BEFORE DEPARTING SMITH POND, MAINE, THE PILOT CHECKED THE FUEL AND ESTIMATED HE HAD BETWEEN 30 AND 40 GALLONS ON BOARD. HE FLEW TO WATERVILLE, THEN TO KATACHDINE LAKE, AND WAS ON THE NEXT LEG OF THE FLIGHT WHEN THE ENGINE LOST POWER. HE SWITCHED TANKS AND THE ENGINE STARTED FOR A FEW SECONDS, THEN LOST POWER AGAIN. THIS OCCURRED OVER LEVEL TERRAIN COVERED WITH TREES, BUT WITH NO CLEARING. THE FLOAT PLANE WAS BADLY DAMAGED DURING A FORCED LANDING IN THE WOODED AREA. THE PILOT STATED THAT THIS WAS A NEWLY PURCHASED AIRCRAFT AND THE FUEL GAUGES READ FULL AT THE TIME OF THE ACCIDENT. THE PILOT SUSPECTED A PROBLEM WITH THE FUEL TANK VENTS. HOWEVER, AN INSPECTION REVEALED THEY WERE CLEAN AND HAD NO SIGNS OF BLOCKAGE. THE AIRCRAFT HAD TRAVELED ABOUT 216 MILES AFTER DEPARTING SMITH POND. THE ESTIMATED CRUISE SPEED WITH FLOATS WAS ABOUT 110 MPH. THE PILOT REPORTED THAT THE FUEL FLOW METER WAS INDICATING ABOUT 15 GAL/HR IN FLIGHT. THE ENGINE RAN SATISFACTORILY DURING AN OPERATIONAL CHECK ON 5/27/82.