Step 1: Understanding the Concept:
The question asks for the provision in the Code of Civil Procedure (CPC), 1908, that empowers and encourages courts to refer disputes to methods of settlement outside the formal court adjudication process. This provision is the cornerstone of court-annexed Alternate Dispute Resolution (ADR) in India.
Step 2: Detailed Explanation:
Let's analyze the given sections of the CPC:
\begin{itemize}
\item Section 98: Deals with the decision where an appeal is heard by two or more Judges.
\item Section 89: This section is titled "Settlement of disputes outside the Court." It was inserted by the CPC (Amendment) Act, 1999. It provides that where it appears to the court that there exist elements of a settlement which may be acceptable to the parties, the court shall formulate the terms of settlement and refer the same for:
\begin{enumerate}
\item arbitration;
\item conciliation;
\item judicial settlement including settlement through Lok Adalat; or
\item mediation.
\end{enumerate}
This section is the principal statutory provision promoting ADR within the civil justice system.
\item Section 99: Deals with the principle that no decree shall be reversed or modified for error not affecting merits or jurisdiction.
\item Section 88: Deals with Interpleader suits, where a person holding property claimed by two or more rival claimants can institute a suit to have the court decide the rightful owner.
\end{itemize}
Therefore, Section 89 is the specific provision for the settlement of disputes outside the court.
Step 3: Final Answer:
The section that deals with the settlement of disputes outside the court is S.89.