I have become an aficionado of these circumstances, and a bit of an expert I might say…
When President William McKinley was shot in 1901 by a would-be assassin, the President was visiting the Pan-American Exposition in Buffalo, New York. McKinley was treated in Buffalo, and Vice President Theodore Roosevelt traveled to be at the President’s side. Because McKinley didn’t seem to be in danger, Roosevelt’s presence seemed unnecessary, and he was urged to leave Buffalo.
Roosevelt then resumed his vacation, traveling to Newcomb in New York’s mountainous Adirondack region, and staying at the Tahawus Club with his family. On September 13, 1901, the Vice President and several others in his group climbed Mount Marcy, and were having lunch after descending the high peak a short distance to the shore of Lake Tear of the Clouds, the highest pond source of the Hudson River. A forest ranger approached the group at the small lake with news that the President’s health had deteriorated. Roosevelt and the others returned to their camp and were again informed late that night that McKinley was near death, and the Vice President was summoned to Buffalo immediately.
Roosevelt accompanied a driver in a horse-drawn wagon (buckboard), and in the darkness of that Adirondack night they made their way over perilous roads toward the train station in North Creek. When they arrived at the station, Roosevelt was informed that William McKinley had died. Somewhere on that "rough ride", at 2:15 A.M. September 14, 1901, near Newcomb, Theodore Roosevelt had become President of the United States.
Roosevelt boarded a private rail car and traveled overnight by rail to Buffalo. In Buffalo, McKinley’s close friend wanted Roosevelt to be sworn-in at his house, but Roosevelt instead chose to take the oath of office at the home of his own friend, Ansley Wilcox. The Wilcox Mansion still stands today on Delaware Ave., and is a National Historic Site.
PS: An interesting side note -
The doctor who attended to McKinley treated him with all the usual standards of the time. Nevertheless, the President succumbed to a complication that now is considered quite treatable - an infection. It has been said that a second doctor who would have been McKinley’s primary care physician, had he not been out of town when the shooting happened, would have treated McKinley a bit differently. That doctor had been practicing a new technique that treated patients in such a way as to prevent the common infection - that man’s name, the medical director of the Pan-American Exposition, was Dr. Roswell Park, namesake for Buffalo's famous Roswell Park Cancer Institute.
(As president, Roosevelt hated the nickname Teddy, but the public loved it and the name endured.)