  Motivated by a recent experiment by Yacoby et al.\ [preprint, 1994], we
calculate magnitude and phase $\alpha$ of the transmission amplitude through a
quantum dot. We work in the Coulomb blockade regime, assume the electrons not
to interact, and consider tunneling through isolated resonances. Assuming a
non--resonant background, we find that $\alpha$ increases by $2 \pi$ over each
resonance, with a sharp rise by $\pi$ over an energy interval much smaller than
the thermal width. This is consistent with the experimental data. Our
assumptions can be tested by further experiments.
