Step 1: Permanent hardness of water is mainly due to soluble salts of calcium and magnesium.
Step 2: The important hardness-producing ions are:
\[
Ca^{2+}
\]
and
\[
Mg^{2+}
\]
Step 3: In the permutit process, sodium zeolite exchanges its \(Na^+\) ions with \(Ca^{2+}\) and \(Mg^{2+}\) ions.
Step 4: This removes calcium and magnesium ions from hard water.
Step 5: Hence, \(Na^+\) ions are exchanged with:
\[
Ca^{2+},\ Mg^{2+}
\]
\[
\boxed{Ca^{2+},\ Mg^{2+}}
\]