Radio-frequency E1 transitions between nearly degenerate, opposite parity levels of atomic dysprosium were monitored over an eight month period to search for a variation in the fine-structure constant. During this time period, data were taken at different points in the gravitational potential of the Sun. The data are fitted to the variation in the gravitational potential yielding a value of $(-8.7 pm 6.6) times 10^{-6}$ for the fit parameter $k_alpha$. This value gives the current best laboratory limit. In addition, our value of $k_{alpha}$ combined with other experimental constraints is used to extract the first limits on k_e and k_q. These coefficients characterize the variation of m_e/m_p and m_q/m_p in a changing gravitational potential, where m_e, m_p, and m_q are electron, proton, and quark masses. The results are $k_e = (4.9 pm 3.9) times 10^{-5}$ and $k_q = (6.6 pm 5.2) times 10^{-5}$.
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