La risoluzione dell'equazione di Laplace nel campo esterno a uno sferoide

Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q ₁,Q ₃, ....Q _2s–1 tali che la sommatoria delleQ _2i–1/^2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.

---

Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q ₁,Q ₃ ....Q _2s–1 in such a way as to make the summatory of theQ _2i–1/^2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.

     

Propagation of surface waves on a nonhomogenous spherically aeolotropic shell

Summary This paper studies the propagation of Surface Waves on a spherically aeolotropic shell surrounded by vacuum. The elastic constantsc _ij and density of the material of the shell are assumed to be of the form _ij r ^l and _o r ^m respectively, where _{ij o} are constants andl, m are any integers.     

Reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating

Simple models are discussed to evaluate reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating. By comparing various single well and doublet production schemes, it is shown that reinjection of heat depleted water greatly enhances heat recovery and reservoir lifetime, and can be optimized for maximum heat production. It is concluded that geothermal aquifer production should be unitized, as is already done in oil and gas reservoirs.Nomenclature a distance between doublets in multi-doublet patterns, meters - A area of aquifer at base temperature, m² drainage area of individual doublets in multidoublet patterns, m² - D distance between doublet wells, meters - h aquifer thickness, meters - H water head, meters - Q production rate, m³/sec. - r _e aquifer radius, meters - r _w well radius, meters - R _g heat recovery factor, fraction - S water level drawdown, meters - t producing time, sec. - T aquifer transmissivity, m²/sec. - v stream-channel water velocity, m/sec. - actual temperature change, °C - theoretical temperature change, °C - water temperature, °C - heat conductivity, W/m/°C - _r rock heat conductivity, W/m/°C - _aC_a aquifer heat capacity, J/m³/°C - _aC_r rock heat capacity, J/m³/°C - _WC_W water heat capacity, J/m³/°C - aquifer porosity, fraction     

Physical parameters governing the formation of Pele's hair and tears

The physical parameters that affect the formation of Pele's hair and Pele's tears during lava fountaining are discussed. Experiments on ink jets produced from a nozzle under different Weber number (We) and Reynolds number (Re) show the following results: if (Re) is relatively large compared with (We), an ink droplet is produced. However, if (Re) is relatively small and (We) is large, the spurting ink becomes thread-like. I define the Pele number (Pe) as (We)/(Re), which is expressed as v/₀, where v is the spuring velocity from an erupting vent, and are viscosity and interfacial tension of the erupting magma, and and ₀ are density of air and magma. The experimental results from ink jets suggest that Pele's hair will be produced for larger (Pe), while Pele's tears are very likely produced for relatively small (Pe). I conclude that Pele's hair could be produced when the spurting velocity of erupting magmas is high, and Pele's tears when it is relatively low. As an additional point of interest, the similarity of SEM photographs of the characteristic shape of Pele's hair to those of the failed products of commercial glass fibre are shown.     

Computation of the scattering functions of the haze from skylight measurements,considering the multiple scattering

Summary The primary scattering of atmospheric haze is computed by modification of an approximative method evolved byde Bary, basing on skylight measurements carried out on the Musalla, a mountain of 3000 m height in Bulgaria, at various altitudes of the sun and in different horizontal circles at a wavelength of 450 nm. This measured total radiation is reduced by the radiation induced by the scattering at molecules as well as by secondary or multiple scattering at turbidity aerosol. The single scattering of the atmospheric haze thus computed is discussed for various assumed Linke turbidity factors.The concluding deductions relate to a comparison of haze scattering functions with theoretical scattering functions, the results attained agreeing closely with superimposed logarithmic Gaussian distributions and only partly with the scattering functions computed byBullrich. These deductions prove optically the increase of larger particles (r ₀0.64 m) during forenoon. The analysis of the scattering functions conductes to a shortage of particles withr ₀=0.2 m in agreement with other investigations.

---

Zusammenfassung In Abwandlung einer vonde Bary angegebenen Approximationsmethode wird die Primärstreuung des atmosphärischen Dunstes berechnet. Zugrundegelegt werden Himmelsllichtmessungen, die auf dem etwa 3000 m hohen Mus Alla in Bulgarien bei verschiedenen Sonnenhöhen und in verschiedenen Horizontalkreisen bei einer Wellenlänge von 450 nm durchgeführt wurden. Von dieser gemessenen Gesamtstrahlung werden die Anteile substrahiert, die durch Streuung an Molekülen sowie durch zwei-oder mehrfache Streuung an Trübungsaerosol hervorgerufen werden. Die so berechnete Einfachstreuung des atmosphärischen Dunstes wird für verschiednee angenommene Linke'sche Trübungsfaktoren diskutiert.Abschließend werden die Dunststreufunktionen mit theoretischen Streufunktionen verglichen, wobei eine gute Übereinstimmung mit überlagerten logarithmischen Gauß-Verteilungen und nur teilweise mit vonBullrich berechneten Streufunktionen erzielt wurde. Es kann dabei optisch die Zunahme großer Teilchen (r ₀0,64 m) im Laufe des Vormittags gezeigt werden. Die Analyse der Streufunktionen führt zu einem Fehlen von Teilchen mitr ₀=0,2 m in Übereinstimmung mit anderen Untersuchungen.

     

Humidity effects on gravitational settling and Brownian diffusion of atmospheric aerosol particles

The dependency on relative humidity of the settling velocity of aerosol particles in stagnant air and of the diffusion coefficient due to Brownian motion of aerosol particles was computed for six aerosol types and different particles sizes in dry state. The computations are based (1) on mean bulk densities of dry aerosol particles obtained from measurements or from the knowledge of the chemical composition of the particles, (2) on micro-balance measurements of the water uptake per unit mass of dry aerosol substance versus water activity at thermodynamic equilibrium, and (3) on measurements of the equilibrium water activity of aqueous sea salt solutions. The results show a significant dependence of the settling velocity and Brownian diffusion of aerosol particles on relative humidity and on the particle's chemical composition.Nomenclature A surface parameter of a particle - B surface parameter of a particle - c _L velocity of sound in moist air - C 1+Kn[A+Qexp(–B/Kn]=slip correction - D diffusion coefficient of a particle - D ₁ D(=1)=diffusion coefficient of a spherical particle - f P _w /P _we (T,P)=relative humidity (f=0 dry air,f=1 saturated air) - g acceleration due to gravity - g |g| - k 1.3804×10^–16 erg/°K=Boltzmann constant - Kn _L /r=Knudsen number of a particle - Kn _{0 0L} /r ₀=Knudsen number of a dry particle - m 4r ³/3=mass of a particle - m _L 4r ³ _L /3=mass of the moist air displaced by a particle - M mobility of a particle - M ₀ molar mass of dry air - M _w molar mass of water - Ma |u–u _L |/c _L =Mach number of the particles motion relative to the ambient air - n particle number per unit volume of air - P P ₀+P _w =pressure of the moist air - P ₀ partial pressure of the dry air - P _w partial pressure of the water vapour - P _we P _we (T,P)=equilibrium partial water vapour pressure over a plane surface of water saturated with air - Q surface parameter of a particle - r equivalent radius of a particle (radius of a sphere with the particles volume) - r ₀ equivalent radius of a particle in dry state - R 1+0.13Re ^0.85=inertia correction - R ₀ specific gas constant of dry air - R _w specific gas constant of water - Re 2r _L u–u _L / _L =Reynolds number of the particles motion relative to the ambient air - t time - T absolute temperature - u velocity of a particle - u (amount of the) settling velocity of a particle in stagnant air - u ₁ u(=1)=(amount of the) settling velocity of a spherical particle in stagnant air - u _L velocity of the ambient moist air (far enough from the particle where the flow pattern remains undistorted) - W drag coefficient of a particles equivalent sphere - empirical parameter in equation (3.1) - dynamic viscosity of a particles liquid cover - _L dynamic viscosity of moist air - _0L dynamic viscosity of dry air (at the same pressure and temperature like the moist air) - celsius temperature - dynamic shape factor of a particle (=1 for a sphere) - ₀ dynamic shape factor of a dry particle - _L mean free path of the molecules in moist air - _0L mean free path of the molecules in dry air (at the same pressure and temperature like the moist air) - _Po mean free path of the molecules in dry air at the pressureP ₀ of the dry air and the temperature given - factor of solid to liquid change-over (=1 for a solid particle) - mean bulk density of a particle - _L density of the moist air - _0L density of the dry air at the same pressure and temperature like the moist air - ₀ mean bulk density of a dry particle - ₀ mean diameter of the molecules of dry air - _w diameter of water molecules - relaxation time of a particle - gradient operation - 3.141593     

La funzione dello strato elettricamente conduttivo sottile

Riassunto L'A. esamina l'influenza e.m. della variazione dellospessore di un interstrato conduttivo in un, suolo altamente resistivo, per eccitazione del suolo stesso con c.a. (dipolo orizzontale), a bassa frequenza. Il problema ha la sua particolare importanza pratica nella valutazione del tonnellaggio dei minerali conduttivi, riconosciuti geoelettricamente.I calcoli, laboriosi, per addivenire a soluzioni soddisfacenti, portano a valutazioni analitiche del campo elettrico, tabulabili e diagrammabili. Si deduce, tra l'altro, una nozione di orizzonte elettrico (meno vaga di quella in uso di semplice reperto), quale strato sottile, conduttivo, esteso, di spessore critico, a reazione e.m. massima (nozione implicitamente acquisita, per altra via daH. P. Evans).L'A. dimostra dapprima che l'influenza e.m. dell'interstrato (ovviamente diminuente con la profondità), risente, a seconda la profondità stessa, in modo caratteristico della variazione del suo spessore,diminuendo sostanzialmente con l'aumentare di questo.Mentre per giaciture minerali poco profonde la valutazione del tonnellaggio di minerale si può fare in genere per difetto, per quelle relativamente più profonde tale calcolo riesce in genere più esatto (utilizzando entrambe le componenti del c.e. orizzontale in fase e in quadratura).Dato però che tale influenza e.m. è in funzione più propriamente del fattore di induzione, ci si avvale di questa proprietà per introdurre una nuova prassi (a variazione di frequenza) di rilevamento a pseudorisonanza a massimo effetto geoelettromagnetico.

---

Summary The Author examines the e.m. influence of the thickness change of a conductive interlayer in a soil of high resistivity, for excitation of the soil itself with a.c. (horizontal dipole) of low frequency. The problem has its particular practical importance in the estimation of the conductive minerals tonnage, geoelectrically, acknowledged.The laborious calculations, for obtain satisfactory solutions, lead to analytical estimations of the electric field, that may be expressed in tables and diagrammes. The Author deducts, among other, a notion of electrical horizon as conductive and extensive thin layer of critical thickness (notion already acquired, in other way, byH. P. Evans).First the Author demonstrates that the interlayer e.m. influence (obviously decrising with depth), feels, according to the depth itself, in a caracteristic way of the change of its thickness,decrising substantially with incrising of this. While for little deep mineral layers the estimation of the mineral tonnage can be made generally for defect, for those relatively deeper such a estimate is usually more exact, utilizing both the components of e.c. (horizontal) in phase and in quadrature. Given, therefore, that such e.m. influence is more properly a function of the induction factor, is made use of this property to introduce a new praxis (to frequence variation) of socalled pseudoresonance to maximum geoelectromagnetic effect.

---

Zusammenfassung Der Verf. untersucht den elektromagnetischen Einfluss, den die Aenderung der Mächtigkeit einer in einem Boden von hohem spezifischen Widerstand befindlichen leitenden Zwischenschicht infolge Erregung durch Wechselstrom mit Niederfrequenz (wagerechter Dipol) ausübt. Das Problem ist in parktischer Hinsicht besonders wichtig bei der Schätzung des Tonnengewichtes der leitenden geoelektrisch festgestellten Mineralien.Die für eine zufriedenstellende Lösung mühevollen Berechnungen führen zu analytischen Schätzungen des elektrischen Feldes, die in Form von Tabellen und Diagrammen zusammengestellt werden können. Es lässt sich daraus u.a. die Kenntnis eines elektrischen Horizontes ableiten (die klarer ist als die übliche einer einfachen Feststellung) in Form einer leitenden, ausgedehnten dünnen Schicht von kritischer Mächtigkeit und von höchster elektromagnetischen Wirkung (diese Kenntnis wurde auf anderem Wege vonH. P. Evans indirekt abgeleitet).Zuerst ergibt der Verf. den Nachweis, dass der elektromagnetische Einfluss der Zwischenschicht (der selbstverständlich mit der Tiefe abnimmt), je nach der Tiefe selbst, in kennzeichnender Weise von der Aenderung ihrer Mächtigkeit abhängt und zwar, dass er wesentlich mit ihrer Zunahmeabnimmt. — Während man für die wenig tiefen Minerallagerungen das Tonnengewicht meist ungefähr abschätzen kann, erhält man für verhältnismässig tiefere Lagerungen gewöhnlich eine genauere Berechnung; indem beide, sowohl gleichphasigen als auch um 90 Grad verstellten Komponenten des elektrischen (wagerechten) Feldes berücksichtigt werden. Da aber dieser elektromagnetische Einfluss eigentlich eine Funktion des Induktionsfaktors ist, benutzt man diese Eigenschaft zur Einführung einer neuen Vermessungsweise (mit Frequenzänderung), die sogenannte Pseudoresonanz mit höchster geoelektromagnetischer Wirkung.

---

---

I principali risultati del presente studio vennero comunicati alla Terza Assemblea Generale della Società Italiana di Geofisica e Meteorologia (Genova: 15–17 Aprile 1955).     

Formation of cracks due to moving source over a thick crust

Summary In this paper the problem of a point source of stress moving over the surface of a thick aelotropic plate resting of a rigid foundation has been considered. Following the method ofAleksandrov & Vorovich (1960) the stress componentsZ _x andZ _z have been expanded in series of ascending powers of 1/h when the source velocity is less than (c ₄₄/)^1/2. When the velocity exceeds (c ₄₄/)^1/2 it has been shown that two cracks are produced in different directions and their successive reflections at the upper and lower surface are also obtained.     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

---

¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Gravity topographic corrections computed from a square grid of height points

Summary Computation of terrain corrections from a map with a square grid of mean height points

---

uu mnauu nna n am ¶rt;u m u¶rt; a¶rt;am mu m nm.

     

Propagation of surface waves on the surface of a non-homogeneous aeolotropic cylindrical shell

Summary The object of the present paper is to investigate the propagation of surface waves on a non-homogeneous aeolotropic cylindrical shell surrounded by vacuum. The elastic constantsc _ij (i, j=1,2...) and density of the material of the shell are assumed to be of the form and respectively, where _ij, ₀ are constants andk ₁,k ₂ are any integers.     

Meridional Turner angles and density compensation in the upper ocean

The World Ocean Atlas 1998 is used to determine the global field of the meridional density ratio R ^hy =T/S, where temperature and salinity changes T and S are evaluated along meridians, in and below the mixed layer. The focus of the analysis is the identification of regions where the R ^hy field matches the values R =2 sometimes suggested as the commonly perceived state of the ocean and R =1, the condition of density compensation. Results are presented through fields of the meridional Turner angle Tu ^hy =arctan(R ^hy ) and through histograms of Tu ^hy for the Pacific, Atlantic and Indian Oceans at the ocean surface and at 300 m depth. At the 300-m depth level, which in the subtropics is representative of conditions in the permanent thermocline, the most frequently encountered values of the meridional density ratio are R ^hy =3.2 in the North and South Pacific, R ^hy =2.0 in the South Atlantic and Indian and R ^hy =1.6 in the North Atlantic Ocean. Conditions in the mixed layer are more variable and show seasonal differences, but R ^hy =2.0 occurs prominently in all ocean regions during winter and in all regions but the Atlantic during summer. Summer values for the Atlantic Ocean are R ^hy =3.2 in the Northern Hemisphere and R ^hy =2.4 in the Southern Hemisphere. Detailed analysis of R ^hy across the Subtropical Front (STF) confirms the most frequently observed values but shows zonal variation along the front in some oceans. Nearly complete density compensation (R ^hy =1) in the mixed layer is encountered in the STF of the eastern North Pacific, the eastern South Pacific and the eastern Indian Ocean. The eastern Indian Ocean south of Australia is also the only region where complete density compensation in the STF occurs below the mixed layer.Responsible Editor: Neville Smith AcknowledgementWe thank Dan Rudnick for helpful comments and discussion during the preparation of this paper.     

Accuracy of integral migration transformation in dependence on space-time sampling

Summary The accuracy of wave field extrapolation is studied with respect to the discretization of field data and integral extrapolator. Assuming a far-field approximation of the Rayleigh-Sommerfeld solution for a two-dimensional scalar wave equation, the minimum and the maximum transmitted frequency are expressed as functions of the sampling intervals t, x, and the half-width x₀ and angle _a of the migration aperture. The theoretical limitation of the transmitted frequency band is tested on numerical examples.

---

aamuam mm manuu auumu m ¶rt;umuauu n u uma manu nama. ¶rt; u uma u -¶rt;a ¶rt; ¶rt; a au, ¶rt; nuuuu ¶rt;a n mu ¶rt; uua u aua n¶rt;aa amm a uu m a -nmam ¶rt;umuauu t u , nuu ₀ u a _a uau anm. mu n¶rt;u amm ¶rt;uanaa mmua a u nua.

     

The secular variation of the geomagnetic field in Egypt in the last 5000 years

The palaeo-intensities (F _a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F _a=36.2 T at 3100 B.C., F_a=46.8 T at 3000 B.C.,F _a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I _a) at some ages are found to be:I _a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF _a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF _a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.     

A relationship between phonon conductivity and seismic parameter Φ for silicate minerals

Summary The relationship between the phonon conductivity at room temperature (K _N ) and the seismic parameter () for silicate minerals is suggested. The considerations are based on the Debye model of thermal energy transport phenomena in solids and on the seismic equation of state for silicates and oxides given byAnderson (1967). The semiempirical relationship is the formK _N = 0.43^0.82 where is in km²/s² andK _N in mcal/cm s K, and the empirical relationship isK _N =(0.528±0.006) –(8.18±2.11). The laboratory data on thermal and elastic properties for several silicates were taken fromHorai andSimmons (1970).     

Physical properties of the Earth's core

Calculations of the compression and temperature gradient of the core are facilitated by the use of the thermodynamic Grüneisen ratio, =3Ks/C _P . A pressure-dependent factor in is found to have the same numerical value for the core as for laboratory iron, justifying the use of a constant value for (1.6) in core calculations. The density of the outer core is satisfied by the assumption that it contains about 15% of light elements, particularly sulphur, whereas the inner core is probably ironnickel with very little lighter component. The presence of sulphur in the outer core reduces its liquidus at least 600° below pure iron, so that the adiabatic gradient does not intersect the liquidus, as Higgins and Kennedy have shown would occur in a pure iron core. The inner core is probably close to its melting point, 4700 K, and the adiabatic temperature gradient of the outer is calculated with this as a fixed point, giving 3380 K at the core-mantle boundary. The estimated electrical resistivity of the outer core, 3×10^–6 m, corresponds to a thermal conductivity of 28 W·m^–1·deg^–1, which, with the adiabatic core gradient gives a minimum of 3.9×10¹² W of heat conduction to the mantle. The only plausible source of this much heat is the radioactive decay of potassium in the core. As pointed out by Goles, Lewis, and Hall and Murthy, the presence of potassium becomes geochemically probable once sulphur is admitted as a core constituent. Thus it appears that the recognition of sulphur in the core resolves the two major difficulties which we have faced in attempting to understand the core.List of Symbols a equilibrium atomic spacing at zero pressure, also a constant - A surface area of core - b a constant - c a constant - C _V ,C _P specific heat at constant volume, constant pressure - D dimension of core (or core eddy) - E(r) atomic interaction energy - E energy due to atomic displacement from equilibrium - lattice energy of material - f ₁,f ₂ structure-dependent constants - F(P) pressure dependent factor in Grüneisen's ratio - g gravitational acceleration; also a constant (Equation (13)) - H latent heat of solidification - I integral (Equation (23)) - k Boltzmann's constant - K incompressibility (bulk modulus) - K _T ,K _S isothermal, adiabatic incompressibilities - N number of atoms in a volume of material - P pressure - dQ/dt core to mantle heat flux - r atomic spacing - r _e equilibrium value ofr under pressure - R _m magnetic Reynolds number - T temperature - T _c critical temperature - T _R reduced temperature (Equation (39)) - U specific internal energy of a material - v velocity of internal core motion - V volume - 3 volume expansion coefficient - compressibility - thermodynamic Grüneisen ratio (Equation(2)) - magnetic diffusivity - thermal conductivity - _e electronic contribution to - ₀ permeability of free space - density - _e electrical resistivity - R reduced conductivity,eM/e     

Vertical motion and diabatic heating over the Indian monsoon region during the Bay of Bengal depression of 5–8 July, 1979

The vertical velocity, , and the diabatic heating were computed at 800, 600, 400 and 200 mb surfaces using the Omega equation. The highest contribution to is from the diabatic heating produced by condensation associated with the precipitations appearing to be the main source of diabatic heating. The net radiative cooling and the thermal advection in the upper troposphere over the warm anticyclone result in diabatic cooling over the eastern part of the Bay of Bengal and adjoining northern and eastern regions.List of Symbols Used C _p Heat capacity at constant pressure - f Coriolis parameter - g Acceleration due to gravity - P Atmospheric pressure - Q Diabatic heating rate per unit mass - R Gas constant of air - S Static stability parameter - t Time - U, V Zonal and meridional wind components - Specific volume - Relative vorticity - Absolute vorticity - Potential temperature - Geopotential - Vertical velocity (dP/dt) - ₁ Adiabatic vertical velocity - ₂ Vertical velocity due to certain forcing - ₃ Diabatic vertical velocity - Isobaric gradient operator - ² Laplacian operator - J(A, B) Jacobian operator     

Sulla variazione della densità nell'interno della terra

Riassunto L'Autore considera dapprima un geoide di rotazione di cui esprime la densità mediante sviluppo in serie di potenze del raggio vettore con i coefficienti dipendenti dalla latitudine . Risolve l'equazione di Poisson relativa al geoide, dimostra che la funzione potenziale si sviluppa in serie di potenze pari di e mette in evidenza la influenza dei termini dipendenti dalla latitudine nel rapporto fra i momenti di inerzia e nella variazione della gravità in superficie. Considera poi il geoide sferico e determina, in due esempi, l'andamento della densità, basandosi nel presupposto che l'energia del campo di gravità sia la più alta possibile compatibilmente allo stato attuale della Terra; ne risulta una densità centrale compresa fra 15 e 19.

---

Summary The Author first considers a rotational geoid the density of which he introduces through potential series development of radius vector with coefficients as functions of latitude . He solves Poisson equation of the geoid, demonstrates that its potential function develops through potential series even of , points out the influence of the terms deriving from the latitude in the ratio from the inertia moments and the variation in surface gravity. Then he considers a spheric geoid and, by two demonstrations, he establishes the density, basing his theory on the assumption that gravity field energy is the highest one can trace in the present condition of the Earth; the result give a central density ranging from 15 to 19.

     

Influence of the IMF sector boundaries on cosmic rays and tropospheric vorticity

Summary The effect of the IMF sector boundary crossing (IMF SBC) in the vorticity area index (VAI) — the well-known dip in the VAI after IMF SBC — is found to be independent of the IMF SBC effect in the cosmic ray flux. This finding refutes a recent suggestion by Lundstedt [1] that the IMF SBC effect in VAI is caused by a decrease in cosmic ray flux, but supports the concept of the IMF SBC effects in the ionosphere and atmosphere developed by Latovika [2–4]. Cosmic rays seem to affect the troposphere in another way.

---

¶rt;mu nu mau nam aum n ( ) a u¶rt; na¶rt;u aumu () — um uu n — a¶rt; auu m ma nm uu . mm mam nam ¶rt;a n¶rt;u ¶rt;m¶rt;a [1], m m a nuu nma uu , n¶rt;¶rt;uam nu m u u am, aum amu [2–4]. am m uu u m um a mn ¶rt;u a.

     

Les formes différentielles extérieures dans la géodésie I: Courbure de Gauss

1) , 2) 3) .