  We observe a thermo-mechanical effect when a chemical potential difference is
created by a temperature difference imposed between two liquid reservoirs
connected to each other through Vycor rods in series with solid hcp 4He. By
creating a temperature difference, $\Delta T$, between the two reservoirs, we
induce a rate-limited growth of a pressure difference between the two
reservoirs, $\Delta P$. In equilibrium $\Delta P {\it vs.} \Delta T$ is in
quantitative agreement with the thermo-mechanical effect in superfluid helium.
These observations confirm that below $\sim$ 600 mK a flux-limited flow exists
through the solid helium.
