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I. A perturbation theory of the approach toward sedimentation equilibrium in the ultracentrifuge and an analysis of a proposed fast method for reaching equilibrium. II. The detailed interpretation of the anomalous electron diffraction photographs of some symmetrical gas molecules with the aid of complex scattering amplitudes

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  • Mathematics


I. The transient concentration distribution in the ultracentrifuge is obtained in the form of a power series expansion in a small parameter by a perturbation treatment of the appropriate differential equation. The problem reduces in zero order to that of sedimentation in a constant gravitational field. The theory is used for determining which initial step distributions lead to the fastest approach to equilibrium. The saving in time as compared to the conventional uniform initial distribution is also calculated. II. The neglect of a phase shift in the theory of scattering has been shown by Schomaker and Glauber to be the reason why electron diffraction investigations in the past led to distorted structures for certain molecules otherwise expected to be symmetrical. Complex scattering amplitudes for use in calculating theoretical intensity patterns are now available as a result of the work of Hoerni and Ibers. In the present investigation we reinterpret the diffraction photographs of a number of these molecules in terms of symmetrical structures. The bond lengths in these molecules are thus determined accurately. In addition, further confirmation is provided for the theory.

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