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.

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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.

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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.     

On the frequency equation for love waves due to abrupt thickening of the crustal layer

Summary The effect of thickening of the crustal layer in mountainous region on the dispersion curve of Love waves has been studied. Perturbation method has been applied to obtain the modified frequency equation for Love waves through the surface of separation between a semi-infinite material and a layer the thickness of which abruptly increases throughout a certain length of the path. The effect is to decrease the phase velocity of the waves particularly in the low period range. It has been pointed out that by proper study, the amount of thickening may be obtained.     

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Ohne Zusammenfassung     

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.     

Disturbances in an infinite slab due to torsional forces applied on a cylindrical cavity

Summary The paper deals with the disturbances in an infinite slab of finite thickness, the medium being homogeneous, isotropic and perfectly elastic.     

Correlation of atmospheric occurences over the United States with some physical and chemical parameters. Part III: Frequencies of precipitation

Summary Correlation between some physical and chemical variables, measured at 28 stations of the United States Weather Bureau Network, and seasonal and annual frequencies of precipitation, has been attempted with the aim of gaining insight into the bearing of such variables, on occurrence of precipitation. — Concurrent trends of frequencies with local temperature functions, altitude parameters, precipitable water vapour increments, and some chemical species have been found.Contribution of the «Centro Nucleazione Aerosoli» of the National Research Council of Italy, Via Vettore 4 (Monte Sacro),Roma.