  We report new bounds on Local Lorentz Invariance (LLI) violation in Cs and
Hg. The limits are obtained through the observation of the the spin- precession
frequencies of 199Hg and 133Cs atoms in their ground states as a function of
the orientation of an applied magnetic field with respect to the fixed stars.
We measure the amplitudes of the dipole couplings to a preferred direction in
the equatorial plane to be 19(11) nHz for Hg and 9(5) microHz for Cs. The upper
bounds established here improve upon previous bounds by about a factor of four.
The improvement is primarily due to mounting the apparatus on a rotating table.
New bounds are established on several terms in the standard model extension
including the first bounds on the spin-couplings of the neutron and proton to
the z direction, <7e-30 GeV and <7e-29 GeV, respectively.
