A DC8-73 ACFT PILOT REJECTED TAKEOFF AFTER TWO ATTEMPTS DUE TO TAKEOFF WARNING HORN SOUNDED AFTER 35 KTS GROUND SPEED.

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PERFORMED A LOW SPD (30 KTS GND SPD) REJECTED TKOF DUE TO TKOF WARNING HORN. EXITED RWY AND STOPPED ACFT TO EVALUATE THE SITUATION. THE DC8 SYS MANUAL STATES THE TKOF WARNING HORN WILL SOUND INTERMITTENTLY WHEN THROTTLES #1 AND/OR #3 ARE ADVANCED BEYOND THE IDLE STOP AND THE GND SPOILERS ARE NOT FULLY RETRACTED; AND/OR THE FLAPS ARE NOT BTWN 6 DEGS AND 35 DEGS (TKOF POS). THE FLAPS AND SPOILERS APPEARED TO BE IN NORMAL POS (THE BLUE SPOILER EXTEND LIGHT WAS NOT ILLUMINATED AND THE FLAPS WERE INDICATING 18 DEGS). WE DECIDED TO CYCLE THE GND SPOILERS AND FLAPS IN AN ATTEMPT TO ENSURE EACH WAS IN THE CORRECT DETENT. WE THEN ADVANCED THE THROTTLES WHILE STOPPED AND DID NOT GET A TKOF WARNING HORN. I CALLED MAINT CTL AND EXPLAINED THE SITUATION THAT WE CYCLED THE FLAPS AND GND SPOILERS; ADVANCED THROTTLES AND DID NOT GET A TKOF WARNING HORN. THROUGH RADIO CONVERSATION WITH MAINT WE JOINTLY DECIDED TO ATTEMPT ANOTHER TKOF. THE TKOF WARNING HORN SOUNDED AGAIN AS WE REACHED APPROX 80% N1. WE DID A BLOCK TURN AND MAINT MET THE ACFT. THEY PERFORMED INSPECTIONS ON FLAPS AND GND SPOILERS AND SIGNED OFF THE LOGBOOK. WE REFUELED PRIOR TO BLOCK-OUT AGAIN. ON THE RWY; WHILE HOLDING THE BRAKES; WE ADVANCED THROTTLE #1 FORWARD AND HORN DID NOT SOUND. THEN WE DID THE SAME FOR THROTTLE #3 AND HORN DID NOT SOUND. WE BROUGHT ALL 4 ENGS UP FOR TKOF TO APPROX 75% AND ASKED FOR TKOF THRUST FROM THE FE. THE HORN AGAIN SOUNDED AS N1'S REACHED OUR REDUCED THRUST TKOF SETTING OF 86%. WE REJECTED AGAIN AT APPROX 35 KTS GND SPD AND RETURNED TO THE RAMP VIA BLOCK TURNBACK.