This is a partial pressure suit, first used in 1951. Developed from an emergency suit used on three flights in the US Navy's D-558-II rocket-powered airplane, popularly known as the Douglas Skyrocket. It has "capstans" running up the outer sides of the legs and arms. Capstans are tubes that, when inflated, pull the suit fabric tightly against the pilot's body thereby applying counter pressure against the internal expansion of gases and water vapor in blood vessels and body tissue.
The T-1 suit was manufactured by the David Clark Company, which later on was the prime contracter for the NASA Gemini spacesuits.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.