues ondes dans la vapeur d'eau pour l'étude des domaines suivants: construction de diagrammes du rayonnement, programmation pour le calcul des flux de rayonnements par des calculatrices électroniques, calcul du taux de vapeur d'eau dans la stratosphère par des observations dans l'infra-rouge, dépouillement des données du rayonnement fournies par les satellites artificiels. Le présent travail est un essai de solution de ce problème au moyen de paramètres spectroscopiques et théoriques; on y indique cependant aussi les limites utiles de la méthode. Lors de l'utilisation d'un modèle aléatoire du spectre de la vapeur d'eau, le problème crucial est le choix d'une unité adéquate pour la mesure des intervalles spectraux. Cela implique l'examen de la position des lignes d'absorption en rapport avec la répartition aléatoire, la réunion ou la séparation de lignes spectrales rapprochées et l'appréciation de la mesure dans laquelle le résultat est influencé par le choix des différentes enveloppantes des bandes spectrales. On a développé des méthodes appropriées à ce but. La valeur de l'absorption continue, provoquée par des lignes distinctes, mais fortement marquées doit également être prise en considération dans l'espace compris entre les bandes du spectre. Dans ce cas, il se pose un problème particulier: celui du calcul des flux de rayonnement pour des couches atmosphériques inhomogènes.

---

---

With 4 Figures

---

Published by permission of the Director, Meteorological Branch, Department of Transport, Canada, and dedicated toDr. W. M?rikofer on the occasion of his 70th birthday.     

Measurements of radio noise at 0.700 mc and 2.200 mc from a high-altitude rocket probe

Radio noise observations at frequencies of 0·700 Mc and 2·200 Mc were made at altitudes between 3000 and 11,000 km from a Blue Scout Jr. high-altitude rocket probe on 30 July 1963. A steady background flux of (7·5₋₃⁺⁶) × 10⁻¹⁹ W m⁻²)(c/s)⁻¹ at 0·700 Mc and (1·8^+1.0_−0.5 × 10⁻¹⁹ W m⁻² (c/s)⁻¹ at 2·200 Mc was observed. Assuming a galactic origin of the observed fluxes at both frequencies, the averaged sky brightnesses are b(0·700 Mc) = (6₋₃⁺⁵) × 10⁻²⁰ W m⁻² (c/s)⁻¹ sr⁻¹b(2·200 Mc) = (1.4^+1.0_−0.5 × 10⁻²⁰ W m⁻² (c/s)⁻¹ sr⁻¹ The observed brightness at 2·200 Mc is in reasonable agreement with the results of other observers. The apparent brightness at 0·700 Mc is, however, greater than was expected from previous observations. An alternative source of the 0·700 Mc flux in the terrestrial exosphere, as well as characteristics of several noise bursts observed during the flight, is briefly discussed.     

Acoustic-gravity wave propagation in an atmosphere with two sound channels

Summary In order to interpret the observed features of pressure records produced by waves from large explosions in the earth's atmosphere, the writers have obtained numerical solutions of the homogeneous equations governing acoustic-gravity wave propagation in a stratified compressible fluid. Theoretical dispersion curves and variations of perturbation kinetic energy with altitude are presented for 11 normal modes. It is shown that the step-like character of the phase velocity curves in the velocity-period plane can be interpreted as being the result of interference between two families of normal modes-«quasi-horizontal modes» representing energy propagation in the lower atmosphere (below the ozonosphere) and «quasi-vertical modes» representing energy propagation in the upper atmosphere (above the ozonosphere). The theoretical prediction that several normal modes contribute to the observed barogram traces is verified by Fourier analysis of a number of wave records.Lamont Geological Observatory Contribution No. 611. — This research was supported by National Science Foundation Grant NSF-G-11997, Office of Naval Research Contract Nonr 266 (70), and National Science Foundation Grant NSF-GP-550. — Part of this research was done at the NASA Institute for Space Studies, New York, N. Y.     

Equivalent thickness of the outer ionosphere obtained by evaluation of Faraday records

With an appropriate system of higher order approximations the Faraday-effect is calculated for instantaneous ionospheric models the data of which are derived from the results of vertical soundings. Only one parameter which corresponds to the thickness of the outer ionosphere is left open; it is determined by global comparison with simultaneous Faraday-observations of satellite emissions. The thickness parameter shows various forms of variation with latitude; an increase towards north is the rule for quiet daytime conditions. Comparison with local methods shows considerable differences due to the indetermination of the absolute number of rotations.     

The volcano-magnetic effect

Summary A geometrically simple volcano is considered, havig a spherical magma chamber of 2.5 km radius centred at 10 km depth. The Curie point isotherm is assumed to be a plane at 20 km depth, except for the spherical volume which is also non-magnetic. The stress pattern in the vicinity of the spherical chamber, due to regional stress of sufficient intensity to cause an eruptions, is used to calculate the change in magnetization which results from the piezomagnetic effect through the volume of solid rock. The consequent magnetic field anomaly at the surface is then obtaied by numerical integration of the dipole law of force over the stressed volume. For rocks of the type found on the volcanic island of St. Vincent (West Indies), this model gives a maximum local volcano-magnet c effect of about 7 gammas.     

IDENTIFYING AND ASSESSING PROBLEM AREAS IN SOIL EROSION SURVEYS USING AERIAL PHOTOGRAPHS

Gully erosion has for many years been a problem in Rhodesia1s Tribal Trust Lands. This paper describes how Soil Conservation Service staff, with no previous ground knowledge of these areas, used good quality 1/25,000 scale aerial photographs to measure the extent of the gully erosion and to pinpoint erosion “black spots.” This enabled quick and reliable estimates of the cost of reclamation work to be made without the need for time-consuming field survey. The survey method discussed is capable of wide application wherever gully erosion occurs and needs to be brought under control.     

Climatic satellite monitoring of the external heat balance of the oceans and Black Sea

The long-wave outgoing radiation, effective cloudiness equal to the product of the total cloud amount by their optical density, and the sea-surface temperature determined from the satellites are used to determine the annual course of the components of external heat balance on the sea surface whose climatic anomalies, parallel with the meridional heat and water transfer in the ocean-atmosphere system, specify the intraannual and interannual large-scale variations of weather in different regions of the Earth. The development of these studies is connected with the progress of satellite hydrophysics because the data obtained from the space become sufficiently exact, regular, and global. The increase in the existing data array on the external heat balance of the oceans from ∼15–20 to 100 yr and more would promote the solution of the problem of oscillations of Earth's climate. We present examples of coordinated numerical analysis of the heat balance of the upper (0–100 m ) layer of the Black Sea performed on the basis of the shipborne and satellite data. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 59–75, November–December, 2007.