  The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are
compared to set new constraints on a possible violation of Lorentz invariance.
We determine the variation of the oscillator frequency as a function of its
orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike
test) with respect to a preferred frame candidate. We constrain the
corresponding parameters of the Mansouri and Sexl test theory to $\delta -
\beta + 1/2 = (1.5\pm 4.2) \times 10^{-9}$ and $\beta - \alpha - 1 = (-3.1\pm
6.9) \times 10^{-7}$ which is equivalent to the best previous result for the
former and represents a 30 fold improvement for the latter.
