What is the permutit method, how can it be used for softening hard water?
Permutit is an artificial zeolite. Chemically, it is hydrated sodium aluminum orthosilicate with the formula $$Na_2Al_2Si_2O_8.xH_2O$$. For the sake of convenience, let us give it the formula $$Na_2P.$$
A tall cylinder is loosely filled with lumps of permutit. Ions get exchanged when hard water containing calcium and magnesium ions percolates through these lumps. Sodium permutit is slowly changed into calcium and magnesium permits, and the water becomes soft with the removal of calcium and magnesium ions.
When no longer active, a permutit is regenerated by running a concentrated solution of brine over it and removing calcium chloride formed by repeated washing.