PA28 PLT MAKING TOUCH AND GOES AT LVK ARPT OVERHEARS A XMISSION ON THE RADIO ABOUT SOMEONE WHO CUT IN DANGEROUSLY CLOSE TO ANOTHER ACFT.

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I WAS FLYING AT THE LIVERMORE ARPT ON JUL/XB/99. AT APPROX XA10 HRS A RADIO CALL WENT OUT THAT A PLANE CUT IN FRONT OF ANOTHER ON FINAL APCH TO RWY 25R. ANOTHER RADIO CALL WAS XMITTED THAT STATED THE PLANE THAT CUT IN WAS 'DANGEROUSLY CLOSE.' THIS FORM IS BEING SENT IN RESPONSE TO THIS INCIDENT. I AM THE PLT OF THE PLANE THAT CUT IN FRONT OF THE OTHER ONE. I WAS FLYING IN THE PATTERN; SHOOTING TOUCH AND GOES. THIS WAS MY FOURTH CIRCUIT. THERE WERE 2 OTHER PLANES IN THE RWY 25R PATTERN AT THE TIME; PLUS OTHER TFC FOR RWY 25L. I WAS FLYING MY PA28-A AND THE SECOND PLANE IN THE INCIDENT WAS A CESSNA (150/152 I THINK); ALSO DOING TOUCH AND GOES. ON THE DOWNWIND LEG; APPROX 1 MI FROM THE ACTIVE END OF THE RWY; I PASSED ABEAM OF THE PLANE (CESSNA CARDINAL) CLRED #1 TO LAND. THERE WAS A RADIO XMISSION FROM THE TWR TO THIS PLANE ASKING FOR HIS POS; AND HE RESPONDED AS 1 MI OUT. THE #2 PLANE THEN QUERIED THE TWR ASKING IF HE COULD TURN BASE. THE TWR RESPONDED THAT HE WAS NOT IN SIGHT; THERE WAS NO RADAR AT LIVERMORE AND HE WAS CLRED TO LAND. THE TWR THEN CAME TO ME ASKING MY POS. I RESPONDED AS BEING 3 1/2 MI DOWNWIND (ALMOST TO THE LAWRENCE LIVERMORE LABORATORY). I WAS CLRED AS #2 TO LAND; FOLLOWING THE CESSNA. A HIGH WING PLANE HAD PASSED BY DURING THIS XMISSION; AND I THOUGHT THIS WAS THE PLANE I WAS FOLLOWING. MY ALT WAS APPROX 1500 FT ABOVE MSL (PATTERN ALT IS 1400 FT) AT THIS POINT AND I PROCEEDED WITH MY TURN TO BASE AND THEN TO FINAL. MY FLT PATH WAS EVIDENTLY ABOVE THE #2 CESSNA. I WAS NOT AWARE OF THE OTHER PLANE UNTIL THE RADIO CALL CAME THROUGH. I HAVE NO IDEA HOW CLOSE I CAME TO THE CESSNA. THE TWR THEN CLRED ME AS #1 TO LAND AND I PROCEEDED TO LAND. AFTER I LANDED; I WENT TO THE TWR AND ASKED IF I COULD TALK WITH THEM ABOUT WHAT HAPPENED. I WAS TOLD THE TWR WAS SHORT HANDED AND I WOULD HAVE TO COME BACK THE NEXT DAY AND TALK WITH THE MGR. AFTER THINKING ABOUT WHAT HAPPENED I HAVE THESE THOUGHTS: SCANNING FOR OTHER TFC IS SOMETHING I WORK HARD AT; AND IN MY LOW WING AIRPLANE I DIDN'T LOOK 'DOWN' ENOUGH. CONTRIBUTING TO THIS IS THE FACT THAT I THOUGHT THE TFC I WAS FOLLOWING WAS WELL AHEAD OF ME IN THE PATTERN. I NEVER SUSPECTED THAT I HAD PICKED UP THE TFC FOR RWY 25L. ANOTHER INCIDENTAL FACTOR; I WAS FLYING THE APCH TOWARD THE SETTING SUN.