In 1916, he attempted to capture Death, but instead entraps Dream (Morpheus) as he is returning, after a significant event, far from Earth. The event and the lengthy journey back, had weakened him considerably, and he was returning in a vulnerable condition. It was only because of this vulnerability that the spell cast by Burgess was able to capture him, it was a fluke that he was able to succeed in capturing one of the Endless at all.
He takes Morpheus' helmet, his bag of sand, his ruby, and his clothing, then seals him in a glass bubble behind a magic circle in the basement. Throughout the rest of his life, Burgess tried to bargain with Dream for immortality in exchange for release. He never succeeds in making Dream say even a single word. Maenwhile, the imprisonment of Dream causes the sleepy sickness throughout the waking world, and initiates the unraveling of the Dreaming.
Still imprisoned, Dream watched Burgess fall apart, bitter and angry over his mortality. In 1947 he died after a heart attack at 83 years old. His son, Alex Burgess, succeeded his father, inheriting the estate, the notorious magical order, and the imprisoned Dream.
His first Appearance was The Sandman #1 - Sleep of the Just