J3 ON APCH TO EKY EXPERIENCES CONFLICT WITH OPPOSITE DIRECTION B350.

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WE BEGAN FLYING; REMAINING IN THE PATTERN AT EKY. WE MADE A FUEL RUN TO EET; SHELBY COUNTY LATER. ON RETURNING TO BESSEMER EKY; WE ENTERED A STANDARD L DOWNWIND PATTERN FOR RWY 23. THERE WAS NO WIND AND WE SAW NO TFC IN THE PATTERN AND IT WAS THE EASIEST ENTRY FROM OUR POS. I AND MY REAR SEAT PAX BOTH NOTED THAT WE SAW NO TFC ON DOWNWIND; BASE; OR THE RWY. ON FINAL APCH WE SAW THE KING AIR OFF TO OUR R THAT HAD JUST COMPLETED A LOW APCH. THE KING AIR HAD APPARENTLY SEEN US AS WELL AND WAS VEERING OFF TO OUR R AND WAS 1500-2000 FT AWAY FROM US AND A LITTLE ABOVE US. WE CONTINUED ON TO A NORMAL LNDG. THE PROB AROSE FROM A RELATIVELY FAST KINGAIR DOING A LOW APCH FROM THE OPPOSITE RWY 5. OUR PLANE HAS NO RADIO OR ELECTRICAL SYS; THUS WE WERE NOT IN CONTACT WITH THE OTHER ACFT. BOTH I AND MY PAX WERE ON THE LOOKOUT WHILE IN THE PATTERN FOR OTHER ACFT. ONCE ON FINAL APCH MY ATTN WAS FOCUSED ON THE LNDG. I MADE A CALL TO THE BIRMINGHAM CTL TWR JUST TO CHK IN. I WAS ASKED TO MAKE BETTER USE OF THE RADIO. I EXPLAINED THAT WE HAD NO RADIO. I DON'T BELIEVE ANY RULES WERE BROKEN AND THE SYS ACTUALLY WORKED IN THAT NEITHER PLANE WAS IN ANY SERIOUS PERIL AS BOTH PLANES SAW ONE ANOTHER AND AVOIDED TROUBLE. THERE ARE NO KNOWN ISSUES AFFECTING HUMAN PERFORMANCE IN THIS CASE.