TKOF MINIMUMS CEILING. ACR CREW DEPARTED WITH THE WX SHOWING A CEILING BELOW THE TKOF MINIMUMS.

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ON MAY/THU/95 I WAS FO ON A FLT DEPARTING FYV-BNA. WE INADVERTENTLY TOOK OFF BELOW FYV TKOF MINIMUMS. WE DEPARTED THE GATE AT XC00 AM. IT WAS MY FLT LEG. RELEASE WX AT XF54Z (XA54 AM) WAS 400 FT OVCST WITH 5 MI VISIBILITY LIGHT DRIZZLE/FOG. FYV TKOF MINIMUMS RWY 34 500 FT AT 1 KT. DUE TO A LAST MIN ACFT SWAP (FYV HAD SET UP THE WRONG ACFT FOR FLT) I WAS VERY BUSY COMPLETING THE PREFLT INSPECTION; COCKPIT CHKS; CREW LOG; TO/LNDG CARD; PERFORMANCE CALCULATION (VAQ); ACFT LOAD MANIFEST; RTE PLANNING AND PRESTART CHKLIST. THERE WAS NO ATIS AVAILABLE. WE REQUESTED RYV TO BRING CURRENT WX SINCE RELEASE WX WAS 1 HR OLD; THEY COMPLIED. COMPLETING THE AFTER START CHKS; I REQUESTED TAXI FROM TWR; WE PROCEEDED TO AND HELD SHORT OF RWY 34. TWR ADVISED ATIS WAS UP. WE LISTENED TO ATIS (400 FT OVCST; 1 MI VISIBILITY). WE BOTH LOOKED AT TKOF PROC AND NOTICED THE 1 MI VISIBILITY AND NOTED THE DEP PROC. I WAS JUST CATCHING UP TO THE ACFT AND DID NOT CATCH THE 500 FT CEILING MINIMUM. AT THAT TIME; TWR INTERRUPTED US TO TELL US NEW ATIS WAS UP (HE DID NOT READ THE SA). WE FLIPPED UP ATIS AGAIN TO HEAR 300 FT 1 KT. WITH ALL THE INTERRUPTIONS; IT DID NOT REGISTER TO ME THAT THE CEILING WAS BELOW TKOF MINIMUMS. TWR CLRED US TO TKOF AT XC14 AM; OFF XC15 AM. APPARENTLY THIS IS A CASE OF TKOF MINIMUMS BEING OVERLOOKED AT LEAST 3 TIMES. THE DISPATCHER CUT THE RELEASE WITH 400 FT OVCST; THE CAPT AND MYSELF. FOR MYSELF; I WAS VERY BUSY COMPLETING MY DUTIES AND SEVERAL ITEMS SET OUT IN THE COMPANY FLT MANUAL WHICH ARE THE RESPONSIBILITY OF THE CAPT (IE; CREW LOG AND LOAD MANIFEST). IN ADDITION; I WAS PUSHED BEHIND THE CURVE BY THE LAST MIN ACFT SWAP. I WILL BE THE FIRST TO ADMIT THAT IN THE FUTURE I WILL NOT BE PLACED IN THIS COMPROMISING POS OF TRYING TO FORCE AN ON- TIME DEP. SAFETY AND PLANNING COMES FIRST! SUPPLEMENTAL INFO FROM ACN 305467: WHILE I PERFORMED ENG CHKS; FO COPIED ATIS. WX APPEARED TO BE IMPROVING AND FO STATED WE ARE LEGAL TO DEPART. I RESTATED OUR IFR DEP PROC AND RWY FOR EMER RETURN AND CALLED READY ON RWY 34. TWR THEN CLRED US FOR TKOF AND A NORMAL TKOF AND DEP WERE PERFORMED. I WAS NOTIFIED 5 HRS LATER THAT CEILING WAS STILL 400 FT AT DEP. I SHOULD HAVE QUESTIONED THE FO WHEN HE STATED WE WERE LEGAL TO GO.