  We consider the interaction between two rods embedded in a fluctuating
surface. The modification of fluctuations by the rods leads to an attractive
long-range interaction between them. We consider fluctuations governed by
either surface tension (films) or bending rigidity (membranes). In both cases
the interaction falls off with the separation of the rods as $1/R^4$. The
orientational part of the interaction is proportional to $\cos^2\left[
\theta_1+\theta_2 \right]$ in the former case, and to $\cos^2\left[
2\left(\theta_1+\theta_2\right) \right]$ in the latter, where $\theta_1$ and
$\theta_2$ are angles between the rods and the line joining them. These
interactions are somewhat reminiscent of dipolar forces and will tend to align
collections of such rods into chains.
