Гидродинамика

ЬиММАРчУ 185 method is applied in the investigation of a conical cavity (§ 22, Figs 10 and 11), of a cavity formed by rotation of mutually intersecting hyperboles and of a ring-shaped cavity bounded by hyperbololds (§ 23, Fig. 12). As an example of direct solution is given the case of a cavity In the shape of a hemisphere (§ 24, Fig. 13). Turning to the discussion of multiply-connected cavities Prof. Joukowsky first extends the interpretation of the motion of a rigid body about a fixed point, by means of the cone of the principal moments of momenta and of the invariable plane, to the case when the body has a gyroscope attached to it (§ 25, 26 and Fig. 14). At the end of the second chapter is considered a doubly-connected cavity in the shape of an infi ­ nitely thin closed tube of arbitrary shape ( § 27, Fig. 151; it Is shown (§ 28) that for all thoroldal cavities the principal mo ­ ment of the initial momentum is equal to the product of the mass of the liquid by the velocity clruclation divided by 2~. In Chapter 11 Prof. Joukowsky first considers the case of a vortical motion of the liquid in the cavities of a moving body and forms equations which must be satisfied by the components of the angular velocity of the body ( § 30, formula 4) and by the components of the vortex (§ 30, formula 5); to these lie annexes the formula for the pressure of the liquid (§ 31, for ­ mula 6). The general theory is illustrated by the examples of a cylindrical cavity ( § 32) and of an elliptical cavity (§ 33); there are also described tests for an experimental verification of theo ­ retical trajectories of particles ( § 32). The author next proceeds to a consideration ot the motion of a liquid when friction is taken into account. After deducing the corresponding equations of motion of the body (§ 30, for ­ mula 5) and of the liquid ( § 34, formula 35) and formula fur the pressure (§ 34, formula 36) the author states Helmholtz's problem of oscillations about a fixed axis, of a body containing viscous fluid within a spherical cavity and subjected to the action of a couple proportional to the angle of rotation of the boay (§ 35 and § 36). In addition, the author solves (§ 37) a new problem, that of the motion of a closed tube filled with a hquia. This pioblem