"I want to ask you whether if I can persuade Root to stay until a year hence, you cannot come back and take his place."
During the first decade of the 20th century, President Theodore Roosevelt wrote that sentence to someone who was currently serving abroad.
For easier analysis, I have changed it to: "If I can persuade Root to stay for another year, I want to ask you whether you cannot come back at that time and take his place."
My question: If President Roosevelt had used can (instead of "cannot"), how would that have changed the meaning that he wished to deliver?
Source: Doris Kearns Goodwin, The Bully Pulpit / Theodore Roosevelt, William Howard Taft, and the Golden Age of Journalism (2013), page 391.
The rather dated negative form adds a diffident tone, in my opinion.