ACFT 1; HAVING MADE A PRACTICE MISSED APCH; IS BEING VECTORED BY RPTR FOR ANOTHER ILS. RPTR OBSERVING THAT ACFT 2 IS DEPARTING ON A CONVERGING COURSE TO ACFT 1; INSTRUCTS THE TWR LCL CTLR TO TURN ACFT 2 ON COURSE. DUE TO ACFT 1'S HDG; THERE IS LOSS OF SEPARATION WHEN ACFT 2 TURNS INSIDE ACFT 1.

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WORKING ALL OF THE N AIRSPACE COMBINED (ARRS; DEPS; OVERFLTS; ETC) ACFT 1 (PA-28) WAS PRACTICING IFR APCHS (ILS 5 PVD). ACFT 1 CALLED ON HIS MISSED APCH. NORMAL PROCS CALL FOR A 30 DEG R TURN ON PLANNED MISSED APCHS. ACFT 1 WAS TOLD 'RADAR CONTACT; VERIFY TWR ASSIGNED HDG?' HE ANSWERED 020 DEGS. THE VERY NEXT XMISSION WAS TO ACFT 1; ROGER TURN R HDG 160 (THIS WAS FOR HIS NEXT APCH). ACFT 2 APPEARED ON THE SCOPE AT THE RWY; I REALIZED ACFT 1 WAS L OF CTRLINE AND IMMEDIATELY CALLED THE TWR TO GIVE ACFT 2 (DC-9) A R TURN ON COURSE (320 DEGS) AND CLB TO 8000 FT (5000 FT BEING THE NORMAL PROC) TO ENSURE SEPARATION. ACFT 2 DEPARTED AND TURNED INSIDE THE PA-28 BUT WITH LESS THAN 3 MI AND 1000 FT WITH HIM IN SIGHT. I BELIEVE THIS WAS A CLASSIC READBACK; HEARBACK SIT. EVEN THOUGH HE HAD STATED THAT HE WAS HDG 020; I 'KNEW' IT WAS 080 AS THE SOP STATES. I BELIEVE A CONTRIBUTING FACTOR ALSO WAS THAT MY TAB LIST HAD BEEN MOVED TO ACCOMMODATE THE COORDINATOR POS THAT WAS OPEN TO MY L. I NORMALLY KEEP THE TAB LIST JUST NE OF OUR PRIMARY ARPT (PVD) SO THAT WHEN THE TWR FLASHES A DEP (THEY BLINK IN THE TAB) IT'S SEEN RIGHT AWAY. IN RETROSPECT I'VE LEARNED THAT IF YOU ASK FOR INFO; MAKE SURE YOU'RE LISTENING FOR THE ANSWER. NOT WHAT YOU THINK THE ANSWER SHOULD BE.