The aircraft was engaged in the transfer of passengers from Cape Flattery to Cooktown. It was observed to overshoot from the first approach and to carry out a low level circuit subsequently landing with the gear retracted. The pilot reported that during the circuit following the missed approach, he was required to adjust the circuit pattern because of heavy rain in the area, and as a consequence flew a tighter than normal circuit. He also stated that during the circuit he was interrupted by radio conversations with another aircraft which was approaching Cape Flattery. An inspection of the aircraft revealed that the gear was in the locked up position and no damage had been caused to the main gear doors. No fault was found with the landing gear system that could have caused it not to extend when correctly selected down. The pilot believed that it was possible that when moving the gear selector lever to the down position he had not moved it fully down. He does not recall checking that the gear down indicator lights illuminated.