We study mesoscopic fluctuations of the differential capacitance of a
dot connected to a lead by a single-mode quantum channel with adjustab
le conductance G. We show that the amplitude of the fluctuations reach
es its maximum at a partially opened channel G less than or equal to e
(2)/pi h. Parametric correlations of fluctuations at different values
of the applied voltage and magnetic field can be studied experimentall
y, and we find the corresponding correlation functions for the differe
ntial capacitance.