PHL ATCT MISJUDGES SEPARATION WITH DH8 WHILE VECTORING A FA10 THROUGH 3 OTHER CTLRS' AIRSPACE.

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WHILE WORKING YARDLEY SECTOR AT PHILADELPHIA TWR; I WAS VECTORING A TRENTON TWR DEP TOWARD DITCH INTXN. THE DEP; A FALCON CPR JET; NEEDED TO CLB THROUGH PHILADELPHIA N ARR AIRSPACE. I COORDINATED WITH N ARR TO CLB THE FALCON AND TURN HIM TOWARD DITCH INTXN. I TOLD THE CTLR WORKING THAT SECTOR I WOULD MISS ALL HIS TFC. WHEN I RELEASED THE FALCON; I ALSO RELEASED A CITATION ROUTED OVER POTTSTOWN VORTAC. I TOLD THE CTLR AT TRENTON TO TURN THE CITATION TO A 270 DEG HDG; AND CLB HIM TO 4000 FT. AT THIS TIME; THE FALCON WAS ON A 240 DEG HDG AND CLBING FIRST TO 6000 FT; THEN TO 7000 FT; EVENTUALLY I WANTED TO HAVE THE FALCON AT 9000 FT TO HDOF TO S DEP. WHEN THE OVERLYING AIRSPACE IS CTLED BY ZDC; WE CALL IT THE 'TUB.' I HAD TO KEEP THE FALCON DOWN UNTIL HE WAS CLR OF THE ZDC AIRSPACE. WHEN THE FALCON REACHED 7000 FT; I TURNED HIM SBOUND TOWARD DITCH INTXN. AT THAT TIME; I PLANNED TO CLB HIM TO 20000 FT WHEN HE CLRED THE 'TUB.' THE TRENTON CITATION HAD JUST DEPARTED. THE CITATION CHKED IN AT 2000 FT ON RWY HEADING; HEADING TOWARD NEW YORK APCH AIRSPACE. I TURNED THE CITATION AND ASKED THE TRENTON CTLRS IF THEY HAD TURNED THE CITATION. THE FALCON WAS STILL HEADING SBOUND AT 7000 FT BECAUSE I HADN'T GONE BACK OT CLB HIM. AT THE SAME TIME; A DASH 8 AT 7000 FT WAS HEADING TOWARD ROBBINSVILLE VORTAC AT 7000 FT. THE S DEP CTLR HAD COME OVER AND ASKED IF THE FALCON AND DASH 8 WERE ALL RIGHT. I LOOKED AT THE DISPLAY AND COULDN'T TELL IF THEY WERE SEPARATED; SO I CLBED THE FALCON TO 8000 FT AND TURNED HIM TO 270 DEGS; TO MAKE SURE HE PASSED BEHIND THE DASH 8. THE CONFLICT ALERT NEVER WENT OFF AND THE PLT DIDN'T RPT ANY TCASII ALERT. I BELIEVE THEY WERE SEPARATED; BUT; I TOOK THE ACTION TO MAKE SURE. IN THE FUTURE; I WILL ASK THE N ARR CTLR IF HE HAS ANY ROBBINSVILLE TFC AT 7000 FT BEFORE I SAY I WILL MISS ALL HIS TFC.