sions of Part A with considerable mathematical care.
The last two articles by V. V. Rumyantsev and N. N. Moiseev, deal with two different approaches to the same main problem: the dynamics of bodies containing liquid-filled cavities. The former treats the full non-linear perturbation equations according to Lyapunov's methods, while the latter treats linearized small oscillations. Lyapunov's method consists of finding the Lyapunov functions, which are expressed in terms of the first integrals of motion, and the stability criterion is the positive definiteness of these Lyapunov functions. The problem is completely solved for a solid body with a cavity totally filled by a liquid; but for part~ally-filled cavities, only stability "with respect to part of the variables" can be obtained by this method. In the latter paper, the procedure consists of linearizing the equations of motion, and determining the frequency of natural oscillations (the eigenvalues) by, say, the Ritz method. Stability is characterized by the eigenvalues. Both of these papers contain theorems which permit the reduction of problems involving liquid-filled cavities to equivalent solid bodies, and both papers contain large numbers of concrete problems.