PA28 PLT WHILE TRANSITING ACROSS THE ILS APCH COURSE; IS REQUIRED TO TAKE EVASIVE ACTIONS TO AVOID ANOTHER ACFT AT COU.

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I CONTACTED COLUMBIA TWR OVER FULTON; MO; REQUESTING TRANSITION THROUGH THEIR AIRSPACE. I HAD CURRENT ATIS INFO WITH RWY 20 IN USE. COLUMBIA'S PRIMARY RADAR WAS OTS. MY ALT WAS 2600 FT MSL AND GND SPD WAS ABOUT 105 KTS; AS INDICATED BY A LORAN RECEIVER. COLUMBIA TWR CLRED ME THROUGH THEIR AIRSPACE. THE LIGHTING WAS CHANGING FROM DUSK INTO NIGHT. COU TWR ANNOUNCED TO ME 'A LEARJET IS ON THE APCH FOR RWY 20.' THE JET WAS HIGHER AND ABOUT 5 MI FROM MY POS; OFF OF MY R WING (ABOUT 2 - 2:30 O'CLOCK POS). I RADIOED BACK TO THE TWR I HAD THE TFC IN SIGHT AND WAS ABOUT 1 MI FROM THE RWY EXTENDED CTRLINE. ABOUT 20 SECONDS LATER; I STILL HAD NOT CROSSED THE RWY CTRLINE. I REALIZED THAT MY CURRENT FLT PATH AND ALT WOULD PUT ME ON AN INTERCEPT COURSE WITH THE LEARJET. MY EVASIVE ACTION WAS TO APPLY FULL THROTTLE AND PUT THE AIRPLANE INTO AN IMMEDIATE DSCNT TO 300 FT LOWER TO 2300 FT MSL. I LATER HEARD THE LEARJET PLT MAKE A COMMENT TO THE TWR ABOUT THE CLOSENESS OF THE 2 ACFT. TWR MADE A REPLY; BUT I DO NOT REMEMBER WHAT WAS SAID. THE PROBS WERE: 1) THE PRIMARY RADAR FOR SEPARATION. 2) IMPROPER JUDGEMENT OF DISTANCE ON MY PART TO THE RWY CTRLINE TO MY CURRENT POS WHEN SIGHTING THE LEARJET. 3) NOT BEING AWARE OF THE LEARJET'S GND SPD DURING THE APCH. EVASIVE MANEUVER I COULD HAVE TAKEN WOULD BE MAKING A L-HAND 180 DEG TURN ON MY PART. (A R-HAND TURN WILL ALLOW THE ACFT CLOSE MORE QUICKLY.) TO PREVENT THIS POSSIBLE PROB; I COULD HAVE TAKEN A RTE ABOVE COU AIRSPACE; OR TAKE A RTE THROUGH COU AIRSPACE XING AT MIDFIELD.