Did Thomas Jefferson father a child by one of his slaves? Did Old Hickory's wife already have an old man? And, say, what COULD you see by the dawn's early light?

Historians - professional know-it-alls who usually save questions for students - admit to a few intriguing doubts of their own in the December issue of American Heritage.The magazine asked American historians to name the one mystery in U.S. history each would like solved. Responses ranged from "Were Sacco and Vanzetti guilty?" to "Who invented the hamburger?"

Walter Lord wonders what Francis Scott Key saw the morning he wrote "The Star-Spangled Banner" during the War of 1812.

Key was forced to observe the British bombardment of Fort McHenry in Baltimore Harbor from a flag-of-truce boat eight miles away. He later said he composed the song's lyrics at dawn, when the sight of the flag assured him the attack had been repelled.

But that was unlikely, Lord suggests. Although the fort's regular flag might have been visible from eight miles, the night's rain would have forced the use of a lighter, smaller "storm flag" that probably could not have been seen through smoke and rain in early light.

Lord argues that it's more likely Key saw an ensign flag raised by the victorious Americans over the fort's guns - a flag that a British officer saw raised around 9 a.m., not dawn.

Key however, "knew that dawn is a more magic hour than 9 a.m.," Lord writes. "It was time to resort to a little poetic license."

Another historian, Charles O'Neill, wonders if the space shuttle Challenger was sent aloft despite less than optimal temperatures because the White House wanted a dramatic background for President Reagan's 1986 State of the Union address, originally scheduled for the night of the launch.

He writes:

"By examination of White House logs or otherwise, I'd like it clearly proven or disproven whether word . . . went to (NASA officials), bidding those in charge not to be too finicky - given the upcoming address - about getting the Challenger into the air, cold weather or no cold weather."

Columbia University historian Henry Graff wonders why former President James Monroe repeatedly sued the government for expenses after leaving office. He suspects Monroe was ashamed of "the substantial charges . . . that he misapplied public money while in official posts" (even that he had personally profited from his refurbishing of the White House after its torching by the British)."