  We have measured the 1S - 2S transition frequency in atomic hydrogen via two
photon spectroscopy on a 5.8 K atomic beam. We obtain $f_{1S-2S} = 2 466 061
413 187 035 (10)$ Hz for the hyperfine centroid. This is a fractional frequency
uncertainty of $4.2\times 10^{-15}$ improving the previous measure- ment by our
own group [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)] by a factor
of 3.3. The probe laser frequency was phase coherently linked to the mobile
cesium fountain clock FOM via a frequency comb.
