  The main object of this note is to study the conormal module $M$ and the
computation of the second symbolic power $\bar I^{(2)}$ of an ideal $\bar I$ in
the residue ring $R/H$ of a polynomial ring $R$ over a field of characteristic
zero. The torsion part $T(M)$ of $M$ and the torsion free module $M/T(M)$ are
expressed by the primitive ideal of $I$ relative to $H$. Two characterizations
for $M/T(M)$ to be free are proved. Some immediate applications are worked out.
