  I have measured the early stages of the growth of branched metal aggregates
formed by electrochemical deposition in very thin layers. The growth rate of
spatial Fourier modes is described qualitatively by the results of a linear
stability analysis [D.P. Barkey, R.H. Muller, and C.W. Tobias, J. Electrochem.
Soc. {\bf 136}, 2207 (1989)]. The maximum growth rate is proportional to
$(I/c)^\delta$ where $I$ is the current through the electrochemical cell, $c$
the electrolyte concentration, and $\delta = 1.37 \pm 0.08$. Differences
between my results and the theoretical predictions suggest that
electroconvection in the electrolyte has a large influence on the instability
leading to ramified growth.
