ON CERTAIN CONSERVATION PROPERTIES IN GAS DYNAMICS.

A previously unknown invariant of the vertex lines of a stationary barotropic, ideal gas flow is discovered. An analogue of this invariant and of other invariants of the stream and vortex lines is obtained for the more general case of non-barotropic flow. An equation is obtained describing the variation in the projection of the vorticity on the direction of the velocity in three-dimensional ideal gas flow. Examples are shown where the projection does not vary along the stream lines, and this yields an additional integral of the gas-dynamic equations.