The pilot, a pilot rated passenger, and their wives were taking off from an uncontrolled airport, about 32 minutes before sunrise. Witnesses reported that the ramp, and the departure and approach ends of the airport were obscured by ground fog. No flight plan was filed for the flight, nor was there any record of a weather briefing. A mechanic reported that he heard the aircraft take off, then he heard about 5 seconds of silence before he heard the aircraft crash. The aircraft crashed into a corn field in a steep, nose low attitude, and was destroyed by impact forces and fire. The crash site was located about 600 feet south of the departure runway, and about 1,100 feet short of the departure end. An examination of the propeller revealed evidence of rotation at impact. The engine ran successfully on a test stand after the accident. The pilot had mentioned that the vacuum pump did not work on an airplane that he had been flying; however, examination of the pump and gyro instruments did not reveal evidence of a mechanical malfunction.