  We demonstrate a reliable continuous-wave (cw) laser source at the
1\,$S$--2\,$P$ transition in (anti)hydrogen at 121.56\,nm (Lyman-$\alpha$)
based on four-wave sum-frequency mixing in mercury. A two-photon resonance in
the four-wave mixing scheme is essential for a powerful cw Lyman-$\alpha$
source and is well investigated.
