  The charging energy of a quantum dot is measured through the effect of its
potential on the conductance of a second dot. This technique allows a
measurement of the scaling of the dot's charging energy with the conductance of
the tunnel barriers leading to the dot. We find that the charging energy scales
quadratically with the reflection probability of the barriers. In a second
experiment we study the transition from a single to a double-dot which exhibits
a scaling behavior linear in the reflection probability. The observed
power-laws agree with a recent theory.
