Radio-frequency electric-dipole transitions between nearly degenerate, opposite parity levels of atomic dysprosium (Dy) were monitored over an eight-month period to search for a variation in the fine-structure constant, $alpha$. The data provide a ra
te of fractional temporal variation of $alpha$ of $(-2.4pm2.3)times10^{-15}$ yr$^{-1}$ or a value of $(-7.8 pm 5.9) times 10^{-6}$ for $k_alpha$, the variation coefficient for $alpha$ in a changing gravitational potential. All results indicate the absence of significant variation at the present level of sensitivity. We also present initial results on laser cooling of an atomic beam of dysprosium.
