  It has been proposed that the radio-frequency electric-dipole (E1) transition
between two nearly degenerate opposite-parity states in atomic dysprosium
should be highly sensitive to possible temporal variation of the fine structure
constant ($\alpha$) [V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. A
{\bf 59}, 230 (1999)]. We analyze here an experimental realization of the
proposed search in progress in our laboratory, which involves monitoring the E1
transition frequency over a period of time using direct frequency counting
techniques. We estimate that a statistical sensitivity of $|\adota| \sim
10^{-18}$/yr may be achieved and discuss possible systematic effects that may
limit such a measurement.
