A note on the application of the von Zeipel method to degenerate Hamiltonians

Through the introduction of a term at each order of the generating function dependent only on the long-period variables, a technique is shown whereby both short- and long-period variables in a degenerate Hamiltonian can be eliminated simultaneously in one transformation with the von Zeipel method, rather than the traditionally separate transformations. The technique is applied to the lunar theory as an example.     

Observed heights of EUV lines formed in the transition zone and corona

The heights of formation of a number of extreme ultraviolet lines in active regions have been measured from OSO-IV spectroheliograms. Using the Lyman continuum at 2000 km above the white light limb as a reference, we find heights for Hei, Heii, Ciii, Niii, Oiv, Ovi, Neviii, Mgx, Sixii, Fexv and Fexvi that are in approximate agreement with models based on analysis of EUV emission intensities. The height of Cii is anomalously high. The accuracy of measurement is typically about 2000 km. The data suggest that the transition zone is less steep than calculated from EUV emission intensities; however, higher resolution observations are necessary to resolve the discrepancy.     

Comparaison de catalogues de crateres lunaires

Résumé La partie systématique des différences entre les positions des cratères de plusieurs catalogues est développée en harmoniques sphériques. L'application du test en ² détermine l'ordre du développement. La méthode a été appliquée pour comparer le système de référence de Arthur avec les catalogues de Schrutka-Rechtenstamm et Gavrilov. On obtient les surfacesf (l, b) des différences systématiques de ces catalogues. La zone centrale de la face visible de la lune (± 40° en latitude et longitude) est bien déterminée, mais la zone marginale présente des différences systématiques qui peuvent atteindre le kilomètre.

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The systematic part of the differences between positions in crater catalogues is expanded into spherical harmonics. The application of the ² test determines the highest order of the expansion. The method was applied to compare the Arthur System with the Schrutka-Rechtenstamm and Gavrilov catalogues. The surfacesf (l, b) of systematic differences from these catalogues were obtained. The central zone of the near side of the Moon (± 40° in latitude and longitude) is well determined but the marginal zone presents systematic differences that can be as large as one kilometer.