A quasi-thermodynamic theory of liquid helium is developed based on very general assumptions regarding the energy spectrum of the liquid. Below the $\lambda$-point helium can be considered as a mixture of two fluids capable of two velocity fields. The macroscopic hydrodynamic equations of this system are derived. These are in the same relation to ordinary hydrodynamics as a two-body is to a one-body problem in point mechanics. The flow connected with the center of mass coordinate is associated with the transport of mass at constant entropy, the one connected with the relative coordinate (internal convection) is associated with an entropy transport at constant density. The results are in excellent agreement with experiment, in particular with the measurements of the temperature waves (second sound), the existence of which was predicted by the theory. The Bose-Einstein liquid introduced earlier is a possible molecular model consistent with the macroscopic results. Landau's theory is discussed.

• Received 17 May 1947

DOI:https://doi.org/10.1103/PhysRev.72.838