  We investigate the feasibility of the method for reconstructing the equation
of state and the effective potential of the quintessence field from SNIa data.
We introduce a useful functional form to fit the luminosity distance with good
accuracy (the relative error is less than 0.1%). We assess the ambiguity in
reconstructing the equation of state and the effective potential which
originates from the uncertainty in $\Omega_M$. We find that the equation of
state is sensitive to the assumed $\Omega_M$, while the shape of the effective
potential is not. We also demonstrate the actual reconstruction procedure using
the data created by Monte-Carlo simulation. Future high precision measurements
of distances to thousands of SNIa could reveal the shape of the quintessential
potential.
