  The $\psi'\to J/\psi\pi^+\pi^-$ decay process provides a new way to extract
the $\pi\pi$ $S$ wave phase shifts up to $0.59GeV$. In this paper we derive the
formulae for extracting the $\pi\pi$ $S$ wave phase shifts from the invariant
mass spectrum of $\pi\pi$ in the $\psi'\to J/\psi\pi^+\pi^-$ decay.
