  We have measured the stability boundary for steady electrically-driven
convective flow in thin, freely suspended films of Smectic-A liquid crystal.
The thinness and layered structure of the films supress two- and
three-dimensional instabilities of the convection pattern. As the voltage
applied across the film, or the length of the film, is varied, convective
vortices are created or destroyed to keep the wave number of the pattern within
a stable range. The range of stable wave numbers increases linearly with the
dimensionless control parameter $\epsilon$, for small $\epsilon$, and the
vortices always appear and disappear at the ends of the film. These results are
consistent with a mechanism for boundary-induced wavelength selection proposed
by Cross {\it et al.} [Phys. Rev. Lett. {\bf 45}, 898 (1980)].
