We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm 199Hg+ optical clock transition to the ground state hyperfine splitting in 133Cs. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of <5.8x10(-6) per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of |alpha/alpha|<1.3x10(-16) yr-1, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and 171Yb+ vs other 133Cs standards yield a coupled constraint of -1.5x10(-15)
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