ATC APCH CTLR DID NOT ISSUE APPROPRIATE INSTRUCTIONS FOR A RESOLUTION TO AN OVERTAKING ACFT RESULTING IN LTSS DURING AN APCH VECTOR.

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I WAS AT THE CTLS OF FLT NUMBER; DEPARTING SL NDB ON AN ASSIGNED HDG OF 290 DEGS WITH A CLRNC TO DSND TO 8000 FT. ACR FLT NUMBER; A WDB; WAS APPROX 1/2-1 MI AHEAD OF US MAINTAINING 8000 FT. OUT SPD AT THIS POINT WAS GREATER THAN THE WDB AND THE DISTANCE BTWN US WAS CLOSING AT A STEADY RATE. AT THIS POINT THE CTLR APPARENTLY SAW WHAT WAS HAPPENING AND ATTEMPTED TO RECTIFY HIS MISTAKE. I CAN ONLY ASSUME THAT HE PANICKED AND BEGAN TO THINK IN A STRICTLY 1 DIMENSIONAL MANNER; AS HIS ONLY ATTEMPT TO KEEP OUR 2 ACFT SEPARATED WAS BY REPEATED CALLS FOR 1 OF THE ACFT TO 'REDUCE TO MIN SPD.' UNFORTUNATELY; HE WAS INSTRUCTING THE WRONG ACFT (NUMBER); WHICH WAS THE LEAD ACFT) TO MAKE THE SPD REDUCTION. FORTUNATELY; THE WX WAS CLR AND I HAD THE WDB IN SIGHT. I MAINTAINED VISUAL SEPARATION BY LEVELING OFF AT 9000 FT. THE CTLR CONTINUED TO CALL FOR AN AIRSPD REDUCTION BY FLT NUMBER (HIS VOICE BECOMING HIGHER AND MORE OUT OF CTL WITH EACH ENSUING CALL) UNTIL HE WAS RELIEVED (I AM ASSUMING THAT IT WAS NOT MERELY A FORTUITOUS CHANGE OF SHIFT) BY A CALMER SOUNDING CTLR WHO PROCEEDED TO SORT THE SITUATION OUT WITH A COMBINATION OF VECTORS AND SPD ASSIGNMENTS. THE FLT WAS NORMAL FROM THIS POINT ON. HAD WE BEEN IN IFR CONDITIONS AND NOT HAD THE WDB IN SIGHT; I WOULD ESTIMATE THAT THERE WAS AT LEAST A 90 PERCENT PROBABILITY THAT A MIDAIR COLLISION WOULD HAVE ENSUED.