The variational equation of the three-body problem

Letx ₀ (t),x ₀ ⁴ be a homothetic solution of the planar three-body problem with total energyh, described in relative coordinates with respect to one body. It is shown that the variational equation of the problem atx ₀ (t) can be solved explicitly in terms of hypergeometric functions. This is done by using the scaled true anomaly of the one-dimensional Kepler motion as the independent variable.The classical theorems about hypergeometric functions allow a simple calculation of all the values needed in applications. By means of this theory the past of a homothetic triple close encounter may be described in a linearized approximation.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

The spectrum of the Cr star epsilon ursae majoris

Fourteen coudé spectrograms (eight with dispersion 12.4 Å mm^–1 and six 7 Å mm^–1) of the Cr star UMa (Ap) have been studied. The observations were made at the Haute Provence Observatory. The radial velocities of the various ions have been measured. The existence of Balmer progression in radial velocity is doubtful. The variability of some lines is in the opposite sense of K of Caii. Both a rough and a fine analysis have been made. The results of these analyses are compared and found to be in good agreement. The results of the fine analysis indicate a defect of Al, Si and Ca; Sc, Ti, Fe and Sr are normal, Mg and Ni are in slight excess. V, Cr and Mn are in excess by factors of 3, 12, 19; Y, Zr and Ba are in excess by factors of 9, 15, 30. Rare earths are in excess by factors ranging between 100–1000. These results are compared with the majority of the Cr–Eu–Sr stars.The observations have been made at the 152 cm coudé telescope of the Haute Provence Observatory.     

The nature of chemical bond of magnetite and consequences

Summary Types of chemical bonding in magnetite are discussed. Magnetite spinel lattice is characterized by tetrahedral covalent bonds and octahedral electrovalent bonds. The consequences for oxidation processes are studied in connection with hitherto existing experimental and theoretical results.

---

Zusammenfassung Der Charakter der chemischen Bindung im Magnetit wird diskutiert. Für das Spinellgitter des Magnetits sind tetraedrische kovalente und oktaedrische elektrovalente Bindungen typisch. Die Auswirkungen dieses Bindungszustandes auf den Ablauf der Oxydationsvorgänge wird überprüft an Hand der bisher vorliegenden experimentellen und theoretischen Teilergebnisse.

---

---

Dr. Dr. habil.F. Frölich, Dr.H. Stiller, Geomagnetic InstituteFotsdam, German Academy of Science at Berlin, Mitteilung Nr. 133.     

Buchbesprechungen

Ohne Zusammenfassung     

Neue Ungarische geoelektrische Instrumente

Zusammenfassung Die Einleitung gibt einige Gesichtspunkte der heutigen geoelektrischen Instrumentenentwicklung in Ungarn. Dann werden zwei neue ungarische geoelektrische Instrumente u.z.w.: 1) ein den spezifischen Widerstand unmittelbar lieferndes Instrument und 2) ein isolationsfehlerloses geophysikalisches Fotoregistrier-instrument mit ihren theoretischen Grundlagen behandelt. Am Ende des Artikels werden einige technische Daten der Instrumenten mitgeteilt.

---

Summary The introduction deals with the general aspects of the development of modern geoelectrical instruments in Hungary. Then two hungarian geoelectrical instruments: 1) an instrument giving directly the value of the resistivity and 2) a geophysical recording instrument free from isolation errors are discussed from the point of view of the theoretical problems of the instrument-constructions. Finally some technical data of the instruments are presented.

     

Vergleich einiger Methoden zur Untersuchung von geochemischen Vorgängen bei der Verwitterung

Summary Chemical analyses are used by many authors to describe processes of soil development or laterite formation. In this paper some methods of balance calculations are compared by using samples of a laterite profile on granite from India as testing material. It should be proved which of these calculations of transported matter between the different layers are fitting to the mineral analyses of the laterite profile.Only the results of the method proposed byMashall by using an index-mineral as a base for comparison is confirmed by the mineral analyses.The method ofStreng differs from the above described calculation by using a chemical element as an index. FollowingStreng it is supposed that this element remains unchanged during the weathering processes. But certain chemical elements can be constituents of several minerals of a parent rock. During laterite formation all or almost all minerals of the original rock will be altered and the elements will be transported by weathering solutions. Therefore chemical elements do not serve as an index for balance calculations within a laterite complex.UsingGrossers method one cannot decide wether the abundance of a certain element is caused by accumulation of this element or by lost of other constituents and vice-versa.The use of the method developed byMillot u.Bonifas is not advisable except the structure of the original rock is preserved unaltered during laterite formation. This is not indicated in our case.     

Initialer Magmatismus und Tektonik in Ostthüringen

Ohne Zusammenfassung     

Die geophysikalischen Grundlagen der Kontraktionshypothese

Ohne Zusammenfassung