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Abstract

THIS book may be regarded as a pendant to the author's “Foundations of Hydromechanics” and extends the same rigorous methods to the treatment of the problem of the equilibrium of rotating masses of liquid under their own gravitational attractions. It summarises researches carried out by the author and his pupils during the past six years, mainly on existence problems of figures of equilibrium, of rotating masses of liquid in the neighbourhood of known figures of equilibrium, of homogeneous and also of heterogeneous masses of such liquid. An integro-differential equation is constructed in each case and solutions are sought by the method of successive approximations, both for classical problems, such as those of Laplace and Liapounoff, and for new ones concerning one or more coaxial rings, Roche's satellites, liquid double stars with and without solid centres.

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Von Prof. Leon Lichtenstein. Pp. viii + 175. (Berlin: Julius Springer, 1933.) 15.60 gold marks.