Pressure of thermal excitations in superfluid helium

We find the pressure, due to the thermal excitations of superfluid helium, at the interface with a solid. The separate contributions of phonons, $R^{-}$ rotons and $R^{+}$ rotons are derived. The pressure due to $R^{-}$ rotons is shown to be negative and partially compensates the positive contribution of $R^{+}$ rotons, so the total roton pressure is positive but several times less than the separate $R^{-}$ and $R^{+}$ roton contributions. The pressure of the quasiparticle gas is shown to account for the fountain effect in $HeII$. An experiment is proposed to observe the negative pressure due to $R^{-}$ rotons.