## Abstract

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0$\cdot $05 to 1$\cdot $0 cm at temperatures between 0$\cdot $25 and 0$\cdot $7 degrees K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path $\lambda $ varies with temperature, and may be either greater or less than the diameter of the tube d. When $\lambda \gg $ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when $\lambda \ll $ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation $\lambda $ = 3$\cdot $8 $\times $ 10$^{-3}$ T$^{-4\cdot 3}$ cm. This result is inconsistent with the temperature dependence of $\lambda $ as T$^{-9}$ predicted theoretically by Landau & Khalatnikov (1949).