A DC9 IN CRUISE AT FL350 HAD THE FO LEAVE THE COCKPIT TO RESOLVE A PAX DISPUTE.

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THE LEAD FLT ATTENDANT PHONED THE COCKPIT AND INFORMED US THAT THERE WAS A DISPUTE BTWN 2 PAX. AFTER A SHORT DISCUSSION BTWN THE FLT ATTENDANT ON THE PHONE; SHE CAME TO THE COCKPIT. SHE SAID THE SIT WAS GETTING WORSE AND SHE REQUESTED ONE OF US TO COME BACK AND TALK TO THE PAX. THE CAPT ASKED IF I WANTED TO GO BACK OR IF I WANTED HIM TO GO BACK. I SAID I WOULD GO BACK. JUST IN CASE SOMETHING HAPPENED; HE WOULD BE ABLE TO FLY THE ACFT. I THEN ASKED ABOUT HIS THOUGHTS ON PLTS LEAVING THE FLT DECK; EXCEPT FOR PHYSIOLOGICAL REASONS -- PER FARS. HE RESPONDED THAT IT WOULDN'T BE A PROB AND THERE WAS NO NEED TO DECLARE AN EMER. THEREFORE; I WENT BACK AND SPOKE TO THE PAX INVOLVED. THE SIT AROSE FROM A PAX SITTING DIRECTLY FORWARD OF THE OTHER RECLINING HIS SEAT AND NEARLY TIPPING OVER A DRINK ON THE TRAY TABLE. THE 'REAR' PAX WAS TRYING TO START A PHYSICAL ALTERCATION. I MADE IT CLR THAT IF A PHYSICAL ALTERCATION OCCURRED THE ACFT WOULD BE LANDED AT THE NEAREST SUITABLE ARPT AND THE AUTHS WOULD BE STANDING BY. WITH THE SIT UNDER CTL; I RETURNED TO THE FLT DECK. IN TALKING TO THE LEAD FLT ATTENDANT WE DISCOVERED THAT THE 'REAR' PAX HAD STOPPED HER DURING HER CABIN SVC AND DEMANDED HER TO MAKE THE 'FORWARD' PAX STOP RECLINING HIS SEAT. SHE TOLD THE PAX THAT IF HE 'INTERFERED' WITH HER DUTIES SHE COULD HAVE HIM ARRESTED. THIS IS WHEN TEMPERS BEGAN TO FLARE. I BELIEVE THAT IF THE FLT ATTENDANT HAD ATTEMPTED TO MANAGE THE SIT INSTEAD OF BEING 'HVY HANDED' THE ENTIRE SIT MAY HAVE BEEN AVERTED. WE CONTINUED THE FLT WITHOUT FURTHER INCIDENT.