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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. 810^-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 | { }|<1. 310^-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. 510^-15< /<0. 410^-15 yr^-1 and -2. 710^-15<ddtln{₂ₒ}{₁}<8. 610^-15 yr^-1.
Fortier et al. (Fri,) studied this question.