Early in the trip, Gilder was stationed on the Siberian coastline with a few other men and a cache of supplies while the Rodgers moved on in its search. He and his compatriots would establish one potential refuge for the survivors of the missing expedition, should they be found. As such, he wasn't on the Rodgers when it caught fire and was destroyed, forcing the rest of the crew to abandon ship. He did, however, hear of the event soon after from another crew member. Gilder had previous experience with long-distance sledge journeys in the Arctic, having once covered 3,251 miles during a search for the lost Franklin expedition, so it made sense that he was the man to make the long journey to the closest telegraph station, notifying the Navy of this most recent disaster.
To get Gilder's account of that journey, you'll just have to come in and read his report for yourself. There are other items stored with it, including a sketch of the Rodgers burning, diagrams of sledges, and a rough map of the bodies eventually recovered from the Jeannette expedition. Ask for Stefansson Mss-45, Box 2.