Army Signal Corps Collection in the United States National Archives Churchill, F.D.R. and Stalin at Yalta.

The most provocative evidence the authors present is that Roosevelt had a left-sided hemianopsia — a loss in vision — toward the end of his life. This indicated a mass in the right side of his brain. Dr. Lomazow and Mr. Fettman arrive at this conclusion based on an ingenious bit of research. On March 1, 1945, Roosevelt had given a speech to Congress, reporting on his recent trip to Yalta to meet with British Prime Minister Winston Churchill and the Soviet leader Joseph Stalin. During the speech, Roosevelt appeared confused: He skipped words in his prepared remarks, ad-libbed and repeated several points. Critics later seized on this speech as evidence that the president was deteriorating mentally.

Dr. Lomazow and Mr. Fettman obtained both a video of Roosevelt giving the speech and the text he used. Comparing the two, they concluded that the president could not see the left side of the page. His seeming mistakes and confusion reflected his attempts to compensate.

The research casts doubt on the impression left by F.D.R.’s physician that high blood pressure caused the hemorrhage, and is of “great importance,” Mr. Lerner writes. “It is the latest to demonstrate the conflicts of interest that presidential physicians encounter as they serve both their patients and the public.”

“If Lomazow and Fettman are right,” he adds, “Republican Thomas E. Dewey or a different Democrat should have been elected president in 1944. In that case, Harry S. Truman, F.D.R.’s vice president, would almost certainly not have been commander in chief from 1945 to 1952. The Cold War and subsequent American history might have taken a very different path.”