The frequencies of Cs and Rb fountain clocks have been compared to various H-masers to search for periodic changes correlated with the gravitational potential and boost with respect to the cosmic microwave background. The data span about eight years and the main sources of long-term noise are the offsets and linear drifts associated with the H-masers. To circumvent these effects we apply a numerical derivative to the data, which significantly reduces the standard error. We determine a limit for the Local Position Invariance (LPI) coefficient with respect to gravity to be 4.8×10−6 and 10−5 for a Cs-H and Rb- H comparison, respectively. From the same data the boost LPI coefficients were measured to parts in 1011. From these results and others, independent limits on all coefficients of the boost violation vector with respect to fundamental constant invariance were determined to parts in 1010.